tag:blogger.com,1999:blog-19313736739469548542020-01-14T14:10:44.303+01:00Prawns and ProbabilityRichard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.comBlogger34125tag:blogger.com,1999:blog-1931373673946954854.post-90545228891873655302018-11-06T11:49:00.000+01:002018-11-06T15:26:59.615+01:00Noise and collective behaviour<div dir="ltr" style="text-align: left;" trbidi="on">"You should never do anything random!", Michael Osborne told the room at large for the umpteenth time during my PhD. Mike, now <a href="http://www.robots.ox.ac.uk/~mosb/" target="_blank">an Associate Professor at Oxford</a>, is still telling anyone who will listen about the evils of using random numbers in machine learning algorithms. He contends that for any algorithm that makes decisions at random, there is a better algorithm that makes those decisions according to some non-random criterion.<br /><blockquote class="twitter-tweet" data-lang="en-gb"><div dir="ltr" lang="en">The strongest arguments for random numbers in computation seem to be their <br /><br />1. low cost and their <br />2. unbiasedness.<br /><br />Below are my best attempts at counter-arguments.</div>— Michael A Osborne (@maosbot) <a href="https://twitter.com/maosbot/status/1045629223388491776?ref_src=twsrc%5Etfw">28 September 2018</a></blockquote><script async="" charset="utf-8" src="https://platform.twitter.com/widgets.js"></script>Having seen this debate sporadically erupt over a decade or so has burned the issue of random decision making deep into my psyche, where it has lurked until I recently had reason to think a bit more deeply about the use of random decision making in my own research area: modelling animal behaviour.<br /><br />Many models of animal behaviour make use of random decisions, or 'noise'. For example, <a href="https://www.sciencedirect.com/science/article/pii/S0022519302930651" target="_blank">an animal may choose a new direction in which to move by averaging the current directions of the other individuals around itself, and then add some random error to that average to give its own new direction</a>. But why should an animal do something random? Surely there is a 'best' action to be taken based on what the animal knows, and it should do this. Indeed, <i>how</i> would an animal do something random? <a href="https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0041531" target="_blank">It is remarkably difficult for humans to write down 'random' series of numbers without the aid of a random number generator, such as a coin or a dice</a>. If you were asked to pick one of two options with a probability of 0.65, how would you do it? Why should an animal be any different?<br /><br />Usually when we ascribe noise to animal or human decisions, what we are really doing is modelling that part of the decision that we either don't understand, or that we choose to ignore. For example, in <a href="https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0206687" target="_blank">a recent paper</a> my coauthors and I looked at factors influencing neighbourhood choice in Stockholm. We modelled choices as being influenced by the characteristics of the moving household and the neighbourhoods they were choosing from, but ultimately being probabilistic - i.e. random. As we say in the paper, this is equivalent to assuming that the households are influenced by many other factors that we don't observe, and that they make the best choice given all this extra information. Because we don't see everything that influences the decision, it appears 'noisy' to us.<br /><br />So far, so good. This is fundamentally no more controversial than treating a coin toss as random, even though we know that the coin is obeying deterministic physical rules. As long as we use a decent model for the stochasticity in these decisions, we can happily treat what are really deterministic decisions as being random, and still make solid inferences about what influenced them. But we can run into trouble when we forget that only <i>we </i>are playing this trick. This becomes a problem in the world of <i>collective behaviour</i>, where we want to understand how animals are influencing and being influenced by each other. Though we might treat individual animals' decisions as being partly random, we cannot guarantee that the animals themselves also do the same thing. Indeed, it is likely that the animals themselves have a better idea about what factors motivate and influence each other than we do. Where we might, in our ignorance, see a random action, another animal might well see a response to some cue that we haven't thought to look for.<br /><br />To illustrate, lets imagine that you and I are trying to choose a restaurant. For the purposes of simplicity I will assume that we like very much the same things in a restaurant - we have the same tastes in food and ambience. We approach two seemingly similar-looking restaurants, A and B. I can smell that the food in restaurant A smells somewhat more appetising than in B. Nonetheless, I see you starting to walk in the direction of restaurant B. I know we can both smell that the food in A is better, so what should I make of your decision? If I assume your decision is partly random, I might just assume you made a mistake - A really is better, but you randomly picked B instead. I am then free to pick A. But if I assume you made the best choice with the information available, I must conclude that you have some private information that outweighs the information we share - maybe you earlier read an excellent review of restaurant B. Since our tastes are very similar, I should also conclude that if <i>I </i>had access to your private information as well, I would have made the same choice, since the choice is determined exactly by the information. So now I really ought to pick restaurant B as well.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-Ca6feERRyLQ/W99TbROwfsI/AAAAAAAAsac/cusBuW8DlvEqJYBvf0xdTyIz3sl9E3dYwCLcBGAs/s1600/Whataburger_hamburger_and_fries.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="480" data-original-width="640" height="240" src="https://1.bp.blogspot.com/-Ca6feERRyLQ/W99TbROwfsI/AAAAAAAAsac/cusBuW8DlvEqJYBvf0xdTyIz3sl9E3dYwCLcBGAs/s320/Whataburger_hamburger_and_fries.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;"><b>This place looked great on the web... </b></span><br />[<a href="https://commons.wikimedia.org/wiki/File:Whataburger_hamburger_and_fries.jpg" target="_blank">Kyle Moore, CC-SA 1.0</a>]</td></tr></tbody></table>Looking at collective decision making this way shows that how individuals should respond to each other depends on how much <i>they </i>ascribe the choices made by others to random chance, not how much <i>we </i>do. We therefore need to be careful not to assume that 'noise' in the behaviour of animals in groups is an intrinsic property of the decisions, but instead remember that it depends on choices we make in deciding what to measure, and what to care about. The animals themselves may make very different choices. The consequences of adopting this viewpoint are laid out in detail in my recent paper: <a href="http://www.pnas.org/content/115/44/E10387" target="_blank">Collective decision making by rational individuals</a>. In short they are:<br /><br />1. The order in which previous decisions have been made is crucial in determining what the next individual will do - the most recent decisions are the most important.<br /><br />2. Because of the above, how animals appear to interact depends strongly on what we choose to measure. Social information isn't something we can measure in a model-free, neutral way.<br /><br />3. Group behaviour should change predictably when we observe animals (or humans) in their natural habitat versus the laboratory. In general, social behaviour will probably be stronger in the lab.<br /><br />None of this is to say that animals or humans always (or ever) <i>do </i>behave rationally. Rather, that they make decisions on the basis of reasons, not the roll of a dice. And their reaction to the choices made by others will be shaped by what they perceive those reasons to be in other individuals. Perhaps, to paraphrase Michael Osborne, we should never assume that other people or animals are doing anything random. Or at least we shouldn't assume that other people are assuming that.........<br /><br /><br /></div>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com0tag:blogger.com,1999:blog-1931373673946954854.post-74713558159800243032018-11-01T14:32:00.002+01:002018-11-03T15:02:01.847+01:00Yet more reasons to fund diverse basic science<div dir="ltr" style="text-align: left;" trbidi="on">Research is an incremental, iterative process. New advances build on those that came before, and open up new lines of research to follow afterwards. But not all research leads anywhere. The office drawers of academics are full of manuscripts that never got published, or data from studies that never showed any results. Whole fields such as <a href="https://en.wikipedia.org/wiki/Phrenology">phrenology</a> enjoy periods in the sun before fading away (if you know of any modern research that directly descends from phrenology, let me know in the comments).<br /><div><br /></div><div>In this respect, research is a lot like the <a href="https://en.wikipedia.org/wiki/Tree_of_life_(biology)">Tree of Life</a>, with each project or study being a species. Species may give rise to new species (new research questions), or they may go extinct, but the Tree of Research (hopefully) endures. </div><div><br /></div><div>Mathematicians have tools for understanding tree-generating processes such as these: <a href="https://en.wikipedia.org/wiki/Birth%E2%80%93death_process">birth-death models</a>. These specify what types of tree are likely to be generated based on the rates of speciation and extinction for individual species.</div><div><br /></div><div><a href="https://onlinelibrary.wiley.com/doi/10.1111/evo.13593">Graham Budd and I recently published a study investigating the properties of these processes</a>. Trees generating by birth-death processes are very vulnerable; a newly created tree with only a few species can easily stop growing if all of those species go extinct. On the flip side, trees that have already generated many species can be very robust and are hard to push towards extinction. A consequence of this is that trees that <i>do</i> survive a long time tend to have bursts of rapid diversification at the start. Looking more deeply into the trees that survive, we find that the surviving <i>lineages </i>(those species that have modern descendants) are <i>always </i>diversifying like crazy, speciating at twice the rate we would otherwise expect.</div><div><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><img height="230" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/960b81f6-90eb-4ff2-8110-131afd0d5ad6/evo13593-fig-0001-m.png" style="margin-left: auto; margin-right: auto;" width="640" /></td></tr><tr><td class="tr-caption" style="font-size: 12.8px;"><b><span style="font-size: small;">Trees that survive for a long time tend to diversify quickly when they are small (Budd & Mann 2018)</span></b></td></tr></tbody></table><div><br />What does this have to do with research funding? Increasingly research funding is allocated on the basis of competitive grant applications.<a href="http://prawnsandprobability.blogspot.com/2016/02/some-thoughts-on-academic-funding.html"> I have written before about the waste involved in this</a>, but another consequence is that research diversity suffers. To get a grant in the UK for example, you must convince the funder and reviewers that you have a very good chance to make notable findings and have impact in academia, industry and elsewhere. This requirement, along with the<a href="https://nexus.od.nih.gov/all/2012/02/13/age-distribution-of-nih-principal-investigators-and-medical-school-faculty/"> notable and growing bias</a> towards <a href="https://www.nature.com/news/the-best-kept-secrets-to-winning-grants-1.22038">funding senior academics</a> who have substantial previous funding, favours research that is predictable, which follows the researcher's previously demonstrated expertise and where preliminary results are already available. This in turn reduces the diversity of possible research avenues that might be explored. </div><div><br /></div><div>What is the result of reducing diversity? Our research suggests that if we depress the diversification of research we risk extinguishing the Tree of Research altogether. If we focus research efforts too narrowly <a href="https://www.theguardian.com/education/2012/jul/09/research-funding-for-star-academics">we put too many eggs in too few baskets</a>. The future success of those research areas is less predictable than we might like to think - few phrenologists thought that their expertise would one day be seen as quackery. If those bets don't pay off then scientific progress may slow down or stop altogether.</div><div><br /></div><div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td><img height="265" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/f28edbc1-f757-40ad-8402-04dbe535f79c/evo13593-fig-0003-m.png" style="margin-left: auto; margin-right: auto;" width="640" /></td></tr><tr><td class="tr-caption" style="font-size: 12.8px;"><div style="text-align: justify;"><b>Lineages that give rise to long-term descendants are always diversifying quickly (red lines). Green lines diversify slowly and go extinct (Budd & Mann 2018)</b></div></td></tr></tbody></table></div><div><br /></div><div>But surely, you might reply, isn't it a good idea to check on the track record of scientists and look at their ideas before giving them lots of public money? No doubt there is some value in scrutiny, but given the competition for academic jobs I think we can safely say that most academics have already been scrutinised before they start asking for money. As stated above, I believe our ability to predict what will be a success is highly limited. Moreover, several<a href="http://blog.mrtz.org/2014/12/15/the-nips-experiment.html"> studies have shown</a> t<a href="http://www.pnas.org/content/early/2018/02/27/1714379115">hat we can't even agree</a> on what is good or not anyway, reducing weeks or months of labour to a lottery. Just as importantly, <a href="http://www.pnas.org/content/114/20/5077.full">as another of my recent papers</a>, this time with Dirk Helbing, has shown, the way that we allocate rewards and resources based on past success can distort the things that people choose to research, and as a result reduce the collective wisdom of academia as a whole. <a href="http://www.pnas.org/content/114/20/5077.full">Dirk and I showed</a> that too much diversity in what people choose to research is greatly preferable to too little: as a collective we need the individuals who research seemingly mad questions with little chance of success. Unfortunately, the most natural ways to reward and fund academics based on their track record would seem to create far too little diversity of research.</div><div><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><img alt="Fig. 2." src="http://www.pnas.org/content/pnas/114/20/5077/F2.medium.gif" height="400" style="margin-left: auto; margin-right: auto;" width="387" /></td></tr><tr><td class="tr-caption" style="font-size: 12.8px;"><span style="font-size: small;"><br /></span><br /><div style="text-align: justify;"><b><span style="font-size: small;">Rewards influence diversity and collective wisdom. Too much diversity (orange line) is better than too little (black and blue lines). (Mann & Helbing 2017).</span></b></div></td></tr></tbody></table><div>So what can be done? Dirk and I showed that collective intelligence can be optimised by retrospectively rewarding individuals who are proved right when the majority is wrong. This mirrors approaches in statistics for ensemble learning called <a href="https://en.wikipedia.org/wiki/Boosting_(machine_learning)" target="_blank">Boosting,</a> wherein we train models to predict data that other models were unable to predict accurately. So I would be in favour of targeting grants to those who have gone against prevailing opinion and been proved right. However, we also showed that if agents choose what to research at random this will create greater collective intelligence than many reward schemes. This would support funding many scientists with unconditional funding that supports research wherever their curiosity takes them. This would have the additional advantage of removing <a href="https://prawnsandprobability.blogspot.com/2016/02/some-thoughts-on-academic-funding.html" target="_blank">much of the deadweight cost of grant applications.</a><br /><br /></div><div><b>References:</b></div><div><br /></div><div>Budd & Mann (2018): <a href="https://onlinelibrary.wiley.com/doi/10.1111/evo.13593">History is written by the victors: The effect of the push of the past on the fossil record</a>. <i>Evolution</i></div><div><i><br /></i></div><div>Mann & Helbing (2017): <a href="http://www.pnas.org/content/114/20/5077.full">Optimal incentives for collective intelligence</a>. <i>PNAS</i><br /><i><br /></i>Pier <i>et al. </i>(2018) <a href="http://www.pnas.org/content/115/12/2952" target="_blank">Low agreement among reviewers evaluating the same NIH grant applications.</a> <i>PNAS</i></div><div><i><br /></i>Price (2014), The NIPS Experiment: <a href="http://blog.mrtz.org/2014/12/15/the-nips-experiment.html">http://blog.mrtz.org/2014/12/15/the-nips-experiment.html</a></div><div><div><br /></div><div></div></div></div>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com0tag:blogger.com,1999:blog-1931373673946954854.post-24529423340934850622018-05-21T10:17:00.000+02:002018-05-21T10:17:19.613+02:00What crosswords can teach us about collective intelligence<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: left;">Dear reader: it is only fair to give you advance warning that this post will be a thinly-veiled excuse for me to crow about winning the prize for the weekly Times Jumbo Cryptic Crossword...</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">...that being said, I have long meant to write a post about crosswords, and in particular what they can teach us about collective intelligence. So here we go:</div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-7gFkL11fNfY/Wv7tNwjOJEI/AAAAAAAAsHY/wLl7kRfJY1gZYzfPyMcoSGY4UnqnaP0RgCLcBGAs/s1600/DaFyuAoV4AAELjs.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1200" data-original-width="1114" height="320" src="https://3.bp.blogspot.com/-7gFkL11fNfY/Wv7tNwjOJEI/AAAAAAAAsHY/wLl7kRfJY1gZYzfPyMcoSGY4UnqnaP0RgCLcBGAs/s320/DaFyuAoV4AAELjs.jpg" width="297" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>Alexander wept, for there were no more worlds to conquer.</b></td></tr></tbody></table><div class="separator" style="clear: both; text-align: left;">Most weeks I complete several <a href="https://www.crosswordclub.co.uk/">crosswords in The Times</a> (London not New York). I'm not an especially good crossword solver, and solving a typical crossword might take me anywhere from 30min to several hours depending on the difficulty. Clearly solving a cryptic crossword is a task that requires 'intelligence' to perform, though exactly how transferable that concept of intelligence is can be debated. You don't need to be a maths whizz or a language expert - most of it is about learning a few basic rules of cryptic clueing and fostering a reasonably open mind. In the case of The Times it also helps to absorb a lot of weirdly specific knowledge and jargon of the sort that a certain demographic of person possesses - picture an English man in his 50's-70's who went to private or grammar school and then Oxbridge, and who grew up on a diet of Enid Blyton books and cricket. For reasons that are <a href="https://english.stackexchange.com/questions/69013/why-is-money-called-rhino">completely inexplicable</a> you also need to know that 'rhino' can be a synonym for 'money'. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">All of that is to say that I am not positing crosswords as a benchmark for general intelligence, but that they can be used as an example of a task that requires some type of intelligence to perform. In terms of crosswords, we can measure 'intelligence' firstly by how many clues one gets right, and among those who get all clues right, by the speed of completion.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">What does this have to do with collective intelligence? Well, on many occasions I complete crosswords together with my friend <a href="https://en.wikipedia.org/wiki/Graham_Budd">Graham Budd</a> [1]. As the saying goes, two heads are better than one, and when solving together we typically finish the crossword more quickly than on my own, despite us wasting time bemoaning the particularly excruciating clues and otherwise dwelling on our perceptions of ongoing societal collapse. As such, this is an example of collective intelligence - together we are able to solve a problem with greater intelligence than either of us alone.</div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-8ZkhrrANZRE/WwG2KwQEhjI/AAAAAAAAsIM/3gYC50hq_I8hEi0N6DZ5LHoUKK7ocDBPACLcBGAs/s1600/Screen%2BShot%2B2018-05-20%2Bat%2B18.53.17.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="140" data-original-width="442" height="101" src="https://1.bp.blogspot.com/-8ZkhrrANZRE/WwG2KwQEhjI/AAAAAAAAsIM/3gYC50hq_I8hEi0N6DZ5LHoUKK7ocDBPACLcBGAs/s320/Screen%2BShot%2B2018-05-20%2Bat%2B18.53.17.png" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>An excruciating clue: Sunday Times Crytic 4619</b></td></tr></tbody></table><div class="separator" style="clear: both; text-align: left;">So far this is not especially noteworthy. Of course we are faster together! We can divide the labour. When one of us gets a clue we both get it. Even if we don't agree to split the clues, neither of us has the solve all the clues ourselves. However, what is surprising is that we often finish the crossword in less than half the time it would take me alone. That means that our 'intelligence' has more than doubled. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Such a case is called <i>superadditive; </i>If I write the performance of some individuals as f(Individuals) then:</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><b><span style="font-size: large;">f(Me + Graham) > f(Me) + f(Graham)</span></b></div><div class="separator" style="clear: both; text-align: left;"><b><br /></b></div><div class="separator" style="clear: both; text-align: left;">Or in plain language, Graham and I are 'more than the sum of our parts'</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Conversely, many cases of collective intelligence are <i>subadditive, </i>i.e.</div><div class="separator" style="clear: both; text-align: left;"><span style="font-size: large;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><b><span style="font-size: large;">f(Me + Graham) < f(Me) + f(Graham)</span></b></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">For instance, one of the most famous examples of collective wisdom <a href="https://www.nature.com/articles/075450a0">comes from Francis Galton</a>. Galton observed punters guessing the weight of a bull at a fair, and noted that the average of their guesses was uncannily accurate. We know that this is a consequence of the<a href="https://en.wikipedia.org/wiki/Law_of_large_numbers"> Law of Large Numbers</a>, and thus we also know that the error in the average guess scales as 1/<span style="font-family: "arial"; font-size: 11pt; white-space: pre-wrap;">√</span>N, where N is the number of guessers. This is a <i>subadditive </i>relation. If we double the number of guessers we do not halve the error, but only reduce it by a factor of about 1.4. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">These illustrate two fundamentally different regimes of collective intelligence. The superadditive relationship is one we typically see when groups have evolved specifically to work together, such as a colony of insects or the cells in your brain. An termite colony is truly more intelligent than the sum of its parts: <a href="http://jeb.biologists.org/content/220/1/83?utm_source=TrendMD&utm_medium=cpc&utm_campaign=J_Exp_Biol_TrendMD_1">no single termite could build the large intricate nest that the colony inhabits</a>, even if it were given a huge amount of time to try. Likewise, no single neuron in your brain could learn...almost anything. The interactions between individuals produce something far beyond what they can do alone. In these situations the group can grow very large, as the benefits of group living increase with each new member. </div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-1nLfAAGjGC8/WwHiZKIFLSI/AAAAAAAAsIk/hijMHY8z3EcoUWwb21qa9MWqn7tGlsn-gCLcBGAs/s1600/Cathedral_Termite_Mound_-_brewbooks.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1234" height="320" src="https://4.bp.blogspot.com/-1nLfAAGjGC8/WwHiZKIFLSI/AAAAAAAAsIk/hijMHY8z3EcoUWwb21qa9MWqn7tGlsn-gCLcBGAs/s320/Cathedral_Termite_Mound_-_brewbooks.jpg" width="246" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>Grand designs</b></td></tr></tbody></table><div class="separator" style="clear: both; text-align: left;">On the flipside, subadditive collective intelligence is what we often see in groups of unrelated individuals, like the punters guessing the weight of Galton's bull. Other examples with similar properties are seen in the way that navigating birds pool their knowledge about how to fly home, or how groups of fish become better at avoiding predators. In each case the group is better than one individual, but there are diminishing benefits of adding more and more group members. In such situations the benefits of being in a group are naturally limited: for example, you might get better at finding or catching food, but then you have to share it with more other individuals. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Humans are not like insect colonies - we do not live in groups of genetically identical individuals who specialise and collaborate for the common good. But the most interesting examples of human collective intelligence occur when, despite this, we still find superadditive scenarios, where we can become more than the sum of our parts. Some problems naturally lend themselves to this type of collective solution. A good example is mathematics, where someone may work on a problem for years until they meet just the right person with the right knowledge to solve a problem together. On a more humdrum level, consider Graham and I completing the crossword. Despite sharing some things in common, we also have a lot of different knowledge. This means that Graham will easily solve some of the clues I find most difficult and vice versa. And due to the nature of the puzzle, when Graham solves a clue he may make the one I am looking at easier, by giving me some of the letters. We don't just divide the clues at random, we naturally each tend to look at the ones we are most likely to solve. <a href="http://science.sciencemag.org/content/330/6004/686.full">Researchers in the USA have in fact shown</a> that group intelligence is more related to the diversity of group members and the extent to which all individuals are able to participate than it is to the intelligence of the individuals themselves. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">In the example of the crossword, this diversity of skills is a happy accident. But in other cases there are incentives for people to be specialised. <a href="https://en.wikipedia.org/wiki/Division_of_labour#Adam_Smith">Adam Smith noted</a> that division of labour made industrial production much more efficient. Similarly, markets such as the stock exchange can reward a diversity of knowledge - the best way to make a profit is to know something about a company that other people do not.<a href="http://www.pnas.org/content/early/2017/04/25/1618722114.full"> Some of my recent research</a> has looked at how these incentives can be manipulated, and we find exactly this: rewarding people for accurately predicting something that other people were unable to predict creates the best environment for fostering collective intelligence. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">What is the future for collective intelligence. Globalisation, increasing urbanisation and the internet have created ever greater rewards for specialisation. This has fostered economic growth and associated improvements in health and education, especially in what were once under-developed countries now enjoying the fruits of industrialisation. There has thus naturally been a drive to follow this trend further. But we should be wary of continuing this drive to specialisation indefinitely for the sake of group performance. One of the most depressing anecdotes I have ever heard [2] relates to specialisation: an accountant, finding his job rather unfulfilling, began spending large amounts of time playing the online multiplayer game World of Warcraft. In this game [3], players typically join together in 'guilds' to complete 'quests' together. Completing quests can gain players experience points and prizes which can be used to improve their characters in the game. However, when a guild completes quests together, the resources they expend or win, and the new materials they buy or sell must be managed and divided equitably. Slowly over time this accountants guild found they needed to devote more and more time to managing resources - a task that called for some specialisation. Eventually our hero finds himself coming home from 8 hours of real world accountancy only to spend his evening doing the guild's accounts, while other players do the fighting on his behalf! As this anecdote illustrates, if we follow our specialities too closely we may eventually become alienated and lose our motivation to participate in the group at all, which will then reduce the group performance.</div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-TEGfaQQq9oY/WwHGwKcQlGI/AAAAAAAAsIY/SHHtTDF1qMYN6NNhPAaSvKIzvkbFYqp8QCLcBGAs/s1600/accountant-2302101_640.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="640" data-original-width="640" height="320" src="https://2.bp.blogspot.com/-TEGfaQQq9oY/WwHGwKcQlGI/AAAAAAAAsIY/SHHtTDF1qMYN6NNhPAaSvKIzvkbFYqp8QCLcBGAs/s320/accountant-2302101_640.png" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>Feel the wrath of my double-entry bookkeeping [4]</b></td></tr></tbody></table><div class="separator" style="clear: both; text-align: left;">In contrast, as I noted at the start, I am not a particularly good crossword solver. It can easily take me 4-5 hours in total to solve one of the 'Jumbo' crosswords on Saturdays. Given that one is unlikely to win the prize even if the crossword is completed correctly, and that the prize is a set of books that one could get for about £50 on Amazon, this is not an efficient way for me to acquire an atlas and a dictionary. I complete the crosswords because I find the puzzle intrinsically interesting and diverting. What's more, I value my ability to do a range of tasks, some of which I might even be actively bad at (as erstwhile members of Uppsala Wanderers FC will attest). <a href="https://en.wikiquote.org/wiki/Time_Enough_for_Love">Robert Heinlein said</a> 'specialisation is for insects', and I'm inclined to agree; while a degree of specialisation is useful, too much goes against what makes us human, and deprives us of motivation and intrinsic reward in activities. To perform well, and to lead fulfilling lives, we need not just diversity between individuals, but also diversity within ourselves and our own minds - to experience the joy of mastering multiple tasks, and to have agency over our own lives rather than to feel like ever smaller cogs in an every larger machine. This also makes us more flexible and robust. Mastering one task makes you vulnerable to that task becoming redundant. Being able to work in many different groups in a multitude of ways makes you more able to contribute as society's needs change. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">So in conclusion, as someone who studies collective intelligence, I am most interested in finding how this can be fostered without crushing individual autonomy. I don't want us to end up looking like an insect colony. I'd rather we ended up like Graham and me, coming together to solve tasks that bring us satisfaction in a job collectively well done. I for one will be enjoying my atlas far more than any I could have bought on Amazon!</div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-i91i_ywcLDw/Wv7s_idkbUI/AAAAAAAAsHU/lliUjIt33nQpzWqHqEzs55fJM18EYkT2wCLcBGAs/s1600/2018-05-16%2B18.02.13.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1200" data-original-width="1600" height="240" src="https://3.bp.blogspot.com/-i91i_ywcLDw/Wv7s_idkbUI/AAAAAAAAsHU/lliUjIt33nQpzWqHqEzs55fJM18EYkT2wCLcBGAs/s320/2018-05-16%2B18.02.13.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>To the victor, the spoils</b></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">[1] Though not in the case of my immortal triumph in <a href="https://www.thetimes.co.uk/puzzleclub/crosswordclub/puzzles/crossword/38741">Cryptic Jumbo 1313</a>!</div><div class="separator" style="clear: both; text-align: left;">[2] I vaguely recall this coming from <a href="http://www.swansea.ac.uk/staff/science/biosciences/strombomd/">Daniel Strömbom</a>, of <a href="http://rsif.royalsocietypublishing.org/content/11/100/20140719.short">robot sheepdog fame</a>.</div><div class="separator" style="clear: both; text-align: left;">[3] My knowledge of WoW is all at least 3rd hand so please excuse any inaccuracies in this description.</div><div class="separator" style="clear: both; text-align: left;">[4] As an academic statistician, I'm aware that I really shouldn't be nerd-shaming anyone.</div><br /></div>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com0tag:blogger.com,1999:blog-1931373673946954854.post-4715811568722362552017-11-06T14:51:00.000+01:002017-11-06T14:52:21.042+01:00Feedback in academic selection<div dir="ltr" style="text-align: left;" trbidi="on">I recently finished reading Cathy O'Neil's excellent book, <a href="https://weaponsofmathdestructionbook.com/">'Weapons of Math Destruction'</a>, which describes how large scale use of algorithms and metrics are creating dangerous systems that create and perpetuate unfairness and pathological behaviour. I highly recommend it to anyone interested in how the seemingly opaque systems that increasingly govern our lives work, and came into existence.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://images-na.ssl-images-amazon.com/images/I/51eUw-v0X%2BL._SX329_BO1,204,203,200_.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="499" data-original-width="331" height="320" src="https://images-na.ssl-images-amazon.com/images/I/51eUw-v0X%2BL._SX329_BO1,204,203,200_.jpg" width="212" /></a></div><br /><br />One thing that O'Neil wrote about that struck a chord with me was about systems that have no feedback to tell them whether they are working well. For instance, O'Neil writes about the use of baseball statistics to select a winning team. In this case, if the algorithms don't work, the steam won't win and the team's statisticians are forced to change their models. She compares this to university ranking systems, where the true quality of a university is measured via a range of proxies, such as entrance scores, employment stats, publication metrics etc. In this case their is no external factor that can determine whether these measures are right or wrong, so in effect the proxies <i>become</i> the quality. As a result universities spend a lot of time chasing good scores on these proxies, rather than attending to their fundamental purpose of research and education<br /><br />As I was reading this I started thinking about how many systems in academia, and elsewhere, operate with a similar lack of useful feedback. As a result, many decisions are being made without any meaningful opportunity to reflect on whether these decisions, and the criteria on which they were based, were any good. For example, in the past few years I have sat on both sides of various hiring committees. These typically involve a group of faculty members interviewing several candidates, reviewing their work and watching their presentations, before collectively deciding which would best serve the needs of the department. This collective decision can be more or less equally shared between members of the committee, and may focus on particular immediate needs such as teaching shortages, or more generalised goals such as departmental research directions and reputation. In some institutions the candidates face a relatively short interview, while in others (particularly in the USA), they meet with many members of the department over several days. Different systems no doubt have their own particular merits and downsides.<br /><br />What is rarely done though is to precisely define what the department hopes to achieve with this hire. Even rarer is to evaluate later whether the hire was a right decision. For instance, a department may want to increase its research reputation. This is a goal which may mean different things to different people - some may think it implies gaining more research funding, others may consider that publications in top tier journals are more important. To define a measure of success, the department could decide that it wants the hired candidate to publish as many papers as possible in a defined set of acceptable journals, or to bring in as much grant income as they can. It can then measure the success of the decision with respect to these numbers later.<br /><br />But there remains a problem here. What threshold determines a good decision? The goal of the hiring committee was to select the best candidate. They should not be considered a success if they picked one good candidate from many others, nor a failure if they hired one poor candidate from a generally weak field. To decide if the hiring process was successful or not, it is necessary to keep track of the paths not taken, the candidates not selected. Academics are fairly easy to keep track of online - we have a strong tendency to build up <a href="http://www.richardpmann.com/">elaborate online presences to advertise our research</a>. Therefore it should be possible to keep an eye on shortlisted candidates who were not hired, and see how they perform.<br /><br />Such a process raises statistical and ethical issues. Selected candidates may perform better simply because they were given a chance while others were not. Would it be ethical or wise for the department to make tenure contingent on outperforming the other shortlisted candidates (I would argue not, but this would be similar to the practice of hiring more assistant professors than the department plans to give tenure to). Nonetheless, applied sparingly and with a little common sense, it could give some idea as to whether hiring committees were able to accurately judge which candidates were genuinely the best for the job better than picking from the shortlist at random. This could then be as evidence for improving hiring procedures in the future. For example, a department aiming to improve its research ranking might choose to employ young academics with papers in top journals, only to find that they struggled to replicate this success without the support of their previous supervisor. Over time they could recognise this pattern and look for more evidence of independent work and research leadership.<br /><br />Similar questions could be asked of selection procedures for allocating grant money and publishing papers. In some cases there is a process for evaluating success (grant funders ask for reports, journals check their citations and impact factors), but all too rarely do those doing the selecting evaluate whether the people, papers or proposals that they rejected would have been better than those they selected, i.e. whether they succeeded in the task of selecting the best. Without this feedback, it is easy for institutions to lapse into making selections based on intuitively sensible criteria which have little hard evidence to support them.<br /><br /><br /></div>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com1tag:blogger.com,1999:blog-1931373673946954854.post-71889573812808339892017-09-16T00:05:00.003+02:002017-09-16T00:05:44.489+02:00Guest post on Academic Life Histories<div dir="ltr" style="text-align: left;" trbidi="on">I have a new <a href="http://academiclifehistories.weebly.com/blog/outrageous-good-fortune-and-selection-bias-in-academia">guest post </a>up on the <a href="http://academiclifehistories.weebly.com/blog">Academic Life Histories</a> blog, detailing how luck and selection biases influence how we perceive success in academia.<br /><br /><a href="http://academiclifehistories.weebly.com/blog/outrageous-good-fortune-and-selection-bias-in-academia"><img border="0" height="368" src="https://3.bp.blogspot.com/-tvvBmShibzE/WbxOmA7cVJI/AAAAAAAArB4/h40rNTezZe0uMbe480hY5mh55RYydtxygCK4BGAYYCw/s640/Screen%2BShot%2B2017-09-15%2Bat%2B23.04.47.png" width="640" /></a><br /><br /></div>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com0tag:blogger.com,1999:blog-1931373673946954854.post-16143492417335711672017-06-16T21:36:00.000+02:002017-06-16T22:43:53.715+02:00Rethinking Retractions: Rethought<div dir="ltr" style="text-align: left;" trbidi="on">Four years ago I published what turned out to be one of my most popular blogposts: <a href="http://prawnsandprobability.blogspot.ch/2013/03/rethinking-retractions.html">'Rethinking Retractions'</a>. In that post I related the story of how I managed to mess up the analysis in one of my papers, leading to a horrifying realisation when I gave my code to a colleague: a bug in my code had invalidated all our results. I had to retract the paper, before spending another year reanalysing the data correctly, and finally <a href="http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1002961">republishing our results in a new paper.</a><br /><br />Since I wrote that blogpost I have found there are a lot of people out there who want to talk about retractions, the integrity of the scientific literature and the incentives researchers face around issues to do with scientific honesty.<br /><br />Here a few of the things that have resulted from that <a href="http://prawnsandprobability.blogspot.ch/2013/03/rethinking-retractions.html">original blogpost</a>:<br /><br /><ul style="text-align: left;"><li><a href="https://www.cs.toronto.edu/~duvenaud/">David Duvenaud </a>(who spotted the original bug in my code) created <a href="https://www.cs.toronto.edu/~duvenaud/talks/sanity2.pdf">a presentation</a> and<a href="https://arxiv.org/pdf/1412.5218.pdf"> a paper</a> on the pitfalls of creating code for analysis, and sanity checks the analyst can use to avoid the same thing happening to them</li><li>The story was picked up <a href="https://www.timeshighereducation.com/features/how-likely-are-academics-confess-errors-research">by Times Higher Education</a> </li><li>I was invited to tell my story at a symposium at the <a href="http://wcri2017.org/">World Conference on Research Integrity 2017</a>. The symposium was organised by Elizabeth Moylan, who with co-authors wrote <a href="http://biorxiv.org/content/early/2017/03/21/118356">a proposal </a>for a new system of post-publication article alterations. </li><li>After speaking at the symposium, the story of my retracted paper was <a href="https://www.statnews.com/2017/06/01/shrimp-study-error/">covered by the founders of Retraction Watch in STAT</a> and <a href="http://www.sciencemag.org/news/2017/06/how-avoid-stigma-retracted-paper-dont-call-it-retraction">then by Science</a></li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-rreZGlzGCS0/WUQuRBDMq8I/AAAAAAAAqfI/O5nR6GVr5SwIqU_7ihlOe9zrp3wxIIniQCLcBGAs/s1600/wcri.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="900" data-original-width="1600" height="225" src="https://4.bp.blogspot.com/-rreZGlzGCS0/WUQuRBDMq8I/AAAAAAAAqfI/O5nR6GVr5SwIqU_7ihlOe9zrp3wxIIniQCLcBGAs/s400/wcri.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Speaking at the World Conference on Research Integrity<br /><br /><br /></td></tr></tbody></table>Looking back now at the original blogpost, I can see the situation with some more distance and detachment. <b>The most important thing I have to report, five years after the original cock-up and retraction, is that I never suffered any stigma from having to retract a paper.</b> Sometimes scientists talk about retractions as if they are the end of the world. Of course, if you are forced to retract half of your life's work because you have been found to have been acting fraudulently then you may have to kiss your career goodbye. But the good news is that most scientists seem smart enough to tell the difference between an honest error and fraud! There are several proposals going around now to change the terminology around corrections and retractions of honest errors to avoid stigma, but I think <b>the most important thing to say is that, by and large, the system works </b>- if you have made an honest mistake you should go ahead and correct the literature, and trust your colleagues to see that you did the right thing.<br /><div><br /></div><div>Meanwhile, I'm just hoping I still have something to offer the scientific community beyond being 'the retraction guy'...<br /><div><br /></div></div></div>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com0tag:blogger.com,1999:blog-1931373673946954854.post-63041664534274569092017-06-16T20:36:00.004+02:002017-06-16T21:43:02.491+02:00Analogues between student learning and machine learning<div dir="ltr" style="text-align: left;" trbidi="on"><div class="page" title="Page 1"><div class="layoutArea"><div class="column"><b>Back in 2014 I was trying to make some progress towards my <i>docent </i>(Swedish habilitation) by fulfilling the requirement to undertake formal pedagogic training. As it happens, I left Sweden before either could be completed, but I recently went back through my materials, and found this essay I had written as part of that course. In the absence of anything else to to do with it, here it now lies...</b><br /><br /><span style="font-family: "cmbx12"; font-size: 14.000000pt;"><b>Introduction </b></span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11.000000pt;">Over time people have developed increasingly sophisticated theories of learning and education, and correspondingly teaching methods have changed and adapted. As a result, much is now known about what activities most promote student learning, and the differences between individuals in their learning techniques and strategies. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11.000000pt;">At the same time, computer scientists have developed increasingly powerful artificial intelligences. The creation of powerful computational methods for learning patterns, making predictions and understanding signals has drawn attention to a more mathematical understanding of how learning happens and can be facilitated. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11.000000pt;">Some of the parallels between these fields are obvious. For example, the development of artificial neural networks was driven by the analogy between these mathematical structures and the neuronal structure of the brain, and encouraged scientists to describe the brain from a computational perspective (</span><span style="font-family: "cmti10"; font-size: 11.000000pt;">e.g. </span><span style="font-family: "cmr10"; font-size: 11.000000pt;">in [Kovács, 1995]). However, the analogies between theories of learning in education and computer science are deeper than these surface resemblances, and go to the heart of what we consider useful </span><span style="font-family: "cmti10"; font-size: 11.000000pt;">information </span><span style="font-family: "cmr10"; font-size: 11.000000pt;">and </span><span style="font-family: "cmti10"; font-size: 11.000000pt;">knowledge</span><span style="font-family: "cmr10"; font-size: 11.000000pt;">, and what we mean by </span><span style="font-family: "cmti10"; font-size: 11.000000pt;">understanding</span><span style="font-family: "cmr10"; font-size: 11.000000pt;">. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11.000000pt;">In this report I will review elements of both the pedagogical and machine learning literature to draw attention to specific examples of what I consider to be direct analogues in these two fields, and how these analogies help organise our knowledge of the learning process and motivate approaches to student learning. </span><br /><span style="font-family: "cmbx12"; font-size: 14.000000pt;"><br /></span><span style="font-family: "cmbx12"; font-size: 14.000000pt;"><b>Learning to learn </b></span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11.000000pt;">When computer scientists first began creating an artificial intelligence, their first approach was to try to encode useful knowledge about the world directly in the machine, by explicitly inclusion in the computer’s programming. For example, in attempting to create a computer vision system that could recognise handwriting letters, the programmer would try to describe in computer code what an ‘A’ or a ‘B’ looked liked in terms that the computer could recognise in the images it received. However, this procedure generally proved dramatically ineffective. The sheer range of ways in which an ‘A’ can be written, the possible permutations on the basic design and the different angles and lighting that the computer could receive defeated the attempt to systematically describe the pattern in this top-down fashion. </span></div></div><div class="layoutArea"><div class="column"><br /></div></div></div><div class="page" title="Page 2"><div class="layoutArea"><div class="column"><span style="font-family: "cmr10"; font-size: 11.000000pt;">Instead, success was first achieved in these tasks when researchers tried the radically different approach not of teaching the computer each concept individually, but instead teaching the computer </span><span style="font-family: "cmti10"; font-size: 11.000000pt;">how to learn </span><span style="font-family: "cmr10"; font-size: 11.000000pt;">itself. In 1959 Arthur Samuel defined machine learning as a ‘Field of study that gives computers the ability to learn without being explicitly programmed’ [Simon, 2013]. By providing the computer with algorithms that allowed it to observed examples of different letters, and learn to distinguish these itself from the examples, much greater success was possible in identifying the letters. In essence, by teaching the computer good methods for learning, the computer could gain much greater understanding itself, and with less input from the programmer. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11.000000pt;">The parallel here with the teacher-student relationship is very direct. A teacher is responsible, of course, for providing a great deal of information to a student. But the best teachers are more successful because they teach the students how to learn for the themselves, how to fit new examples into their existing understanding and how to seek the new information and examples they need. At the higher levels of tuition, encouraging and enabling this self-directed learning is essential. Anne Davis Toppins argues that within 30 minutes ‘I can convince most graduate students that they are self-directed learners’ [Toppins, 1987]. However, much as programmers initially tried to directly tell computers what they needed to know, before realising the greater efficiency of teaching them to learn for the themselves, so has the pedagogical approach taken a similar path [Gustafsson et al., 2011]: </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;"><br /></span> <span style="font-family: "cmr10"; font-size: 11.000000pt;">'For some lecturers, thinking in terms of emphasising with and supporting the students’ learning and “teaching them to learn”, i.e. supporting them in their development of study skills, can constitute a new or different perspective. [...] </span><span style="font-family: "cmr10"; font-size: 11pt;">Some teachers claim that since the students have studied for such a long time in other school situations, the higher education institution should not have to devote time to the learning procedure.'</span><br /><span style="font-family: "cmr10"; font-size: 11pt;"><br /></span> <span style="font-family: "cmr10"; font-size: 11.000000pt;">In other words, there have been, and indeed still are many lecturers who view their role primarily in terms of transmitting information, rather than in developing the students’ abilities to think and learn for themselves. </span><br /><span style="font-family: "cmbx12"; font-size: 14.000000pt;"><br /></span><span style="font-family: "cmbx12"; font-size: 14.000000pt;"><b>Conceptual understanding </b></span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11.000000pt;">In the modern teaching literature, much importance is placed on aiming for, and testing students conceptual knowledge. That is, students are expected to learn not simply a series of factual statements, or isolated results, but instead to incorporate their knowledge into higher level abstract concepts that they can use to understand unfamiliar situations, solve unseen problems and extrapolate their knowledge to new domains. The prevailing doctrine of </span><span style="font-family: "cmti10"; font-size: 11.000000pt;">constructive alignment </span><span style="font-family: "cmr10"; font-size: 11.000000pt;">[Biggs, 1999] that forms the basis for recommended teaching approaches in European countries under the Bologna process is designed to make sure that teaching methods, student activities and assessment assignments all align towards this goal of promoting and testing whether students understand the ‘big picture’. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11.000000pt;">According to a computer scientists view of knowledge and information, there is a very good reason why we should aim to promote such a concept-centred approach for students. Identifying unifying principles that tie knowledge together and understanding how apparently different fields may link together reduces the amount and the complexity of the information that a student or computer must </span><span style="font-family: "cmr10"; font-size: 11pt;">store, access and process, and maximises the effectiveness of extrapolating to new domains.</span><br /><span style="font-family: "cmr10"; font-size: 11pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11pt;"><span style="font-family: "cmr10"; font-size: 11pt;">Consider as a simple example the data shown in figure 1. How can this data be effectively stored? The simplest method would be the record each pair of (</span><span style="font-family: "cmmi10"; font-size: 11pt;">x, y</span><span style="font-family: "cmr10"; font-size: 11pt;">) co-ordinates. Assuming we use a 1 byte per number (single-precision floating point accuracy), this will take us 20 bytes (10 </span><span style="font-family: "cmmi10"; font-size: 11pt;">x</span><span style="font-family: "cmr10"; font-size: 11pt;">’s, 10 </span><span style="font-family: "cmmi10"; font-size: 11pt;">y</span><span style="font-family: "cmr10"; font-size: 11pt;">’s). But visually we can immediately recognise an important pattern; the data clearly lie along a straight line. If we know the gradient of this line we can immediate translate any value of </span><span style="font-family: "cmmi10"; font-size: 11pt;">x </span><span style="font-family: "cmr10"; font-size: 11pt;">into a value of </span><span style="font-family: "cmmi10"; font-size: 11pt;">y</span><span style="font-family: "cmr10"; font-size: 11pt;">. Therefore we can reproduce the whole data set by specifying just 12 numbers – the 10 values of </span><span style="font-family: "cmmi10"; font-size: 11pt;">x, one value for the intercept </span><span style="font-family: "cmr10"; font-size: 11pt;">and one value of the gradient. Therefore by understanding one big idea, one concept about the data, that they lie along a line, we have almost halved the effort of learning and storing that information. Furthermore, we can now extrapolate to any new slue of </span><span style="font-family: "cmmi10"; font-size: 11pt;">x</span><span style="font-family: "cmr10"; font-size: 11pt;">, immediately knowing the correct corresponding value of </span><span style="font-family: "cmmi10"; font-size: 11pt;">y</span><span style="font-family: "cmr10"; font-size: 11pt;">. If we had simply memorised the 10 pairs of co-ordinates we would have no way to do this. In the field on machine-learning this line of reasoning has been formalised into the principles of Minimum Message Length or Minimum Description Length, first proposed by Chris Wallace [Wallace and Boulton, 1968] and Jorma Rissanen [Rissanen, 1978] respectively. This states that the best model, or description of data set is the one which requires the least information to store. Modern texts on machine-learning theory focus heavily on the superiority of the simplest possible models that enable reconstruction of the necessary information and stress the connection to the well established principle of Occam’s Razor (</span><span style="font-family: "cmti10"; font-size: 11pt;">e.g. </span><span style="font-family: "cmr10"; font-size: 11pt;">[MacKay, 2003]). Applications of machine learning theory to animal behaviour have further suggested that animals apply the same principles to maximise the value of their limited processing and storage capabilities [Mann et al., 2011], so it is likely that humans also apply similar methods</span></span></div></div></div><div class="page" title="Page 3"><div class="section"><div class="layoutArea"><div class="column"><span style="font-family: "cmr10"; font-size: 11.000000pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11.000000pt;"><br /></span></div></div><div class="section" style="background-color: rgb(100.000000%, 100.000000%, 100.000000%);"><div class="layoutArea"><div class="column"><div style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: left;"><img border="0" data-original-height="1280" data-original-width="1600" height="320" src="https://3.bp.blogspot.com/-85USjKonNck/WUQkfhGLT3I/AAAAAAAAqe4/vWyxGKnXFgI2cIKwgdIymmhVObwHazfUwCLcBGAs/s400/ttc.jpg" width="400" /></div><br /><br /></div></div></div><div class="layoutArea"><div class="column"><span style="font-family: "cmr10"; font-size: 11pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11pt;"><br /></span><br /><span style="font-family: "cmr10"; font-size: 11pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11pt;"><b><br /></b></span><br /><span style="font-family: "cmr10"; font-size: 11pt;"><b><br /></b></span><span style="font-family: "cmr10"; font-size: 11pt;"><b>Figure 1: By observing conceptual patterns in the data we can reduce the amount of memory needed to store it, whether on a machine or in a human mind. In this simple example identifying the linear relation between the X and Y co-ordinates (Y = 2X), we need to store only the X values, the intercept and the gradient, reducing the number of stored numbers from 20 to 12.</b></span><br /><div><br /></div><span style="font-family: "cmr10"; font-size: 11pt;">An analogous example in student learning might be seen in teaching mathematics students to solve equations. The most naive way for students to learn how to solve a particular type of problem in an exam would be to observe many, many examples of the problem, remember the solution to each one and then attempt to identify a match in the exam and recall the solution for the matching equation. Such an approach, while not entirely unknown among students cramming for final exams, </span><span style="font-family: "cmr10"; font-size: 11pt;">is likely doomed to failure. It requires an enormous amount of (trustworthy!) memory to store even a fraction of the possible problems one might see in the exam, and if a new problem is encountered there is no way to generalise from the known solutions to other equations in order to solve it. A much more efficient method is to learn </span><span style="font-family: "cmti10"; font-size: 11pt;">general techniques </span><span style="font-family: "cmr10"; font-size: 11pt;">that can be applied to any possible equation. In this case the student need only remember a few core principles and how to apply them. They can then solve both equations they have seen before, or new examples</span></div></div></div></div><div class="page" title="Page 4"><div class="layoutArea"><div class="column"><span style="font-family: "cmbx12"; font-size: 14.000000pt;"><br /></span><span style="font-family: "cmbx12"; font-size: 14.000000pt;"><b>Strategic learning </b></span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11.000000pt;">A common characteristic of high-achieving students is a </span><span style="font-family: "cmti10"; font-size: 11.000000pt;">strategic </span><span style="font-family: "cmr10"; font-size: 11.000000pt;">approach to learning. They have a good overview of what they need to learn to achieve their life goals. They set realistic but challenging learning goals for themselves to the end of learning this material. And they actively seek out information from teachers, reading materials and other sources to aid their learning. Whether their goals are intrinsic (interest in the subject, desire for knowledge) or extrinsic (obtaining a degree, getting a job), this strategic approach to learning systematically produces better outcomes than passively receiving whatever information is offered. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11.000000pt;">Analogously, in the field of machine learning, recent developments have tended more and more towards ideas termed ‘active learning’ [Settles, 2010]. The previous paradigm of simply offering many examples to the computer to learn from and then assessing or using the results of that process has been overturned. Instead, the programmer/mathematician devises a </span><span style="font-family: "cmti10"; font-size: 11.000000pt;">strategy </span><span style="font-family: "cmr10"; font-size: 11.000000pt;">for the computer to seek out new examples, based on what it wants to achieve (</span><span style="font-family: "cmti10"; font-size: 11.000000pt;">e.g. </span><span style="font-family: "cmr10"; font-size: 11.000000pt;">identifying written letters successfully) and what it currently knows. For example, if the computer has a good idea how to recognise an ‘A’, but frequently confuses a ‘U’ and a ‘V’, it will seek out or request more examples of these letters so that it can improve its knowledge. This way it does not waste time learning redundant material, but maximises the result of its effort by focusing on the most rewarding areas. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11.000000pt;">Likewise a high-performing student will focus their attentions on areas where they are weak and/or particularly crucial concepts that provide a pivot for understanding. They will ask their teachers for more feedback on their efforts in these areas, spend more time on mastering them and prioritise them ahead of areas of less importance or that are already understood. Mckeachie’s Teaching Tips [McKeachie and Svinicki, 2013] devotes a chapter to the importance encouraging strategic and self-regulated learning. One of their descriptions of a strategic learner states: </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;"><br /></span> <span style="font-family: "cmr10"; font-size: 11.000000pt;">‘Strategic learners know when they understand new information and, perhaps more important, when they do not. When they encounter problems studying or learning, they use help-seeking strategies’. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;"><br /></span> <span style="font-family: "cmr10"; font-size: 11.000000pt;">This emphasis on the importance of know where understanding is </span><span style="font-family: "cmti10"; font-size: 11.000000pt;">lacking </span><span style="font-family: "cmr10"; font-size: 11.000000pt;">and the resultant help- seeking strategy perfectly aligns with what information theory tells us is the optimal way to gain useful knowledge. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11.000000pt;">Mckeachie’s Teaching Tips [McKeachie and Svinicki, 2013] also focuses on the importance of student learning goals. My own research in the field of active-learning corroborate this view, demonstrating that even when a learner has a good learning strategy, the success of that strategy depends intimately on the goals that the learner sets themselves. Indeed, without a suitable goal the learner is unable to define a useful strategy [Garnett et al., 2012]. Thus, in order to develop students strategic learning skills, it is essential first to help them define, and identify what their individual </span><span style="font-family: "cmr10"; font-size: 11pt;">goals are. A student for whom this is an essential course, but who is otherwise uninterested, may be best helped by helping them to clarify what they wish to achieve (a certain final grade for instance), and then working with them to establish what strategy will most likely allow them to reach that outcome. A student with greater intrinsic motivation for the course may need help setting specific staged learning goals that enable a learning strategy. The teacher’s experience in understanding the most effective path through the material would therefore be essential in establishing effective goals that the student can then apply a strategy to achieve.</span></div></div></div><div class="page" title="Page 5"><div class="layoutArea"><div class="column"><span style="font-family: "cmbx12"; font-size: 14.000000pt;"><br /></span><span style="font-family: "cmbx12"; font-size: 14.000000pt;"><b>Discussion </b></span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11.000000pt;">While student and machine learning are clearly not direct parallels of each other (could one imagine a machine equivalent for tiredness, or skipping class to watch TV?), the analogies that do exist be- tween the two help us to understand why certain approaches to student learning are more successful than others, via the large body of technical knowledge that exists regarding how machines can be taught. In this report I have analysed a selection of those analogies, aiming to draw conclusions about how students should be taught. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11.000000pt;">In particular, a common theme of modern pedagogical approaches is to move from information transfer to a student directed learning approach. In a sense, computer scientists have been down this path already, switching from a programmer-led to a computer-led learning approach that has resulted in far superior learning outcomes. This should motivate and support the equivalent transition in student learning </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11.000000pt;">In teaching computers how to think and learn, we have also needed to help them establish goals and strategies for learning, and this is now the forefront of machine learning research. The dramatic improvement in computer learning outcomes when well-developed strategies are employed should remind us that it is the manner in which the student approaches new information and requests help and feedback that matter at least as much as the amount of information they are presented with. Such knowledge demands that we devote time to monitoring and developing students learning strategies and discussing what they hope to achieve via our courses. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;"><br /></span><span style="font-family: "cmr10"; font-size: 11.000000pt;">Students, like all of us, are presented with a great deal more information than they can easily process and digest. If computer science in the 21st century has taught us anything, it is the importance of identifying general patterns in the vast body of information we are now exposed to via the media, the Internet and other sources. Without relatively simple general principles, information can easily become overwhelming. That the same principle applies in student learning should not surprise us. How is a student to retain all the information we attempt to transfer to them without organising it into general principles rather than a huge array of specific cases? The content of any course therefore should revolve as much around this organisational structure as the raw information itself, demanding generalised understanding rather than specific regurgitation. Thankfully this is the direction modern pedagogy is taking, with such concepts of constructive alignment and the SOLO taxonomy. </span></div></div><div class="layoutArea"><div class="column"><br /></div></div></div><br /><div class="page" title="Page 6"><div class="layoutArea"><div class="column"><span style="font-family: "cmbx12"; font-size: 14.000000pt;"><b>References </b></span></div></div><div class="layoutArea"><div class="column"><span style="font-family: "cmr10"; font-size: 11.000000pt;">[Biggs, 1999] Biggs, J. (1999). What the student does: teaching for enhanced learning. </span><span style="font-family: "cmti10"; font-size: 11.000000pt;">Higher Education Research & Development</span><span style="font-family: "cmr10"; font-size: 11.000000pt;">, 18(1):57–75. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;">[Garnett et al., 2012] Garnett, R., Krishnamurthy, Y., Xiong, X., Schneider, J., and Mann, R. (2012). Bayesian optimal active search and surveying. In </span><span style="font-family: "cmti10"; font-size: 11.000000pt;">Proceedings of the International Con- ference of Machine Learning</span><span style="font-family: "cmr10"; font-size: 11.000000pt;">. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;">[Gustafsson et al., 2011] Gustafsson, C., Fransson, G., Morberg, </span><span style="font-family: "cmr10"; font-size: 11.000000pt; vertical-align: 2.000000pt;"> ̊</span><span style="font-family: "cmr10"; font-size: 11.000000pt;">A., and Nordqvist, I. (2011). Teaching and learning in higher education: challenges and possibilities. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;">[Kovács, 1995] Kovács, I. (1995). </span><span style="font-family: "cmti10"; font-size: 11.000000pt;">Maturational windows and adult cortical plasticity</span><span style="font-family: "cmr10"; font-size: 11.000000pt;">, volume 24. Westview Press. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;">[MacKay, 2003] MacKay, D. J. C. (2003). </span><span style="font-family: "cmti10"; font-size: 11.000000pt;">Information Theory, Inference and Learning Algorithms</span><span style="font-family: "cmr10"; font-size: 11.000000pt;">. Cambridge: Cambridge University Press. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;">[Mann et al., 2011] Mann, R., Freeman, R., Osborne, M., Garnett, R., Armstrong, C., Meade, J., Biro, D., Guilford, T., and Roberts, S. (2011). Objectively identifying landmark use and predicting flight trajectories of the homing pigeon using gaussian processes. </span><span style="font-family: "cmti10"; font-size: 11.000000pt;">Journal of The Royal Society Interface</span><span style="font-family: "cmr10"; font-size: 11.000000pt;">, 8(55):210–219. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;">[McKeachie and Svinicki, 2013] McKeachie, W. and Svinicki, M. (2013). </span><span style="font-family: "cmti10"; font-size: 11.000000pt;">McKeachie’s teaching tips</span><span style="font-family: "cmr10"; font-size: 11.000000pt;">. Cengage Learning. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;">[Rissanen, 1978] Rissanen, J. (1978). Modeling by shortest data description. </span><span style="font-family: "cmti10"; font-size: 11.000000pt;">Automatica</span><span style="font-family: "cmr10"; font-size: 11.000000pt;">, 14(5):465–471. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;">[Settles, 2010] Settles, B. (2010). Active learning literature survey. </span><span style="font-family: "cmti10"; font-size: 11.000000pt;">University of Wisconsin, Madison</span><span style="font-family: "cmr10"; font-size: 11.000000pt;">, 52:55–66. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;">[Simon, 2013] Simon, P. (2013). </span><span style="font-family: "cmti10"; font-size: 11.000000pt;">Too Big to Ignore: The Business Case for Big Data</span><span style="font-family: "cmr10"; font-size: 11.000000pt;">. John Wiley & Sons. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;">[Toppins, 1987] Toppins, A. D. (1987). Teaching students to teach themselves. </span><span style="font-family: "cmti10"; font-size: 11.000000pt;">College Teaching</span><span style="font-family: "cmr10"; font-size: 11.000000pt;">, 35(3):95–99. </span><br /><span style="font-family: "cmr10"; font-size: 11.000000pt;">[Wallace and Boulton, 1968] Wallace, C. S. and Boulton, D. M. (1968). An information measure for classification. </span><span style="font-family: "cmti10"; font-size: 11.000000pt;">The Computer Journal</span><span style="font-family: "cmr10"; font-size: 11.000000pt;">, 11(2):185–194. </span></div></div><div class="layoutArea"><div class="column"><br /></div></div></div></div>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com1tag:blogger.com,1999:blog-1931373673946954854.post-1863856910620616192017-06-07T16:41:00.000+02:002017-06-09T11:02:51.487+02:00General election 2017: Opinion Polls vs Betting Markets<div dir="ltr" style="text-align: left;" trbidi="on"><b>Update, June 9:</b> The results are in, and the <a href="http://www.bbc.co.uk/news/election/2017/results">BBC gives the vote share for each party</a>. Although the polls gave a wide variety of different predictions between different polling companies, the average of the polls appears to have outperformed the betting markets again!<br /><br /><a href="http://www.bbc.co.uk/news/election/2017/results"></a><a href="http://4.bp.blogspot.com/-jqM32kXX7lg/WTpiBrFdWHI/AAAAAAAAqd4/m5UeOWTXtB4ikRDpxBRefdOpf9b2AmDjQCK4B/s1600/Screen%2BShot%2B2017-06-09%2Bat%2B09.53.11.png" imageanchor="1"><img border="0" height="205" src="https://4.bp.blogspot.com/-jqM32kXX7lg/WTpiBrFdWHI/AAAAAAAAqd4/m5UeOWTXtB4ikRDpxBRefdOpf9b2AmDjQCK4B/s400/Screen%2BShot%2B2017-06-09%2Bat%2B09.53.11.png" width="400" /></a><br /><br />See my recent <a href="https://theconversation.com/a-simple-reward-system-could-make-crowds-a-whole-lot-wiser-76763">article in The Conversation</a> for some reasons why betting markets may have been performing so badly in predicting elections and referenda in recent years, or<a href="http://www.pnas.org/content/114/20/5077.abstract"> read the original research here</a><br /><br />------<br /><br />Tomorrow is the polling day in the <a href="https://en.wikipedia.org/wiki/United_Kingdom_general_election,_2017">UK General Election 2017 </a>(make sure you vote!). Today's news will be full of the latest opinion poll numbers, and pundits making predictions. Increasingly people are also <a href="https://theconversation.com/a-simple-reward-system-could-make-crowds-a-whole-lot-wiser-76763">looking to betting and prediction markets to get an idea of what is likely to happen as wel</a>l. Both opinion polls and betting markets have made some very significant errors in recent years. Before the Brexit referendum <a href="http://prawnsandprobability.blogspot.co.uk/2016/06/predicting-brexit-vote-from-betting.html">I did an analysis</a> of what bets on Betfair were telling us about the predicted vote share for Leave/Remain. <a href="https://theconversation.com/a-simple-reward-system-could-make-crowds-a-whole-lot-wiser-76763">Punters got that one wrong, just like the election of Trump in the USA</a>, while polls were more accurate in predicting tight races.<br /><br />Before we go to the polls tomorrow, lets compare what opinion polls and betting markets are telling us, so we can evaluate which is more accurate on this occasion. I'll focus simply on raw vote share for the two main parties (ignoring constituency effects), and I'll use the <a href="https://ig.ft.com/elections/uk/2017/polls/">Financial Times poll-of-polls</a> as a benchmark for the opinion polls and Betfair's vote share markets for betting markets.<br /><br />First the opinion polls: https://ig.ft.com/elections/uk/2017/polls/<br /><br /><a href="http://3.bp.blogspot.com/-AmDyN16RVl8/WTgN2Gy43CI/AAAAAAAAqdA/p5CBAPcSKjAMSEoVNqUIlQ0_-ThOAYUFQCK4B/s1600/Screen%2BShot%2B2017-06-07%2Bat%2B15.21.44.png" imageanchor="1"><img border="0" height="292" src="https://3.bp.blogspot.com/-AmDyN16RVl8/WTgN2Gy43CI/AAAAAAAAqdA/p5CBAPcSKjAMSEoVNqUIlQ0_-ThOAYUFQCK4B/s400/Screen%2BShot%2B2017-06-07%2Bat%2B15.21.44.png" width="400" /></a><br /><br />This gives a central forecast of Conservatives on 43%, Labour on 37%<br /><br />To calculate the predicted vote share from Betfair I'll be repeating the analysis<a href="http://prawnsandprobability.blogspot.co.uk/2016/06/predicting-brexit-vote-from-betting.html"> I did here</a> (see <a href="http://prawnsandprobability.blogspot.co.uk/2016/06/predicting-brexit-vote-from-betting.html">previous post </a>for R code), fitting a beta-distribution to the vote share divisions given on the market. I've taken screenshots of the Conservative and Labour markets, as these will no doubt change after I post this:<br /><br />Conservative:<br /><br /><a href="http://3.bp.blogspot.com/-u3NLTE99qX0/WTgOb0HVI7I/AAAAAAAAqdM/-qSb_U54RqQX4ydRcVScx2H6vrQEnXddACK4B/s1600/Screen%2BShot%2B2017-06-07%2Bat%2B15.12.43.png" imageanchor="1"><img border="0" height="168" src="https://3.bp.blogspot.com/-u3NLTE99qX0/WTgOb0HVI7I/AAAAAAAAqdM/-qSb_U54RqQX4ydRcVScx2H6vrQEnXddACK4B/s400/Screen%2BShot%2B2017-06-07%2Bat%2B15.12.43.png" width="400" /></a><br /><br />Labour:<br /><br /><a href="http://4.bp.blogspot.com/-mQtxw8xjxIE/WTgOgOvtWFI/AAAAAAAAqdU/fuSl1lB-Yx02mi9kUJZrDQwchAA3edCswCK4B/s1600/Screen%2BShot%2B2017-06-07%2Bat%2B15.12.03.png" imageanchor="1"><img border="0" height="141" src="https://4.bp.blogspot.com/-mQtxw8xjxIE/WTgOgOvtWFI/AAAAAAAAqdU/fuSl1lB-Yx02mi9kUJZrDQwchAA3edCswCK4B/s400/Screen%2BShot%2B2017-06-07%2Bat%2B15.12.03.png" width="400" /></a><br /><br />Performing the analysis to get the predicted vote share gives the following results:<br /><br /><a href="http://3.bp.blogspot.com/-XSjZ3dkgeoE/WTgO1vrmmUI/AAAAAAAAqdc/1itz8KoAQrk3aaVMy2p0hdB4TBfw0m2bQCK4B/s1600/election.jpg" imageanchor="1"><img border="0" height="347" src="https://3.bp.blogspot.com/-XSjZ3dkgeoE/WTgO1vrmmUI/AAAAAAAAqdc/1itz8KoAQrk3aaVMy2p0hdB4TBfw0m2bQCK4B/s400/election.jpg" width="400" /></a><br />This puts the Conservatives on 44% and Labour on 34% - almost identical for the Conservatives as the opinion poll, but somewhat lower for Labour.<br /><br />Labour have recently surged in the polls from a very low position. It seems that the betting markets don't fully trust this. Come tomorrow night we'll have a good idea which of the polls or the market has been more accurate.<br /><br /><br /><br /></div>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com2tag:blogger.com,1999:blog-1931373673946954854.post-50313948698336065362017-05-02T13:53:00.000+02:002017-05-02T18:02:22.923+02:00A simple reward system could make crowds a whole lot wiser<span><a href="https://theconversation.com/profiles/richard-mann-367883">Richard Mann</a>, <em><a href="http://theconversation.com/institutions/university-of-leeds-1122">University of Leeds</a></em></span> <p>There’s a problem with the wisdom of crowds. <img src="https://counter.theconversation.edu.au/content/76763/count.gif?distributor=republish-lightbox-basic" alt="The Conversation" width="1" height="1" /></p> <p>Market economies and democracies rely on the idea that whole populations know more about what is best for them than a small elite group. This knowledge is potentially so powerful it can even predict the future through stock markets, betting exchanges and special investment vehicles called prediction markets. </p> <p>These markets allow people <a href="http://www.nature.com/news/the-power-of-prediction-markets-1.20820">to trade “shares” in possible future outcomes</a>, such as the winner of upcoming elections. Anyone with new information about the future has a financial incentive to spread it by buying these shares. Prediction markets now routinely inform bookmakers odds and are <a href="http://www.cnbc.com/2016/06/13/polls-say-brexit-is-likely-but-the-betting-markets-say-it-isnt.html">quoted in news coverage of elections</a> alongside more traditional opinion polls.</p> <p>But prediction markets are having a crisis of confidence in the abilities of the crowd. They have been systematically wrong about a series of high profile political decisions, including the <a href="http://www.newstatesman.com/politics/2015/01/who-do-betting-markets-think-will-win-election">UK general election of 2015</a>, the <a href="http://www.economist.com/blogs/graphicdetail/2016/06/polls-versus-prediction-markets">Brexit referendum</a> and the <a href="http://www.cnbc.com/2016/11/07/betting-sites-see-record-wagering-on-us-presidential-election.html">US presidential election of 2016</a>. </p> <p>We shouldn’t expect perfect accuracy on every occasion, just as we know opinion polls <a href="https://theconversation.com/can-we-trust-the-opinion-polls-in-election-2017-76496">are often flawed</a>. But to be wrong so consistently about such prominent events points to possible flaws in the assumptions we make about crowd intelligence. For example, people don’t always act on the information they have and so it might never become part of the crowd’s decision. The dynamics of crowds and markets might also stop people from paying attention to some sources of information at all.</p> <p>However, there might be a way forward. My colleagues and I have come up with a model that overcomes this problem by giving people a incentive to seek out new sources of information, and an extra reason to share it.</p> <p>An important question for markets is “where do individuals get their information?” <a href="https://dx.doi.org/10.1038/scientificamerican1155-31">Research shows</a> that our opinions and activities very often match those of our peers. We also tend to look for information in the most obvious places, in line with everyone else.</p> <p>To give an example, if you look around on any public transport in the City of London you’ll probably see people holding copies of the Financial Times. This is a problem because if everyone has the same information, the crowd is no smarter than a single individual. Studies show that having a <a href="http://dx.doi.org/10.1002/ejsp.2016">diverse collection of opinions</a>, especially <a href="http://dx.doi.org/10.1126/science.1102081">including minority views</a>, is crucial for creating a smart group.</p> <figure class="align-center "> <img alt="" src="https://cdn.theconversation.com/files/167166/width754/file-20170428-12987-1hba5mi.jpg"> <figcaption> <span class="caption">Thinking the same.</span> <span class="attribution"><span class="source">Shutterstock</span></span> </figcaption> </figure> <p>So why do we tend to narrow the sources of our opinions? One reason is because we have an innate desire to <a href="http://dx.doi.org/10.1073/pnas.1008636108">imitate our peers</a>, to behave in ways that are safe and acceptable within our community. But it may also be because of a rational, profit-seeking motivation.</p> <p><a href="http://www.pnas.org/cgi/doi/10.1073/pnas.1618722114">We studied</a> how theoretical profit-motivated people behave when faced with the types of rewards seen in market-like situations. To do this, we created a computer simulation of a prediction market, where people received a reward for making correct predictions. Rewards were larger when fewer people guessed the right answer, just like in a prediction market or a betting exchange.</p> <p>The reward an individual received was a fixed amount divided by the number of other people who made a correct prediction. This was supposed to give people an incentive to look for right answers that other people wouldn’t find. But we found that people still gravitated towards a very small subset of the available information – just like London bankers with their copies of the Financial Times.</p> <p>The more complex the situation was, the smaller the percentage of available information people actually used. The problem was that the more niche, unused information, though it might be useful to the group, was so rarely useful to the individual that possessed it that there was no incentive for them to seek it out. </p> <h2>New reward system</h2> <p>To counter this, we created a theoretical new prediction market system, where people would only be rewarded if they expressed accurate views but were also in the minority. For example, if someone predicted that Donald Trump would win the US election, against the consensus view, they would have received a reward once the result was known. Conversely, if most people accurately predict the Conservative Party will win the upcoming UK election then they wouldn’t receive any reward.</p> <p>We found that this “minority reward” system, which explicitly favours those who go against popular opinion if they turn out to be correct, produced much more accurate collective decisions. This was especially the case when the situations were complex, influenced by many factors.</p> <p>Intuitively, this makes sense. If your opinion supports the existing popular view, you can’t change whether the group will be correct or not. In our model, people have an incentive to go hunting for more esoteric sources of information about possible future outcomes. For example, rather than reading the Financial Times, they might follow obscure blogs, or read local newspapers looking for information on companies in the area.</p> <p>They know that only by finding information that very few have access to will they have a chance to correctly go against the prevailing wisdom. This encourages the whole group to bring together a much wider set of information, leading to more accurate collective decisions.</p> <p>Our results are so far confined to a theoretical model, but they give us an insight into why current forms of prediction markets may be prone to failure, and how we might try to improve them in future. We hope that these insights will be used to create more accurate prediction markets, as we could all benefit from better collective foresight.</p> <p>Better predictions and collective decision making could help society decide which political ideas will or won’t work. Improving the ability of stock markets to predict which companies and ideas will do well could improve the return on investment and generate greater economic growth. Even academia is a large-scale exercise in collective wisdom. If changing the way that researchers are rewarded can improve the wisdom of this crowd, it could lead to more important scientific discoveries.</p> <p><span><a href="https://theconversation.com/profiles/richard-mann-367883">Richard Mann</a>, University Academic Fellow in Data Analytics, <em><a href="http://theconversation.com/institutions/university-of-leeds-1122">University of Leeds</a></em></span></p> <p>This article was originally published on <a href="http://theconversation.com">The Conversation</a>. Read the <a href="https://theconversation.com/a-simple-reward-system-could-make-crowds-a-whole-lot-wiser-76763">original article</a>.</p> <script type="text/javascript" src="https://theconversation.com/javascripts/lib/content_tracker_hook.js" id="theconversation_tracker_hook" data-counter="https://counter.theconversation.edu.au/content/76763/count?distributor=republish-lightbox-advanced" async="async"></script>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com0tag:blogger.com,1999:blog-1931373673946954854.post-42590885787836155362016-12-20T17:52:00.000+01:002016-12-24T11:24:01.865+01:00Cheap wins from data in healthcare<div dir="ltr" style="text-align: left;" trbidi="on">There have been many calls for a 'data revolution', or even a '<a href="http://www.forbes.com/sites/bernardmarr/2015/04/21/how-big-data-is-changing-healthcare">Big Data revolution</a>' in healthcare. Ever since the completion of the <a href="https://en.wikipedia.org/wiki/Human_Genome_Project">Human Genome Project</a>, there has been an assumption that we will be able to tailor individual treatments based on data from an individuals DNA. Meanwhile, others dream of using the masses of routinely collected clinical data to determine which treatments work and for whom through data mining. As individuals we are encouraged to <a href="http://www.apple.com/uk/ios/health/">record our health metrics using smartphones</a> to optimise our lifestyles for better health.<br /><br />Each of these aspects of data-driven healthcare has promise, but also problems. <a href="http://www.biometricsociety.org/2014/08/the-truth-about-personalized-medicine/">It is very difficult to reliably associate a disease or drug efficacy with a small number of testable gene allele</a>s, and very easy to identify false positive gene associations. Routinely collected data is very difficult to make reliable inferences from in terms of cause and effect, because treatments are not randomly assigned to patients. <a href="https://prawnsandprobability.blogspot.co.uk/2016/12/machine-learning-doesnt-give-you-free.html">Sophisticated analytics do not stop you needing to think about how your data was collected. </a>Lifestyle optimisation via smartphones probably owes more to Silicon Valley's ideal of the hyper-optimised individual and a corporate desire for ever more personal data than any real health benefits beyond an increased motivation to exercise.<br /><br />However, there are easy wins to be had from data. These are in prediction of future events that involve no medical intervention. It is difficult to predict how a drug will affect a patient, because you need to infer the drug's effect against a background of other potential causes. But it is much easier to tell if a patient arriving at the hospital for a specific operation will need to stay overnight; simply look at whether similar patients undergoing similar operations have done so. If this sounds exceptionally simple, that's because it is. However, the gains could be great. Hospitals routinely have to keep expensive beds available to deal with emergencies, or cancel planned operations to deal with unexpected bed shortages. A reliable system to estimate the length of patient stay after an operation with some accuracy would reduce the need for these expensive, time consuming and inconveniencing issues. On the ground staff already have a good sense for which patients will need to stay longer than others. However, in the maelstrom of an NHS hospital, anything that can help to systematise and automate the making and use of these estimates will reduce pressures on staff.<br /><br />Exploring this possibility,<a href="http://journal.frontiersin.org/article/10.3389/fpubh.2016.00248/full"> we performed an analysis of data the NHS routinely collects </a>for patients and procedures, such as age, year, day and surgery duration (see figure below), and used this to predict stay duration. Our results showed that a substantial portion of the variability in stay duration could be predicted from these data, which would translate to a significant saving for the NHS if generally applied and combined with current estimates of stay given by experts on the ground from their past experience. Note, importantly, we are not suggesting any intervention on the individual as a result of this analysis. For instance we make no judgement on whether the variation by day indicates anything important about treatment, only that this helps planners to know whats likely to come up next. This work is not about <a href="http://www.bbc.co.uk/news/health-34150672">whether the NHS should operate a full weekend service</a>!<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://www.frontiersin.org/files/Articles/216364/fpubh-04-00248-HTML/image_m/fpubh-04-00248-g001.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="421" src="https://www.frontiersin.org/files/Articles/216364/fpubh-04-00248-HTML/image_m/fpubh-04-00248-g001.jpg" width="640" /></a></div><div style="text-align: center;"><b><span style="font-size: x-small;"><br /></span></b></div><div style="text-align: center;"><b><span style="font-size: x-small;">The variation in predicted stay duration based on four possible indicators. Black line indicates median prediction, grey region is a 95% confidence interval. From <a href="http://journal.frontiersin.org/article/10.3389/fpubh.2016.00248/full">Mann et al. (2016) Frontiers in Public Health</a></span></b></div><br /><a href="ftp://rammftp.cira.colostate.edu/Connell/pdfs/forecast_competnc.pdf">As with numerical weather forecasts,</a> we envisage this supplementing and supporting existing human expert judgement, rather than replacing it - there are clearly facets of the patient that we cannot capture in a simple data analysis. This provides a minimal cost use of existing data, with little or no complicating causal issues, that could save the NHS money on a daily basis. The size of the NHS means that small gains can be amplified on a national scale, while NHS data provides an enormous potential resource. It may be in these unglamorous aspects of healthcare provision that data analytics has immediate potential.</div>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com0tag:blogger.com,1999:blog-1931373673946954854.post-28633157531101482862016-12-05T21:11:00.000+01:002016-12-24T11:24:22.407+01:00Machine-learning doesn't give you a free pass<div dir="ltr" style="text-align: left;" trbidi="on">A few weeks ago I read<a href="https://arxiv.org/pdf/1611.04135v1.pdf"> this paper </a>on arXiv, purporting to use machine-learning techniques to determine criminality from facial expressions. The paper uses ID photos of "criminals and non-criminals" and infers quantifiable facial structures that separate these two classes. I had a lot of issues with it and was annoyed if not surprised when <a href="http://www.telegraph.co.uk/technology/2016/11/24/minority-report-style-ai-learns-predict-people-criminals-facial/">the media got excited by it</a>. Last week I also saw this <a href="https://medium.com/@katherinebailey/put-away-your-machine-learning-hammer-criminality-is-not-a-nail-1309c84bb899#.5rg2ui89g">excellent review</a> of the paper that echoes many of my own concerns, and in the spirit of shamelessly jumping on the bandwagon I thought I'd add my two-cents.<br /><br />As someone who has dabbled in criminology research, I was pretty disturbed by the paper from an ethical standpoint. I think this subject, even if it is declared fair game for research, ought to be approached with the utmost caution. The findings simply appeal too strongly to some of our more base instincts, and to historically <a href="https://en.wikipedia.org/wiki/Eugenics">dangerous</a> <a href="https://en.wikipedia.org/wiki/Phrenology">ideas</a>, to be treated casually. The sparsity of information about the data is troubling, and I personally find the idea of publishing photos of "criminals and non-criminals" in a freely-available academic paper to be extremely unsettling (I'm not going to reproduce them here). The paper contains no information on any ethical procedures followed.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-8Fw9ayaKnJY/WEXFEm_IYKI/AAAAAAAAqMk/hGvqX98_YS01DFoBq368WsoswEfs5wHygCLcB/s1600/PhrenologyPix.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://1.bp.blogspot.com/-8Fw9ayaKnJY/WEXFEm_IYKI/AAAAAAAAqMk/hGvqX98_YS01DFoBq368WsoswEfs5wHygCLcB/s400/PhrenologyPix.jpg" width="321" /></a></div><br />Aside from these issues, I was also disappointed from a statistical perspective, and in a way that is becoming increasingly common in applications of machine-learning. The authors of this paper appear not to have considered any possible issues with the causality of what they are inferring. I have no reason to doubt that the facial patterns they found in the "criminal" photos are distinct in some way from those in the "non-criminal" set. That is, I believe they can, given a photo, with some accuracy predict which set it belongs to. However, they give no consideration to any possible causal explanation for why these individuals ended up in these two sets, beyond the implied idea that some individuals are simply born to be criminals and have faces to match.<br /><br />Is it not possible, for example, that those involved in law enforcement are biased against individuals who look a certain way? Of course it is. Its not like there isn't <a href="https://www.ncjrs.gov/App/Publications/abstract.aspx?ID=70171">research on exactly this question</a>. Imagine what would happen if you conducted this research in western societies: do you doubt that the distinctive facial features of minority communities would be inferred as criminal, simply because of well-documented police and judicial bias against these individuals? In fact, you need not imagine,<a href="https://www.propublica.org/article/machine-bias-risk-assessments-in-criminal-sentencing"> this already happens</a>: machine-learning software analyses prisoners risk of reoffending, and entirely unsurprisingly attributes higher risk to black offenders, even though race is not explicitly included as a factor.<br /><br />If this subject matter was less troublesome, I would support the publication of such results as long as the authors presented the findings as suggesting avenues for future, more careful controlled studies. However, in this case the authors resolutely do not take this approach. Instead, they <a href="https://arxiv.org/pdf/1611.04135v1.pdf">conclude</a> that their work definitively demonstrates the link between criminality and facial features:<br /><blockquote class="tr_bq"><i>"We are the first to study automated face-induced inference</i><br /><i>on criminality. By extensive experiments and vigorous</i><br /><i>cross validations, we have demonstrated that via supervised</i><br /><i>machine learning, data-driven face classifiers are able</i><br /><i>to make reliable inference on criminality. Furthermore, we</i><br /><i>have discovered that a law of normality for faces of noncriminals.</i><br /><i>After controlled for race, gender and age, the</i><br /><i>general law-biding public have facial appearances that vary</i><br /><i>in a significantly lesser degree than criminals."</i><br /><div><i><br /></i></div></blockquote>This paper remains un-reviewed, and let us hope it does not get a stamp of approval by a reputable journal. However, it highlights a problem with the recent fascination with machine-learning methods. Partly because of the apparent sophistication of these methods, and partly because many in the field are originally computer scientists, physicists or engineers, rather than statisticians, there has been a reluctance to engage with statistical rigour and questions of causality. With many researchers hoping to be picked up by Google, Facebook or Amazon, the focus has been on predictive accuracy, and on computational efficiency in the face of overwhelming data. <a href="https://www.wired.com/2008/06/pb-theory/">Some have even declared that the scientific method is dead</a> now that we have Big Data. As <a href="https://medium.com/@katherinebailey/put-away-your-machine-learning-hammer-criminality-is-not-a-nail-1309c84bb899#.5rg2ui89g">Katherine Bailey has said</a>: "Being proficient in the use of machine learning algorithms such as neural networks, a skill that’s in such incredibly high demand these days, must feel to some people almost god-like ".<br /><br />This is dangerous nonsense, as the claim to infer criminality from facial features shows. It is true that Big Data gives us many new opportunities. In some cases, accurate prediction is all we need, and as we have argued in a<a href="http://journal.frontiersin.org/article/10.3389/fpubh.2016.00248/full"> recent paper</a>, prediction is easy, cheap and unproblematic compared to causal inference. Where simple predictions can help, we should go ahead. We absolutely should be bringing the methods and insights of machine-learning into the mainstream of statistics (this is a large part of what I try to do in my research). Neil Lawrence<a href="https://www.youtube.com/watch?v=2Shx0cW1bMI&feature=youtu.be"> has said</a> that Neural Networks are "punk statistics", and by God statistics could do with a few punks! But we should not pretend that simply having a more sophisticated model, and a huge data set, absolve us of the statistical problems that have plagued analysts for centuries when testing scientific theories. Our models must be designed precisely to account for possible confounding factors, and we still need controlled studies to carefully assess causality. As computer scientists should know: <a href="https://en.wikipedia.org/wiki/Garbage_in,_garbage_out">garbage in, garbage out</a>.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-pqnt0RUPXDI/WEXGViHrzfI/AAAAAAAAqMs/GqsrVlcfEzslEna-F9I7YEZG4TMTAtliQCLcB/s1600/physicists.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://2.bp.blogspot.com/-pqnt0RUPXDI/WEXGViHrzfI/AAAAAAAAqMs/GqsrVlcfEzslEna-F9I7YEZG4TMTAtliQCLcB/s400/physicists.png" width="265" /></a></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: x-small;"><a href="https://xkcd.com/793/">XKCD:793</a></span></div><br />This is not a plea for researchers to 'stay in their lane'. I think criminology and statistics both need fresh ideas, and many of the smartest people I know work in machine-learning. We should all be looking for new areas to apply our ideas in. But working in a new field comes with some responsibility to learn the basic issues in that area. Almost everyone in biology or social science has a story about a physicist who thought they could <a href="https://en.wikipedia.org/wiki/Spherical_cow">solve every problem in a new field </a>with a few simple equations, and I don't want data scientists to do the same thing. I fear that if modern data science had been invented before the discovery of the Theory of Gravity, we would now have computers capable of insanely accurate predictions of ballistics and planetary motions, and absolutely no idea how any of it really worked.<br /><br /><br /><br /></div>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com0tag:blogger.com,1999:blog-1931373673946954854.post-72698855665298123222016-08-21T17:50:00.002+02:002016-08-22T12:23:56.862+02:00A Bayesian Olympics medals table <!DOCTYPE html> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"><meta http-equiv="Content-Type" content="text/html; charset=utf-8" /><meta name="generator" content="pandoc" /> <title></title> <script 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oPEio8DsNzZQqgUMoq0%2BNMALrygrOlErJohXvIJ%2F0IqziZok6OuApG2eoGAEFsTc6yWf9eRcklYZRO3PkA%2BW8aN5ME8aLNC3Kdwtm64WyqytOEW1WQIg6bOFHAs1ovo3OfCvvZASxBcxg2SRCRTTJDBKajFH0LL1kSBroe6L9xvVxMCIFS7Zo6y4ZOEIkAI9QtGVIKKBlCvUUEq2S8FiR7VkJGbvBFaS6UzQV%2BayV6NKw62tbJbEjkJ7AMC17DK399DZr%2FtE5sUtaAPwaHNj9VCoVB4VAG0iNI9IjDo0mr97FWjYeDRSr3pstZTVZ6nj5Vp3IbssG3g0r9E2eSmHY97LYobIHPnEGkKDJP15WPWtwMgS8HeLd6NEnP4mIFlRJB4zLeDeoBElpUNRIQMzLbRQsGLj3DZhQytDQPLAUE9JWHiLKAJxVTOJNZsObEiutLqwox%2BM51t7vJQhBeQm2i5bTa4D8qIUjqI1sL9G6Vha6U6IPUabeCUMIufG%2F%2F6USyxymXNlfnVinkNvKZGUjz0EWKIgZEC4WkUEr%2BgP%2BFpkIPUVM%2BQEJPxFxKDlpBEeiUSaTgCm4sEfRnBxu0eF%2FLgLp0IFHMEt8aZrsQzTF3wRw8TdpzHNGMZrHHa6nU8KCQppWBVpJ8b2Xjq278mtoTfrgfAMSAm3cYEcDw%2BzcSsXTaUyd2PH6DCU0DdBiauxpsyoKlAh9IUAzS32X%2F0d3x7h4gL36Q5sC4YzkbttmSwhenP5pxxrBEEcoAohUGB1jHGtB2%2BI0FEcCM2y8EY1e2NPXJS7wp7APp46lC7gSit7FEFQCIDnNX%2F196lJs%2BgXTyJrXAze%2FQ%2B9GEFC7p5W7W5FEooh5QlO01B1OcYDH4VTmRSO8fHPjRo4FkT9GrnUZw9pXnDplu0YFyOaAsLOkxdsu2gfYJ%2BDzBNihSUutbDbDy7VKS3KwwUTChYQkWCmldyS%2Fy05EvDGbLbpkDfbbHNGEhTSiaAEDmoKTERX3pEuKYJT%2FlNS4IawkdDACC5Jk4hgNa2EGV8yblsXoSHDrqHDJs4JDXLLA67oCyia7LABDzBMInY5gnZCpFuyyuaWXjKHRgy409j2wNaI1bGlosUnhaB5iqHHZf2%2BbDPpsIwoahsWRL69BhhyPHQBUNCyBR%2BUJzMOBRMxTVhNsS0%2B1n5kboqmNZcC%2Bt6HYVscRaBeox%2Fvv3%2FxwdoUoRvs6CamykRGihd8HTNaL%2BxRuoo3QVZvFT7xS9opWLiNbQRti9PXbNg0J5WDsxaNesdmkYOcwpiqsURuor%2BS8hhgWniGGll%2BtD55enFSsyATy9MonNXUJV5Q7eAouzR%2FP4HlA5YWBYYjm6NDAEk%2Bx9On0MGm65%2FEm1GKndnRp4cv%2FjFAdM7hnXsaXnGKAeK4aE%2F6BhOq1%2FAWmgCMQ4zC8G0wBzhuMSeeVhgAl0jpwicoR64K%2BBYlYbWz0gTGAGtI3puhx3F5%2F5QKXradYFuhJPYWq3ITCUUNLpugdVBegedngCO%2FDN5mJBWzGEL932jL1YntvCgzzLeR0WczKl0J4g8Gcbo6p5LOslpYBw4kE3ZDMiHPjBGyAUjkrWXqYTrl7gRUwex0zKVekIhoI0dsFRDtQxsLctjOlRs5Y2gYpQeBORQFR4C3hXh8EnZUzuloqFLFATXzpzv6k5XoHB3fZLNUiPV5DvAfroLwH8tYhkcOxWnHqePfQulM0DCPTadXa%2FTpoHYkh9BeeAwpmi9Kbo%2Fm88ob17pFzKP2lJpfWxbyD3PccS041A0MQWUqNDHOPOFt57Q6TiHQEKJQsI4v1JqcD7Q3orOdsLvExRQwS0nlUtV%2FpQbx0wSlrRSneWAQ%2FJhPaT6rMvIcid93ahrnKe34YxGA3D30BI2lEiLGh5iAUkBLBoXRshvpjGJGLzGcvonIqzVubgEJv4mbEl7JggQUWb6AYaQMmGUXEwIjylByVLbgcEbUQL5RFiRkX%2FbOhzb9XavzmFpR0cOdx3etgoaCPbiL5gR8o0wJNdPMCYcmyP0SDmmsW8o0O%2Fy5HNRxqz3IhmaxvIT%2FxpN8Pj%2Bx4i%2FGawfTOod%2BpvHN9BMNQUKG555l7yAKsma4r8JwVm6gxqBECXHA3e%2BdCsONR41WrcokynYzYqB0xlCdg9Nu%2FVL4rgwOiTVy8K70TghEjAOHeFBYvGwmkrDIzlwQsyBsr3K%2FEBFKO8UQ6J1hU%2FYGFA8fGgTnBoNnAmZc%2B9S%2BXnpbpJ4QKgdip6TZnI6woSQaYgxGpdaxxSuQkxu0avCBOSwchx0SS0x5HgR6iz9AkbeoDFTnGInFfbnMUP%2B8p3uSQu2CVkHxeVeEMICXKlVDsj89UY7AfyMvxTyws7ilT3y4zYSLVToLb1IwDJHJ804mZKVSKgSOa0mHCQrjWQLaz9LrCiISicIHspx5moJ%2F3Ng4rjU8aMqTDl5gjJAFgAMupkEoWEalYEtHh8CvvMqUP0Ra4v6BRr%2BdgNXFRLo%2BjKWRhaP4x63qqfsnw%2B%2FlDAo2doOxQP7GwahE%2BiZ2OX2l5DodFT8bGiL0YglcRmgDoYIEaRBLqdbj7HFD8xfZz45H2Tg6upN9XjuGCxtdxuVuRjssowtewrBo9gBM3T7d77hNjF9rd8QTMjwGLx3oWax6aa17t0I2gcG6kcQgw%2FphwfsB4gsCGgMGZU8P%2BORAg4iQDmTP9XqByg%2BjtRqWtpaHjiHSL8CNah084UP6Rfjx8GU2eaRw4mH%2BA9Ad42DummqhAj0%2FeMNS3V8lEHUSc1ntW779KspgJUBtJQEpS59ODiBRghAyioIrf%2FKoPh0eAJWqxh%2BSurG%2F5xVdzZBLgKEiYy4izBuKhCRIhfoADEt%2FB%2BirTWSOZVkcfzWBbA%2FAO817phMFhWQnvTwzjirEna6JgrjgHyk%2B8nWk0k06KkkSOOryl2OrOta3U1Vai9SLWxcE3cY161P64wA5VUgBExRGc8qtWCkEHIJfWtybVbTm%2BhrXnbVSsP4ucJTC9onJ8N4r9lRaV%2Fc4a2SZKmPNCgEUW7LDBXhvFxUvZYtnIuGD61WQtIrDXUc13hksUbImFeHrIBgvnG4ogmKBk5CClzY5DWqCCMzdrHBGSSOTyO%2BE8inLMGSApQqKJB3XKm%2F%2FMFoO17KuwfwqcaqjAyaJ5JOWW1Myr%2Fs7ZQiw%2FPqVAMH%2BlK6DYqjGUMcAXnVxy6z6CDl6j5mDa5EG4j8C6pr0hKyRNnoiR1vl9DWOfC2%2BM4v44bO3onXro%2BNlz00ZlGV2ICJ5CcCazVCJHIETBqVFhGT7KSBdNDv5ILpSacSTL0S6fX%2FP1CEIT5NZgcwpI0rkV7LqiHRoLUAPjXEqCZ5mLntX5JkkUEelCsU2tXCMZ6cZivQI6hYQNbXl4nc1sSNtBUTkQ8Y442KxRe7Uy5yOzB%2BUlA3MhvFmXweJJj%2F%2BG%2BqwJFWFLNYp0JhzD%2B4sl4JYn6a%2FvShCCo8hchMfrswjZgUqiToKfoOGaHdIAnKE%2BiEedBkyLwMSoNVX83TJERFy8PLMpBjsXtBITuS9lpPCTVl%2Fvs2Aqzlzwnj7lpl6VX%2FQ74tWqUSzaKziwue1phr9BpcZjNc%2FGXuJUq15TMDnCsJS0X2wAtW5JQA5MaTyUH4cDRif3MDxZx3Se89P4WSIvEEeLjToJbXf%2FrRhBMtRevJxuf%2Fs8EK4woZOFli3yTq3xqjBjrlierqgmUpFA15HFkeUOuLDjuhzLDjAGKK6WThTynzd%2FtCQWU3Nzd8%2Fa0q%2FxwZYn%2FUPEHU6lsdG%2Fn8gN%2BYACURCU%2BW%2FldrXpdUK7WxhgWmNd%2BLDoQFCU0sFyHn3KqFz%2BIg9e2C5oe9EOi7KdTBxPE1k4k5tkX%2FoZzSih8DJDFd%2BrITKNSsAAGtscSW9VDasqkEamMzeUOhRqRRAj9lc%2B7An2YOdL46GdcOLAsgYaFsR9hs0ToUzZ9rFRLG1%2F7eYLz1l5ijumbe1druwaHNFzZjtwt%2Bn7paZaMZu2EIx%2BlxX%2F2SBrWJQQM0wmE19eWrGPIVMeAzVWWRp76m1skeqzaBBZ6So4eD8Gpv31bn%2BnO4WG%2FOg%2FB7xQu9kpA3eZL3w9cwzrZfMmbUSk5OiF3Qx7bQYhL0VoUQQP3Hmps1bBJDQU0qAJpWwnb4iFOMBthzwP81ilVnh1bIuk0C9Xe%2B1kSK%2FK%2FMYOh7vIa7ghqGEKzCiHrehs3cA1pzgec5NpLDtCqMPp1GVECA4QZKiZX0hQ%2FGqjOhhObmpH0vwx0WHctTrmGC84Ub6BOQVdXIqoxqMVNhQjd%2B0CYMRk1zp6%2FPnIOsW7k%2BhQEruSB7%2BDEGv1lziYEEwur9gsigQBG8EJ3zeigdA74WvD0h2IbdNzPw3okAFsdmi3qKH41lxijDPDtvZcEzXwUnRNn4WpCP3vPNHhO8czUiYjRn6GRIQ4SymW9MhjUu%2FjbWOhOqNeh9OSRNh1EaFZcalxYnJMLCpTlEDttzYxhNCcZ86PUpbEkFmkU5HRiAF9AahZ8jQ769NUzJGkq9YLj9HWZLEK%2BIryXyPLZHAAHsBSe5moWq2RRQT655EACRYKQ1AR2mNQU6hNdrqLyfpSeJ5PrccWf3dXVxmIidWyyIkCm1v1oFYgyGcXwrCRPXPMLYHRFvGVuYyAUhzgYntJmDhE4VCNKoSxWlSFiFuMGumZHJnCJyAdT%2BHcgUhIEJZgWOjmy%2FZWisKRYo4JjuPntQGSxlJg3XJ5DBsFM3kGGQjqECyjqYFW6ccOkCDy3EhUt6taBIaHclyblt3Xxs353KjciddJC7gI4cZaPj4zBxOVNfei9MW9cLUHspngSFFni3AL7sLsbqo3totPWMf0yD2bdWKWuK2a4eF5jKcYCZyvORgcHeETtqeqhAYtIyiFGAYJQMOX4VJzPjyDKiavWJRtjWCnaTUdPR6FRkTfFAARc%2B3Ln3oFDETvxxiaDT3roIpaWwEEjRlhjvs9ZKiU2o1HJOMuVRFAA5fWzMgAqSKDaSLNQcQZbaFzsgKxXWIvjaOqsoiS0kA1bx2TN4NrJBVMJcmRWNIqrjepyobiDa9yXYKmJvgQWZhEBvF8wEx0pMQqCzcf9JemmcVMROHpvzARvqDrI5WOXmah0Zkh%2B6PIozOYm78ieRAJObTPxSCLuwQiRlWaLSxJ5hgIIrjsEUKPWMqRFuMgh1FsNDFw5jPGKPTWzyiSEIS6IPweoS55G9SZZ6wcpW%2BHYMSkoSETssJ3QQM9bQRo1JdCQdS1np6F5WR9wujL48y6xB4M6Y7FMnX7f22J6F5gyYVK0QlgEQxVXFUuC964aXqqhT5cX8XaZv5hVzeTU7bSoy40QuTOUjLVShZVi5iWJMAbFhku4I5QyO1x0Pm%2BcTesk5XsjnzwoAIsmXCFbWyIZQuawuVuXuR8DK92lWJDrNrbFtNbCj5sTTCx7e2Wb0UydtbZ%2F0CSIT7OnVIY0fRntwN3jNOdh7nGpmmq9CbBm1uLafMptryjPHHp7tKZEuAL7OjXHySRjUkXydXE%2BSrNxA2Um5Al8Dh3EZC5V4SFynxsMTKCAIMqEqNKzuJCQM3tvVBjRfT7xHSuCO72a6pSo2wn8%2FaXBmKI9sW2BccnPF8aML8%2Bohhb7ciWy%2Fxch7McUey2CPGCyVKaKDX8%2BSBNgqZqMLbCgZ4NPkIF6NfeH7gtElIrOqbudNqU8yyyewVZneKXuzObCUxU5b2tecTa7Jn7SE6UlSYMTkMfCs3Q7fVCaqK5k6pf%2F2wW%2F%2FosIJEgW3skUNgQHyb%2BsAi4ECMNcyjicIITuXGyXkkRIXyN50Jg3r1FpMmaQSUl9pGxnNMp8jf24vS5eX%2FyJYlMUISy9e6JooaPn7fiuG4QEscaDgCZpra85ygZUcJInLV6C314YPJdG2UL6qljb1QV1ZhrNcFecs0j2qb5gvkKHOFxHphwdBgEJc3y8qihwdZCQpJ62h1voTUccffiDJEzkU8jbXRvLFdPbcmVBUhArEuTKQFe570IglefLJ30dWmVAtx23vIGmF7N6auVNpZUQVHNmAlGgjNet51laJgLQSpfZyxBEqLwoCEGlF6ISp0NUmhUHT5a12%2FZElPE5UGO9AVnKpae3D5llVvXAHK0FIH3uE8AXFPF%2FSwx3OdCN6aViMIxEVcqv1UsLJo03R0grVOHRogBCiYVrK%2FqFBPmGrDyXLgr6DxBMSKnf1uSBgiRjCiwL1QoM981XHZnusKIVJ405xXwx6aBUuM2YXS0jaCPwaC2Zdp07J8gxM1KnpWMqNkRCfPaYTelLbBmd97YeNAOFaFOlV29YQn0qIInmIeMFxikX4U1pEusNYtOX6tKZKkgVONLhIF9ZPpxNWGA5fslgv82Lx49LF6FltT3Qp7q4Rcu4hKczn2m1GTA4unFBAkDCqY%2BD5s2dyVIfDeGeBgwDnPbGYXQqwM0E%2FBCl69QtVYbUwkQZAtSB618VkAzCPAs93Ip9qWnBMX%2BRUX0PFxCACZQwpfvNvAMGrD69RE6JSyNNOvRD8v3gzw46n8oB8mFQiYiwgidAyJgrfY1SaNrL5QDEjIIgYLECALRSK49wPmSO8jZLnesJ8oFZjWJyTrfBrNRCeOMoaVxOojhX6WVAhhJ6dvBPZ4AbMXC37YPHBFKUgA7t8mCk8U07mFgWg3wbOZDgsEZBOC%2FApoLJL8CzpXhZuoEh0ntzsvrUPhE40%2BUUkCAm26DxGMecbxuJ%2BpPJct9BZL6lVcWLmHps6SSRwqmRJeypwrd3vNnIawZkqBn%2BumMrwB%2Fc%2F%2BIAx3X3Ehjr%2FzJIVUK8Luxlv5IeNoBQPnIhvJDZfGo8KIpLh8O4iRusiuQOtytJ61yCvQUGFmCxEEliRlQmkN5wrVLkx3CUrlDG3ABe14lLsoysj9hXY%2FTJpUb3tCvpw8Ez7Wb20lfIScq%2F6wGFIrBkgzjtNLBoYqAgJoKvDHcdkTRNbmMKP7Fha6v0z1qPmfqQzKW%2Bi9g0kSWn1vQuqaJyaTAX7hrJwJgfaPjJvb6wXroHZRAD5NH2E2KaWtBw9TGd9mIea9%2BPrxlBpyjnQhg6rLogT7414uB8V19PPcBZUhnNx%2Fhr1%2BtX%2F1jKG4nnHv2EtR3VOjo9oWEibOHX8508Tra1pFg4lnAwoQ2u2JcsDi7diOc%2Fuhvd8qexCvYgoI6m9VYAg7Vl0PRXiuCdgHdKDIIHG0j73u07ULaOJJ60Y178Lsgtd7zYdOUGlMCYhR2Uhyglt3KUjPCpM8MKjVS6OgTHgqD1SSQ%2BqhzInvSk8VzFP1cI8vLxtdDvH35uPzMi4mQtJCrVUqhBWbQRke9Sjt9laOS7Y9YqUkXldpaAoofKmUNsx0D7eYLc%2BspsKbO71qdmmaGglAJjo4kj6XlnIWS1hQZORC%2Fh4i%2FCdcbaFFuxb0AYMJ7EdQExeIHEdPRtCxVECvtxHzbEyldDvie9cGKwImUuI0xEL9W%2B7FhefRJ05ePV427NJDYmhOCwBDNBP5LrIiblD6aw7pSeWFA%2FlDoWYMm%2BZEcF16VDdA3ALq7hDBlLUzNTL9AoVyczpCwb7xHucfK6T64W0AnDzYLg0HYWadOMPdoP%2FlliqiAlAWP4rio6stY02elA%2FLOPBnEr6rsAqtMRsS2g6HJtNANGwpxTdZEP5Xt5mE2gPs7dE0gyQv%2BFdd8QTBEqmAeMHtNnjBtKvg7KmIZCj9303GT9mWQXZxolBupTHIhJT%2B0WN7uu1FbRp6NnSRDIj1aXRJD25s%2FAD5%2FIc2OQ0iDp7%2F3Dbv3Oa8McFBhXrPpAKzhrFANFpcnLmEVTXjq0MO5sJAPVxFbMh93VfD%2FDppG4mBzXSgVfXJeWNNxoKF8QTwcQFXwQPB7QLE2PENdF%2F4vDL9zn0ZgQ1i6Nyr35KAwetsESlUtEENQbCFOeUFb9lg4Q%2FW5lUNo2fsscGbWY4T6pynpP0Krl%2BJFEfY%2BGGHI3aj8aBO0K%2FndAEPa5FX51Niq7CEOhoB2hSpGAgBT5%2BuzxAMzSuVEeQmZIbYew4tM4UsHYdZtT%2F9ibeR1u6rlX6lBQlSBT6LQ9YUEAgmAxLkAKQL9PSm%2F3NQF4w7ZvdqRqMJ5DYZh3j3I1rDmyXyti0llyZjkLnoPtHHwZd%2BfwWVz9ztMTMCFjpKBVWAdcYhRV6wY0kRv47nqddzEhQvXsqNstE6GNiLTd8iliAfI5vfm2KjfTQwbxz2uFzaUL0A9VKWzB7VrWS0QvlqVw9VCXOB6RDSgbNtW05PB7pEz%2FHZkv%2BXQTUD8mSQ3mJk%2FEUe3%2F2ixiuDVAOBfyIscXixo%2Frh7BHtl5KSBigokAOClzsk5pj5X5S9GLKgu5AbQNotZBWU5zoIzScHQKjeFNr0MiX0Mp%2BlHmHKuaDcfU2H%2F%2FhJmeXl1nPE8E%2Fk8ULZ%2FCLYtwJWG4CHI8h5ySfOAFbkRVFJyi0KYkQ%2FfhDAjciw08ETminGEMzG%2FwOERVW0AEslZEl4sfr5AYRKGVSMzkDSQ%2FnhkipQ8y8EF9ZRGKCOxRzfpNMubhc%2Bs9lZBHqNegMaRLozjP%2Bg8CUsaVzp5Wd0ZI5SaeSdNAD1HIc0vTPw7SLi4Jpa1gGgtEY865KzsFCn6I1RvKT3r6BVdYGsBPWdVzeLfbxKi8BVQVzd9f83goEpezGYiAXT8S%2FpW37TxnZ6f%2Bog248Vvj9otMMAmzAfvCpPYmXIx6ZAKAwBH737j2KJpWyuPMnFIBfqRrEBYiTiWVjvdx5T7k0dwFjgjLrLVm28m%2FXLNfjkSOzkoh3hangxcOjvxzVDIGSxYBxI9ak%2BDsrVTPAlMWZD7OThbuxdkWjCtGwtH4QzQdpmaBsHV8Yrg1iAK64TC2WMbQJAFFciwJFPSRQ86OtUrnPSODgRE%2FhD4qWAHDlWBDy1KPUCEbpodyyU4TnaIFzU%2BtJJAes10UhzVTNE6fGDGUN33wCgAZYoIz44wHk6fDO7wGbAEwmcVQg1HGGByFjYGdwJD1joA5AM8olCJ1LlTUGB%2FkhlrmbJbCbD4Uj0GZTy06zCTjOeVkJKZzqk0nE4%2B3RmlgDHpJwCwwZKOl8SEEH%2B8TQK7R6TiIPAy%2F5M08zWqjpXg4KWF%2FMNQpvipZJ4KZfGsivxCXyinAY16NjMD%2Bkgtfc8pGpAgSyN27l%2BuW3OjjOCnldBAJLpzjAYdBoh3b0yuYkLj7c6iwxR9NHW9WBeGVYjvaTEHVq2t96HA16vtKz3ZgtNuJgpjnNZRGEjbmQuiQEBJ2BdgHxFDqf0F1dQJcS4sIvDHlCASh65anDjgr07Qa98i8Jb1rAbSdOOz0cM9wlKXm7ugzOMTmi8EbeTBIoHrudZ9RSwEtADDsgyFwnxyfzXecDzLGFMmkRrGWCdnWVnSMMcc4cl7NaF%2Bt%2BgTHgy9s1SV05LLaw7YYgNxNKt2kpiEgpahsRp%2F0tarSWdfS3AdWYIAnrT68WTwX1vtPgL7EMcIzmOpOxL7oZh%2BcoizveUkJVmjedZZlkwkno1E7%2BjVJIoz8APlgweTgHUL%2FGciPnYgtfrq4TtxE4adiNQ2ZgyJHWYWmrMlW6ebFkPaAUwzKsAhoGXxXGRGKFObHKQOqFOnGgkyLajFNwhUa4fqva2yI2DlREZ6p0CNOGwR4XCrS4K3SH8pDQGvZIaDcMPtJUoLRM0owJ0iT9QcdRK5IRIIpAOzsUotf3TbAVvbQH8n5voA6kUzw6LqVnwPkmnYxgJLYiQ7hQYlEsYL4k5GCZvd58ypvZfwO5t1fXMTj11hE8GuAZhX78JMPsK%2FJ0yQqDPk4Z%2BJbbXS1tia0EBwCjgWUJsUI18clQ%2FL%2FH39pOY3jRcZFFfW7bC5v98f%2FwQjY4osg1CYvJfYmKVWbiPLEpDvlTEGLjUbCmh74cUqKtsVVr9hspTEdTKrKSRjqUHkhwgyUQeNizUsUp3cLmGnOoxPIuzYDGHFJxwclXasrQR5Pp4%2FX9adXL0zyaNRcp5govE%2FKIiLMyYKgb3rKpuxbm7t8U7GiR8qcIvzarYOuIr0z8D1QgHRWmwQj1jMXJlqpuDBiVUQD80Fnr7quJElyEAs47dXRoms8yEtA2VxNaYbJmUQ%2BlsKhyYLlk2q0QMXQSsMctgTGOka0GYae3AxbsfNKwpf8YnyAYZzDx20P8xvD5aQ4OkVtbj%2FxeO9gPGmBGT3BiXsWroQWXXm7Mw8XnUAttSlNyNEsqWLOLy5MJLmMa9m7Abm0SuOJF9RWA8VDp5xMP%2FI6LaAKUmkqt6%2Fxs1XyWrgcDo5hjmvshCSHhWpwCludJPk5i4bpUhqFw%2BRmK4VAI0O11JGtbQ64l%2By0LUdW7GarSUUwP47kW2CYDEdvsA%2FTXw0I4OPf2SvJ0FKjn7aZxxwVp2xjhpWMTDxaZMkiOxaFFLydXq16fefH2qVJybgXVpioGcKFhS4AjNTEa5T37zLo22Qv1apFD5qUjB9w8yA0vSc2RMiA7xIsRIGBTWOjHH9SZlK6QJGru7w%2Bq2GoC22fzSVxkr%2BWlT9rAABqi3RiLzDxns68PSEUIxqrqFw8oMUhIeL%2BSdTHAvw8M5C0b29DIIfScMQS0TKwvPEq3kAQvxMTC0D%2B7tnB7QNRliGiWl0NuVnIUY7QMwRkP%2FgVT2WDBX08%2BWLDc%2BiW0mz2CZ3IAvWqesMkIe3lWqMvUDL5Q33McSklm9U0P9SHgPGGVlX40diyUBp%2BpfWi%2Fh9sKTOvCRCj%2BeFIWvUXobOyAxrHlhKFGhOiw1vyKUiNMgN3k9No1jfVEpQEU35laY1OWX0u%2BF%2F3AcQq9opTw0RwEyxVosGLDgIkSdn7hs%2BIHrv2jR%2BJUh2kADlTtyX8HxtYxLUhMLj3%2FFpJAhfxzoRspqTIQicEOQtI1iv4n0xi9GiED3BLS%2BriXyEyU1v6KfcGAWCaq%2FgQ5kImR6wna1UoP6KtpT9XLI4EebxCRQriHsHkCOgDlZM8hJEHcCfGIERpbdeZFFHtE3lBjH2cIQ5p7TNVfRTwBkflxGhmddY2YfZbMF0bFv76YdpbH3dxSKmVVsblZW2xdvOxqSIQqbw536IFhJKhELagVlMG3LQqHU43e%2BRZjx4BJExsLcLX1oShyJFvhFevBTFOUF3Exw2yNBWwMCW5QA%2B7UmPhwM7AMOXRddPg6OxuaNAmiDYRKlcHo4FwUeta%2FLSOUyYddHQi3OFkb4z35KYG%2BxJAOZ8LTMyJ%2FCgARNXgZ%2FC%2BfKy8W7VwKPzhRpDnIMS0ClN6sPMpa421GfuLwApsG0C4FpdCsaLM0NtsctgKVSkeql94%2BXUmITqdGBajY4m4NmDFEk2HiFjYtNLmZSxNY1QM4KakEvIQIFts%2BOJ0QCRKvhCmQcfRAjN4VmYgb58CBUMiSUpcyuEfRFZS0SThDQPO4aFcJiNJUvlFdO0s8RaeSdpOSHscV%2BJAIchHCniOYTsEqhdLZtWVSiAw6hEDO7LI4or%2BkXTE6zB0CA9o4NUeZIpS0Fn7Q8lU4X9sZNCO0uPfjoWqOaqDVcbxBJSAs8RV9IcKmOPY%2FLDUnXDLSYfFT1xyNTWRLKRW0kFxctTIuvuU6R%2F%2F9ApGo0EHrqGH7dEmsI%2BgA0UXpfNwWFxUHz9CYK9toXP6IlTFRhuGh7z3bhwL5qzzoRAF8dkwboKslbtuftJDrshFMoBNaIvpSXyAFRCCKFOKEkzCkB3NDQB2qtV%2FANwHNea%2BAUDr6WWScJazRx4glReLp8vQ8sFtz%2BhqehlJO6MM5NMIc8%2FkWnwbE768NqCDKBi%2BpY288WynJ1CT2Kq9%2Bo6rhlUpRatsVIsacJhA%2Bq8M9X%2FUQMRZhshDAvsXwlZfxDn%2BWCfyJyLFA2s54on9a54PSC3WgchQWZLZgEl8xGrFUqCofhkvqYtXjA9XyewEKlnAtD26XlSvqtdhXOT%2Bi5BrX6S6hHVcqbZ8qbh%2BEzffUpCfTG5HULg9DQQaQ6ENkkq3DvUSAQwcxh24qkmtdRoIMDxOVDdy0T2w3afIBABsQGxnqJaAOY1gWawTUuhslaSivzrXaPcRyGhUkH0R541UbNvLKiY070WOGYY4R%2Fg1rfKhHcjoV4p45o21tldJXmpG0XsOekNlYucZlkAWkVUHtjkSeUbdfBMKrGATodKL9arS5JFVovaKRlOWbNJIS6GHxuLt8CX%2BBYQUYDfxlQrQQhL7z6vChINNDAVVN0rXxaKjegwIPOJf7rXfHBBHGpBNpaeLGFXCBrWAdpIwF6mcE7pE2z4HdIxcWkU0QA3TKjZQ%2FPNc4VwWA3OqmXuoleHBmMRLsU3ENaVgIpVnIWvBLVDYNLzVRdIefms6mo9VoRQZ6cCkQSOdK6KDkWEMZkQyIEM6QUltTfQ1xFpxUL%2FlFho06RSy0MhFQCIEh5FrTToDEgpZU4QcT%2FbYWc9XTPTTM6ZiDUk6d8MHSyFOgi3cE0Oh5I2Tv%2FThHNjxg7A0zwweFEVnLpE0Ai8Q9OWYcdB1zNKwLEBtxjc45oHjshf4AMMWhwwRhRdBnjEU3iL3TIBscW%2BvDMwGJnW4omSkqIJxsnzyWwZBg9lQCsSZ2CK25fZnAEtrlT3WZ1xUoqsQBEiEMEmCZAjQU8EhBFQSUEVhPwf6Ekh%2FQtYOKDqg%2BIfAJ8CuQ0oaANSG8CrQwYJAhV0I0D4CXAOIBYAcYMUAO4A0AuQNYAwAWgJAFzA9A0AgoIOA4ARIJoBoDTBVATUAVA%2FfmHjl6j%2B5Pa79V8K%2Fh%2FQfNvjz3P7ler%2FHHh7%2FPw68DnObsHvPy3cPPA5wScuOB7qBzX7b8SuTXQrw88fvOjUnszbV9wOhztB3%2FrTR53FdNbVFq3a82jxmuwOcluBDDjLjOjALxD3%2FQiP39Y7a5Rt0oNm7G8V06nAGXPxV3oiByNCcCfXAkpuOrai62YwdiJaYXnQsst7b8q9lbH1AhQ4fOtIhMRO4kqFfJyARyYkd8VFgh1WJGVCPlA1ZMLjSDAUNwDDwkxBcqWcEmILYipcSYqtCIqlSAqaSAqUCAqkjRU7GCpiLFSkWKlAgVIxAqRiBUbDiowGFRIMKhYMKgwKK%2FYQV6wYrughXTBCtmAFaz8VpvxWa%2FFYZ4KujsVY%2FYqr%2BxVOdCp85FSnwKkjcVGeoqJdRUiaio4xFRNgKhy0VBtoqArRXysFeyurkV1bquqMqqonq%2Bh2r6EqfoBp%2B%2BNH3jn%2B5M325m%2BzqX6%2F4%2FrnjqtKKqtoqqPhqmWGqVIapJgqjWCqxYKqxeqp52qenapVdqkp2qOnaopdqh52qD3Krsbqs1uquGqqZaqmdqqVmapLZqjdgLkVYtPvgiXswWobLWxLWyK0qjACE6uL48VDS74vVFa9UPr1QitVAa1XzWq9S1XKUq4ilUQUqiClULTqhKdUDSqgSNX2hV9IVfB9XkdViTasMbVeTarwZVcjKrSZVYS6q6XVVS6qiXVCBdUEF1fgqrzlVcsqrdlVbQqrWk%2FZ8n7Vkfagj7JEfYwf7Cj%2FXof68j%2FW8f62DVWIarWDVaUarJi1YsWrEC1XsWq9C1XQWq1iVWMSqMBKoqEqhgSqBxKvuJV7g6ucHVwg6tqHVrg6vuFV6QquaFVwQatsDVrwatGDVnAascDVhwaoyAqiv9UO%2FqhL9UBfq%2Bn6vB%2F7kf%2B2%2Fx%2BtVskpnZEuCUxHC%2B%2FYuIK6NNKiB%2FEzIk5DuCcPq3Ew4GQBYmlqw4gUEVMiRKFQwiMCQcTgAAAAEDAWAAF5ItM%2B6bFophhd3N1nA4zIKh4NARWfqCooqII1UQ4kBYJ2AQsGyO2lAp%2B6Xiqm%2FCkfz5urtugisAuGzxeNHQh1A73Vh4dG0%2FNDkMQKtSO%2FBTm3DojsrbF3jq6kKdaxNxwpKvTKteAnM7mCQ85oHLN5AxXtO3FxElkoEAFo%2FY7SdVN5daSO3q5Y%2BGBpQAYrusw%2BEY9%2FXMmtYT6y1gbXXfGgzHr8ic6AN9hcvHwEYELAoOjr69A1yaVwaL10euR3YUZUZvQl5xZXoT8YeJLqVKFrjMLT83%2BN7REmekLvRn0TLh%2BZMzVhvjjOcuh7%2FDGoSIzhcgAEyu2q%2BgmErl0SoAyvHf0gOOHkuRFZQSSkFEDSG4HCQ838BiFt5mdNnEIYrPlCai6RoN3%2FEdkyVeA7o%2BHQvKrwD5CYAAo2RJZIeP1xRy%2BlJaWuskPYYJ6GKPdNLzxcio1M6LXHJDQbx0X1i8B9YnLsQYerRiZjBe%2B2alDqaPIASEoxCeRAUMVuivCDeCNo43Zi%2BmFz4viBZJrJMbwxhXGCv8CUG%2BGpgMJzaVH06hQdq5woKyZyKYDByVHQl05OpUqPrSuURMAxrqnfhkQENbMcnlzk3MLnnmnljBLSdHj488rWP0ithH7Mq2sETRkNmgYc3AZSu6gL%2BCk4IDhPtHR057XmxZs5enMzU7IR5rdjAD5bhqPdP0mGax4%2FBC5rzvd%2FNmFSTuivxBTftCPQY%2BTO9CX4l81r5FFfrkZ1yrTcaX%2FE35vu8hUNdTlgS2iD0q93mIVdiG%2Bzz6ZoWvKaG4axR1VGYKVxYs%2FhBQR7uUeb1mU%2F3VlT93WVa55WteFObdmuaGauUaHua6G9Lh9q5rpXj%2Fwgi3iPylvEGKzMA9lXBUjbXHUnsEBSjM4dcmrgF7f0G9lwAQt4RLmuXHbpvBr9TrIO6tAdGiB79MRHozMKD8uVjof8zfR8GjzHzhs033A2Py%2BejgTAGqXxpL%2Fw2WVk1lFTJqz%2B0kBeRuJCR5GRySPRQSmUbztwmWP9kLIWUhlXSVdCicr0AP0QVDW1JhE6NsgqFunp2ST1zYgQv6Qnhu0JlL3GiFmbc6pMG8mzBJsoRi1z3Z5NTM0f1ndDFjciaUQqsNg6uq3fi8dFUAWOQGs1VX8XhLFmvpemPhnFsJ4EJp5fMYZskQQsqfYfD9NJDx6cnQ0sTSuR2L40hG49L%2Bmrs3RoC4ghACgxYOijJAtdpXHsZI0rFXEhZYgy3algwWFOreuLxQmZTNtXroCxgYhVHmAFChJHArQSkYK5FLPlzPCQ38AzsClDlC4ke6RHiVatgqkBMcH5a6mGXLmcLkgxPCTi3IYssNhBMcXoBJkK7iAw%2Fq1cJO27YZZ1dgwK6TjpcOKZhOClzaJK94ByvnLhalwYwwHNGbpKKrMoiCUVvMU4ZDGftbGmdYDSWM4M18njvCm2QeRAFzCJCDrWq4fFsh0jgTZAy3lAyEhSb5p3l%2B7zqhPPDOxcQ5kAj9XEi83gCXQDB330FUKUN8JTMzokg%2BMHLm0D3oGAQxNjGVUC4qv3mNqY80W8Wma%2FG%2FRJg0Pokw2Jil%2BUKRbOEH5QZhYg2DwSICOBEYPtpPgwWBiCfyJ0YCZEGKrTfFYsGyw21JEW52PoQdw%2BSszylGkFpTMhd5kWLnyTIQai8z1ij55qLRN75GxKwkR9E1MhMUCbxmmw63GyiBjM6OORqQNMpJtSUqMssFsiIRB3bOWC1CBqx4cDrtymvUnfKZrNpclIQX0iC%2B0SWyKIyxEbrSIkB4ly9nnkYJu6fFFI5UkewzCvGzpCmkfDtvWO%2FvOQBSKG%2Bw4WeOGpxQqahRKjqs7pmglalwleZKZnV2WNi1CBepIZxSes8CtZlRI0GWmUOVcYlpvK0hUKRhWaEyXRViM53DzUU8eSDYlUJQqDMmUYc2RuqTtfeLBUIWJzpxmeJiOCoAXmCaSqYM441iWisAz0U0EQHSkfuH3o9uyZk0g2C%2B1Huy1lYiCySpvTSdjMKwTiKdQVCax08qRNA1Vs2wiL2IyamfCpg%2BlZwXvOo2sB1QB9xIdX6Bj6VzRgd4UoHI9PenyASnBA8k3EjsE1S2ipMclWB3LPJeWzSHOikaNhJsFX5zoP45XxaGhDK%2FpP%2FDIYztiS6vqMPACWcgP2kpZWjOfJBHYRQNI4tp3WUQGWpE8ZqoZEFvYJaFCTkUJPdTqeYpTEWodgDyHYOTQomy%2BoKxLC8BtejPZfK3UMphCswZ56qASoLK60kVHNgZzT8%2FUWcqkls5xsQ57uoPAv%2BCrnsSCROispXTpjPKe4ND10sCf%2FElOsPgR%2B1K2fX5hXhJfNGzBWCpiE4EjGUBgUzovLqcdL1yqDbTutsHLe0YqwBcpKRqcP65%2Fvot41Eg4cbCrFOObHzAyIO3Np2zmgIymMqrmdZ5wgWiOKMA%2BV8kKigbnyOAnZzQK1uMozbw7SBWI%2BtpCLJTN4yFsnUOPsR6JqbOmnG2mYUYJV0I%2FFDRgDb2YBKeBAzYRv4d82IRIjKNJ6kthxBIf4f6tg5Rewqogb%2BBL89Xa%2B8Y7mPwJBnr%2BqyHL3Me2KqwE3nnFG4NiIrI%2BvziW0DG1jcQIHeE7iAwtWHXwFYTmEfOmdkgt4Pr1n2vJwnSQymN0R0NLRTgAHjDVSIfITmkvlvfz7MU64jgUChw5hCXsYgG5gXyQ1osKsxCRhvPgsghFG5zI1CXCBIAwKkjyKLeqBc%2BfEUFiCvfGOta3gR%2FU26my2RNT0gywIO1yxoMTM8Mlfo35lpDQ4jfU18jrE6QiUumMhcIndvm8iDoRH8amzyNFXNUKcSoCnh5AQYr61lElsUE1avUS%2FnDanpv%2FZFa3VH2JIq5OrC2wDxYOhlkZf5BIr5I2JAQY6MewSa45Ob%2Fz%2BEjpgzBQTlG3AdVyHpu2GkjfOxGCSQ%2F4KBsYV%2B4WC4tHrRIEC3vi8DWBGimk2R3cQNWDhpiR%2F9KQZE618tdreVPJR485XjWwoxbnLTn6IZ4EjKrhRraDtVPs4zmDldmpWjWM5L49vWKkkh21cJ0GELX5Hje5CUKJRNkIrvqKWk7bw8b7gYD5fEhk7VgXTHJI0UsIqSimKH3B62CsLrQWXjB%2BoWwKWamDL6RlAYnwhMdNFIyfJuJIyo2hI%2BRLmmREVRHaJdaBYDQo4bDl91nK3Zy7hcqlXpT%2F%2Fg9jl5m4DVYTnaJOAoq7zjeA2QzPBWRnDjFKG0AJybS5gxwd7oVkVIAgAqWCrwA2TuCFHn%2BlQSxm2EjeZemixAGSIByWTtmzQII9iyI6QxlnEfiedIUpRSDRKzAojtJx830mEfqcSqHRLRGSUmpIkhYAfBXhL3h5wRAsiPnzp5CmVoG70nYHSlNBsQEOYNSYjVHmDMCMyyhMYHx%2BhksBoo78rYc0vB6ClzXpCsSQL0xuJj0lRG0q3NgS%2FgqHn0%2FdBeijOqfmwAAwNmamjdRSr62goEAhLCK0y0mqVtUz8B3F3pE3rUMN9wQoCtpvRAK3sFTK3tcPZnt6Z27rdUEcCb1qxd8b7ARVibBsC%2BRyonUCCcPwOsBKtzEuPpnx3V%2BQo3FTRLkQsTzT%2Ft5GIpAhUffp2BuiRh%2FhQEK3waIhUoJczWFQtyb9PP5ODdKmoRpQHa5EoivjH117VzUEyb9h3I8XFhYGY2GgobkujLXrm%2BbJ7HN7wo3WOTojHaQLy5ZQH60wuIar4h1s2FLyTWktIBtEtP6PSDSPebTewSizvHczvHVzmh8LyM8TZbIzBlYhsTDRW2MtA4tMbKoUyaOwZNB0EcTEoAHayrWzlDMhazQx8GCH8%2BXZI4EskKhE1hnN1De89ZjtBMDWCxLN%2B4bn5AnyOhxpTflbO1kA%2F0EGhUliSyMtWT0UMb%2BqEPinhEFYyHEbAUyp8tYuqYDRipLscjyGJA3zbmKdMTMI8V72v2ZQ8R1C6WY4qjndJBCREkDNEWaBovAOsU5JvqCCECn5%2Fq30Wfs27Q1NX3PB1CxWQYK4rW6gl2DEhCJLvzF%2BBEKd6LLjbQMVuJRpueMSQJN40n5WAdyXvuYQeXUQsoQDysgsemARNTywlJKFiZeuo5AiRfoTmTq6hkwijNVgqADIQ0SrFqBN9hK5RC2ZzmikwVm0CCZzso1HPlzzN0IP%2BQCIQZ%2FzA%2FJ0cIiWLfbbDGvgdRmzRiOWxhWyl0iXpQfpiIVEQuNo2d7rj0OZeiVOeay6x5oKlhwZCcg8KUij44xrtH4IX6UM37YQMPXh6QvlpkcPG94IVYA3iwMJ0L8LuuaogTlCTJsenAjL0PQ7L1Pi8hmGJdOqOJeVo7ECLPOdRHN4hjBEITrTPlmX622a1Nkllc%2BXvRIMYsWFbQasKlkKf0TuoImAklJXaN12zLmMOiREi6fUAhVGrkOVhqjWR2eenOmgUY7GLcmbnAqWpftrThQTmBEC5zJQBDcPyN4AoXnInBM2UJew3uo3Osd%2FVotG4JFRB1dhhN21R2ig74o0Jw8ZN7VnA0lWB0lDFZ5PDtyXLlhvcGuF0S6Wr3U2CqpnkDjwB2mBQdPGRuL5x1IFo03LEOsHEh4MKRvE9edrMh0Snaf0cShzOIJdiyBYWbPeMzTRGYsBHAfX1laNIl1ZVxzggRI5m51PG59wVXQ7HQGRYRRnGy89qI5okgmTpsdUtZgAxPvJ%2BWcqIbSWx6tf5yN%2BuJkKOjROUqEcP4y6WDOTFIXxQkr7hHBS7hmbyT8AljD77OJLW4CQGYAb2Pei8bNTgMttEECV0uBXZksyIJd39JlDyojumSt0T2TM5i3S2cviYGBEzQtmTKzAFB8QEcXkZq4YmJ%2FTDWdYLS0Kazft%2Ba%2BC7HwNZAJaVEY3kfqPHY2SBxchsqiGqJLn5a%2FmjEa8QgmABHka5AWJ%2BG18I9w3WjonkFGEwKhtgp0j8YPUeYEncSOLNhhwVJnEiplRLfp6lN7z5sAMYVx%2BA71pVUbhIzIaaNzUbAarADBLMSSoXqKXumbEiOijClhzIbSA5gGB2qtutd0MjQyWBaAzJmfqki7MMaEQAOCXbwaXixbEGNFnHCqmWg8qjxIZ0oeAxEPKD1A7yRyuS4AIRwOrQJ6DxVHVPpAc7aCkBHpHC9GMxBqe9Qt62zjQGJy9sjB5efNIj3%2Fyv2r6z%2BSM%2FzuFE0Za9wOJ37u2rcQy7P6SvWZqCuEJKtvjAUTarXAcyMQRrVOlrD0HTsN2KDiUivtwmgj5U9inAK5%2BC4IqL6iNHhU7OH98NmQILOWxNwJiPwwlnf1QAEMLagJuGLoYUdlqBRDn8QcRAg9AuLhe4myJn%2FEoxUfepXHhZ8Dk0BKaH6znSNmNJJ2IRdEvxoTfFkKRNn0cEvSio6ek7OG7AZljFvqNgRejEgmOwp7toPkAA5CIjKCsWmYPIlxUdVDDj%2F6UQEQZwMPCocey9jKiCj3ryLWjtGlYDdewTAsT%2FytgOZKoG6jDf%2FUzE%2BDBwpk%2FPx891KJ7wcBDtmnc4Zr8PjCwfnWIE7Tz5Wh4XZOloMKHqBYibF9JCb589kpcmC6MqgAH60Nwcj%2BnBhrvYWI7IfIiYD0IThyXLu%2BBjtuDKdFNmVqTy8ELHUIcco0LUngtn%2BupQtGnWSsHRGOZxzUOEULCoCKWugvY7ZqEN0MDmNHqeKtmwQSOPoR%2FZ0KGKGB2wdDYj1CrZsodEQx2TukU2%2FMDvJyPuRgDSC80jH6IO5DbRYrS0rIXfANDM017avY1V29khrSTX8G%2FWm5HQ3j02j1MGoCeHm%2B25tIebrUOsJUhfKhD0EIEeXj3%2B%2BQ43UQYWPGKRd5tI6RgOxzkuNv3Ji8YcsIU0cpJNn1rQt1eBb5t%2Fe6vSIMsxyrbVRxAHaSs8%2Fijk5AW1W3ajQf6DP51FkKbjEEaQp7ThQOL8pUajXNZgjP%2BAGWp2PntYtYtaMRzL3lOTlAMAU2jKG8l3wMD%2BbxPb8RDFLiiPnwnwm42DzJDXbmbGIZ0jLkON0Ub4bgHg3f5pBR%2FoVAu0YDFztE%2Bzps%2BP3bAAWSgSxlY2S3LazAF0KZAmzACvKJ%2FMz0beXxl%2BeIEFgZCLRMTD0eI7mFnojAK95ZgCTCfQOybhXCo6576fGouBIpcPFCU9ALkeU0pQaG70p3LmSrRNvUUN3vI9R8lCXjgQBKD9twFivCVAT47aBVWQPv7zSwNj8Un%2FSFG3FqLOS5c%2BWZHKZKVGCPSmIgHEwoN5C6HgtxiaB5%2BUvBrgQmTbO5rMJ%2BCuldZzfzxgdXp9XgD508hFWCeR8zw0tDDW2xoicZACrgqgnQ48NRFvjGjGQLa0bZ%2FYIPRHYC9plKdMERvlMGhAQeqDBMhf6LZGmyElMCwEIYOo1BZ6PH7%2BWHUp1YWZa7wqK1XoOCvECZSwoJH1Mkaogtg1cnvzmDI1q5S6K8zNTnhUkglWVoNqdHdJkfg0Fxp37eM%2FnNEjkRlbYvQhIWSCHT%2FqEBqUlbxYgGY%2BMSFSRxt4bg1PVnRhKNZIXooJOn0HVNY%2FcfiwOh4kjntxHmybS7MJkM71QCMhZGbYSMrJ68qAj1YN82a3v5utE6PJoWbuOva8RkRMPNZOJG3h4NcQ9LTUNP7WRG34U%2B6pZFDjhFpbJyEq7ddJp5LrxHhOcWeKH5m0I1Q2anhxKm%2BO1yIfm7BGh7B%2FjqYiPKEBJ6cFrT2ZB6TmSyLIpnTVkU%2FYqVla2WfZcp7SSoTzv6vLYtG8AgtXlxfWZxN6Gzmta1EwxIU6yE9s0x%2FZlSkSYE8X5a7%2FVPKA%2Flig684F00nmacRk4WooPYSFBnHTa1ebr6zgD%2BMcOV4BeWlJJLrL0qnYZSAVtBA5UxpOASkxyTpYRBUMiUqxjxU%2Bce5iSPwywJQRsno2JDcLSzoQnpUALmNJE%2BWSFPdsteXHMocr%2FC0IqI26humQ1wKQoHcGmUNYBVwIFZqI1azUTzdFmIOugxHeiO7FGrlsIVmnE3L1JrCuYeQCJCpQc%2F0JCGgQIe79NvrOoYeDQJ2REZcyhK7ihxb2NeHkVj0aI0LIicFJjQk21YaBO4G64TBu2IKBTzYheH2CASyWnlbZNFDbFlJqA1Q4kIljGpwnmhmXbOSQEgWsMmsHkBZYKRUWBv9HZZ1N1JSN64WPlCBOt7zqAJMKpczyNBpzQk5o%2F%2FxDjQg86ozQyN4waltVoDaLJOfWjYqewlULt9QO8N4AqlP%2Fo1ZIqJMaZ%2FORyILlDFoGoeY2%2FswI7MBMVXSMJXCUeRsJjHIU6kNEsAqZoBDoHo8Y8pZtM%2BGL8OLfcPdBbsbvRZuDQcyyrZ42OoTsMJ2GH21od%2FRCfgHrkeCyZfMOkWTSYgXtqYxGIGLcI5gKg%2FZR2xnb1upteR3rcNGITv8oKHpUWdLK9kIZlFfEtPUNAgnOY66o0dWYJq2a0UT3usCxxDZm0UIViE7Q13vLoyXH6VgLZoJt476o2dZ1DSsnihertfmTnTdREBRHm5ASIGxMbMSITKCmV5fMqgFiewxFtxqh5yfCPkmlKNcrJfmvyKlbaqps0Oa%2FBSPXk4FJjtWF2wOHfpFY63qA49US3T180HXmbqEjYsSpRFkkOVMCBH1C9JAJTRgjCWNAjl2MSA%2BvZjADldAJGTIoWBOcOEUI4qwvBSI4hMj8m7WHoFosA0M4Q4yS8XtN%2B5emVGJDGqX8D5SVbE%2F0bWETJRyRFYKQ8umFTkY2ZnV9Lz%2BVW9hgHq%2BHYhsrghzcANy%2B02yEIiJuDFngZnEHSFnTnqDAicaKOgtLZkRXBqGS3bgcqBK6B%2BmV5G4%2BxzA1IlYTTtL30wAPCkFZuhlgsViFEnA5Rg4UXmBbXBAW7JuNvZlXTVsYDMV305DdUPX6QyUFMwndSexwLkpBDsIQ4lUnD9QoEF8QmpcQk8FJckIIkVwvETqBSrIvHRim18B7iqFwNCcFoUKmSj9cSfX37WL%2BCT4mAKH%2BS76AYlpBE3eYErTSL68qrzEKiOZo1mbN1ujQapDrmTWb1s3iBTeQMCYcYfVeS5ks0rTlCPWr9AjV%2FbgZ8To6s7qOr3%2BkRUCKT5GAAUzFlHOkmV3fJEImmhCZ4S5ivYOcC3SUx70Is%2BgfKTQfQBsES9NEX4x0WTcQkWV5JKEJNl0UV8pDmBNnC%2F4qRYIkjLTUknCCTbfLBLJzy4rnSGTntJHjdpYIWlqzxK%2BG%2BRBy22IJ8gMQIibkjgh8Y9Q2H5aenHLwEJg2iDmhQybR8G3gfKxBAZwppQkDi9rFMfLSe8Fgalu2z9mKNwe%2BF24HWYNjNI3zoQfXsIck6YiAwCMhAsEDMvxfp9PxAAxF94h42eFp8V8BZxS3g%2FoQhPG05yIyOc5GxA27VgPq%2FN9uxGcdZCP9PAWYlmmiIlMHE%2FRj3IzE8YKgGEh8OmOkN4KuO6GYyNnRhoWNSgmY9%2BVfMfhBm7xIwZPp7ggg%3D%3D%29%3Bsrc%3Aurl%28data%3Aapplication%2Fvnd%2Ems%2Dfontobject%3Bbase64%2Cb08AABFOAAACAAIABAAAAAAABQAAAAAAAAABAJABAAAEAExQAAAAAAAAAAAAAAAAAAAAAAEAAAAAAAAAjPL%2FpQAAAAAAAAAAAAAAAAAAAAAAACgARwBMAFkAUABIAEkAQwBPAE4AUwAgAEgAYQBsAGYAbABpAG4AZwBzAAAADgBSAGUAZwB1AGwAYQByAAAAeABWAGUAcgBzAGkAbwBuACAAMQAuADAAMAAxADsAUABTACAAMAAwADEALgAwADAAMQA7AGgAbwB0AGMAbwBuAHYAIAAxAC4AMAAuADcAMAA7AG0AYQBrAGUAbwB0AGYALgBsAGkAYgAyAC4ANQAuADUAOAAzADIAOQAAADgARwBMAFkAUABIAEkAQwBPAE4AUwAgAEgAYQBsAGYAbABpAG4AZwBzACAAUgBlAGcAdQBsAGEAcgAAAAAAQlNHUAAAAAAAAAAAAAAAAAAAAAADAHa4ADV2ADV8AC1cEs3pishg2FfJaEtxSn94IlU6ciwvljRcm9wVDgxsadLb0%2FGIypoPBp1Fx0xGTbQdxoAU51YoZ9RXGB0bXNPyK3JLMApRwa%2FIMy1PPoJDx39kimekZX1c%2BDSW41tEZBuFiwdwx1dRoPVA2vWPSlsSDqhNkqYfhrqlVUGD0J3HEAgZavmtLnDC5WBriSpD8Uk02KsUkJ9vCFz2CZXAd5viwGZ2xcVYRPa1bEIai51nMYlbL2ERuB2TCzLAbPWWRZ3%2FsZ%2FKBjLk8%2FgAZzK1OaxNw4oGBbsNhx6Reg5HRFVCrwa15kGmJEy5kX1YypVm%2FHo7TjKP3l%2B%2FnuCTOyiOa6S8QEJbuiGYNlCnM7tHChCHRRQHXQh7yPXASlcvc5KrNKol6orb35kbo%2BiEwl8d230cfWPwTy00bFDRYURYGchbwsoDcaR2AJsFGCrbWCzBdQ0qCobWwLfueqAzSkzaHX3yCjDlGYPV0VZqVXlqbr4poRaG5NNPMDv5MCHkLSFyABMRBhMiGSZiDgABYmwsLWDjUZCUnHwvXt0VAUy4%2FqjwVgjfUqp1evzUqutJB7DW99Cq5aEhGePsa4omKUp7LnSQUz%2BZq51pU72ApMxkaVZE9jF3IGKVnF0GlK1E6iqLJXFzy1BEv6Kr0ngCzIgVANRwCkVHYJj86Sv2dzqgVrjYKlg8W94FbPGQghEbTakZ4AoS9h0u39DOoRJTA2iirs9xa5m9Ir0KwkogoqFNVDbTIGO0%2FWuJYfp61Kq0bhgbcbnvbTDj4HBESsXMdvrvpp7Owf%2FS2EbndoEoglO%2FjigGAuLUTUmG07ZGlRCZ4QZLu81tPEgTtAvF99BxfnxNslgVYH5Jc4AfHwsiktDBO4wjgjizFMsIeBTGmIYrhtrK3tvtBu5tYB0PDMXILUkFYPM%2B5yLLGOU9DtoDLYWLQig%2B8wNRZbJZZWeK5JyKNwumLgP7X6pqgiZMFUvfCTl6Urx1gUOjzhcICumUUsiNESZCmTANkgHoh%2BKU0t1fgQYOBkNfp4MRiJysezS1Vz%2BahE7ohM0iJBn4I%2BT9RJN%2FuQk6SjQGwC%2Bom%2FSD7Zq2RxvcSjtdxHfo7NtktA46mEg5gBkTtMKu7oFb1KgqwqBLzQqZI%2Fs4QSRhYF3ani1URTcMD38kDDqlc3DChmYJTCR9WpaWrYFiXeNi7jYa1Oe%2BSP30gxVyeC10DYOakGpWaU1qkQ9OXlujEbM4A6A%2BQ243TA2QnI8mKzNXNo1HPN1CFawST6uC9dkyQTqq5bOKkkuGjz0nkj35Sr%2BQ%2FkLGg2iQMrTKImSGshnX7%2F0Jyh0JziDbTzxp3IrbosXgpchLcBJpLLUBrFbt%2FU6qXqAaNFJoeBItBoqgQlPZkpTq31s5VZsgIkFupAno5G9oKwCGRqv5294xFqOrEpewcjx%2Be06mxDkN85c0ckmWmMzbkFX9YHAf83p0EsnBywjZbcPxZw91kqg7voxasp3VfDhEDAufUx0MTddLO5kCyKkUBwOm%2FMurQH4bJQgK%2Bp14dkBBhgxpBUkTlSbTE8DDu9qKiDSCtvmPY7FRMn0wuS6XR7J%2BnpjjeaDNwiOgIKUWCP9aLb%2BXpc4toQCryp6gjCVq1Cl1Di%2BtEx4WnBp2hmGZpEksZwTSggXuqAWD4B7WAMcir2wmA%2BI43ECxUSeTDT%2BxgR3O4XFPOGxHh09lxpScampLahUbICao0db7%2F%2F%2B4CBMcCokQ7aOQ02MOzh0NEaJGGOvPR1t4sY1I55lNfQ3IkF04onnAomXxiNg2EbBbPTMBBlv%2BggPSmkb4GNFW6Ehd6nDzJlnIXFfzr1bVWQlfylDodFBbhCDf%2FVB13j441dc2rx3h4hfAWIJuZqbH%2Fwbuafg%2FnTQJ9bnMfR3U6TwYgDQJIOPOtmZW4ZHsR2VifZGaC6Pzv4ZzC2nSAaqSe09F9MxuI4UmUVA2RAUqBUIETEIAhB%2BtBhsxhVMXUmv3RPe1grhYWLM%2BPHwwO5W069qIgDXtETXZQ3741DSk%2BvO6y8k%2F7Mg6GFC5fSK02yXZ1XV0NZe8iknoIbSFnDm%2BbMP%2BBCQhoLKOeU3FVNQ%2BgPEntwkHT950cQYEYQc%2FXuL4nxwcRW2bIN%2ByskPaD5Rz6lN8LW5IDLYfuvhxlLcjWXSADeTshWsJk%2FHCuRbwjqLcx66fc6UlF33HipliQ1cvfKlgRpVcsmIsiYnJjzJIovUyqi%2F2OTQcIwt%2B3WW44BAQh%2F2GymOIscSpIt0YUePiwOCJN%2BQ60lqkSRbWi10lotzgWZsqzEI7OGFGeIoFyqli41%2FNn7LfLQ0qtxkaAwbsKZQ0D9s%2FwhBqoxhAlxCVNVF%2FJ6rsUBQ49MLtR3ICtKPLKZ%2FQPEeIRgWUNLbNR3v3tTaL8uiXO%2BOj3tSJc56KJHol9nGPuclbrQpCn4keT05ETSOQ%2FDwwKjCRLgIzBi7x%2BU7ByTZGUWcGLPY0VtXWC7kQ38C5thIGJx%2FxLM3KsoGyRwC5AFUNWPzU0QBCaVXo6z1NCclLuPVA8%2FwWuNhiAG9CPPSSlIOCuh2AQM1d6MyIEIQArIa9YenQ5ug37h9gPNDHVLImcjE91ewI7pz7HgOEVqTD%2FjREYRtEoDIfgxzDePkVvHWJAtcpCJ%2Bg2o4akZpphRUQ0U92lJcKZGJI9mnpl8UVzpMi8SBGXUAPpgcS2cDAusSE6q0hNibhCgZHLReLsA%2BSv8wF6LiDL3TogB1DsO%2FHeMg0ETucRO2hIOvbp1NVkFMclluNmBQbTy%2Bosr2bJ7oWdUtSHi1s%2B2vWxq8njY1eW4BCVr2EqSyIUuFKS9iwVF5FBGeg0hRcHwCKMtqYLBfvVSYXHdGZK3Ug95C2d%2B3t9ZWEYqq6F4TocgcDS4tI8cvEEXK1%2ByB9RofdKpHoA3eP9%2FB%2FEBG%2BIgvmwZ4Iir1SOYFEtUG%2FoVkECQqoPTdHoNpQKpA9K9k7TisAUBsKPtWgBriyeOxs1o%2B4KCIFumN744dH3Yf7X8F426LGtEhFLULhlKFgXF8Wq2D6kFSBkViLad9D9U%2FP6A%2Fr8SE7jsr9s%2Bsb5ODWI5uS6BkZJI5RQ5QDVZ5%2FKOG6Dzc1RLQKAdGkgwLiZLQdEYQ9yhQLtD5kWr4wGHTv4GqloWePyHYyuy3Ek3iQVQkdkAz0MxcsHzccdMLO8KFh7ywo4jXywraIhIicAI4dWdD5wEXBhsMklzbWc8zi8opC3IlPsLXHCWOqOgq4iPU6xyDS2tdSLnlhSFjsCCWvMRt5TAI30EHR4f16NYyzoG%2FoKgCUsW4182Wvj5gpb0bGGLe8YRIYRGVgF2hwIlEfm7eUwwLZWW%2BmmBZPggPnIKI0b6G%2BlHCncx0wkaVPRQpZKWIIrzh4yC4Ar2vTKzhVKSutNi1dSzmM73AGUXSBJrQH5J4Dfb%2BRU25tYrIVdLr4ogiwTE2i2hl39ffJWHNTSWq3PvVJplNqDTJgJcvCHYoQAuHeOew0gZGfmX3p4D0aSr1BhXbXRA1qipfS6LiggtiT1eDg4FTCWwCdAFC9FCOZ52EdrFetMBxUdC0dfnqpr0mELJE2m5FVMvwplyf0XIKclHa6%2FQrw%2FFOVkVKK71Ab5iAVWm4GA3HnkCJhYkW06XJ3TDGB9YhVW9RuC39AFUcFWwU5eTNzuck7IQty7ZC9IjAGNHuZhQ8yDWZhGUoNyhDcKYQiUDqAC782makzJ1o3XJFIEDXgObv%2BTlS%2FdAr5rn2C%2FCDmkI0WO3cSTJwSLrS5dBdkyfpxAu4XghB3jgGShG8UCorOibUp7NciZgEDLmT6eOxDegpLRk7HomganEaTmRZAAMrhobApDjFWtOxht%2BNQngtKVgGL2yy6Qnsmju6DAg4d%2FRvxHa5mBaEMcBekCMtwaPPGeKFPMsgAJTidusMLUbTAUBJMOmXRwhONkoLPqBhpTuLSYN%2Bf8aeX1NKSxF2OUST9ezObkHETTsr04iWClpoFDE8OdIiDPQJqkHhnUPTcE43OsKBGS%2Fzk6F57sqVmhZKjPxle2S%2BiIE%2BMXOiTOoRKF0Q7mbNRYGPZDp5eIdPOZHboa4CTvwnlZb0zCOW6kZJh6klDDvYghmQ2FCDKB5DD%2B0nImiNcfSzaGT8aSPzEZjMQ2GPpA1Ws4Xeysyv0zSSMVVsiOoiowo2SfYFdapUBsWIoRXMAKYdguyVcwqX%2BzVWYLiNddi8p%2BxMV4dQIoUs6SQ4C1%2FBjtBw0ocOzLmMkEv5D8N4%2FZu4gYA4ryDb5Y3gkIxdb37qMCWYmDGgsyEE00y3BZ4FgyT%2FdJLHxMQwx0gViQjWL0QyBfcufCgRYYGiCHrxez874MrcqldLCEQLkCCK6pWCnULCh%2BVK6FW%2B1nm%2BN668e16QTKWprvRw3mkwitjPefHt5QKrVumkXsvsVrHdAJrodfWckxhhzknXZ8cMVIvKphJVfhvWbhoZbbgo3fygOr8PlKcVEYLTmUbjp8rTFlPRtPrdA8tljZ0REfnhwApCZ65Igtn1gBROJdPCCb9ZIqlQUq3W89ZjSgSnUz8nEBW03JCcQ%2FSxouQtYBE7ichYHbASPB5J1%2FzVfPINn38CqTMws1KKo%2FyvNXpDgBvCI08SBLSwX5Szp6WlpzoPEio8DsNzZQqgUMoq0%2BNMALrygrOlErJohXvIJ%2F0IqziZok6OuApG2eoGAEFsTc6yWf9eRcklYZRO3PkA%2BW8aN5ME8aLNC3Kdwtm64WyqytOEW1WQIg6bOFHAs1ovo3OfCvvZASxBcxg2SRCRTTJDBKajFH0LL1kSBroe6L9xvVxMCIFS7Zo6y4ZOEIkAI9QtGVIKKBlCvUUEq2S8FiR7VkJGbvBFaS6UzQV%2BayV6NKw62tbJbEjkJ7AMC17DK399DZr%2FtE5sUtaAPwaHNj9VCoVB4VAG0iNI9IjDo0mr97FWjYeDRSr3pstZTVZ6nj5Vp3IbssG3g0r9E2eSmHY97LYobIHPnEGkKDJP15WPWtwMgS8HeLd6NEnP4mIFlRJB4zLeDeoBElpUNRIQMzLbRQsGLj3DZhQytDQPLAUE9JWHiLKAJxVTOJNZsObEiutLqwox%2BM51t7vJQhBeQm2i5bTa4D8qIUjqI1sL9G6Vha6U6IPUabeCUMIufG%2F%2F6USyxymXNlfnVinkNvKZGUjz0EWKIgZEC4WkUEr%2BgP%2BFpkIPUVM%2BQEJPxFxKDlpBEeiUSaTgCm4sEfRnBxu0eF%2FLgLp0IFHMEt8aZrsQzTF3wRw8TdpzHNGMZrHHa6nU8KCQppWBVpJ8b2Xjq278mtoTfrgfAMSAm3cYEcDw%2BzcSsXTaUyd2PH6DCU0DdBiauxpsyoKlAh9IUAzS32X%2F0d3x7h4gL36Q5sC4YzkbttmSwhenP5pxxrBEEcoAohUGB1jHGtB2%2BI0FEcCM2y8EY1e2NPXJS7wp7APp46lC7gSit7FEFQCIDnNX%2F196lJs%2BgXTyJrXAze%2FQ%2B9GEFC7p5W7W5FEooh5QlO01B1OcYDH4VTmRSO8fHPjRo4FkT9GrnUZw9pXnDplu0YFyOaAsLOkxdsu2gfYJ%2BDzBNihSUutbDbDy7VKS3KwwUTChYQkWCmldyS%2Fy05EvDGbLbpkDfbbHNGEhTSiaAEDmoKTERX3pEuKYJT%2FlNS4IawkdDACC5Jk4hgNa2EGV8yblsXoSHDrqHDJs4JDXLLA67oCyia7LABDzBMInY5gnZCpFuyyuaWXjKHRgy409j2wNaI1bGlosUnhaB5iqHHZf2%2BbDPpsIwoahsWRL69BhhyPHQBUNCyBR%2BUJzMOBRMxTVhNsS0%2B1n5kboqmNZcC%2Bt6HYVscRaBeox%2Fvv3%2FxwdoUoRvs6CamykRGihd8HTNaL%2BxRuoo3QVZvFT7xS9opWLiNbQRti9PXbNg0J5WDsxaNesdmkYOcwpiqsURuor%2BS8hhgWniGGll%2BtD55enFSsyATy9MonNXUJV5Q7eAouzR%2FP4HlA5YWBYYjm6NDAEk%2Bx9On0MGm65%2FEm1GKndnRp4cv%2FjFAdM7hnXsaXnGKAeK4aE%2F6BhOq1%2FAWmgCMQ4zC8G0wBzhuMSeeVhgAl0jpwicoR64K%2BBYlYbWz0gTGAGtI3puhx3F5%2F5QKXradYFuhJPYWq3ITCUUNLpugdVBegedngCO%2FDN5mJBWzGEL932jL1YntvCgzzLeR0WczKl0J4g8Gcbo6p5LOslpYBw4kE3ZDMiHPjBGyAUjkrWXqYTrl7gRUwex0zKVekIhoI0dsFRDtQxsLctjOlRs5Y2gYpQeBORQFR4C3hXh8EnZUzuloqFLFATXzpzv6k5XoHB3fZLNUiPV5DvAfroLwH8tYhkcOxWnHqePfQulM0DCPTadXa%2FTpoHYkh9BeeAwpmi9Kbo%2Fm88ob17pFzKP2lJpfWxbyD3PccS041A0MQWUqNDHOPOFt57Q6TiHQEKJQsI4v1JqcD7Q3orOdsLvExRQwS0nlUtV%2FpQbx0wSlrRSneWAQ%2FJhPaT6rMvIcid93ahrnKe34YxGA3D30BI2lEiLGh5iAUkBLBoXRshvpjGJGLzGcvonIqzVubgEJv4mbEl7JggQUWb6AYaQMmGUXEwIjylByVLbgcEbUQL5RFiRkX%2FbOhzb9XavzmFpR0cOdx3etgoaCPbiL5gR8o0wJNdPMCYcmyP0SDmmsW8o0O%2Fy5HNRxqz3IhmaxvIT%2FxpN8Pj%2Bx4i%2FGawfTOod%2BpvHN9BMNQUKG555l7yAKsma4r8JwVm6gxqBECXHA3e%2BdCsONR41WrcokynYzYqB0xlCdg9Nu%2FVL4rgwOiTVy8K70TghEjAOHeFBYvGwmkrDIzlwQsyBsr3K%2FEBFKO8UQ6J1hU%2FYGFA8fGgTnBoNnAmZc%2B9S%2BXnpbpJ4QKgdip6TZnI6woSQaYgxGpdaxxSuQkxu0avCBOSwchx0SS0x5HgR6iz9AkbeoDFTnGInFfbnMUP%2B8p3uSQu2CVkHxeVeEMICXKlVDsj89UY7AfyMvxTyws7ilT3y4zYSLVToLb1IwDJHJ804mZKVSKgSOa0mHCQrjWQLaz9LrCiISicIHspx5moJ%2F3Ng4rjU8aMqTDl5gjJAFgAMupkEoWEalYEtHh8CvvMqUP0Ra4v6BRr%2BdgNXFRLo%2BjKWRhaP4x63qqfsnw%2B%2FlDAo2doOxQP7GwahE%2BiZ2OX2l5DodFT8bGiL0YglcRmgDoYIEaRBLqdbj7HFD8xfZz45H2Tg6upN9XjuGCxtdxuVuRjssowtewrBo9gBM3T7d77hNjF9rd8QTMjwGLx3oWax6aa17t0I2gcG6kcQgw%2FphwfsB4gsCGgMGZU8P%2BORAg4iQDmTP9XqByg%2BjtRqWtpaHjiHSL8CNah084UP6Rfjx8GU2eaRw4mH%2BA9Ad42DummqhAj0%2FeMNS3V8lEHUSc1ntW779KspgJUBtJQEpS59ODiBRghAyioIrf%2FKoPh0eAJWqxh%2BSurG%2F5xVdzZBLgKEiYy4izBuKhCRIhfoADEt%2FB%2BirTWSOZVkcfzWBbA%2FAO817phMFhWQnvTwzjirEna6JgrjgHyk%2B8nWk0k06KkkSOOryl2OrOta3U1Vai9SLWxcE3cY161P64wA5VUgBExRGc8qtWCkEHIJfWtybVbTm%2BhrXnbVSsP4ucJTC9onJ8N4r9lRaV%2Fc4a2SZKmPNCgEUW7LDBXhvFxUvZYtnIuGD61WQtIrDXUc13hksUbImFeHrIBgvnG4ogmKBk5CClzY5DWqCCMzdrHBGSSOTyO%2BE8inLMGSApQqKJB3XKm%2F%2FMFoO17KuwfwqcaqjAyaJ5JOWW1Myr%2Fs7ZQiw%2FPqVAMH%2BlK6DYqjGUMcAXnVxy6z6CDl6j5mDa5EG4j8C6pr0hKyRNnoiR1vl9DWOfC2%2BM4v44bO3onXro%2BNlz00ZlGV2ICJ5CcCazVCJHIETBqVFhGT7KSBdNDv5ILpSacSTL0S6fX%2FP1CEIT5NZgcwpI0rkV7LqiHRoLUAPjXEqCZ5mLntX5JkkUEelCsU2tXCMZ6cZivQI6hYQNbXl4nc1sSNtBUTkQ8Y442KxRe7Uy5yOzB%2BUlA3MhvFmXweJJj%2F%2BG%2BqwJFWFLNYp0JhzD%2B4sl4JYn6a%2FvShCCo8hchMfrswjZgUqiToKfoOGaHdIAnKE%2BiEedBkyLwMSoNVX83TJERFy8PLMpBjsXtBITuS9lpPCTVl%2Fvs2Aqzlzwnj7lpl6VX%2FQ74tWqUSzaKziwue1phr9BpcZjNc%2FGXuJUq15TMDnCsJS0X2wAtW5JQA5MaTyUH4cDRif3MDxZx3Se89P4WSIvEEeLjToJbXf%2FrRhBMtRevJxuf%2Fs8EK4woZOFli3yTq3xqjBjrlierqgmUpFA15HFkeUOuLDjuhzLDjAGKK6WThTynzd%2FtCQWU3Nzd8%2Fa0q%2FxwZYn%2FUPEHU6lsdG%2Fn8gN%2BYACURCU%2BW%2FldrXpdUK7WxhgWmNd%2BLDoQFCU0sFyHn3KqFz%2BIg9e2C5oe9EOi7KdTBxPE1k4k5tkX%2FoZzSih8DJDFd%2BrITKNSsAAGtscSW9VDasqkEamMzeUOhRqRRAj9lc%2B7An2YOdL46GdcOLAsgYaFsR9hs0ToUzZ9rFRLG1%2F7eYLz1l5ijumbe1druwaHNFzZjtwt%2Bn7paZaMZu2EIx%2BlxX%2F2SBrWJQQM0wmE19eWrGPIVMeAzVWWRp76m1skeqzaBBZ6So4eD8Gpv31bn%2BnO4WG%2FOg%2FB7xQu9kpA3eZL3w9cwzrZfMmbUSk5OiF3Qx7bQYhL0VoUQQP3Hmps1bBJDQU0qAJpWwnb4iFOMBthzwP81ilVnh1bIuk0C9Xe%2B1kSK%2FK%2FMYOh7vIa7ghqGEKzCiHrehs3cA1pzgec5NpLDtCqMPp1GVECA4QZKiZX0hQ%2FGqjOhhObmpH0vwx0WHctTrmGC84Ub6BOQVdXIqoxqMVNhQjd%2B0CYMRk1zp6%2FPnIOsW7k%2BhQEruSB7%2BDEGv1lziYEEwur9gsigQBG8EJ3zeigdA74WvD0h2IbdNzPw3okAFsdmi3qKH41lxijDPDtvZcEzXwUnRNn4WpCP3vPNHhO8czUiYjRn6GRIQ4SymW9MhjUu%2FjbWOhOqNeh9OSRNh1EaFZcalxYnJMLCpTlEDttzYxhNCcZ86PUpbEkFmkU5HRiAF9AahZ8jQ769NUzJGkq9YLj9HWZLEK%2BIryXyPLZHAAHsBSe5moWq2RRQT655EACRYKQ1AR2mNQU6hNdrqLyfpSeJ5PrccWf3dXVxmIidWyyIkCm1v1oFYgyGcXwrCRPXPMLYHRFvGVuYyAUhzgYntJmDhE4VCNKoSxWlSFiFuMGumZHJnCJyAdT%2BHcgUhIEJZgWOjmy%2FZWisKRYo4JjuPntQGSxlJg3XJ5DBsFM3kGGQjqECyjqYFW6ccOkCDy3EhUt6taBIaHclyblt3Xxs353KjciddJC7gI4cZaPj4zBxOVNfei9MW9cLUHspngSFFni3AL7sLsbqo3totPWMf0yD2bdWKWuK2a4eF5jKcYCZyvORgcHeETtqeqhAYtIyiFGAYJQMOX4VJzPjyDKiavWJRtjWCnaTUdPR6FRkTfFAARc%2B3Ln3oFDETvxxiaDT3roIpaWwEEjRlhjvs9ZKiU2o1HJOMuVRFAA5fWzMgAqSKDaSLNQcQZbaFzsgKxXWIvjaOqsoiS0kA1bx2TN4NrJBVMJcmRWNIqrjepyobiDa9yXYKmJvgQWZhEBvF8wEx0pMQqCzcf9JemmcVMROHpvzARvqDrI5WOXmah0Zkh%2B6PIozOYm78ieRAJObTPxSCLuwQiRlWaLSxJ5hgIIrjsEUKPWMqRFuMgh1FsNDFw5jPGKPTWzyiSEIS6IPweoS55G9SZZ6wcpW%2BHYMSkoSETssJ3QQM9bQRo1JdCQdS1np6F5WR9wujL48y6xB4M6Y7FMnX7f22J6F5gyYVK0QlgEQxVXFUuC964aXqqhT5cX8XaZv5hVzeTU7bSoy40QuTOUjLVShZVi5iWJMAbFhku4I5QyO1x0Pm%2BcTesk5XsjnzwoAIsmXCFbWyIZQuawuVuXuR8DK92lWJDrNrbFtNbCj5sTTCx7e2Wb0UydtbZ%2F0CSIT7OnVIY0fRntwN3jNOdh7nGpmmq9CbBm1uLafMptryjPHHp7tKZEuAL7OjXHySRjUkXydXE%2BSrNxA2Um5Al8Dh3EZC5V4SFynxsMTKCAIMqEqNKzuJCQM3tvVBjRfT7xHSuCO72a6pSo2wn8%2FaXBmKI9sW2BccnPF8aML8%2Bohhb7ciWy%2Fxch7McUey2CPGCyVKaKDX8%2BSBNgqZqMLbCgZ4NPkIF6NfeH7gtElIrOqbudNqU8yyyewVZneKXuzObCUxU5b2tecTa7Jn7SE6UlSYMTkMfCs3Q7fVCaqK5k6pf%2F2wW%2F%2FosIJEgW3skUNgQHyb%2BsAi4ECMNcyjicIITuXGyXkkRIXyN50Jg3r1FpMmaQSUl9pGxnNMp8jf24vS5eX%2FyJYlMUISy9e6JooaPn7fiuG4QEscaDgCZpra85ygZUcJInLV6C314YPJdG2UL6qljb1QV1ZhrNcFecs0j2qb5gvkKHOFxHphwdBgEJc3y8qihwdZCQpJ62h1voTUccffiDJEzkU8jbXRvLFdPbcmVBUhArEuTKQFe570IglefLJ30dWmVAtx23vIGmF7N6auVNpZUQVHNmAlGgjNet51laJgLQSpfZyxBEqLwoCEGlF6ISp0NUmhUHT5a12%2FZElPE5UGO9AVnKpae3D5llVvXAHK0FIH3uE8AXFPF%2FSwx3OdCN6aViMIxEVcqv1UsLJo03R0grVOHRogBCiYVrK%2FqFBPmGrDyXLgr6DxBMSKnf1uSBgiRjCiwL1QoM981XHZnusKIVJ405xXwx6aBUuM2YXS0jaCPwaC2Zdp07J8gxM1KnpWMqNkRCfPaYTelLbBmd97YeNAOFaFOlV29YQn0qIInmIeMFxikX4U1pEusNYtOX6tKZKkgVONLhIF9ZPpxNWGA5fslgv82Lx49LF6FltT3Qp7q4Rcu4hKczn2m1GTA4unFBAkDCqY%2BD5s2dyVIfDeGeBgwDnPbGYXQqwM0E%2FBCl69QtVYbUwkQZAtSB618VkAzCPAs93Ip9qWnBMX%2BRUX0PFxCACZQwpfvNvAMGrD69RE6JSyNNOvRD8v3gzw46n8oB8mFQiYiwgidAyJgrfY1SaNrL5QDEjIIgYLECALRSK49wPmSO8jZLnesJ8oFZjWJyTrfBrNRCeOMoaVxOojhX6WVAhhJ6dvBPZ4AbMXC37YPHBFKUgA7t8mCk8U07mFgWg3wbOZDgsEZBOC%2FApoLJL8CzpXhZuoEh0ntzsvrUPhE40%2BUUkCAm26DxGMecbxuJ%2BpPJct9BZL6lVcWLmHps6SSRwqmRJeypwrd3vNnIawZkqBn%2BumMrwB%2Fc%2F%2BIAx3X3Ehjr%2FzJIVUK8Luxlv5IeNoBQPnIhvJDZfGo8KIpLh8O4iRusiuQOtytJ61yCvQUGFmCxEEliRlQmkN5wrVLkx3CUrlDG3ABe14lLsoysj9hXY%2FTJpUb3tCvpw8Ez7Wb20lfIScq%2F6wGFIrBkgzjtNLBoYqAgJoKvDHcdkTRNbmMKP7Fha6v0z1qPmfqQzKW%2Bi9g0kSWn1vQuqaJyaTAX7hrJwJgfaPjJvb6wXroHZRAD5NH2E2KaWtBw9TGd9mIea9%2BPrxlBpyjnQhg6rLogT7414uB8V19PPcBZUhnNx%2Fhr1%2BtX%2F1jKG4nnHv2EtR3VOjo9oWEibOHX8508Tra1pFg4lnAwoQ2u2JcsDi7diOc%2Fuhvd8qexCvYgoI6m9VYAg7Vl0PRXiuCdgHdKDIIHG0j73u07ULaOJJ60Y178Lsgtd7zYdOUGlMCYhR2Uhyglt3KUjPCpM8MKjVS6OgTHgqD1SSQ%2BqhzInvSk8VzFP1cI8vLxtdDvH35uPzMi4mQtJCrVUqhBWbQRke9Sjt9laOS7Y9YqUkXldpaAoofKmUNsx0D7eYLc%2BspsKbO71qdmmaGglAJjo4kj6XlnIWS1hQZORC%2Fh4i%2FCdcbaFFuxb0AYMJ7EdQExeIHEdPRtCxVECvtxHzbEyldDvie9cGKwImUuI0xEL9W%2B7FhefRJ05ePV427NJDYmhOCwBDNBP5LrIiblD6aw7pSeWFA%2FlDoWYMm%2BZEcF16VDdA3ALq7hDBlLUzNTL9AoVyczpCwb7xHucfK6T64W0AnDzYLg0HYWadOMPdoP%2FlliqiAlAWP4rio6stY02elA%2FLOPBnEr6rsAqtMRsS2g6HJtNANGwpxTdZEP5Xt5mE2gPs7dE0gyQv%2BFdd8QTBEqmAeMHtNnjBtKvg7KmIZCj9303GT9mWQXZxolBupTHIhJT%2B0WN7uu1FbRp6NnSRDIj1aXRJD25s%2FAD5%2FIc2OQ0iDp7%2F3Dbv3Oa8McFBhXrPpAKzhrFANFpcnLmEVTXjq0MO5sJAPVxFbMh93VfD%2FDppG4mBzXSgVfXJeWNNxoKF8QTwcQFXwQPB7QLE2PENdF%2F4vDL9zn0ZgQ1i6Nyr35KAwetsESlUtEENQbCFOeUFb9lg4Q%2FW5lUNo2fsscGbWY4T6pynpP0Krl%2BJFEfY%2BGGHI3aj8aBO0K%2FndAEPa5FX51Niq7CEOhoB2hSpGAgBT5%2BuzxAMzSuVEeQmZIbYew4tM4UsHYdZtT%2F9ibeR1u6rlX6lBQlSBT6LQ9YUEAgmAxLkAKQL9PSm%2F3NQF4w7ZvdqRqMJ5DYZh3j3I1rDmyXyti0llyZjkLnoPtHHwZd%2BfwWVz9ztMTMCFjpKBVWAdcYhRV6wY0kRv47nqddzEhQvXsqNstE6GNiLTd8iliAfI5vfm2KjfTQwbxz2uFzaUL0A9VKWzB7VrWS0QvlqVw9VCXOB6RDSgbNtW05PB7pEz%2FHZkv%2BXQTUD8mSQ3mJk%2FEUe3%2F2ixiuDVAOBfyIscXixo%2Frh7BHtl5KSBigokAOClzsk5pj5X5S9GLKgu5AbQNotZBWU5zoIzScHQKjeFNr0MiX0Mp%2BlHmHKuaDcfU2H%2F%2FhJmeXl1nPE8E%2Fk8ULZ%2FCLYtwJWG4CHI8h5ySfOAFbkRVFJyi0KYkQ%2FfhDAjciw08ETminGEMzG%2FwOERVW0AEslZEl4sfr5AYRKGVSMzkDSQ%2FnhkipQ8y8EF9ZRGKCOxRzfpNMubhc%2Bs9lZBHqNegMaRLozjP%2Bg8CUsaVzp5Wd0ZI5SaeSdNAD1HIc0vTPw7SLi4Jpa1gGgtEY865KzsFCn6I1RvKT3r6BVdYGsBPWdVzeLfbxKi8BVQVzd9f83goEpezGYiAXT8S%2FpW37TxnZ6f%2Bog248Vvj9otMMAmzAfvCpPYmXIx6ZAKAwBH737j2KJpWyuPMnFIBfqRrEBYiTiWVjvdx5T7k0dwFjgjLrLVm28m%2FXLNfjkSOzkoh3hangxcOjvxzVDIGSxYBxI9ak%2BDsrVTPAlMWZD7OThbuxdkWjCtGwtH4QzQdpmaBsHV8Yrg1iAK64TC2WMbQJAFFciwJFPSRQ86OtUrnPSODgRE%2FhD4qWAHDlWBDy1KPUCEbpodyyU4TnaIFzU%2BtJJAes10UhzVTNE6fGDGUN33wCgAZYoIz44wHk6fDO7wGbAEwmcVQg1HGGByFjYGdwJD1joA5AM8olCJ1LlTUGB%2FkhlrmbJbCbD4Uj0GZTy06zCTjOeVkJKZzqk0nE4%2B3RmlgDHpJwCwwZKOl8SEEH%2B8TQK7R6TiIPAy%2F5M08zWqjpXg4KWF%2FMNQpvipZJ4KZfGsivxCXyinAY16NjMD%2Bkgtfc8pGpAgSyN27l%2BuW3OjjOCnldBAJLpzjAYdBoh3b0yuYkLj7c6iwxR9NHW9WBeGVYjvaTEHVq2t96HA16vtKz3ZgtNuJgpjnNZRGEjbmQuiQEBJ2BdgHxFDqf0F1dQJcS4sIvDHlCASh65anDjgr07Qa98i8Jb1rAbSdOOz0cM9wlKXm7ugzOMTmi8EbeTBIoHrudZ9RSwEtADDsgyFwnxyfzXecDzLGFMmkRrGWCdnWVnSMMcc4cl7NaF%2Bt%2BgTHgy9s1SV05LLaw7YYgNxNKt2kpiEgpahsRp%2F0tarSWdfS3AdWYIAnrT68WTwX1vtPgL7EMcIzmOpOxL7oZh%2BcoizveUkJVmjedZZlkwkno1E7%2BjVJIoz8APlgweTgHUL%2FGciPnYgtfrq4TtxE4adiNQ2ZgyJHWYWmrMlW6ebFkPaAUwzKsAhoGXxXGRGKFObHKQOqFOnGgkyLajFNwhUa4fqva2yI2DlREZ6p0CNOGwR4XCrS4K3SH8pDQGvZIaDcMPtJUoLRM0owJ0iT9QcdRK5IRIIpAOzsUotf3TbAVvbQH8n5voA6kUzw6LqVnwPkmnYxgJLYiQ7hQYlEsYL4k5GCZvd58ypvZfwO5t1fXMTj11hE8GuAZhX78JMPsK%2FJ0yQqDPk4Z%2BJbbXS1tia0EBwCjgWUJsUI18clQ%2FL%2FH39pOY3jRcZFFfW7bC5v98f%2FwQjY4osg1CYvJfYmKVWbiPLEpDvlTEGLjUbCmh74cUqKtsVVr9hspTEdTKrKSRjqUHkhwgyUQeNizUsUp3cLmGnOoxPIuzYDGHFJxwclXasrQR5Pp4%2FX9adXL0zyaNRcp5govE%2FKIiLMyYKgb3rKpuxbm7t8U7GiR8qcIvzarYOuIr0z8D1QgHRWmwQj1jMXJlqpuDBiVUQD80Fnr7quJElyEAs47dXRoms8yEtA2VxNaYbJmUQ%2BlsKhyYLlk2q0QMXQSsMctgTGOka0GYae3AxbsfNKwpf8YnyAYZzDx20P8xvD5aQ4OkVtbj%2FxeO9gPGmBGT3BiXsWroQWXXm7Mw8XnUAttSlNyNEsqWLOLy5MJLmMa9m7Abm0SuOJF9RWA8VDp5xMP%2FI6LaAKUmkqt6%2Fxs1XyWrgcDo5hjmvshCSHhWpwCludJPk5i4bpUhqFw%2BRmK4VAI0O11JGtbQ64l%2By0LUdW7GarSUUwP47kW2CYDEdvsA%2FTXw0I4OPf2SvJ0FKjn7aZxxwVp2xjhpWMTDxaZMkiOxaFFLydXq16fefH2qVJybgXVpioGcKFhS4AjNTEa5T37zLo22Qv1apFD5qUjB9w8yA0vSc2RMiA7xIsRIGBTWOjHH9SZlK6QJGru7w%2Bq2GoC22fzSVxkr%2BWlT9rAABqi3RiLzDxns68PSEUIxqrqFw8oMUhIeL%2BSdTHAvw8M5C0b29DIIfScMQS0TKwvPEq3kAQvxMTC0D%2B7tnB7QNRliGiWl0NuVnIUY7QMwRkP%2FgVT2WDBX08%2BWLDc%2BiW0mz2CZ3IAvWqesMkIe3lWqMvUDL5Q33McSklm9U0P9SHgPGGVlX40diyUBp%2BpfWi%2Fh9sKTOvCRCj%2BeFIWvUXobOyAxrHlhKFGhOiw1vyKUiNMgN3k9No1jfVEpQEU35laY1OWX0u%2BF%2F3AcQq9opTw0RwEyxVosGLDgIkSdn7hs%2BIHrv2jR%2BJUh2kADlTtyX8HxtYxLUhMLj3%2FFpJAhfxzoRspqTIQicEOQtI1iv4n0xi9GiED3BLS%2BriXyEyU1v6KfcGAWCaq%2FgQ5kImR6wna1UoP6KtpT9XLI4EebxCRQriHsHkCOgDlZM8hJEHcCfGIERpbdeZFFHtE3lBjH2cIQ5p7TNVfRTwBkflxGhmddY2YfZbMF0bFv76YdpbH3dxSKmVVsblZW2xdvOxqSIQqbw536IFhJKhELagVlMG3LQqHU43e%2BRZjx4BJExsLcLX1oShyJFvhFevBTFOUF3Exw2yNBWwMCW5QA%2B7UmPhwM7AMOXRddPg6OxuaNAmiDYRKlcHo4FwUeta%2FLSOUyYddHQi3OFkb4z35KYG%2BxJAOZ8LTMyJ%2FCgARNXgZ%2FC%2BfKy8W7VwKPzhRpDnIMS0ClN6sPMpa421GfuLwApsG0C4FpdCsaLM0NtsctgKVSkeql94%2BXUmITqdGBajY4m4NmDFEk2HiFjYtNLmZSxNY1QM4KakEvIQIFts%2BOJ0QCRKvhCmQcfRAjN4VmYgb58CBUMiSUpcyuEfRFZS0SThDQPO4aFcJiNJUvlFdO0s8RaeSdpOSHscV%2BJAIchHCniOYTsEqhdLZtWVSiAw6hEDO7LI4or%2BkXTE6zB0CA9o4NUeZIpS0Fn7Q8lU4X9sZNCO0uPfjoWqOaqDVcbxBJSAs8RV9IcKmOPY%2FLDUnXDLSYfFT1xyNTWRLKRW0kFxctTIuvuU6R%2F%2F9ApGo0EHrqGH7dEmsI%2BgA0UXpfNwWFxUHz9CYK9toXP6IlTFRhuGh7z3bhwL5qzzoRAF8dkwboKslbtuftJDrshFMoBNaIvpSXyAFRCCKFOKEkzCkB3NDQB2qtV%2FANwHNea%2BAUDr6WWScJazRx4glReLp8vQ8sFtz%2BhqehlJO6MM5NMIc8%2FkWnwbE768NqCDKBi%2BpY288WynJ1CT2Kq9%2Bo6rhlUpRatsVIsacJhA%2Bq8M9X%2FUQMRZhshDAvsXwlZfxDn%2BWCfyJyLFA2s54on9a54PSC3WgchQWZLZgEl8xGrFUqCofhkvqYtXjA9XyewEKlnAtD26XlSvqtdhXOT%2Bi5BrX6S6hHVcqbZ8qbh%2BEzffUpCfTG5HULg9DQQaQ6ENkkq3DvUSAQwcxh24qkmtdRoIMDxOVDdy0T2w3afIBABsQGxnqJaAOY1gWawTUuhslaSivzrXaPcRyGhUkH0R541UbNvLKiY070WOGYY4R%2Fg1rfKhHcjoV4p45o21tldJXmpG0XsOekNlYucZlkAWkVUHtjkSeUbdfBMKrGATodKL9arS5JFVovaKRlOWbNJIS6GHxuLt8CX%2BBYQUYDfxlQrQQhL7z6vChINNDAVVN0rXxaKjegwIPOJf7rXfHBBHGpBNpaeLGFXCBrWAdpIwF6mcE7pE2z4HdIxcWkU0QA3TKjZQ%2FPNc4VwWA3OqmXuoleHBmMRLsU3ENaVgIpVnIWvBLVDYNLzVRdIefms6mo9VoRQZ6cCkQSOdK6KDkWEMZkQyIEM6QUltTfQ1xFpxUL%2FlFho06RSy0MhFQCIEh5FrTToDEgpZU4QcT%2FbYWc9XTPTTM6ZiDUk6d8MHSyFOgi3cE0Oh5I2Tv%2FThHNjxg7A0zwweFEVnLpE0Ai8Q9OWYcdB1zNKwLEBtxjc45oHjshf4AMMWhwwRhRdBnjEU3iL3TIBscW%2BvDMwGJnW4omSkqIJxsnzyWwZBg9lQCsSZ2CK25fZnAEtrlT3WZ1xUoqsQBEiEMEmCZAjQU8EhBFQSUEVhPwf6Ekh%2FQtYOKDqg%2BIfAJ8CuQ0oaANSG8CrQwYJAhV0I0D4CXAOIBYAcYMUAO4A0AuQNYAwAWgJAFzA9A0AgoIOA4ARIJoBoDTBVATUAVA%2FfmHjl6j%2B5Pa79V8K%2Fh%2FQfNvjz3P7ler%2FHHh7%2FPw68DnObsHvPy3cPPA5wScuOB7qBzX7b8SuTXQrw88fvOjUnszbV9wOhztB3%2FrTR53FdNbVFq3a82jxmuwOcluBDDjLjOjALxD3%2FQiP39Y7a5Rt0oNm7G8V06nAGXPxV3oiByNCcCfXAkpuOrai62YwdiJaYXnQsst7b8q9lbH1AhQ4fOtIhMRO4kqFfJyARyYkd8VFgh1WJGVCPlA1ZMLjSDAUNwDDwkxBcqWcEmILYipcSYqtCIqlSAqaSAqUCAqkjRU7GCpiLFSkWKlAgVIxAqRiBUbDiowGFRIMKhYMKgwKK%2FYQV6wYrughXTBCtmAFaz8VpvxWa%2FFYZ4KujsVY%2FYqr%2BxVOdCp85FSnwKkjcVGeoqJdRUiaio4xFRNgKhy0VBtoqArRXysFeyurkV1bquqMqqonq%2Bh2r6EqfoBp%2B%2BNH3jn%2B5M325m%2BzqX6%2F4%2FrnjqtKKqtoqqPhqmWGqVIapJgqjWCqxYKqxeqp52qenapVdqkp2qOnaopdqh52qD3Krsbqs1uquGqqZaqmdqqVmapLZqjdgLkVYtPvgiXswWobLWxLWyK0qjACE6uL48VDS74vVFa9UPr1QitVAa1XzWq9S1XKUq4ilUQUqiClULTqhKdUDSqgSNX2hV9IVfB9XkdViTasMbVeTarwZVcjKrSZVYS6q6XVVS6qiXVCBdUEF1fgqrzlVcsqrdlVbQqrWk%2FZ8n7Vkfagj7JEfYwf7Cj%2FXof68j%2FW8f62DVWIarWDVaUarJi1YsWrEC1XsWq9C1XQWq1iVWMSqMBKoqEqhgSqBxKvuJV7g6ucHVwg6tqHVrg6vuFV6QquaFVwQatsDVrwatGDVnAascDVhwaoyAqiv9UO%2FqhL9UBfq%2Bn6vB%2F7kf%2B2%2Fx%2BtVskpnZEuCUxHC%2B%2FYuIK6NNKiB%2FEzIk5DuCcPq3Ew4GQBYmlqw4gUEVMiRKFQwiMCQcTgAAAAEDAWAAF5ItM%2B6bFophhd3N1nA4zIKh4NARWfqCooqII1UQ4kBYJ2AQsGyO2lAp%2B6Xiqm%2FCkfz5urtugisAuGzxeNHQh1A73Vh4dG0%2FNDkMQKtSO%2FBTm3DojsrbF3jq6kKdaxNxwpKvTKteAnM7mCQ85oHLN5AxXtO3FxElkoEAFo%2FY7SdVN5daSO3q5Y%2BGBpQAYrusw%2BEY9%2FXMmtYT6y1gbXXfGgzHr8ic6AN9hcvHwEYELAoOjr69A1yaVwaL10euR3YUZUZvQl5xZXoT8YeJLqVKFrjMLT83%2BN7REmekLvRn0TLh%2BZMzVhvjjOcuh7%2FDGoSIzhcgAEyu2q%2BgmErl0SoAyvHf0gOOHkuRFZQSSkFEDSG4HCQ838BiFt5mdNnEIYrPlCai6RoN3%2FEdkyVeA7o%2BHQvKrwD5CYAAo2RJZIeP1xRy%2BlJaWuskPYYJ6GKPdNLzxcio1M6LXHJDQbx0X1i8B9YnLsQYerRiZjBe%2B2alDqaPIASEoxCeRAUMVuivCDeCNo43Zi%2BmFz4viBZJrJMbwxhXGCv8CUG%2BGpgMJzaVH06hQdq5woKyZyKYDByVHQl05OpUqPrSuURMAxrqnfhkQENbMcnlzk3MLnnmnljBLSdHj488rWP0ithH7Mq2sETRkNmgYc3AZSu6gL%2BCk4IDhPtHR057XmxZs5enMzU7IR5rdjAD5bhqPdP0mGax4%2FBC5rzvd%2FNmFSTuivxBTftCPQY%2BTO9CX4l81r5FFfrkZ1yrTcaX%2FE35vu8hUNdTlgS2iD0q93mIVdiG%2Bzz6ZoWvKaG4axR1VGYKVxYs%2FhBQR7uUeb1mU%2F3VlT93WVa55WteFObdmuaGauUaHua6G9Lh9q5rpXj%2Fwgi3iPylvEGKzMA9lXBUjbXHUnsEBSjM4dcmrgF7f0G9lwAQt4RLmuXHbpvBr9TrIO6tAdGiB79MRHozMKD8uVjof8zfR8GjzHzhs033A2Py%2BejgTAGqXxpL%2Fw2WVk1lFTJqz%2B0kBeRuJCR5GRySPRQSmUbztwmWP9kLIWUhlXSVdCicr0AP0QVDW1JhE6NsgqFunp2ST1zYgQv6Qnhu0JlL3GiFmbc6pMG8mzBJsoRi1z3Z5NTM0f1ndDFjciaUQqsNg6uq3fi8dFUAWOQGs1VX8XhLFmvpemPhnFsJ4EJp5fMYZskQQsqfYfD9NJDx6cnQ0sTSuR2L40hG49L%2Bmrs3RoC4ghACgxYOijJAtdpXHsZI0rFXEhZYgy3algwWFOreuLxQmZTNtXroCxgYhVHmAFChJHArQSkYK5FLPlzPCQ38AzsClDlC4ke6RHiVatgqkBMcH5a6mGXLmcLkgxPCTi3IYssNhBMcXoBJkK7iAw%2Fq1cJO27YZZ1dgwK6TjpcOKZhOClzaJK94ByvnLhalwYwwHNGbpKKrMoiCUVvMU4ZDGftbGmdYDSWM4M18njvCm2QeRAFzCJCDrWq4fFsh0jgTZAy3lAyEhSb5p3l%2B7zqhPPDOxcQ5kAj9XEi83gCXQDB330FUKUN8JTMzokg%2BMHLm0D3oGAQxNjGVUC4qv3mNqY80W8Wma%2FG%2FRJg0Pokw2Jil%2BUKRbOEH5QZhYg2DwSICOBEYPtpPgwWBiCfyJ0YCZEGKrTfFYsGyw21JEW52PoQdw%2BSszylGkFpTMhd5kWLnyTIQai8z1ij55qLRN75GxKwkR9E1MhMUCbxmmw63GyiBjM6OORqQNMpJtSUqMssFsiIRB3bOWC1CBqx4cDrtymvUnfKZrNpclIQX0iC%2B0SWyKIyxEbrSIkB4ly9nnkYJu6fFFI5UkewzCvGzpCmkfDtvWO%2FvOQBSKG%2Bw4WeOGpxQqahRKjqs7pmglalwleZKZnV2WNi1CBepIZxSes8CtZlRI0GWmUOVcYlpvK0hUKRhWaEyXRViM53DzUU8eSDYlUJQqDMmUYc2RuqTtfeLBUIWJzpxmeJiOCoAXmCaSqYM441iWisAz0U0EQHSkfuH3o9uyZk0g2C%2B1Huy1lYiCySpvTSdjMKwTiKdQVCax08qRNA1Vs2wiL2IyamfCpg%2BlZwXvOo2sB1QB9xIdX6Bj6VzRgd4UoHI9PenyASnBA8k3EjsE1S2ipMclWB3LPJeWzSHOikaNhJsFX5zoP45XxaGhDK%2FpP%2FDIYztiS6vqMPACWcgP2kpZWjOfJBHYRQNI4tp3WUQGWpE8ZqoZEFvYJaFCTkUJPdTqeYpTEWodgDyHYOTQomy%2BoKxLC8BtejPZfK3UMphCswZ56qASoLK60kVHNgZzT8%2FUWcqkls5xsQ57uoPAv%2BCrnsSCROispXTpjPKe4ND10sCf%2FElOsPgR%2B1K2fX5hXhJfNGzBWCpiE4EjGUBgUzovLqcdL1yqDbTutsHLe0YqwBcpKRqcP65%2Fvot41Eg4cbCrFOObHzAyIO3Np2zmgIymMqrmdZ5wgWiOKMA%2BV8kKigbnyOAnZzQK1uMozbw7SBWI%2BtpCLJTN4yFsnUOPsR6JqbOmnG2mYUYJV0I%2FFDRgDb2YBKeBAzYRv4d82IRIjKNJ6kthxBIf4f6tg5Rewqogb%2BBL89Xa%2B8Y7mPwJBnr%2BqyHL3Me2KqwE3nnFG4NiIrI%2BvziW0DG1jcQIHeE7iAwtWHXwFYTmEfOmdkgt4Pr1n2vJwnSQymN0R0NLRTgAHjDVSIfITmkvlvfz7MU64jgUChw5hCXsYgG5gXyQ1osKsxCRhvPgsghFG5zI1CXCBIAwKkjyKLeqBc%2BfEUFiCvfGOta3gR%2FU26my2RNT0gywIO1yxoMTM8Mlfo35lpDQ4jfU18jrE6QiUumMhcIndvm8iDoRH8amzyNFXNUKcSoCnh5AQYr61lElsUE1avUS%2FnDanpv%2FZFa3VH2JIq5OrC2wDxYOhlkZf5BIr5I2JAQY6MewSa45Ob%2Fz%2BEjpgzBQTlG3AdVyHpu2GkjfOxGCSQ%2F4KBsYV%2B4WC4tHrRIEC3vi8DWBGimk2R3cQNWDhpiR%2F9KQZE618tdreVPJR485XjWwoxbnLTn6IZ4EjKrhRraDtVPs4zmDldmpWjWM5L49vWKkkh21cJ0GELX5Hje5CUKJRNkIrvqKWk7bw8b7gYD5fEhk7VgXTHJI0UsIqSimKH3B62CsLrQWXjB%2BoWwKWamDL6RlAYnwhMdNFIyfJuJIyo2hI%2BRLmmREVRHaJdaBYDQo4bDl91nK3Zy7hcqlXpT%2F%2Fg9jl5m4DVYTnaJOAoq7zjeA2QzPBWRnDjFKG0AJybS5gxwd7oVkVIAgAqWCrwA2TuCFHn%2BlQSxm2EjeZemixAGSIByWTtmzQII9iyI6QxlnEfiedIUpRSDRKzAojtJx830mEfqcSqHRLRGSUmpIkhYAfBXhL3h5wRAsiPnzp5CmVoG70nYHSlNBsQEOYNSYjVHmDMCMyyhMYHx%2BhksBoo78rYc0vB6ClzXpCsSQL0xuJj0lRG0q3NgS%2FgqHn0%2FdBeijOqfmwAAwNmamjdRSr62goEAhLCK0y0mqVtUz8B3F3pE3rUMN9wQoCtpvRAK3sFTK3tcPZnt6Z27rdUEcCb1qxd8b7ARVibBsC%2BRyonUCCcPwOsBKtzEuPpnx3V%2BQo3FTRLkQsTzT%2Ft5GIpAhUffp2BuiRh%2FhQEK3waIhUoJczWFQtyb9PP5ODdKmoRpQHa5EoivjH117VzUEyb9h3I8XFhYGY2GgobkujLXrm%2BbJ7HN7wo3WOTojHaQLy5ZQH60wuIar4h1s2FLyTWktIBtEtP6PSDSPebTewSizvHczvHVzmh8LyM8TZbIzBlYhsTDRW2MtA4tMbKoUyaOwZNB0EcTEoAHayrWzlDMhazQx8GCH8%2BXZI4EskKhE1hnN1De89ZjtBMDWCxLN%2B4bn5AnyOhxpTflbO1kA%2F0EGhUliSyMtWT0UMb%2BqEPinhEFYyHEbAUyp8tYuqYDRipLscjyGJA3zbmKdMTMI8V72v2ZQ8R1C6WY4qjndJBCREkDNEWaBovAOsU5JvqCCECn5%2Fq30Wfs27Q1NX3PB1CxWQYK4rW6gl2DEhCJLvzF%2BBEKd6LLjbQMVuJRpueMSQJN40n5WAdyXvuYQeXUQsoQDysgsemARNTywlJKFiZeuo5AiRfoTmTq6hkwijNVgqADIQ0SrFqBN9hK5RC2ZzmikwVm0CCZzso1HPlzzN0IP%2BQCIQZ%2FzA%2FJ0cIiWLfbbDGvgdRmzRiOWxhWyl0iXpQfpiIVEQuNo2d7rj0OZeiVOeay6x5oKlhwZCcg8KUij44xrtH4IX6UM37YQMPXh6QvlpkcPG94IVYA3iwMJ0L8LuuaogTlCTJsenAjL0PQ7L1Pi8hmGJdOqOJeVo7ECLPOdRHN4hjBEITrTPlmX622a1Nkllc%2BXvRIMYsWFbQasKlkKf0TuoImAklJXaN12zLmMOiREi6fUAhVGrkOVhqjWR2eenOmgUY7GLcmbnAqWpftrThQTmBEC5zJQBDcPyN4AoXnInBM2UJew3uo3Osd%2FVotG4JFRB1dhhN21R2ig74o0Jw8ZN7VnA0lWB0lDFZ5PDtyXLlhvcGuF0S6Wr3U2CqpnkDjwB2mBQdPGRuL5x1IFo03LEOsHEh4MKRvE9edrMh0Snaf0cShzOIJdiyBYWbPeMzTRGYsBHAfX1laNIl1ZVxzggRI5m51PG59wVXQ7HQGRYRRnGy89qI5okgmTpsdUtZgAxPvJ%2BWcqIbSWx6tf5yN%2BuJkKOjROUqEcP4y6WDOTFIXxQkr7hHBS7hmbyT8AljD77OJLW4CQGYAb2Pei8bNTgMttEECV0uBXZksyIJd39JlDyojumSt0T2TM5i3S2cviYGBEzQtmTKzAFB8QEcXkZq4YmJ%2FTDWdYLS0Kazft%2Ba%2BC7HwNZAJaVEY3kfqPHY2SBxchsqiGqJLn5a%2FmjEa8QgmABHka5AWJ%2BG18I9w3WjonkFGEwKhtgp0j8YPUeYEncSOLNhhwVJnEiplRLfp6lN7z5sAMYVx%2BA71pVUbhIzIaaNzUbAarADBLMSSoXqKXumbEiOijClhzIbSA5gGB2qtutd0MjQyWBaAzJmfqki7MMaEQAOCXbwaXixbEGNFnHCqmWg8qjxIZ0oeAxEPKD1A7yRyuS4AIRwOrQJ6DxVHVPpAc7aCkBHpHC9GMxBqe9Qt62zjQGJy9sjB5efNIj3%2Fyv2r6z%2BSM%2FzuFE0Za9wOJ37u2rcQy7P6SvWZqCuEJKtvjAUTarXAcyMQRrVOlrD0HTsN2KDiUivtwmgj5U9inAK5%2BC4IqL6iNHhU7OH98NmQILOWxNwJiPwwlnf1QAEMLagJuGLoYUdlqBRDn8QcRAg9AuLhe4myJn%2FEoxUfepXHhZ8Dk0BKaH6znSNmNJJ2IRdEvxoTfFkKRNn0cEvSio6ek7OG7AZljFvqNgRejEgmOwp7toPkAA5CIjKCsWmYPIlxUdVDDj%2F6UQEQZwMPCocey9jKiCj3ryLWjtGlYDdewTAsT%2FytgOZKoG6jDf%2FUzE%2BDBwpk%2FPx891KJ7wcBDtmnc4Zr8PjCwfnWIE7Tz5Wh4XZOloMKHqBYibF9JCb589kpcmC6MqgAH60Nwcj%2BnBhrvYWI7IfIiYD0IThyXLu%2BBjtuDKdFNmVqTy8ELHUIcco0LUngtn%2BupQtGnWSsHRGOZxzUOEULCoCKWugvY7ZqEN0MDmNHqeKtmwQSOPoR%2FZ0KGKGB2wdDYj1CrZsodEQx2TukU2%2FMDvJyPuRgDSC80jH6IO5DbRYrS0rIXfANDM017avY1V29khrSTX8G%2FWm5HQ3j02j1MGoCeHm%2B25tIebrUOsJUhfKhD0EIEeXj3%2B%2BQ43UQYWPGKRd5tI6RgOxzkuNv3Ji8YcsIU0cpJNn1rQt1eBb5t%2Fe6vSIMsxyrbVRxAHaSs8%2Fijk5AW1W3ajQf6DP51FkKbjEEaQp7ThQOL8pUajXNZgjP%2BAGWp2PntYtYtaMRzL3lOTlAMAU2jKG8l3wMD%2BbxPb8RDFLiiPnwnwm42DzJDXbmbGIZ0jLkON0Ub4bgHg3f5pBR%2FoVAu0YDFztE%2Bzps%2BP3bAAWSgSxlY2S3LazAF0KZAmzACvKJ%2FMz0beXxl%2BeIEFgZCLRMTD0eI7mFnojAK95ZgCTCfQOybhXCo6576fGouBIpcPFCU9ALkeU0pQaG70p3LmSrRNvUUN3vI9R8lCXjgQBKD9twFivCVAT47aBVWQPv7zSwNj8Un%2FSFG3FqLOS5c%2BWZHKZKVGCPSmIgHEwoN5C6HgtxiaB5%2BUvBrgQmTbO5rMJ%2BCuldZzfzxgdXp9XgD508hFWCeR8zw0tDDW2xoicZACrgqgnQ48NRFvjGjGQLa0bZ%2FYIPRHYC9plKdMERvlMGhAQeqDBMhf6LZGmyElMCwEIYOo1BZ6PH7%2BWHUp1YWZa7wqK1XoOCvECZSwoJH1Mkaogtg1cnvzmDI1q5S6K8zNTnhUkglWVoNqdHdJkfg0Fxp37eM%2FnNEjkRlbYvQhIWSCHT%2FqEBqUlbxYgGY%2BMSFSRxt4bg1PVnRhKNZIXooJOn0HVNY%2FcfiwOh4kjntxHmybS7MJkM71QCMhZGbYSMrJ68qAj1YN82a3v5utE6PJoWbuOva8RkRMPNZOJG3h4NcQ9LTUNP7WRG34U%2B6pZFDjhFpbJyEq7ddJp5LrxHhOcWeKH5m0I1Q2anhxKm%2BO1yIfm7BGh7B%2FjqYiPKEBJ6cFrT2ZB6TmSyLIpnTVkU%2FYqVla2WfZcp7SSoTzv6vLYtG8AgtXlxfWZxN6Gzmta1EwxIU6yE9s0x%2FZlSkSYE8X5a7%2FVPKA%2Flig684F00nmacRk4WooPYSFBnHTa1ebr6zgD%2BMcOV4BeWlJJLrL0qnYZSAVtBA5UxpOASkxyTpYRBUMiUqxjxU%2Bce5iSPwywJQRsno2JDcLSzoQnpUALmNJE%2BWSFPdsteXHMocr%2FC0IqI26humQ1wKQoHcGmUNYBVwIFZqI1azUTzdFmIOugxHeiO7FGrlsIVmnE3L1JrCuYeQCJCpQc%2F0JCGgQIe79NvrOoYeDQJ2REZcyhK7ihxb2NeHkVj0aI0LIicFJjQk21YaBO4G64TBu2IKBTzYheH2CASyWnlbZNFDbFlJqA1Q4kIljGpwnmhmXbOSQEgWsMmsHkBZYKRUWBv9HZZ1N1JSN64WPlCBOt7zqAJMKpczyNBpzQk5o%2F%2FxDjQg86ozQyN4waltVoDaLJOfWjYqewlULt9QO8N4AqlP%2Fo1ZIqJMaZ%2FORyILlDFoGoeY2%2FswI7MBMVXSMJXCUeRsJjHIU6kNEsAqZoBDoHo8Y8pZtM%2BGL8OLfcPdBbsbvRZuDQcyyrZ42OoTsMJ2GH21od%2FRCfgHrkeCyZfMOkWTSYgXtqYxGIGLcI5gKg%2FZR2xnb1upteR3rcNGITv8oKHpUWdLK9kIZlFfEtPUNAgnOY66o0dWYJq2a0UT3usCxxDZm0UIViE7Q13vLoyXH6VgLZoJt476o2dZ1DSsnihertfmTnTdREBRHm5ASIGxMbMSITKCmV5fMqgFiewxFtxqh5yfCPkmlKNcrJfmvyKlbaqps0Oa%2FBSPXk4FJjtWF2wOHfpFY63qA49US3T180HXmbqEjYsSpRFkkOVMCBH1C9JAJTRgjCWNAjl2MSA%2BvZjADldAJGTIoWBOcOEUI4qwvBSI4hMj8m7WHoFosA0M4Q4yS8XtN%2B5emVGJDGqX8D5SVbE%2F0bWETJRyRFYKQ8umFTkY2ZnV9Lz%2BVW9hgHq%2BHYhsrghzcANy%2B02yEIiJuDFngZnEHSFnTnqDAicaKOgtLZkRXBqGS3bgcqBK6B%2BmV5G4%2BxzA1IlYTTtL30wAPCkFZuhlgsViFEnA5Rg4UXmBbXBAW7JuNvZlXTVsYDMV305DdUPX6QyUFMwndSexwLkpBDsIQ4lUnD9QoEF8QmpcQk8FJckIIkVwvETqBSrIvHRim18B7iqFwNCcFoUKmSj9cSfX37WL%2BCT4mAKH%2BS76AYlpBE3eYErTSL68qrzEKiOZo1mbN1ujQapDrmTWb1s3iBTeQMCYcYfVeS5ks0rTlCPWr9AjV%2FbgZ8To6s7qOr3%2BkRUCKT5GAAUzFlHOkmV3fJEImmhCZ4S5ivYOcC3SUx70Is%2BgfKTQfQBsES9NEX4x0WTcQkWV5JKEJNl0UV8pDmBNnC%2F4qRYIkjLTUknCCTbfLBLJzy4rnSGTntJHjdpYIWlqzxK%2BG%2BRBy22IJ8gMQIibkjgh8Y9Q2H5aenHLwEJg2iDmhQybR8G3gfKxBAZwppQkDi9rFMfLSe8Fgalu2z9mKNwe%2BF24HWYNjNI3zoQfXsIck6YiAwCMhAsEDMvxfp9PxAAxF94h42eFp8V8BZxS3g%2FoQhPG05yIyOc5GxA27VgPq%2FN9uxGcdZCP9PAWYlmmiIlMHE%2FRj3IzE8YKgGEh8OmOkN4KuO6GYyNnRhoWNSgmY9%2BVfMfhBm7xIwZPp7ggg%3D%3D%29%20format%28%27embedded%2Dopentype%27%29%2Curl%28data%3Aapplication%2Fx%2Dfont%2Dwoff%3Bbase64%2Cd09GRgABAAAAAFsYABEAAAAAoUAAAQAAAAAAAAAAAAAAAAAAAAAAAAAAAABGRlRNAAABgAAAABwAAAAcalXC8EdERUYAAAGcAAAAHgAAACABCAAET1MvMgAAAbwAAABDAAAAYGenS4RjbWFwAAACAAAAARsAAAJySvAJmmN2dCAAAAMcAAAACAAAAAgAKAOHZnBnbQAAAyQAAAGxAAACZVO0L6dnYXNwAAAE2AAAAAgAAAAIAAAAEGdseWYAAATgAABODAAAiTweHjMhaGVhZAAAUuwAAAA0AAAANgJiWP5oaGVhAABTIAAAABwAAAAkCjIED2htdHgAAFM8AAABFAAAAvTBwRGObG9jYQAAVFAAAAGrAAABuDSPVk5tYXhwAABV%2FAAAACAAAAAgAgQBoG5hbWUAAFYcAAABggAAA3zUr5ntcG9zdAAAV6AAAANAAAAIhLlGpmlwcmVwAABa4AAAAC4AAAAusPIrFHdlYmYAAFsQAAAABgAAAAZYr1LmAAAAAQAAAADMPaLPAAAAAM8MFvIAAAAAzwwJLnjaY2BkYGDgA2IJBhBgYmAEwltAzALmMQAADagBDQAAeNpjYGZpZJzAwMrAwszDdIGBgSEKQjMuYTBi2gHkA6Wwg1DvcD8GBwbeRwzMB%2F4LANVJMNQAhRmRlCgwMAIAC2EJ1gB42s2RP0vDYBDG723aSIrSUESsiHcIWqqDXbvFRe0gBJw6tTgUCx2Kk926dusixc0P4OiXaQZzjx2cnNRFhPiagENdHBx84P693P0O7iUihzLbJGM9mb6tTFrnTWhjSAEVyLfZCgnt060U5UDacrdd3vnYNVWvWlJHPa1oTRva1JZ2tKdDHesUHiqooYEjNNFCD0OMcY2bR0qSr10pcc8S6QfRaEF9Fa1roKElnutARzqBgQ9BHQFOEKKDAUaYYJoSTfKWzJMo6epSPI%2Fv44sHJ9qI1malWVEqsi5lWRZXiN%2F5lV%2F4mZ8YfMWX3Ocud7jNLT7jUz7mQw62ouwafyvj0jfW5KzLLTZkX5EpX6B%2FLXfxYfU3U5%2BPg2iWAAAAAI8AKAL4eNpdUbtOW0EQ3Q0PA4HE2CA52hSzmZDGe6EFCcTVjWJkO4XlCGk3cpGLcQEfQIFEDdqvGaChpEibBiEXSHxCPiESM2uIojQ7O7NzzpkzS8qRqnfpa89T5ySQwt0GzTb9Tki1swD3pOvrjYy0gwdabGb0ynX7%2FgsGm9GUO2oA5T1vKQ8ZTTuBWrSn%2FtH8Cob7%2FB%2FzOxi0NNP01DoJ6SEE5ptxS4PvGc26yw%2F6gtXhYjAwpJim4i4%2FplL%2BtzTnasuwtZHRvIMzEfnJNEBTa20Emv7UIdXzcRRLkMumsTaYmLL%2BJBPBhcl0VVO1zPjawV2ys%2BhggyrNgQfYw1Z5DB4ODyYU0rckyiwNEfZiq8QIEZMcCjnl3Mn%2BpED5SBLGvElKO%2BOGtQbGkdfAoDZPs%2F88m01tbx3C%2BFkcwXe%2FGUs6%2BMiG2hgRYjtiKYAJREJGVfmGGs%2B9LAbkUvvPQJSA5fGPf50ItO7YRDyXtXUOMVYIen7b3PLLirtWuc6LQndvqmqo0inN%2B17OvscDnh4Lw0FjwZvP%2B%2F5Kgfo8LK40aA4EQ3o3ev%2BiteqIq7wXPrIn07%2BxWgAAAAABAAH%2F%2FwAPeNq9vQlgG%2BWVADzfzEijWxpJo5FkS7IkS%2FIpxZJlxfGR4Nx3yM2dgIBCOMIVrhAghXK0CYZCKA0tKSyQco6UUNpu2G3pwoq26hnSQrcsvVhajm0hu90m8fC%2F981Ilu0Eyu7%2F%2F3EkzSXNe%2B973%2FvePQzLtDEM%2BQzXwnCMwKRLhMkMlgWefS9bMhr%2BbbDMsbDJlDg8bMDDZcHIHRssEzyeE6NiIifG28gs9e0%2F%2F5lrOfZmG%2FsThjBFpsgv4ZcwMtPKKExGsecUUlWsWaL4M4rnkGLIKu6qImRLAdLJTOvx5KOpgizmxIIsRKWoLKTEuCikCkXCPb%2Fj%2BQq8CKeO1TYPTzqgjtHLAA0G%2FtH7WplFTNnCMJ14c4He3JAtE8bSuW8W4cydRLFlFMshhc0q5qrCZ8tmC54yC%2BbOssWMmxbG3FmyU%2BgCJCrW%2Fsgo6SKj6mb14PiWupmMUpwN%2FBf4Z5gCs4VRshmlrVpuy%2BJPtaXNFI4ohSOSVQwZpTmnGKtKMKtIGcVaLUtWvFByIWTTM0qBQharlkKRLHy6St2kU3FllXRVcWZL%2FaSzFCuIbkXoV7rFsrUl29%2Ffj1Qs5HoL8UKur9CXy8o%2BOd6bZuMxBytEhahRgrcwn8sOs%2FmcUTDGY6k0SRWLlxleL96WWHzV%2Fg82Dxqfyy1ZFPb3z5npIdcX1YNGsgvezdP6Z%2Bek0KIluWciGzc9Xr26dcRGDhcz%2BeLjp%2B544fwLC%2BunBbxdpw4X033FRVeOdDqD09bln7rwqq%2Bmn7yGwTGpkFF%2BCXsA%2BMtNeYGrEoXPlAzayANRK9wtx7YiORlGH8Pavx7Y%2F%2BgD0sW%2FyJ%2FESEyEUbiM4qjCmBHFlynJ8BMlMye6S1axv39aD%2Bf15aLZvt5kPCakSTxmlLyygzguW86%2Bf80TT1yT7up67pIv%2FZIdWUPeX3H50x885dh49S8eCNgcm5Bt4FXkFeAdHuaBhbEzTJ7IBZIQzQYY9QpgcXQF6VIPsuvZ9TD6XUU8qG6u0L3DY4%2Byp6k20jW2F36H%2B%2BjDjz7kX%2BBfYFjGyLgYRkgAexN4Ffp6MyQZE%2Bxk6b%2Bfeog979DaQ%2BfY7Q84W532zf9%2BsnbgdHvK8YDdXqMFwKQwZibHlI3Iz0JV4WAaWTKK6RCQssyZkHM4AzCuicNNkxEY10qJK0aJCNMpHxV5BYE79iaQUhl7fez1YpFN4u87GBPMl2eZFoZJhklhmOTFhJgUHETW93qTgsFBJDhm5FtvX34SID9r0fJ1bvfty%2BetcljGXBYH7H%2F%2BkvagtKGDPXP32F9dcvDyvkJ7QD65wF1msXLf5TyWseWiP8AANeSP3uX%2FhX%2BA8TBNzClM2YEYuTOKXFWaNMZozijkkCJVFcmFskExwBwAdg9Ionsfx7rcrXK%2FYhCB85mS2wFTwNyvyKLi6lea3PsIIxjg%2FLQetwsQkrwC8XmdxBhLEWB31uVr6XMlW2TSDKzWvIx0CcLFJq9JPXj1zspnXyTu735XfZ%2B8h%2BfU31d2Xq0ehJMXCwLpWsZepP75xe%2FCFRp%2FFpn1%2FLP8HCYAHEmUYEZhDiFPOqqlJo2le4fZMJHhjZW8Dk5I88Xpp1599bVd066%2F5qr1fbOvvWXv8PDjt1w7m3PN2rKqm184Z%2B4CvnvVlln91950Y3nNmvKNN10LtProm8x8%2Fj4YewtjA5aKenKeKPGYiYcrLCD%2Ffg97D%2Fmluv1u9SZ1%2Bz33slwLFUV%2FUmcSj%2Foe%2BWf4pHzY%2BBs%2Bxs8odhC%2FVAzxwERypuSnIE%2F4dY8sFORUIZ4Spt5n9r8s%2FM73Fn33naXLjnNH9sqdv%2F3Cjj984ec%2Fn8C7HpjHeZKPJYdIb1%2FWFyJeY1wiEhlNzFT%2BR5mZIKN3EVK8L1fZqihbK7n7iupHdzE4%2F%2Bj3l9B1yco44Xdk4JoIE2dSTCeTgRmhMGUGOYivlvwtICiFjBLLKaaq0ppVrBklmVNsVaUtqzgzSkdOcVWVrqziySjpnOKtKtOyiH84m0NyEKWXjiNf3WeyubytclbhXSii9pntooS7%2FqrSDO8aV4aySkt1X2tb1zQ81eIqReHKRHt3D%2B5y1VIeBZPNCoIp2NTfrzjFUnMIBVQPXS%2Fz8fykF0pBmKVRcpxzvHJ0f7H%2BD8TN2F76OjB%2BkF%2FSeAnKUhBOx7bWjzC6fNPWRifQMMPMZEaYsh2p15UDtJFkoYwySEnTC7wxi9LDRddHP7y7Si2AOBCtvapMz5ZOonwD8qEPJK5PEmFMo7FkgEzcJ59wPgRcIIVCkroZ38e32fUnOpNtOMxe3LAz9sKJzjAgPSfjvpw5i7mUuZG5C9ZqSoXS4EU5pEOpt5hFSpSWbM0hLUpzroT97kzp9C%2FAfmu1tPqWLFBnFKlTciHTmYH52rKUQtNAUs1aAdv91dKC9fjpKm2AY5tvgu0LqqVrbs9mS3dTyuFcGCDabOgksaSY%2F%2Fh9kv%2F%2F9vqQVEGCneCNjP7fzmfre%2BTR420e%2B6%2F%2F6wWwztbkReMYr9V5fJDyeC%2Bd%2FktySnNVmYOjqpyOY6qshhHdMGFE5ROMaGnj8UfP64PdPjichF2jNPk8jgbyPZV9UY36H7f%2FydRmD%2BDO2Bx8P%2F52I83Hv%2F0pKIoyPMTE%2BA%2F4DsbAMLA4pEgqRB7hsgfHvvYj8rJ6OtcLWz%2FG6y5kLuTn8fNATuN1BTORzUQwkwtJUH3rIAmS4EH1LfoGH8MT9w%2FiNbBWTdANUszzE7QDUAviOSVUVaLZcnMI1ZzmJGg8oWbcDEVAv9b1h7YG%2FSEJAiucVRJVpSVbTiTx0kQcvpVM4GayGb6VqGsZ7TDSSdAyyqwPRHa%2FkhAVd78SAK1DdgUbtA7ZDVqHq78UAu1jH2OQ%2FHiuSSx7A6S%2F%2FxN0Dw7keU7KSXEpnv9YPWResQKi%2FhO0EfUUvAile412X6a0izBnHE%2BzapmqWUV1zeo51KyaQx%2BjWz2HulVz%2BBO1Kw6WsY%2FHDLUG8r6O2I5r1VcFH1xlqiH2InG9CIhRXZGR%2BQdAf2iC1X4ug4ajBdDoouuSUC0L1JgTwJhTBFfJBhh5qmWbBw%2FawI5Ck6lkE2CQZH9zHACnmpm7IIE26wVg873JVN7nBg2NjaVZok1g1HfpBJZ%2F9vj5W4%2BQs49sPf%2Fxn522%2B9V3X919Gvl1SCri7CjiAvU8aRt%2BrFC5pnTkSOmaSuGxYfWXz2%2BBq%2BBiYhtfs2DdLTIE5FKprsdMY8o8rjgmWy5HFFdG4REfRMIESFjBTNbQcVZLIpU2BbCwCRjHtb8iGCNdFRj6CkGDhBxWbWh5g6KwAukWZJr4XfwuZj5zMnM2g0ywoqoszih9QL2VlHoLqsoCV2kp3AMWtFVApwUM2lBDwPZLxX1OKdePrNDqLgUyYFiWVgDLlwRQYJTF4j4umpqLZ%2Fvcpc6TkOE93gjrixDBJxdkH2zmsjPZvplE7iukCn2wme%2FNsMkMKSRTQioJm%2FGYkzU6ScooyIIRNg2oFEpeYywZNN7POvzciu7BWw3dPYZkW6wpkzSmM4bPTZ%2B2gvM7yZcMhi8Rl8yt6Br8nKF7mlG7wpDtMtw6kF7BBezs%2FUZy%2FrbyNvjPnhJtTxp7ugyfG0ifzAXhlMFwP2sPcid3DX3O0NWDX27uThpzHYbPzciczAUc2s87AtzJmRmfM2TSxuS0wPpt29afsm0byEKBKX70Ea8YvKD3j2ugBeYOphzFudYK1v603iwsFalMuSPblwN1oakKKiYqFY4uOJ7JULsVzPvgIVx1Wl2lBM7DrNKGmmk50UYlFAMM3eZCeaRMAy3VVeqBre6s0ltV7Nlybw9e1OuBi3pdqGeCUESHAHWi4CJSX0kalhMPqJ3aFrKSB16obnr07aLTQjwD7aSrfYB4LE6H9ehbVkeRu2WgfWxO%2B0CRyhjkM03a8CRrcRbbBwba4XtZq8Nx7BJkvvbBwXb2wNgc9gBYxkf3a5uavQR%2FBon%2FNdggXUzZTPV14HvQz82HUFc3UT0bqQRMXzKYQPAQOlnNJF5zurCj7C0V9SD%2Bsaewt4xtHduLcoRdj%2FyOAvBtkBMORmRiTBmMpU6CXA%2FSzlgtGwkSzGgCieDRZhPVSesUISIpOqzkV2TUYT32jNXBriddAX6b1aHaxs4A9Dg34o4ylmd4%2Fin%2BKZjDHuCB7Qza4M6q4kUhW5a9eBtZgnHx4JBTwxAgsMOouUpeQHD8ogBcJLtwcsO8R6Ox5LWDnLJwDg%2FMrJIow46Zd6Kty5S8TtgTGLsLT3nwlJGINl0Qu1tbeLeL5Vta3boA9qCEkPg9xE3mEPeePer76gH1fd%2BHZO2HH6pPzAeR8Y3GE3v2sGepT3yIp8dUIOlBaiuwHz3IMAYv0BTlVVq3soQcYgwWlTNDHQ9O6nggZmRhlGO6tIqTHAd%2FJMrFOU%2BOixfJsz%2BVHvb%2BhDw79lb7B209bzY9wSvoQDm6gq4FhzW%2FD6vr6No9FzFlK95TuxuYICQ7LirLvIC35hlN9NuBjhYqK0sCD5KKNYOksosgX6lXDL0g6KcEiKjtRf6kvoHyU30Dtn7z7LPUjwciFP14lSKMM%2FAr2PfPAhQyE2bO0TVID53LBhjYCB1YsaqI2kIKymSzqyTBFiiOLbikiqJ7v513y1Q3aBaVcL8iuffbDB5fiI6p7IE1l5jMTFBfUXuH2WyYpUsRqY0kR4U9R87a88bhN%2FacpX2c%2FgFZ%2FcEH6lMrdlV2HSENJ%2BCDZdWnPsDzKp2uwLQTeTbIbKzxrM6iTQ0sipiAjeuv82UzYgJ8uR%2F50ouY%2BEVF6lfgCDKnj2LicSImRoGhetDxWZJrgokcF0%2FEk8uPHNl1Yq5Uz9ZwoUzC1n0KiE%2B7Lk2AR1xUsWcBJW8GRwKMbzOocjxxUJ0sL3qiTTVZmJOjhRwXrXAt%2F0pA1m23OiqVLOnKVjaOPRwgv0LJpSZg4pO3YJk9PIGGEuNn5jXMe6RhgNIQYLDVKRcEyok2IAxvtnA%2Bf30aU0L55CmE8uj6SAvMbMOJyPQhmUHaJ5OJ7IcRf%2BpJOH8nubsCnFvTmZqZVQy6mWFsxYwSADhDFE6A2%2BkqWTReDQOcFoTLwHu8cgCH2CyWJB%2Bu%2BSKOPGHMXgkPB0SFAu0Ns%2BhAjnuNLUkXOpmFqCjAiu4gsq4k7TqifhU0otsvuYeM3v2Vl0EjYn%2F0rqYWbQFVCTSqk%2FHMdaftZjQdj6Hwupgocx1TFnE8YX75qmVfBOe4Lwhz3I7zrmw34AE7gy7ymOacgIHXGDdYLcUBGReqMaK7HwF%2BXjBYLaCbRBH%2BoLtkNiFavggsL1EqHsx4nQGd6JrLDrApiNFCEt3GnBgVQJHpy%2BdgTsZjKcRuy8tfuVvd%2FMXNt5WOLCSj9HOXdphdj4rfdXh2xZESLk34SY8xsOoVdZ49nh9rBaOYMoo%2FhyIumMWgRHMOBy2URWnXkkMxE80ir7XmUHdPZKmJYzpUtrm8qGxYq2WH2wdbqDCAtMOVDZf7BBgaqYaXBxb8IRKVEnntpfmMuFuOvVlzEqEMHH%2Bh1wnd8tryr%2F0f21us7zbIa9SHQF7LOHYtmo7TCiN2CEalbAjioBlQUgdduNQpDgC4CQ86QIdBBYgpteCqxjsMQToz0Kc0MG4w5xq8SaDcaOo5KB9bVpKulVuoInJsK2guIMWp3Vpk17cPVFZu2bKyAgrMXjjP%2FmEX1cR1XYH6gTiYy7K2rmEkAbmJq9J4ApAQ5K5nmITZYVIQHSTNGQVAe%2FC2a7ZefmGxve36W0Zvu%2FJUL9KPjA5Os0ebDMtPJodPnmtpa7PMPRnJwuly6n7g6h7mJOZ8ppxB6gznlGRV6aPjHAIyjei2DK5iMaBNZ1XpdJWysDVQVQZcJRdVG0qzgbWznUAjmzXUTKVJMgOzU3B5vBxytw3WOifKObFuxQyTljCRxvfTbMzBSh5Rc0sgQdEtkZi077CCQrfj98T4%2Bx1085xH3nj7jUfOqdhMe0w2%2BsauH98mHpCSVtJ1408vv%2FynN6oHtb0r4QvwvSvHXiU%2FxAvVXnxv2NbleIVfz73NGEBnY8SoQTRESQHjIzJYBSkwczWpzyo7dsyv%2FSejILMr6pMNh2q%2FxW2mv%2BVk3AxVExyHUL6JehAEfz1RABtDSIGYrf%2F2gbmXXjh7rfar%2Ffnbnv36rX2X3HlPbfy%2BzZ%2FN%2FZX%2BZogZpHEr9BKH9d9G35BHEzwRGB0PrDb7XD5ZW94Jgwqcw6Pxc4BEE2KC1O8PVpIEhrNcQMuIaNCQeygsZwrXXy2cbNw5aiR3A1zH3qyQVwCwJ24tXHLn3VXT%2Fd99YZdpxFT%2B3VtlU90%2FroBUEYGbAwBnlNokM5nZYPstZpYTonF4adocMEbc1XJ7z1yUGcFMOdW5RDNQyonupXgslimxRjgSB4U8C2iWHAtgL1ot9S5Ef%2BcKNFpKhjD6RqslDqOSIc07ZkfTJldV8vDuKqWtnUoHdbnMypbT1M%2BSjpk7y8TqxLskXKUCfGfOAtgeqJaSi%2FDTVVoClBzJKsur5f6heSjLToaLpoVgZfJK%2FkDvTFR9CwlY0Nvap2OosxRrAgp7vNOpnRoXy%2FyMAfTZhN2zzAZfoK8wODRrNiV%2BT1SM59HdkstH0ZmuCUcCLw6EIofqYB5UQ%2BqRwYu0oyAAorirXc2BuCQoQuFFDqPdTUaLRdVGtSw0xFF4dmkWueajh%2B3K2F78wEuobNVlbBcIDYwhHsB3lKfsAfwlelGxAltF7m1kzgqK4814EQpo7hYQvnM0P765Pu5T15PNmvVT5r3NOLr2akkKZbP0GNVcW2nQUPMwoGyxZVGtRX0QTBQryhq0S%2FywBZZrk%2Bbxj1dRSJdcGMwQjP39pSaQ1jScgf5%2FNCGBPCmgmIwrDXxK8JnXP3Gfol2pryKVCvf20RWwxb19zF857bTjfk7Q9QRN1xN0jxZPtTxUZmCKU13PLQBrMEYr1fVED64cZsJ4ZV%2B20NebSsYEAhbu6%2BwBsOh%2BGQqvCofwDYbgVxYn6Ho27nerQ%2BFwCN%2Fo3Cdg%2B%2Fxav28A5Ld2Zzmn3VzxZmu2nVmL%2BNH774f7%2BwKU55rIVAgSOfSeElA4dUB%2Bod0Q3lhrEY9kyYsIktUxCSQF9%2BFkLfao0cQCs1y3yjS910qXEktVsUwwpy0MejQFE501Au4Q3kDplBMLoLuBnhMVi89yXymOuYvs%2Bzx59pgfWLBIhwBj93S9LMH9GMBA7E3COmyUKuRF8mJIOvamFCIH1Ln8Nm847G1Y91A%2Fl0G7OYUpJxBGsJAs1Ga0cLXUCkXIljnLBAuyjaIA3MlmkUFNmm9E0FyzJiuuf85UTPPkAYOhGg%2BTOyp5YItLE4RM4ArDBPWGCPFRlaEC6gCw3LE3823siuEzWZdFHba42JEk67GQwxYPm2StlrG9FhwDmLNzKhX2ta1byam4lh29%2BUsWh8OCbxPyA0JMgukGvriUZiOAqGvPKN2gpmVgMhFM%2FAAsItVyhPonIxnALuIqpejyXsoBKhEYBiXQX%2BpMAUrR1kQLXTS622EvEoujRahExVK6BwSax73fGghmpmmKkZbdoPko0zws2A7WSbMcGHSheY0x1uvD7IcYKn8D7dzbqBzt4p25wqqOSvvKGWmrbRdoSsXRyuhoxTi8fnh4PQHq4FWoNJma5uY7YUfyDrSDKQzXjJIWvGj4TKrv5enYPgs2cQxeGvfZc0q4WmZtKN2JEs%2BUWnUtNA%2BW7EwSlWEYpGg%2BmUoTWOviYAA5iJMQj%2BzJk4vbh1s9p5PbVro68%2BRrsTZ32GhUbzxDvczfbOtwOsmmcvrKEV9f15%2Fe6F43MkI6PGmHnXvrmHtaky0oCORfyStfUL8HPIf%2Bn%2B8Bz7WAlOhhzmXKLQhZtKp9Ejo%2BHVWlJ6NZusBhdJT4Q3ANLlZRWLYwvQa065ZDIjArHaVEGkbJBwPTHoWN5n6lQ4RdpQed%2F4BgniZHpLlU3oDeSxyJMA%2BfJJ5CuwGHKK9txEFHZc2%2B1gj5xTXflqMxqw0I3du55bHlla%2BdctMNZz70%2BSUX7d19ipBr4waa5ZDdKcwnyhcKZxTaTAJny520Zd7qu5dWNq4%2B9ebi9UtXbqzPS%2B5Sqnu36CNBaJgWxIADo94oovR0BAS14OnDIUjlo7KDcxLO6JOlytIrTE9b2uYbzQbydTY6IxYwGG6yTJvfL8zOcCdPb%2FUQjvT3m%2BKphM127F97B439DPvRc7pfyAxzYBtTbtLstTJr8OGCYwOut1GudwHXW4AjklRQahouWp0wW0AHCFFfQ9lPAzn%2BIAZy%2FDSQ0wRf82trk7OKc6ZkAdlaMlDbLdKkxSRsosLDEKRg9hfkuJgTPGIuCjswGp1ElIHdCiKYpJy0ePHiG26A15Fd7IFdWZeUjsYqRXVzsRKLZrwiqH2PP37szce5c3CZDaUkM3vsmWyxmOVWsmYpFaJrUPSjb%2FB3gfxDfO9gQO0CfNkqNVEb0bUA3E4NXcuhT49kCHSbfazJTFDRcfnRGgJRRsUCawL8GRDZSkQE2R2ksnsmASRlAWQfdwLUo49r2BU11L2ZcdTTkit3g0YZ7sd11Me2IOrsnTXU9XyBxngqowsgjHLSZeDT7ockfglaYkf34zvXgu%2B4hsD223TbTyOY62kEcy%2BoLris0IhL5WO3%2Fh5YxUn7nk84PxHW8e3KCcOtdXDI4fqmuvl4R48Db1L3MoJ%2B0Z3B4EAog4kYQxmlt4q5GHq%2BxRCZGCf25D%2FdfiMmxUayVxrHozJhELSQFwDPXlTfVN8%2B3tGPx0vDSMPuk%2FASP3W8%2FPijdaLtcaTIrE%2FYRJRMx80twPyRlTp%2BS2h%2BwRyaQ3M6zaFZTfMLLqL5BcUsYrw1hzGcK0FM3IQ6QtnVMi1Lsw3K%2FrbpaPXc%2FL%2FKDDle5sf%2FjZa1IOfHv6G%2FZcIc%2FsTtT0H1Y6OfZoSMH%2B3Wx8cImmqQ6WBmMItgZUSrPUmz3dJA9cUZNDQ185yuIBiOBylK42CfXrRNSPg495XHHkPzBmcOznOcOTDnu3BbPTg%2B%2F1VbDWoUBWAWohxWbfySo2%2F9vcIO%2FhmpjSI18ONswFdmyrOoP2txRpl1SJldpehO6yn8H3HD0LNHpulo5NPhx7UUo49XKn%2BvHD%2F6FjrV2OQNi4uLdR%2BRwr1NvTrdNHMRphhafx6qYoP15YW108zQfAymxNt15y%2B6XCammYHl0hVh3490dUXG3JEu7hYw1z3snXR%2FC7yTopa4yzXMcxkoe4o%2Bu2G5r4VyaR7FBN9zqIquED38gxkVoQBAJPYrkljyuKniApCVXR4JXRRNouLtn5o4N5MYUsQjRt26Jh908%2Bs9gYDn6F53sPhX0rGIJN495r9o2eZlyzZ3cYfdwaD7mA3e3%2FvGZx8kw%2Bqb5LD6Izy3DOh270cf8s38C4wXtPQhHYOQBnuEwq7lgKAz1qQFrJokIJ2dR1hDCKvA%2BKme4ekFayobJl6qtaf5VBJ5iZoYxnuv%2Fel11%2F%2Fk2oUL%2F7G%2F3xI754wrOme%2BeP%2BFm%2B6%2F%2F9Au9o9bf3Hztlf%2F%2B77L%2F3tkxBzbdOmexZ%2FfRc%2FcjzrVeHxNYhaOR9e8WnTN1xBd82hEldHDJuogYojCgJG9ktcDihJG0Y4bQ8uJsYmhs6VHFWVyxMysfvUItxZguorhuX83OBkf6HkMoM0VwkbU6oU0WwgTuZBmU8m%2BmcRBrppz8RVXhKWFy9ctnZlYtu3Lyy%2F%2F3k3bHKed5hJ8aYuTNZtPL5BdZ37za195acP8u7ZcfcVVn5t7ygPFAd545je3rbwoeLbRt6ht4Y7e3CW76vbyS%2FxnmGYmCmvlOqYcRGo4qxgVwAFL0QHToktIDV%2B11IbUsGEcOBRG01HxiaVIDAliwlCxFNJCHry4ryUWT%2BguSOA2XhYmKDoFSWO9RIGkzIBihrzzKLkk8m31FTQIyeH2gco7j6oHH32H7P8aefBydRP522WXSaejo%2F3Rd4ymb4ORaMMrb6j85tF33rkwSx68DK75n8suW9M8Hs%2B9D%2BZSM5NmFuiYwbSJZZRUVTFrs9mlGAHLDMXSXkWHIlOKuYAFpVArsGDJHIS5lOgv8Ub4TNantmwU4uO45GuokGEuQiQzkWIOAyBjYG9dc%2FdkZB4Pn3%2F%2BWeEQ%2BYz6gOBfMHvt7H4NoxUt62sYPZAHhEg02esxE%2FJTMocM%2F5J1yLnZF4%2FjtZf6AeK4%2FjfpeJm1EWvVcRkP%2B1P%2FGY3wC%2BEI%2Bi8wqyoK42UGRPf5wObXxqvUEm0QXicYLTObIinArWtopKw%2BMhm5taSJLdyhrrxHw0ku1VCaW%2Fk64rRD%2FT2eP%2FmLWn62lpckM3OZshux8FHrEewbs1ao4z2kcFnEzUQLdUouL0xCI5VpPswJssswH1mxxNio541IsEaYSRw%2BzCQPH2bMZ5bQGwoCN%2FU96g2tfE99Dd4r7Gmk7WXtyMvqL9WDL1eoM%2FXlcfv2FqCxB6isRQWtOer202gL8Ej1ZA4tgkHgT1OAKpp6cli10Y2spuWqi8l%2FHN1P3lYX1XIba7IeJX1ZQj%2B53YkZWX56F7GGNVMLSdXuMn4n%2FUY0e2DKzdSAfkN%2F%2FaaEub2up3j1eg7MhREy6O3CnBft129ne%2FE32SSbHP%2BVBn%2FcEuRCoC4tnMGrKF9WmCJ3C10vIwxTmJTQNjnBrXL85N1dx9fe9HsX%2BSX095nCuCtKcwg2fmkXLugN30M6t9Vwpr4KQyPOwDciLNDkMNs79kN%2BCSKMFSrk7SljRGMZINlzNebksyg0AvWfIZPiWXk8BsMzrrSiqoV3gNdz4yYn%2BQYOEtwPswy4t2t8R2F1aHznphVZ1qrOd9Hj3aur8U70PhPuocUfQafh26hO49Z1GlRoUFQgO0%2FWzaNkgpnGLxl7%2FUhdCydOthdo9C1G4P7Gf53m6GLqbepb7Io%2Fqw%2BRjX9m140pfyYbYQtxc330M34lfyVaMwkzKRBZkOAg2ag%2B9Bd2UCJjyov00rGXfISMlTRZxzEc%2FzT%2FNPXnjtDMB0cVS9YQav%2FUzIeAnvmwDzMfqP9CwjRZzHuYmvWQAzmBSmVcinN7iAfkrGfPHvU99YD63h0V%2Bo%2BmO9QP7tlDTqaHJ8DlBB1iPC8J4XI1wGXX4MLcIPsEuGwWjGcwsMTwsGqWiLF%2FMnjRfHQKWFh4cRygptIqS2HS9VV%2F3QmmUUggcEebC8Uoj2DYpSk3lwtyIVVICSlBngzEqld37Hh15054P7hjCixttTPwPhEmcSJM7gaYPHWYHOMwOafABJwlpCZDs4l4ye5n3z1vCiS3qO%2BQ3c%2B8e54WTx2HYzozyFxEIemvKoNUF4hS9bpXG70hOtfCVSWsuWUBvmGAL4zrTbQX1pu0uN%2FMt80YoMOYGtSHUYmKSgdmKpdtzjQq2r1iyUim4JDLood82DCD5hV4jYKDl3PDfL43zWGlpAf4cTKGr9zFOwUja2DNvIP3cB6fSTY4UyE%2FqRjc3bHmeM%2BcnqbsyXOTt0%2FlVzbAGm0WwcCxxOvy2VyElyNDSc7Snl2fzS1p8xv9%2BQ1qujiBPhjJHahxtEQXZDdN4vFVMdeIH3ftltxSjYd9qB1PRbcQxYgnJpwfD7H3yKgWeJwK%2BB1gEBUrcL4xDucHS%2FMCpuzV43ARWhDFZMqOQDRHi6jKtng3jQNMQ%2BlcNjS3o3%2FDUy0L4RT6N3pQcwUVYl8sns7Q4XPDniL1lxhMywn1K0Qsh9vatThePjdMCvmcFGZlQMBBBCmeT5NUDtRxONpXiOdzsAsH4VRO%2Bl7kts9X%2BrZscv%2FgB4HnT6l84fbwBv%2Bliyv39b5SCZy7qLL4Ev9PyeHKDfcFKxXvis%2FOrZy3N%2FrSS03337DwYv%2BPfjTtq5VFF%2Fp%2F%2BAP5ogUVjV8b8%2BYi4zlfnroJWM%2Bb0yUfGn6YM0VzvrzBiclxNC%2FgBMlxDVkPJ0r9WnjbbRfX%2Fp84ffNXDVcxU%2FNVJ%2BMQnIpD0wQc%2FJNwCHwMDoABORH0m3as%2B%2BFO9bETZ%2FjFd6yr7lQfnwJzkw6zj7I%2FXy8O1SR7QIOZFofWcu2cXgqz6NNhdjQdJ9dOJpji5aHpXb2pKVAPs9OLVz75YXXj5ic%2FHJiab3dFkS0Mfzj2wcCHT27eWKtXPof6KYxMkObcYThW125KrAEYm6HKMc1kxuLhsb1snLxEs5l%2FPuX7ep5J7ft1XxXWoIOWpH2fpqx2qQPqLNKtwfBDmKOLYI4aUU8yUC%2BQQHOw%2BCr%2BUIk3NKRVIyA%2FJC%2BSA%2BohrZx5bC%2FWFOLvfAYG4a3a7xhrv0PGfweWCcXYrxdug3ryGdIGsHSoM2u%2FU6PJv1K9DauowZhG0B2ccd4d%2F%2FEgXnWW8g%2FbK7e8%2BvT5JuLUsGBb51zVKGuM8E2xlp%2FlyJScuo4nE%2FjzwEuMyjeT5E719Zvf2UmSN6ubbyaj%2BgHOjEdgF34vxsT5nfxO%2BnsMGLpREWxd7VdiJIUXqa%2BRvTeT1E71tZsVOKJu3q6%2Bxubxx1I71Ne2Y20Nzal8gOrVcWY51dpaqkqc%2BrNDmVpmBWl0Cpk1qy%2FgwuxKm52PxrUs0DjIaTMuVyER6Nk%2F2W9BPGGCajrG61BNR7Fdy6zUPsjaGXzc2%2BeN8zN4v%2FfHkn8aSO%2Ffjp%2BHD3ae%2BjNvKOQlaXgfewlkuKFO1yTTwUxjemGF6WXKKZTkPTkMjqLUhsW4h3Zm6KWdGYYA%2Ft4e0b3favPkZ2hhdzEnRWlyDMDV15vMEKyyd8JUg02cVU7iIF6JlrN6YlgEQrNtCmHMAh%2FF9eRSwrEx61CqJfSfPrdHej8aSg1Z4ix7aRFzwYtczON%2B9Vewedf3DY4WN8u1aBZikVg9pqdS08RRu89vG3WnkyWT10Jo14DDG6Zl%2Fhm31M3cLS%2FZ2tf1Ix999Cf%2BWVo7lB3P88uBtoEpsKVeyk1SvpDGHL9hQ8HLOvg0Gxf6fIW%2BxDAmEaSSMS1WzQu%2FNJs4aXo6c8G5X77j7c90LfrMZZ%2B95vrTVznPcadmF8j0eRs3ndbu402CNyrGvzI0pN51iu%2Bu7%2BYHbzp7%2B8Dgmlx3uD%2F8gvrDn%2BxekzMbPc7CjfZVI3uTM8%2B6aXXWazaEArkrWlpe%2BiHOmUsZGz%2BH%2Fw9mAXAZURZSjppbVea6SoMwFIvgNTgX2GdGH029cXtlWAl9GrBhArCCLhMmiA9f6GNTPtmXSqbSbAE0nDDn4AUjbpNLDeZ58yIjM6a3OVsc3uVrRUPEZzE7Oc7kCLT6%2B%2Bdsmj3LmXz0H3xSar7TvXyVIWfvOH9R2snaeBMhVlfQnZwhC47emeRbI%2BHpN3ZLlsTwUHjkvdSKvcXowi6Pt8Upm6yEN3qbh2ZfMvspsurirjUPGVgh%2BrnX7jNFzrv48VW2gabepjY54OIt6aVrW9KXYJ3695gb%2BPf4HBNlZjLzmdkMLk%2FtVWWGlk66IKMMHlIK1dJCIEIBVL5ZFnMgaGpvyw%2FTPC%2BmZJ4hup9nxNZ0fnhkPhX6QBdjNmyIAFmMsbQhVQgbskCZNJ%2FSio3yvQWj7JMLmJgwFDQ2z1t%2BxZYvjn5xyxXL5zUbg5MP7BZmd5%2B2%2Brqbrl55StcCKymEZvSHe5T%2FUdLn3dpzwQWJJR4vu77N0rZu9Yb5mcz8DavXtWE26MR9y4ahM6d3tuVOH%2FiMgyxMzJ0RWHQKlryvWbjuiq2zL%2FBvaG3FaQq0YIAWCuOjGQ0nMV9jys6aJTqSwWxQpS%2F47aH%2F%2FM9fM1KnRXGmHYrtO4aSg%2FzNodi%2Fozhd%2B6xOm6dzn4u%2BB%2Bh7kL630vcEvpfhbMudLXfGjWCg9SuBfiXYr7T2K4l%2BxdrPPG%2B12V2BYGsirf8jsyxwyOGccDCdVmYFCaPRGtOncySOBC64kaw6gWcSmvoBVxSSMAgsDghfJ%2FiCocHEverL9yZWPnb5BSnL7p89n9h0FyVqRg7PcDpIW9LXnYlN82TIxs7U7JvT9mBQSJx67hfHyS3uPLriLunc86%2Bd7mxT3%2Brb4X78Eo2imXXNK5uCY4%2Ff7UxmkzP9s9gbp93Td9csb1ubrXfT2efR%2FghfBeHopvqGG3PRk9StkQKQBbSkQX2WxCaSj1%2FalDA4Ek3S2DbvdO%2FYtv8iL5AX1Mcx4DNnzvwWviVmaDl6qMj%2BfKy7iIIMu4PU8rUkKnfbYVZj8ihyc0dGSVA568OOOGUfzZL0%2Bc2d5YSvVqNa6gRO9yVguofCaJOZw7DpS1CnfL63r4DeB%2BqPChP0FaQSIvUZZEhcMGKfhYJoMCaLPifZtH7rerLJ6fOL6gPFoOfMN870BIvqA6KfGNu9PQ4yl6waXr9%2BWH1a%2FUdHj7fda7f9Tf3bab5ZXtG8bJlZ9M7ynUaEv9lwNa7le5sndWEowGpSzzllVjHr6tH3PJaZabkwmAUEhj5G3huz0j%2FltuYLObqfXxKSdmHi5C4pVPzYfzT2xL5fuzAkHVtUS2GH9ebv2tL89JzhGv4ZxsK4QJc%2BieppfhpZ9NCkGxNtL8Flx40zQmsRfLDUW8V9gt1N6yhcYKU5cBCHCPZ6QC8pcBmY%2BlFSkLV9WCDX%2FwUXvYfG9qpPEu66Hc%2BpT7KP7bjuITz4l0qFXf8yelBfQpXtup37x%2B7beb12oNFf5gZdUqsBdoEhmZvoZZoYHiNiPJasZYuNPaX%2BpIjZ9JgQpuXPIzcPMFqeFR3%2FBHBzN7OBKUfw983VspmWapgxj0%2FKYg5MRw7N%2Bk6gRpr6UpPYFAMbcXCukpvQDGEZSx5LGeByDlVckDxusRSOALlkTI7TekJJXhAgoKgPG1O9WLzgdRhAlNfaMYGNahTXpPKJgfaIaAUbG%2Fb9qaXnfuU7Xzl3acpvxPZMpItdXzlyWcvpAavV2xxv60r7RdORSsfKbRdetiKXW3HZhdtWkrVaIi9W%2BWG%2Fod8y3%2BQ%2Fw72BWhMno6Ms%2FDuygWz87dg%2Fkd2%2FQ3fZ79jZSOt5zOv8D3mmVhtvJvPYOezIb9WH1D1caOwFdvbv0Amn1dPNYIqGLaDjm2AetTGoU%2BtOGIGq1uiB4QVNRdc2HLiE0QpIGTQoeKFjXXyZdJKuH5Cbf3HsTXLvL8gNuN9ZYQ%2BQJvUPtBUR1rVtVv9AmlCdBxjdMGZPwJhlAdpyDMcrkFO6gPYuJallB2Pwha8im6BsAhWpFbMXMWWxWYtegLJUkpsBpG46KskC8A7oHOj7RM8n52A7CV1R6QjRzzgur3hZNJZMuQ1OR4C7KWloEs%2FEydj3CmsKuyOhjpB6EN6yNI1GnjZ2W0u3gXvS7%2FY8LEpw%2FNhM3u6jszervYe9UqjS4WMacoOxjsPZmAHHozau2LMUl3pFInZdIfmczvRRCQulK3rB62EsXuVu0Qpatd%2FW8n%2Fxt10wVvXfdtL8QYP222IGGbnBPsuRKBgW4%2FeIEmy1pB5suNMxP9aW1aYWOhoISQOPbacyNapVs9HOTtQzhz2cNLccb6YaH8lpTJCDr738MukgHS%2B%2FrB5CDteSyXX%2Bhf8ZsCe3w2820%2BoitEctGdoSajydjIZroihxotL4T8An%2FVH1Fy%2B91JADpgCVtfqChVqGuRKsYmeFEC1RMlDu8VZpWVZTzXcXoVZQOUKbqUWwmRpWaJkjoj69J6f8NBEtc1f2YNAIhGG8JpOO%2BdsHIk8ZWr3sHk%2FC8JR6V1FLtKdDBm9kDfs7X6pbHmul3iy6ru%2FWc3WtIKsKYPXQsmsGC4IVo6vUAbBladl0qcOIfs8gJTAHTDuTSGlezg9yw4YBkhATcY%2FPAfyMHv4US9vZ6HIzljw3GwjwjljQ9wphWd4g8BX2kbEzkhnWYnMauFXeEF%2Fg3g5JyLzYMCDrz9rtR1hB8kXXHAF92sILnIElR449U1HftVlJs0ROVn%2FLraS%2B%2FmdoXgvLLAL6nwf074R1Nq9XEeVoRmskhzLVny2305zq9gTWxfVmtNZD7TnAqqtHi%2BH3DZCCB%2ByCVJIGLASjFEYbuu4ABVTQkDOE0fA0xhY1ed1XzXRet8ptdHvP9ML7quucM7eI3qag2xQuXvjQ8hv%2BMmOGO0get02fN9067SJyphR6msxfus3b4glKnlbiuXGp%2Bq2nAfM2gbOGJHe71yu0%2F1vP0FCPEflTAp3oQf5B1Ldoqyn8S6G3uyCgwzslC7L0x2Vvdu%2Fe3f3msj%2Ft3%2F%2Bn2vYf95EX6Mc%2BevrBrt8s%2B%2BP%2B%2FX9c9puuB7U1uqjXRcSYNKx%2FNK7cdghj5lio4msD1vPWqhaId4BgRAwsbS3xpZ7v4mRBRxFnkpwkRCUunsLgZXFoq%2FNIOvF%2BaCilfrN5KJVtmubYcLe3uKsIhvOLRw7djm2ZPlxc7CfrI53FrpO3CLu6Tm5rfvlfggn1DnL1qwef%2Fc0N6h3FxtqwJTqcm5lyM45qgnp7mRw2A4BVU8CSZ2x2YanHx2G4Yf3kaU2GEtfam2gVu9grQNSwTMZFd9nU1oUucK1et92tdMKqkkYR3kE9STmxIPYOEOQG2aNPwHr6WIZNFiIwBVPRPBcX4jDTPgn3Ioq0sb03kFEggLp3MgEOvgrIk6vpvIT1r2iQ%2BDUU95OYaxl0pbbSFiXtNEPbi2iXe2idfA8t9Rw5Lu7dWnJtN82o7R4E6YJFct2A%2FH6b2OSdSY3CplZAOQ4UEBV%2Ff8nbA5SRB0%2Bi3uWCSIkA0z0BMzpCaElWtLaiEdoqQY566DJHk7ijHSzmv%2BTB8k0ZTJVis8NBLnRYRdvFDusakl6z6eLVm7YLTU71SeExsAESnzU2OX%2FgcrtdaoFYeTMn8DxrsHxxrfo07eC1mLWLCYv5LaNts8Prdly7ZHSZ%2BrQv9XDTKWSV1BaWvCFCWM7A2UwO%2B%2FOr3tVl2rnAN2uZMI2hXEs7omiZorBeT8f6CmVGtjydioPp%2FUi7IbqUYC0CbYIQ6dJqEZBxgNBeF0pAZVALsCQjWFJoa%2BbbKe1CrTThQomICtNf4qZj5Uiqi9KOBSFo0EiBJcCGMFvLYkpx8VgqhzI8WhATAha6CQ5DB0ElMyeeexESyuq42O6yOsjFgjf6lEl90tVk3L5pteUNZ5PxsySxSf36urstBmIAgpl5K1FbuT9W2NmjS8i1Lpdkv8xmfIu3p8SxD%2Bxfa5PIqmK7V336FPLf7636ptVpNXMYaSGqDSmszbWNqLMaHGCx9DEzwEIpF3CuTYc5NZBRpENKAfuZldslKkJnAHlycMCFein280O%2FSzsGWdx9%2Ff0lR4bmdTFY4RNma%2FHvVCKP6VCSmEoancSITVAKw4ZBrA7ow0nlkw2iEMUaso0UdNZuf7hNUp9eNrrkWmfCsdl32qrnfQEN8mwWkTpFNZvY9eyP1fuMnshjAlmLpLlw9SWb1qg%2FW20j9kt81rX3uO11GpEKutK%2Bj4RUXwe7paLHMFjGwr1n8MO63QscM5dR8loPmH6apJ7PKp3VcictwemcDphHs1h8mtKy0mcA5p0YB7SBSl5ypgBzO1X%2FjBEwOWeCrJCw1mSIJLQmkZgF4CScJyqLBgc1SZN5cRBWlVTSSVCTZ12%2Bzfak81qydHQZWeVtf9g%2B9iHMAMuX3yV%2FPUV9ytuWzXKC0e%2F75j2A%2BsKI7xI7sa7JVdOrL7pk9YU4mcha4bFmh1PdDqOuvr7d2Oz8vs%2Ft9pGKVXCZOLv7HvYyijiL%2BjjMkycZB6w0M3R9xUX1Nz2%2FjKbvac1DXTZ0yLq1Hn2Mh1aEl0ze%2FnpNuB42YEEFF8xEMpy159fXPVwPlb27hyRYUJ%2FIPeol7Jrrfr3nrD3qu3oA1EMsr7xIkqTjJV1ffRJgcsGqN123zGAK%2BjSYtGwGi5bKUPJi7yU35nWVLYzYr1Wpo0tLpBBhV0kKErqzC9E8QHRt450r5B4EST2oAUQB1gB6VH39xVdemkKjYZ1GYp06Wvadezz7TkRj1ubsp1aaQcIsPHfJ6tW6zk6gU4J2rSBT6QTraKUGUwORHkXLi4xOhmmpDpO3cdC0vMUGsKQJYLl0sESaHGjDdZBx9U8dyoSZ9qM4Doi0irNyHBg3oyWp6dd8HU4XczvzJebLzFZ9PDuqyvKM8oUMUXZTcDURu17rTvIg5oAx2sCuF2c5HAZPNN46uGjNNbfcese96BuwuGdZ7LHktIFTz9%2FywJepEF7eIbqf903rG5y3YM06vOYL4iyzhfGuv%2BjWHTvvpW5Oz0Se8Bh9gtcnZNE1LIfZgg9dcF4HQaHEFmA6wn%2FsCGwEZRCjqX1pgtuFvkKYlcMkAko5nCkMc4VkAUPlhTSX6kvhjIcrU8aUAyYptocV4D4OnPwFXxbevD4pzRVylKTXUuJpJP2bqckYIzaf3%2BRf7RvuD5nSXEe3kRg%2Bc1U4Fuccabtjnmgeakm7si6eGNt51hQIyh6P1egytjUZbW0Oh4fnE7zBIvh9Rpcp4pbNlvb4TJvVHOmzWYXMSqfH7ewMDpucQ05pmOM8hOshHBfkLKLVLcTMXc2tD5Mp84CcEr262TwvYPXwtrApE%2Bbdi7zzzUaPxcZdEWodjpiJILishLVa4zKbYe0mzpd0hwKh5rDLSIhg8STMJm6hJHdaHB3egNnt4cxWOSW1CCmDnTPwrXGfjeNsbqOFALWElNMqC7HLLrO1ChabyPvXENbI286qxclY%2Fln%2BVsbLMIOkQID0fbJBLoCSniLGWIY42fXRZRv%2BYac6dvdR%2Bz9cv33sKWen89K7Ol3sunNf6Tv93Dvf3vbs6fMyY0%2B5XJcwtAfiBuDNp%2FS8cM03t4LBfgO9VaVArePmDPaVAkMfphPol9OruBQmqjT%2Bkz9U6ukf72lZzlPrLY%2FWG3ZGxJjQ%2F6Jag2CzKdpwaqJRd6JtsEIPqzatdrpS%2BZdxQ%2B9bx9tUH0BHIHugON7fAW0ArNjS6rX0kKrWMVmzq5kSY9INd1ycDKCfCGKRe%2FvYIu4W9eEKv6SIBd7qQWwAwzTaFminJ5gN1INDaFVrKIeagj%2BG1e1aBWgyozgPKTHaddAZQwKCagJg0Ebeca0nIRaGxWlhGHYhZLO47jIlB6y4SkRzD0qNHVPrJR7Ua0fd0rQzbI12pGugvdI%2BgH4GIBz9Rw1jMto%2BoBEKSzppHTozwa7HuKgXtKNaZp47h1F2jKpr4VbMTCA0Fwk9lNgfhStgEFW4ubKzglFX7YN9Td%2BrYEi1gi84wLXQj2MPaCfZt7RrGL1X515%2BL813iYCNPsIsYX6md2x3VtFTviinBKrK3CyWBffTvgS92XIbpVnbSebOWvudpQ0pAbAk6IXrUWsndtpIaqb%2BcFUZdtG4yYLqvsKC2aZOpYdaGwXaB0%2FPfliGSjD2FbA4aFuN0jBI31L3IOg%2FBTAdnjM7PXxGyzoKaz25bKLWG2dfR%2FfgMG62aUk4SlwsZQZw4fGT43X58ekd7%2BKxPupPwC0ZbBGWes20%2FZSghakSWkEA2Ogn6gt0cSTd0iL7lsKrpcUnr2yPXEfM2o7DCXbOghwJt6QjcKqFlE%2FQPug27fzvu6It6ZZvt%2FQYthGHw4c7lrt9odZcbqWvBW9D%2FaO%2FZAb4bwPvLAftCvMdUlW04kCa9MGoVbFXBPZvYEopzDmY2a%2B0iPutzmBTD1JIcpeyOWpEGGG5yWVxVeorEIy3pjCALBDgN71%2FvYCNJeGwfgk26AnDwgNqZoTgN1C5jMdAwpKm4LT4lnkzp0dntafaRHJn3O9sOtVrTp8UV68X5pJrvR65Kel0tY79undh4VSzwTmtNen3ktN7hzb1BeSztpiE046NCXNZw%2Bzpouu85XNXbTq1bb7KkEP%2FtKx%2FVrOrp6OzC3%2F17Mw6kY3G1SuF2eQqn0tuTeEvjsyMD89qbZXw9wp5Xtx99rmn%2Fe0jRhgkH83ef8a6z7VGC374Mc23uILp47%2FHr4cZl2eGGJTC3dSPI2QJkg%2B0Bq2bWIemNWCzjI5mbH0uOLV8HC4HRDVofh0gCHVHYZ0CdlRMsylYhb24jPtkMG2HWbRcY05KJ%2BOKl2656%2Bzz77r5xfi62fNf2iC6Oi%2BfNzJ%2F9rr4E0PDs3xnbFx5mW3W7OEN%2FYtmbLk8t2DwHM712Zduvvmlz6ZPvWj%2BvH%2F%2BrCzPuHneSfPmX3RqumntScO%2BUy89%2FVLb8Lz1zfM3rnrymRXnaPj1f%2FQBfzX%2FT4wf1h7G4wVAYIwJbXqfErADPoyzYKQnQKgQkC7wCSZEL80fgBHvH9kx57QzRkjTyMgOk%2FWCg%2Br1fz3LnQ4VRg6O7BBsFxwkt8J%2BJhyKF0Z2jJxx1iz1DyNk41mzdo7gV749ssNswu%2F8z1nu7umFEcKfAd%2By0G9tEHtyofiFnXBkZET9wyxNrlf03oHYQSWEefA00hqgVrWbemSMWtcXGBnYd2tVGLSDBhU1Gdr%2BpckNyqbR4NMew1AQtZSOmlVciIpRt16ZXxk878EnvlycoYVWimio%2FsvQ2qGhtUXuW1I2HQ6ns9Kx%2BSCx%2F8IeOPYanhia0EvdP54VE8hgozEU0wTjR6lkb6EvKxOfV0DFgYCMJpkf%2FwxUWmvc6XR0OEgT%2FWhV%2F3jwJ2TrTw4SuRV2nU71LSd%2BxNX%2FUg%2F%2B7McMR1KMG%2BzK3zA9wKGzmfsZrGPsoPWNw9lyN089LuhJGKBOSHe17B7AY24Puhzm0AY5sNZlq7hAZl2lLtJZ5t0zMBUQDE5vZJhuuUqzgJAgOpqx5r6pWpqLTY4wu4jtV7pExYyBkG7Ybe9XBsRvMI6m1Awa61fcmDGI3nDQccU0iaf5fK%2BeKcjLcRAKooyV%2BEbMF8Sid483zAGXiQ7ioU1fSerzhnWLjB42PbIsE12%2FfXkxOXflYCf3kKlv0azY4IpCW3l38Utr2gJ7XWKHt1nghxb%2B6Yn1K0lp6TlOspwYHYFM%2F%2FrC6bfNFpYt5z1dMy8YWbDYrlYdgqdr8Nzhzz9hXbpMXNe2iQ2HuvySUQCz3m0aGOt03zprfkCPCZ%2FH3cs%2FDbTdweAqBHYDqChhGk1spo3srNWyhz4QxOPQaSocUvppD%2FrWbNlPux%2F6w%2BbOskD9XwKjVZQ7Na8FUtKPjW%2FZ6SOUYk7xOWukpaMnhzsOt9IFtO3owcUNjUtGLHUNaoHlHNILaEmlSryXPkJDAEsfKJ2T4j7YFoZJrg%2FntIx90ZI0QyY1bMAclOJjfq%2FFzGW6Nz528%2FcfmLOiNbHa2x6Vw395ySRJ7TPiZ0vRL0SXDGbbl6c65J9lU2tlf8EoWUSbaJ5ma2XXF3sKwYG1Z7atL1%2Fdu7g5JHX1N6%2FqyBWz20MDfVYHiYW%2FGJC5EZ4P2qx38w6j3SpaCnfNB5kD1jX%2FjK7LRGr9Px0ZxYbNRJAoJSsYg4qp3lQ0LppZfGdpDAXsZf2TRgFpSQUNhxzbyt2C0T1WlxFG%2BgwF7H7xmN4TxpgDIa1tmmhipbdaYnhgbzvNk6eeuXKIRkdDMrZAwz5LOIosbZah5dXhgwYwtc4uwxct%2BiNfLLSisNSE7chdoLIGstl9bpdkopVyHpRN2Gmjlo6nmERYE8DoNdFaSMUuKiIOqGaLR2nPaQz0aI2QOFFrilQAFZJ9uYIxpNEirb45p3gOOruLBFv2ICFo01c8q7U4OowNiiqVCTRx0DrDGLNHyxcsCRbsPER9koCrifpdQHK6qJO3mYpU31QCCICMUwJkgX9FJIDDReNfoRaNKB4gzr6gxWrSNLwMNt5qJICgESAWwWoD3oDVBqVmF5zzYx2mEmigho49N5kqDdRAGhTrJDlnnBoaBdgD41Q5thVLcigPLtF5xA1csqnWvxRNAnRfACEoU5TtDtrGUMSJLWcUEX1R%2Bzwu0UQf7SLQRyV5aB4hdmSyUuzxIR20A85%2BhuWMtEuEA6tdDTydt7o%2FgyLGYXBDREtL527kZRgzbUxrDA4aOiDCvQ1GDj4oosJ8HA4Chd6NmJTdtL%2B2G9t7YLFYleJgRd%2FVPg8dHTvFU6A4WDQcRMrCFAfPRBx8k3FIUOg1Bk014kBbEBfPacShSIHHP8qVuERSvtTtGgtwJmKxktERsNZqRFz6VKWwOw%2BVBasHlyRgUmw7Sbva%2BixmfAfpq8FtNaE45YxaFUuN4LQvWO2Vk2rihNaD0da2mLrYQHTatrv%2B%2Bt%2FBawV4nRReEDAgfCx0nbC4EV6L7xPgzUlcA8x1eCsakHoz3hODW%2B%2F5qNWdd4zX7jZPLY2W6wXRzNSC7Mn1Y1jQ%2BPD77z2CRYwVraRRq1zU6hi1E%2B%2BcVCt3HGivxdFqsMTQizkJmvhUaFBkyCAWaKklU2r24GbseCXjkyH0dJP3H0ZYsNLykfcmAFkhS9V9COkj72l1mI2QqrYjR8bjfv9reGPj8Eb%2FHnjlJiznrUM0Ad7ikSMatO8%2FPBnaIiCy9P932kY5hLU2zhNhJYePaEyAiACPzGwg7WaAlfKkwUvrC4PMIFNfjqnbBysH3FqnY1AHZNrVGESpQI2oWvaGIooKp%2BXYY0KEJ18HLl%2BDWnvUW6UGFxlFeBCuivqw%2BjA%2BBmxCIS7V814DQXeI%2FyoTxYwfh%2BYbgiWxmUakMRnC16wlQ5Q86PF34kwFwoAtF0HLuI%2FJ9YHhZuhzF%2FoyoImBrsUIxtdMMknvNhjMZrPDZmWdxGE2yerPyZdZVjCbnRb%2BgPrhYhcreNRFXslqctrZCzyiSHjyrM1pM7uMP1d%2FutZTn8uUbn4Y45lMmdPpZsKabCw1CtK8DhCL3vrUtmoTuhTk9MxExSUqzVrnURjSQj6KhZDUY4VZn7R5BKUpjm8mr9Uik8OOyhlnPPoOrkxU6AAxnd%2FS6PctXmDZd2hQQKNsQ01AiGllVutwOumiGgTAEg22mVXz5CRR5QOT7Dl%2FIBxpaUWtF%2FSDOFYtYzWLyRyOxenRoEi9bfUi65Sge920gt9CCvMVE7RqQJ9Ny66rVVQ%2FuGVR8dF3yJ%2FJxvvI4fvUJzSWOHvh9ffWGPS6Ze88aiZr71Nt96kPTaltObVWj9NEH9Lhaaxw0apysKUEWKKBuoeq9iC053mzxeF0e7RKRrkJjhCjYLO7ROaENTqs3ljiRFU68uV7Lr98z4mLdNx4%2BvIGOYa%2BUBfofmm9C7eod3CgD3mUaBGfCfQF%2BnQ6NzqQfbpPsSYLzCxt7Q%2BrvMPK%2B62uY37yAnkRMxmxWyY2l3Va1Pe4FuxGjGwytiXLHOf%2BnZPu%2F%2FfdXEshNE%2B4excWqauzyZnjd2cP0PDU4aNvTbj3jXBv7LtZw11boQ1aY0rQ6GxZvL1Iby%2Fi7aUpuIMZOuHmPezqL6vzdrG3Ntz8u%2BqP2dW71Xn3j83I1p%2FfhXijz9Zfx1yqYgDRoPUi91HMffTWPrx1cDLmciHFJTxYWdoIwMaDGzez3%2BKO3HfwPvKjBvL%2F29mvbjz2JmH%2F8T%2FhjGo%2FHhzpE8Dhyf4doHhkQS7I1gZQth48%2B1UO7%2FY3ck4DMYoHNx4k7wB8977HfuvoH7OaDJPxmRz8s6BJmbDOg6e2n5lWPhmr2HFOK6rHmh8zkfkH1IT6%2FeXsnrEN5CHOdfQV4lKvJnuq3BNj02sysUhxwyrMpQyuHkYYSCMdSHzmhiNbNor0gRI87Jmytef%2FgfwxUhHkpO4hWkrnNIrustkna14hTaTgcwhkWjGOOm4siXiHpCPA8ZWwd9fYnF2YKVYs7uLe9oapEDz2DBboq5tD3PkVyn%2FDtP%2Beh%2BbjzWJQPwQInRRCJxgVZaNzAnjh2kJtpJ2KmZIRRGDZKvv1xvh1oCSQfhSkRAHLo7hxwNR3r9mmfg4hm3v9NWTj9WriN40Qvq6%2Bd82NAGAJTm64Xm3lnqjU5orR4KCwykycPiuxtQGYRENnBY0qQorUaeJpKIvUwTj%2FCfWQ%2BrxOoOITT9xY%2Bz8OivohvYgS6%2Bir9ORNX8f3Cb1J3ZR2F9E1GWjnoLRzoEljdKHKHcRy5BJvytbJ5wQKM%2BOBHLpAOl3Iz9j9x5alTsAgtijxYGk5rOYlJLB2yDKRzvhATkpmTSnnaFa7RufNqo2ip4WhKw00BjsCsHqSCiPaPrhSYY6D02nHwel42EyAvxF4JSRinkcJi0LKVlsA%2FUOwSE5GQR8oLdZvJuMoVID6l1AcaLRfPdiIwyUVOjY6Fvj01BoOFZoPZ6acMrl2QNMQwVzR%2BrcdXcErev86MnqE5g4ni7RrxZib%2FiDGls6D33tGt6m0ztg3Y6Si5AvmsL1JSW6mD4ssWZ05fFxkyebSqSPUWuhaqSsNvRA%2BugpTIlktaFUZNOPVh40NeM7p0mNAbq8kah0btZJPUDlKxAv0MyFhtXRb%2BKNuB%2FqiehHuDmDWv6Zf0h7Ro3rTaLoJBtrL7LdpRA%2Fzcg%2B9TON79V72tbrsGVpdNi29ZmpOFdmKS9M%2Bs0s2Yf9njNWYqcZusVJHYY8mHkX9ycvam1DvZ5HwYrXOeA957UmwxWxW%2F08bhtBGgVYL3W4Nqu8GEuwB2h4ba2Bq75t%2FoJ5Ee2D8czGUj%2FqNBvUK2o9vZcQjXinOjTT2Nl7C5DBDhkYjbTklVy2zVgfau22Zsr85gZXmKXxWwniyaxsmuxpbaFPjaB4hp8%2F2kbAHLZenSX7APjRwiksPboc51OqdBCi8OEAOBxaTUZrJmw0E1M2LA6otsFjdXDsy3ZYkd6pbkrbp04nBLDm4a3wBwk6Hw%2BoWcmf98LHb8bAe29RsJz%2FTzLSAnZxmskzZr2sKvgz1mdNSH7cX3UCZjNb4yO2iLBVoplqcOMVKKuQS2K%2B5bsNHZSkB6KSiJJ%2BQtCxz0E4PotE0WrkAdJl1RfWOYq24AQswUxfQY6hQaVdrBs3YnMrZ6qFi3dwfrZx9dqU4Nu%2BRWx%2BBcXExLv4h%2FiF8RrA7zMlhLjeT9GHBJxAwTVKFYYLpw07iIpHhe847%2F6f3Xx%2BJPCIKnu94el1bdh47d4todHze0e1%2BmPt95x13HTzv%2FHuGouRhd9pxu4MXt5x7bOcWscf7oscoPjwxtx%2FXt4zeXwmf45qheXsnZUoj9AEvTWhfZmCCtYn7ku3ZWZRomJpQIPneYS6LzCvp9VE0K8Hrm0mGyRDpa5ElL3aIBo0%2FzcdjDt5JJAe5mPUlV25emfQRQi52SChkvOGQ9%2Fve0A4yvINuGIPFra9vO%2F2xq4ozu8zm7EFvzkEyWd7eEpC8Tc0WS1b9qSPnxXZ47JNSgI%2FyMekev%2F8eKQabAaliCpzU0y5F29qiVkt9%2FmIecKAefycTO%2FdGpUQ0hT1dJa2LPX2JMn16x0fcN26gj%2BPQus5Xdh2hT6TGf%2Brmou5zqN3DTDvatOoRdm%2BOSjvLIepN1vpUaQuB9gSReuO%2FWoubXH2riKkGtEKIfhT1Hc0cr6VwsAc0rqImJj5LSu%2Bph70UsGpsge5PcNXtnq4Gf4Ko%2BRPw%2BX2iiz4DoCXe1qF1I6D7wZZkW7tW5DmpjR6G2jzoPMxpXf0NOXQogjqBfeiVrewBrLccm7NVoZ2TKMNjLyqgm%2F6UM3IYr1Bt8I7VGns1IUa930XNoff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AxNRE0NjMhMhYVERQGIyEiJhkBNDYzITIWFREUBiMhIiYBETQ2MyEyFhURFAYjISImGQE0NjMhMhYVERQGIyEiJh0VAZAVHR0V%2FnAVHR0VAZAVHR0V%2FnAVHQJYHRUBkBUdHRX%2BcBUdHRUBkBUdHRX%2BcBUdMgGQFR0dFf5wFR0dAm0BkBUdHRX%2BcBUdHf29AZAVHR0V%2FnAVHR0CbQGQFR0dFf5wFR0dAAAJAAAAAARMBEwADwAfAC8APwBPAF8AbwB%2FAI8AdgCyDQAAK7E8bDMzsATNsTRkMjKwHS%2BxTHwzM7AUzbFEdDIysC0vsVyMMzOwJM2xVIQyMgGwkC%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%2BwTDOwHM2wRDKwLS%2BwXDOwJM2wVDIBsGAvsADWsRAgMjKwCc2xFygyMrAJELEwASuxQFAyMrA5zbFIWDIysWEBKwAwMT0BNDY7ATIWHQEUBisBIiYRFBY7ATI2PQE0JisBIgYVPQE0NjsBMhYdARQGKwEiJgE1NDYzITIWHQEUBiMhIiYRNTQ2MyEyFh0BFAYjISImETU0NjMhMhYdARQGIyEiJh0VyBUdHRXIFR0dFcgVHR0VyBUdHRXIFR0dFcgVHQGQHRUCvBUdHRX9RBUdHRUCvBUdHRX9RBUdHRUCvBUdHRX9RBUdMsgVHR0VyBUdHQGlFR0dFcgVHR0VyMgVHR0VyBUdHfz1yBUdHRXIFR0dAaXIFR0dFcgVHR0BpcgVHR0VyBUdHQAAAAEAHQAiBPIEKgAFAAATCQEnAScdAaMDMtT9oc4Bxv5cAzTU%2FaHPAAABAGoAagRGBEYACwAAEwkBNwkBFwkBBwkBagEa%2FubUARoBGtT%2B5gEa1P7m%2FuYBPgEaARrU%2FuYBGtT%2B5v7m1AEa%2FuYAAAMAF%2F%2FsBMQEmQATABsAJwC3ALIOAAArsBIvsBfNsBwvsCMzsB3NsCEyshwdCiuzQBwmCSuyHRwKK7NAHR8JK7AbL7ADzQGwKC%2BwAdawFc2wFRCxJgErsB4ysCXNsCAysiUmCiuzQCUjCSuyJiUKK7NAJhwJK7AlELEZASuwBc2xKQErsSYVERKyAhYbOTk5sCURsBI5sBkSswMXEBokFzmwBRGwBzkAsRcSERKwEDmxHQ4RErMABRUYJBc5sBsRshQZATk5OTAxEhAAIAAVFAcBFhQPAQYiJwEGIyICEBYgNhAmIAM1MzUzFTMVIxUjNRcBHAGQARxOASwHB20IFAj%2B1HeOyIPCARLBwf7uRmTIZGTIAe0BkAEc%2FuTIjnf%2B1AgUCG0HBwEsTgJs%2FvDCwQESwf5ZyGRkyGRkAAADABf%2F7ATEBJoAEwAbAB8AXQCyDgAAK7ASL7AXzbAbL7ADzQGwIC%2BwAdawFc2wFRCxGQErsAXNsSEBK7EZFREStQMCEBIcHSQXObAFEbAHOQCxEg4RErAJObAXEbAQObAbErUBAAcFHB4kFzkwMRIQACAAFRQHARYUDwEGIicBBiMiAhAWIDYQJiADITUhFwEcAZABHE4BLAcHbQgUCP7Ud47Ig8IBEsHB%2Fu5GAZD%2BcAHuAZABHP7kyI15%2FtUHFgdtCAgBLE4CbP7wwsIBEML%2BWcgAAAIAFwAXBJkEsAAbACsARQCwGC%2BwCs0BsCwvsADWsAfNsgcACiuzQAcDCSuwBxCxDAErsBPNsgwTCiuzQAwQCSuxLQErsQwHERKzFxgcIyQXOQAwMRM0EjcVDgEVFBYgNjU0Jic1FhIVFA4CIi4CARQWOwEyNjURNCYrASIGFRfSp2d8%2BgFi%2Bnxnp9Jbm9Xs1ZtbAd0dFWQVHR0VZBUdAli3ASg%2BpjfIeLH6%2BrF4yDemPv7Yt3bVm1tbm9UBDBUdHRUBkBUdHRUABABkAAEEsASxAAMABwALAA8AMACyBAAAK7EIDDMzAbAQL7AE1rAHzbAHELEIASuwC82wCxCxDAErsA%2FNsREBKwAwMTczESMBETMRMxEzETMRMxFkyMgBLMhkyGTIAQEs%2FtQB9P4MAyD84ASw%2B1AAAAIAGgAbBJYElgBHAFEAYgCwEi%2BwUM2wSy%2BwNs0BsFIvsADWsEjNsEgQsU0BK7AkzbFTASuxSAARErELPTk5sE0Rsw8VMzkkFzmwJBKxGS85OQCxUBIRErEHHTk5sEsRswMhJ0UkFzmwNhKxK0E5OTAxExQfAhYfAQcWFzcXFh8CFjMyPwI2PwEXNjcnNzY%2FAjY1NC8CJi8BNyYnBycmLwImIyIPAgYPAScGBxcHBg8CBgU0NjIWFRQGIiYaBpcCDhgDUC08hQUtMQUmKCIbLyYGLi8FhjgwUAMYDwGYBQWYARAXA1AsPIYFLTAGJigiGy8mBTIsBYU7LlADGQ0ClwYBZ36yfn6yfgJZISkmBjEsBYY7LlEDGg0ClwUFlwINGgNRLD2GBSwxBiYoIhwtJgYzKgWGOi9RAxkOAZgFBZgBDhkDUS86hgUvLgYmMBlYfn5YWX5%2BAAAABwBk%2F%2F8EsAUUABkAIwAnACsALwAzADcAiQCyIQAAK7AkzbIoMDQyMjKwJy%2ByKjI2MzMzsBvNsBcvsATNsQ4sMjKwLy%2BwCc0BsDgvsBrWsCTNsCQQsSUBK7AFMrAozbAsMrIlKAors0AlAAkrsCgQsSkBK7AwzbAwELExASuwLTKwNM2wDTKyNDEKK7NANBMJK7A0ELE1ASuwHc2xOQErADAxEzU0NjMhNTQ2MyEyFh0BITIWHQEUBiMhIiYTESERFAYjISImNzMRIxMzESMRITUhEzMRIxMzESNkDwoBEzspASwpOwETCg8OC%2FvmCw5kA4Q7Kf1EKTtkZGTIZGQBLP7UyGRkyGRkBAEyCg9kKTs7KWQPCjILDg78bgMg%2FOApPDwpArz9RAK8ASxk%2B7QCvP1EArwAAAAAAQABAAEFFQTdAAoALACyCQAAK7AEMwGwCy%2BwCdawCM2wCBCxBQErsATNsQwBK7EFCBESsAE5ADAxEwkBIxEhESERIREBApAChMj%2B1P7U%2FtQCWQKE%2FXz9qAGQ%2FnACWAAAAgBkAAAD6ASwAA4AEQAiALIMAAArAbASL7AB1rAGzbIGAQors0AGCAkrsRMBKwAwMTcRNDYzIREhERQGIyEiJgERAWQOCwHbAZAOC%2FyuCw4CWAEsGQR%2BCw7%2BDP1dCw4OAxIBLP7UAAADAAQABASsBKwACwATABkAggCwCi%2BwD82wFC%2BwF82yFxQKK7NAFxUJK7ATL7AEzQGwGi%2BwAdawDc2wDRCxFAErsBfNshcUCiuzQBcZCSuwFxCxEQErsAfNsRsBK7EUDRESswoDDhMkFzmxERcRErMJBA8SJBc5ALEUDxESswcADRAkFzmxExcRErMGAREMJBc5MDESEBIkIAQSEAIEICQSEBYgNhAmIBMRMxEzFQSgARIBRAESoKD%2B7v68%2Fu4W8wFW8%2FP%2BqkdkyAG2AUQBEqCg%2Fu7%2BvP7uoKACX%2F6q8%2FMBVvP9%2FgGQ%2FtRkAAAAAAL%2FnAAABRQEsAALAA8ALgCyAAAAK7AHM7AKL7AMzbAPL7ADzbIDDwors0ADAQkrsAUyAbAQL7ERASsAMDEjATMDMwMzASEDIwMTMwMjZAGv0RWiFNABr%2F3mKfIoMeAbqgSw%2FtQBLPtQAZD%2BcAH0ASwAAAAAAgAAAAAETASwAAsADwBKALILAAArsAzNsA8vsAnNsAEyAbAQL7AE1rAHzbIEBwors0AEAAkrsAcQsQ0BK7AKzbERASuxBwQRErECCTk5sA0RsQgMOTkAMDExESEBMxEhETMBIRElMzUjAer%2B3sgBLMj%2B3gHq%2FuGvrwGQASwB9P4M%2FtT%2BcMhkAAMAAQABBK8ErwAPABcAHgBjALINAAArsBPNsBcvsAXNAbAfL7AB1rARzbARELEZASuwHM2wHBCxFQErsAnNsSABK7EZEREStA0EEhcYJBc5sBwRsB45sBUStAwFExYdJBc5ALEXExEStQEICQAaHiQXOTAxEjQ%2BAjIeAhQOAiIuARIQFiA2ECYgAzMRMxEzAwFfoN703qBfX6De9N6gXPIBVPLy%2FqxQlsiW%2BgHe9N6gX1%2Bg3vTeoF9foAIC%2Fqzy8gFU8v5kASz%2B1P7UAAMABAAEBKwErAALABMAGgBhALAKL7APzbATL7AEzQGwGy%2BwAdawDc2wDRCxGQErsBjNsBgQsREBK7AHzbEcASuxGQ0RErQKAw4TFCQXObAYEbAVObARErQJBA8SFiQXOQCxEw8RErUBBgcAFRgkFzkwMRIQEiQgBBIQAgQgJBIQFiA2ECYgAxsBIxEjEQSgARIBRAESoKD%2B7v68%2Fu4W8wFW8%2FP%2Bqk%2F6%2BpbIAbYBRAESoKD%2B7v68%2Fu6goAJf%2Fqrz8wFW8%2F5iASz%2B1P7UASwAAAACAAAAAASwBLAACwATACkAsgkAACuwDM2wEDKwEy%2BwAs0BsBQvsRUBKwCxDAkRErIEAQ45OTkwMTUREyEbARQGIyEiJhMzFyE3MwMhyAMgxwEOC%2FuCCw7IyDIBLDLIYf2iGQHbArz9RP4lCw4OAebIyAH0AAMABAAEBKwErAALABUAGABGALAKL7APzbAUL7AEzQGwGS%2BwAdawDM2wDBCxEQErsAfNsRoBK7ERDBEStQQJCgMWGCQXOQCxFA8RErUBBgcAFhckFzkwMRIQEiQgBBIQAgQgJBMUFiA2NTQmIAYBEQUEoAESAUQBEqCg%2Fu7%2BvP7uFvMBVvPz%2FqrzAToBKQG2AUQBEqCg%2Fu7%2BvP7uoKABtKzy8qyr8%2FP%2BigGRyAABABcAFwSZBLAAHABTALAFL7ANzbARL7AZzQGwHS%2BwAdawD82wDxCxCgErsAnNsR4BK7EKDxEStQUEExQXGSQXObAJEbEVFjk5ALERDREStAEACRQVJBc5sBkRsBc5MDESFB4CMj4CNSMUBiAmEDYzMhcHIREHJiMiDgEXW5vV7NWbW5b6%2Fp76%2BrGIbpIBkJGdxnbVmwLO7NWbW1ub1Xax%2BvoBYvpRkgGQkXpbmwAAAAIAFwAABJkEsAAQACEAegCyEQAAK7AfL7AWzbIWHwors0AWGgkrsA0vsAXNsg0FCiuzQA0ACSsBsCIvsADWsBDNsBAQsRkBK7AazbEjASuxEAARErEREjk5sBkRtwcFCwoTFB8hJBc5sBoSsQkIOTkAsRYfERKwITmwDRGxCRI5ObAFErAHOTAxEzQ%2BAjMyFzcRITcmIyIGFQMRIQcWMzI2NTMUDgIjIicXW5vVdsadkf5wk3CHsfpJAZCTcIex%2BpZbm9V2xp0CWHbVm1t6kf5wk1D6sf2oAZCTUPqxdtWbW3oAAAoAZAAABLAEsAADAAcACwAPABMAFwAbAB8AIwAnAFAAsAgvsBgzsAnNsBoysAwvsBwzsA3NsB0ysBAvsCAzsBHNsCEysBQvsCQzsBXNsCUyAbAoL7AI1rIMEBQyMjKwC82yDhIWMjIysSkBKwAwMTMhESETESERJTUzFSc1MxUnNTMVJzUzFRMhNSE9ASEVJTUhFSU1IRVkBEz7tGQDhPzgZGRkZGRkZGQB9P4MAfT%2BDAH0%2FgwB9ASw%2B7QDhPx8ZGRkyGRkyGRkyGRk%2FahkZGRkyGRkyGRkAAIAAAAABEwEsAAZACMASgCyFwAAK7AgL7AJzQGwJC%2BwBdawGs2yBRoKK7NABQAJK7AaELEbASuwDs2yDhsKK7NADhMJK7ElASsAsSAXERKzBA4FGiQXOTAxNRE0NjsBNTQ2MyEyFh0BMzIWFREUBiMhIiYBITU0JisBIgYVOylkdlIBLFJ2ZCk7Oyn8fCk7AZABLB0VyBUdZAJYKTvIUnZ2Usg7Kf2oKTs7AuWWFR0dFQAAAAIAZAAABEwETAADABUAFwCyAAAAKwGwFi%2BwANawA82xFwErADAxMxEzERM%2BAR4CPgE3EQ4BLgMGB2RkZDyHeHxyamQpKHuEkId0WhQETPu0AZA8MA0hGwVPUQH0UUUKKCgKRVEAAAAAAwAAAAAEsASXACEAMQBBAGcAsi8AACuwPjOwJs2wNjKwDC%2BwHc0BsEIvsADWsAfNsAcQsSIBK7ArzbArELEyASuwO82wOxCxEAErsBfNsUMBK7EyKxESswwLHRwkFzkAsSYvERK0BxATFAMkFzmwDBGxCA85OTAxERQWOwEyNjURND4BIB4BFREUFjsBMjY1ETQuAiIOAhUTETQ2OwEyFhURFAYrASImJRE0NjsBMhYVERQGKwEiJg4LMgsOjeQBBuSNDgsyCw5jo97o3qNjyAwIoAgMDAigCAwCWAwIoAgMDAigCAwBEwsODgsBLH%2FRcnLRf%2F7UCw4OCwEsdN6jY2Oj3nT91QHMCAwMCP40CAwMCAHMCAwMCP40CAwMAAAAAgAAAMgEWAPoAAUAEQAAESEFEQUhATcnNxc3FwcXBycHASwBLP7U%2FtQCsI2NR42NR42NR42NAZDIAyDI%2FquNjUeNjUeNjUeNjQAAAAIAAADIA3AD6AAFAA8AEgABsBAvsA7WsAnNsREBKwAwMREhBREFISU3FhUUByc2NTQBLAEs%2FtT%2B1AK8RW9qQ1YBkMgDIMg5NYevqYU2boqSAAAAAAMAAAC6BGID9wAFAA8AHQA8ALAAL7ABzQGwHi%2BwDtawCc2wCRCxEwErsBrNsR8BK7ETCRESsxAWFx0kFzkAsQEAERKzCQ4TGiQXOTAxGQEhJRElATcWFRQHJzY1NDcXFhUUDwEXNzY1NC8BASwBLP7UAZJFb2pDVl4He3cHUQaOkAYBkQGQyPzgyAHJNYevqoU3boqRzQiXwb2WCEIIsuPmsggADQAAAAAEsASwAAcAEQAVABkAHQAhAC8AMwA%2FAEMARwBLAE8BAQCyAAAAK7EwRDMzsBLNsikxRTIyMrAaL7InK0wzMzOwG82yJS1NMjIysCIvsQIGMzOwI82wCDKwHi%2BxDkgzM7AhzbE0STIyAbBQL7Aa1rEFHjIysB3NsQMfMjKwHRCxMAErsQ0sMjKwM82wNTKwMxCxLgsrsCoysCXNsEAysi4lCiuzQC4iCSuyAQsPMjIysCUQsTcBK7FESDIysDvNsSZKMjKwOxCxTAErsEIysE%2FNsjk9RjIyMrFRASuxMB0RErUUFRgZND8kFzmxNyURErIoKTg5OTkAsSIbERKzExQ4OSQXObAjEbIEOjs5OTmwHhJACQUWGTY3PD1AQyQXOTAxMSERIzUjFSM1MzUhNTM1IxEhExEhEQERIREDNTMVAzM1IwE1IREzFSMVIzUjNTM1AzUzFQMzETMRITUjNTMRIRMRIREDNSEVATUzFRM1MxUB9MhkyGQBkGRk%2FgxkASz%2B1AEsyGRkZGQBLAEsyGTIZGRkZGRkyAEsyMj9qMgBLMgBLP7UZGRkAfRkZGRkZGQBLPu0ASz%2B1AK8ASz%2B1P2oZGQCvGT%2BDGT%2B1GRkZGTI%2FgxkZAPo%2FtT%2B1MhkAfT%2BcAEs%2FtT84GRkA4RkZP1EZGQAAAAACQAAAAAEsASwAAMABwALAA8AEwAXABsAHwAjAHAAsgwAACuyBBQcMzMzsA3NsRUdMjKyDAAAK7AFzQGwJC%2BwCNawC82wCxCxEAErsAwysBPNsA%2FNsBMQsRQLK7AXzbAXELEYCyuwG82wGxCxIAErsCPNsSUBK7EQCxESsQcGOTmxGxcRErEcHTk5ADAxNTMRIxM1IRUnETMRFzUzFScRMxEVNTMVNREzERU1MxUnETMRZGRkASzIZMhkZMhkZMhkyMgD6PtQZGTIA%2Bj8GMhbW8gD6PwYyFtbyAPo%2FBjIW1vIA%2Bj8GAAAAAIAAAAABLAEsAAHABMAKQCyBwAAK7ASL7AEzQGwFC%2BwAdawCc2xFQErALESBxESsgAGCzk5OTAxERM0NjMhCQEAFBcWMjc2NCcmIgcBDwoB2gK8%2Fgz92B0eUx4dHR5THgK8AdsKD%2F1E%2FgwD41QdHh4dVB0eHgAAAAMAAQAABd0EsAAHABMAGQAxALIHAAArsBczsBIvsATNsBQyAbAaL7AB1rAJzbEbASsAsRIHERK0AAYLFhkkFzkwMRsBNDYzIQkBABQXFjI3NjQnJiIHJTMJAScBAQEOCwHaArz%2BDP3XHh1UHR4eHVQdAgtkArz%2BDDIBwgK8AdsLDv1E%2FgwD41QdHh4dVB0eHrD9RP4MMgHCAAAAAAEAZAAABLAEsAAKAD8AsgAAACuwBy%2BwAs0BsAsvsADWsArNsAoQsQUBK7AEzbEMASuxCgARErICBwg5OTkAsQcAERKyAQQFOTk5MDEzETchEQcRIQchEWSvA51k%2FRJkAu4EAa%2F8GGQD6GT8GAAAAAABAMgAAARMBLEACgAAMwkBETQmIyEiBhXIAcIBwh0V%2FOAVHQG8%2FkUEfhQeHhQAAAADAAAAAASwBLAACwAXACcAWQCyJQAAK7AczbAKL7ADzbIKAwors0AKAAkrsAcysgMKCiuzQAMBCSuwBTIBsCgvsADWsAvNsAIysAsQsQgBK7AFMrAHzbEpASuxCAsRErMMDyciJBc5ADAxNREzFyE3MxEjNSEVExchNwMuASMhIgYHAzc%2BATMhMhYfARYGIyEiJshkAlhkyMj84DUoAlA%2BXgIQCv4%2BChACQiYCEwoB9AoTAiYCCwr9qAoLZAK8yMj9RMjIAtl8fAFaCw4OC%2FuBmAoODgqYCg4OAAAABAAAAGQEsARMAB0AJQAtADEAbwCwAy%2BwJc2wKS%2BwLc2wIS%2BwE80BsDIvsADWsB%2FNsh8ACiuzQB8vCSuwHxCxJwErsCvNsTMBK7EfABESsBk5sSsnERKzISQlICQXOQCxLSkRErMfIiMeJBc5sCERsS4xOTmwExK0CxkaLzAkFzkwMTUUFjMhMjY1ETQmKwEuBCsBIg4CDwEjIgYVADQ2MhYUBiICFBYyNjQmIiU1MxU7KQPoKTs7KZYEDzM3UyrIKVI6LgsMlik7AWSQyJCQyAY%2BWD4%2BWAFYZMgpOzspAlgpOwgbRTUrKTs7FRQ7Kf5wyJCQyJABIFg%2BPlg%2BXmRkAAIANQAABLAErwAeACIAHgCyAAAAK7ANM7AezbICDA8yMjIBsCMvsSQBKwAwMTMhNSIuAT8BIRcWBiMVITUmJy4BLwEBIwEGBw4BDwEBExcTNQFtKT4kE1wBh1IQKzUBoSIoEh4GBv5%2FXf5xGBwMKg8PAWuyLnRCFjYs6t4tV0JCASoTLg4NA%2Bb8EjAbDBoHBwHHAcmM%2FsMAAwBkAAADwwSwACAAKQAxAGUAsiAAACuwIc2yIAAAK7ABzbApL7AqzbAxL7ANzbANELALzQGwMi%2BwBNawIc2wKjKwIRCxLgErsBDNsCUg1hGwHM2xMwErsSUuERKwFjkAsSkhERKwHDmwKhGwFjmwMRKwEDkwMTM1PgE1ETQuAyc1BTIWFRQOAg8BHgQVFA4BIyczMjY1NCYrATUzMjY1NCYjZCk7AgkWJB8B13i6FyEiCwwIG0U0K3amT8ihWYB9Xp%2BLTGyom1kHMygDOxwXHQ0PB0cBsIw3XTcoCAcDDDNBdkZUkU3IYVRagWR7TVJhAAAAAAEAyAAAA28EsAAZACAAsgAAACuwAc2wGDKwCy%2BwDjOwDM0BsBovsRsBKwAwMTM1PgE3EzYmJy4BJzUhFw4DDwEDBhYXFchNcwitCihHBgkFAakCIToiGQUFgAowRzkHQy8DUTgkEwEDATk5CCMnJQwM%2FMc0PAY5AAL%2FtQAABRQEsAAJACUAfgCyGwAAK7AfL7ICBRYzMzOwDM2yHwwKK7NAHxAJK7AKMgGwJi%2BwAdawB82wBxCxCgErsCXNsCUQsR0BK7AYzbIYHQors0AYGgkrsh0YCiuzQB0bCSuwGBCxEAErsA%2FNsScBK7EKBxESsQUIOTkAsR8bERKwCTmwDBGwBDkwMSczESM3FyMRMwcTETMhMxEjNC4DKwERFxUhNTcRIyIOAxVLS0t9fUtLffqWAryWMhAVLiEiyGT%2BcGTIIiEvFBHIAyCnp%2FzgpwNjASz%2B1B0nFQkC%2FK4yZGQyA1ICCRUnHQAAAAIAIf%2B2BI8EsQAJACUAiQCyCAAAK7ACzbAfL7AWM7AMzbIfDAors0AfCgkrsA8yAbAmL7AK1rAlzbAlELEdASuwGM2yGB0KK7NAGBoJK7IdGAors0AdGwkrsBgQsRABK7APzbEnASuxHSURErMCCAkBJBc5sRAYERKzBAYHAyQXOQCxAggRErEABTk5sB8RsgEEGjk5OTAxPwEVITUXBzUhFQMRMyEzESM0LgMrAREXFSE1NxEjIg4DFSGnAyCnp%2FzgZJYCvJYyEBQvISLIZP5wZMgiIS4VEDN9S0t9fUtLA88BLP7UHScVCQL9djJkZDICigIJFScdAAAAAAQAAAAABLAETAAPAB8ALwA%2FAAA1FBYzITI2PQE0JiMhIgYVNRQWMyEyNj0BNCYjISIGFTUUFjMhMjY9ATQmIyEiBhU1FBYzITI2PQE0JiMhIgYVHRUETBUdHRX7tBUdHRUDIBUdHRX84BUdHRUD6BUdHRX8GBUdHRUCWBUdHRX9qBUdMhQeHhRkFR0dFcgUHh4UZBUdHRXIFB4eFGQVHR0VyBQeHhRkFR0dFQAEAAAAAASwBEwADwAfAC8APwAANRQWMyEyNj0BNCYjISIGFREUFjMhMjY9ATQmIyEiBhUTFBYzITI2PQE0JiMhIgYVERQWMyEyNj0BNCYjISIGFR0VBEwVHR0V%2B7QVHR0VBEwVHR0V%2B7QVHcgdFQK8FR0dFf1EFR0dFQK8FR0dFf1EFR0yFB4eFGQVHR0VAfQUHh4UZBUdHRX%2BcBQeHhRkFR0dFQH0FB4eFGQVHR0VAAQAAAAABLAETAAPAB8ALwA%2FACYAsg0AACuwBM2wLS%2BwJM2wHS%2BwFM2wPS%2BwNM0BsEAvsUEBKwAwMT0BNDYzITIWHQEUBiMhIiYTNTQ2MyEyFh0BFAYjISImEzU0NjMhMhYdARQGIyEiJhM1NDYzITIWHQEUBiMhIiYdFQRMFR0dFfu0FR1kHRUD6BUdHRX8GBUdyB0VAyAVHR0V%2FOAVHcgdFQJYFR0dFf2oFR0yZBUdHRVkFB4eAmxkFR0dFWQUHh7%2B6GQVHR0VZBQeHgJsZBUdHRVkFB4eAAQAAAAABLAETAAPAB8ALwA%2FACYAsg0AACuwBM2wHS%2BwFM2wLS%2BwJM2wPS%2BwNM0BsEAvsUEBKwAwMT0BNDYzITIWHQEUBiMhIiYRNTQ2MyEyFh0BFAYjISImETU0NjMhMhYdARQGIyEiJhE1NDYzITIWHQEUBiMhIiYdFQRMFR0dFfu0FR0dFQRMFR0dFfu0FR0dFQRMFR0dFfu0FR0dFQRMFR0dFfu0FR0yZBUdHRVkFB4eAUBkFR0dFWQUHh4BQGQVHR0VZBQeHgFAZBUdHRVkFB4eAAAAAAgAAAAABLAETAAPAB8ALwA%2FAE8AXwBvAH8AUgCyDQAAK7BMM7AEzbBEMrAdL7BcM7AUzbBUMrAtL7BsM7AkzbBkMrA9L7B8M7A0zbB0MgGwgC%2BwANayECAwMjIysAnNshgoODIyMrGBASsAMDE9ATQ2OwEyFh0BFAYrASImETU0NjsBMhYdARQGKwEiJhE1NDY7ATIWHQEUBisBIiYRNTQ2OwEyFh0BFAYrASImATU0NjMhMhYdARQGIyEiJhE1NDYzITIWHQEUBiMhIiYRNTQ2MyEyFh0BFAYjISImETU0NjMhMhYdARQGIyEiJh0VZBUdHRVkFR0dFWQVHR0VZBUdHRVkFR0dFWQVHR0VZBUdHRVkFR0BLB0VAyAVHR0V%2FOAVHR0VAyAVHR0V%2FOAVHR0VAyAVHR0V%2FOAVHR0VAyAVHR0V%2FOAVHTJkFR0dFWQUHh4BQGQVHR0VZBQeHgFAZBUdHRVkFB4eAUBkFR0dFWQUHh78kGQVHR0VZBQeHgFAZBUdHRVkFB4eAUBkFR0dFWQUHh4BQGQVHR0VZBQeHgAABv%2BbAAAEsARMAAYACgAaACoAOgBKACAAsAAvsCYzsAHNsC4yAbBLL7FMASsAsQEAERKwBDkwMQM1MzUXBzUTMxEjExQWMyEyNj0BNCYjISIGFTUUFjMhMjY9ATQmIyEiBhU1FBYzITI2PQE0JiMhIgYVNRQWOwEyNj0BNCYrASIGFWXJpqbIZGTIHRUCWBQeHhT9qBUdHRUBLBQeHhT%2B1BUdHRUB9BQeHhT%2BDBUdHRVkFB4eFGQVHQH0ZEt9fUv%2BDARM%2B%2BYUHh4UZBUdHRXIFB4eFGQVHR0VyBQeHhRkFR0dFcgUHh4UZBUdHRUAAAAABgABAAAFFQRMAA8AHwAvAD8AQwBKABcAskAAACsBsEsvsEDWsEPNsUwBKwAwMTcUFjMhMjY9ATQmIyEiBhU1FBYzITI2PQE0JiMhIgYVNRQWMyEyNj0BNCYjISIGFTUUFjsBMjY9ATQmKwEiBhUBETMRExc1MzUjNQEdFQJYFB4eFP2oFR0dFQEsFB4eFP7UFR0dFQH0FB4eFP4MFR0dFWQUHh4UZBUdAyBkIafIyDIUHh4UZBUdHRXIFB4eFGQVHR0VyBQeHhRkFR0dFcgUHh4UZBUdHRX75gRM%2B7QCJn1LZEsAAgAAAMgEsAPoAA8AEgAtALANL7AEzbAEzQGwEy%2BwANawCc2xFAErsQkAERKwEDkAsQQNERKxERI5OTAxGQE0NjMhMhYVERQGIyEiJgkBESwfAu4fLCwf%2FRIfLAOEASwBEwKKHywsH%2F12HywsAWQBLP2oAAADAAAAAASwBEwADwAXAB8AWQCyDQAAK7AfL7AbzbAXL7AEzQGwIC%2BwANawEM2wEBCxGQErsB3NsB0QsRUBK7AJzbEhASuxHRkRErARObAVEbETEjk5ALEfDRESshATFTk5ObAbEbAUOTAxNRE0NjMhMhYVERQGIyEiJj8BBScBExEhEjQ2MhYUBiIaEgRYExkZE%2FuoEhpk9wEqSgEl7PwYbE5wTk5wLAP0EhoaEvwMEhoa7baDnAE%2B%2FuAB9P7OcE5OcE4AAgCU%2F%2FMEHAS9ABQAHgA9ALINAAArsB0vsATNAbAfL7AA1rAVzbAVELEbASuwCM2xIAErsRsVERKxDQQ5OQCxHQ0RErIHABg5OTkwMRM0PgEzMh4BFAcOAQ8BLgQnJjcUFjMyNjQmIgaUedF6e9B5SUm7OTkKImNdcys%2Fwpdqa5eX1pYC6XzXgX7V9pVy9kJCCSJrb6BLi5Zrl5fWlpcAAAIAAQABBK8ErwAPABUASQCyDQAAK7ATzbAUL7AFzQGwFi%2BwAdawEc2wERCxEwErsAnNsRcBK7ETERESsQ0EOTmwCRGxBQw5OQCxFBMRErMBCAkAJBc5MDESND4CMh4CFA4CIi4BEhAWMxEiAV%2Bg3vTeoF9foN703qBN%2B7CwAd703qBfX6De9N6gX1%2BgAgn%2BnvoDVgACAHUABAPfBQ8AFgAlAAATND4DNx4GFRQOAgcuAjceARc3LgInJjY%2FAQ4BdURtc3MeFUlPV00%2FJU5%2Bmk9yw4B%2BDltbEAcWLgoPAgkJXDcBll64oZ3FYEePdndzdYZFWZlkOwQGXrh%2BUmwaYgYWSihJjTQzbpYAAAADAAAAAATFBGgAHAAhACYAVwCyGgAAK7APzbAIL7AEzQGwJy%2BwANawDM2wDBCxEwErsBbNsSgBK7ETDBESswYdHiAkFzmwFhGxHyI5OQCxCA8RErMVHR8hJBc5sAQRsyAiIyUkFzkwMRkBNDYzBBcHISIGFREUFjMhMjY9ATcVFAYjISImJTcBJwkBFzcvAeulAW4fuv7JKTs7KQH0KTvI66X%2B1KXrAbShAZxy%2FmsB%2BXFxFVwBkAEspesGCLo7Kf4MKTs7KX3I4aXr62oyAZxx%2FmsB%2BHFxVRwAAAAAAgAAAAAElQRMABwALgBIALIaAAArsBDNsCIvsCfNsAkvsATNsAQQsAbNAbAvL7AA1rANzbEwASsAsSIQERKyFR0kOTk5sQkaERKwJTmxBAYRErAmOTAxGQE0NjMhFwYHIyIGFREUFjMhMjY1NxUUBiMhIiYBPgMfARUJARUiDgXrpQEFAoVVkSk7OykB9Ck7yOul%2FtSl6wGnHmdnXx4dAWj%2BmQcYSENWQzkBkAEspetQIFg7Kf4MKTs7KZk1pevrASEmNBMJAQHRAUQBPtgCDhczQ20AAAAAAgAAAAAEqARMAB0AIwBSALIbAAArsBDNsAkvsATNAbAkL7AA1rANzbANELEUASuwF82xJQErsRQNERKzBx4fIiQXObAXEbAhOQCxCRARErMWHyIjJBc5sAQRsSAhOTkwMRkBNDYzITIXByEiBhURFBYzITI2PQE3FRQGIyEiJgkCJwEn66UBLD1Csv6jKTs7KQH0KTvI66X%2B1KXrAVYBGwI3if5SkgGQASyl6xexOyn%2BDCk7OylFyKml6%2BsBjf7kAjeJ%2FlGTAAABAAAAAQSwBLEAFwBFALISAAArsBYvsA4zsALNsAkyAbAYL7AU1rADMrAQzbAIMrEZASuxEBQRErEGEjk5ALEWEhESsQ0XOTmwAhGxAAw5OTAxEQEVMzUjCQEjFTM1CQE1IxUzCQEzNSMVASzIyAEsASfDyAEs%2FtTIw%2F7Z%2FtTIyAJbASjGyAEs%2FtTIxv7Y%2FtTGyP7UASzIxgAAAAABAMgAAAOEBEwAEwAdALIRAAArsAszAbAUL7AA1rANzbAIMrEVASsAMDE3ETQ2OwEyFhURAREBERQGKwEiJsgdFWQVHQH0%2FgwdFWQVHTID6BUdHRX%2BSwHn%2B7QB6P5KFR0dAAAAAQAAAAAEsARMABcAHwCyFQAAK7ENDzMzAbAYL7AA1rARzbAIMrEZASsAMDE1ETQ2OwEyFhURAREBEQERAREUBisBIiYdFWQVHQH0AfT%2BDP4MHRVkFR0yA%2BgVHR0V%2FksB5%2F4ZAef7tAHo%2FhgB6P5KFR0dAAABAIgAAASwBEwABgAUALIGAAArsAQzAbAHL7EIASsAMDETAREBEQERiAI0AfT%2BDAImAib%2BGQHn%2B7QB6P4YAAAAAQDIAAAETARMAAIAADMJAcgDhPx8AiYCJgAAAAIAyABkA4QD6AAPAB8AADcUFjsBMjY1ETQmKwEiBhUBFBY7ATI2NRE0JisBIgYVyB0VyBUdHRXIFR0BkB0VyBUdHRXIFR2WFR0dFQMgFR0dFfzgFR0dFQMgFR0dFQAAAAEAyABkBEwD6AAPAAA3FBYzITI2NRE0JiMhIgYVyB0VAyAVHR0V%2FOAVHZYUHh4UAyAVHR0VAAAAAQAAAAAEKARMAAYAFACyAAAAK7AFMwGwBy%2BxCAErADAxMREBEQkBEQH0AjT9zARM%2FhkB5%2F3a%2FdoB6AAAAQAAAAAEsARMABcAHwCyAAAAK7EQFjMzAbAYL7AU1rAEMrANzbEZASsAMDExEQERARE0NjsBMhYVERQGKwEiJjURAREB9AH0HRVkFR0dFWQVHf4MBEz%2BGQHn%2FhkBtRUdHRX8GBUdHRUBtv4YAegAAAEBLAAAA%2BgETAATAB0AsgAAACuwDjMBsBQvsBLWsAIysAvNsRUBKwAwMSERARE0NjsBMhYVERQGKwEiJjURASwB9B0VZBUdHRVkFR0ETP4ZAbUVHR0V%2FBgVHR0VAbYAAAIAZADIBLAEKAAPABIAEgCwDS%2BwBM0BsBMvsRQBKwAwMTc1NDYzITIWHQEUBiMhIiYRIQFkHRUD6BUdHRX8GBUdBEz92vpkFR0dFWQVHR0BDwI0AAEAuQAHA%2FkEqQAFAAATATcJASe5AlDw%2Fp8BYfACV%2F2w8AFhAWHwAAABARD%2F0gRSBHQACAAAJQkBNwEXBxUBARABYf6f8QI8FQH9sMIBYQFh8P3FFgEB%2FbEAAAAAAgADAAMErQStAAsAFwBCALAKL7AOzbAVL7AEzQGwGC%2BwAdawDM2wDBCxEQErsAfNsRkBK7ERDBESswQJCgMkFzkAsRUOERKzAQYHACQXOTAxEhASJCAEEhACBCAkEzMVMzUzNSM1IxUjA6ABEwFEAROgoP7t%2Frz%2B7YnIyMjIyMgBtgFEAROgoP7t%2Frz%2B7aCgAVHIyMjIyAACAAMAAwStBK0ACwAPAEkAsAovsAzNsA8vsATNAbAQL7AB1rAMzbAMELENASuwB82xEQErsQ0MERKzBAkKAyQXOQCxDAoRErEHADk5sQQPERKxAQY5OTAxEhASJCAEEhACBCAkEyE1IQOgARMBRAEToKD%2B7f68%2Fu2JAlj9qAG2AUQBE6Cg%2Fu3%2BvP7toKABUcgAAAAAAgADAAMErQStAAsAFwAyALAKL7AEzbAEzQGwGC%2BwAdawB82wB82xGQErsQcBERKxDBA5OQCxBAoRErENFTk5MDESEBIkIAQSEAIEICQTFzcXNyc3JwcnBxcDoAETAUQBE6Cg%2Fu3%2BvP7tU9WNjdWOjtWNjdSNAbYBRAEToKD%2B7f68%2Fu2goAEo1Y6O1Y2N1I2O1Y0AAAIAAwADBK0ErQALABEAMgCwCi%2BwBM2wBM0BsBIvsAHWsAfNsAfNsRMBK7EHARESsQwOOTkAsQQKERKxDQ85OTAxEhASJCAEEhACBCAkEwkBJwcnA6ABEwFEAROgoP7t%2Frz%2B7WsBFAGbr%2BxmAbYBRAEToKD%2B7f68%2Fu2goAGE%2FusBm67sZgAAAAADAAMAAwStBK0ACwA4ADwAbACwCi%2BwOc2wPC%2BwJ82wIS%2BwG82wNC%2BwBM0BsD0vsBLWsB7NsB4QsS4BK7AHzbE%2BASuxHhIRErEhNDk5sC4RtAkEKDo7JBc5ALEnPBESsQcAOTmwIRGwKjmwGxKyDA8uOTk5sDQRsQYBOTkwMRIQEiQgBBIQAgQgJBMzMhYyNjQ%2BBToBMzIWFRQGBw4EFzM%2BBDU0LgMjIg4CEzM1IwOgARMBRAEToKD%2B7f68%2Fu3JjwQPBwYCBQIJBA4EEwMTFggXBQ8nHRgByAUSLSIcIzFEMRsyUUUmiMjIAbYBRAEToKD%2B7f68%2Fu2goAIZAgYMCgcFAwIBFBAWDBABBBcfPSYDCikyWDIzTCgYBhg1YP4uZAADAAMAAwStBK0ACwAVABkAOwCwCi%2BwDM2wFS%2BwDjOwEs2wES%2BwFs2wGS%2BwBM0BsBovsRsBKwCxEhURErEHADk5sRYRERKxBgE5OTAxEhASJCAEEhACBCAkNyE1IxEhFTMVIxMzNSMDoAETAUQBE6Cg%2Fu3%2BvP7t7QGQZP7UZGRkyMgBtgFEAROgoP7t%2Frz%2B7aCgiWQBLGTIAZBkAAACAAAAAASwBLAAGAAvAGkAshQAACuwEi%2BwH82wHDKwAC%2ByDhkhMzMzsAHNsgwjLTIyMgGwMC%2BwFNayBRwpMjIysBPNsgceJzIyMrExASuxExQRErMiIy4vJBc5ALESFBESsBU5sQAfERKwHTmwARGyHigpOTk5MDERNTM%2BATc1MxUeAhczFSMOAQcVIzUuASczHgEXNTMVNjcjNTMuAScVIzUOAQczFcMfh4vINnZrEsvLGbdZyIyIHmAYb0vIlTTJyBllSshLbhjRAfTIfZUayMgUUINFyGaoIcXFG5d9SW0Yzs4wnshKahjMyxdsSMgAAAAAAwAEAAQErASsAAsAEwAfAEYAsAovsA%2FNsBMvsATNAbAgL7AB1rANzbANELERASuwB82xIQErsRENERK1BAkKAxQaJBc5ALETDxEStQEGBwAXHSQXOTAxEhASJCAEEhACBCAkEhAWIDYQJiADNyc3FzcXBxcHJwcEoAESAUQBEqCg%2Fu7%2BvP7uFvMBVvPz%2FqpJh4dth4dth4dth4cBtgFEARKgoP7u%2Frz%2B7qCgAl%2F%2BqvPzAVbz%2FduHh22Hh22Hh22HhwAAAAMABAAEBKwErAALABMAGQBGALAKL7APzbATL7AEzQGwGi%2BwAdawDc2wDRCxEQErsAfNsRsBK7ERDREStQQJCgMUGCQXOQCxEw8RErUBBgcAFxkkFzkwMRIQEiQgBBIQAgQgJBIQFiA2ECYgAzcXNxcBBKABEgFEARKgoP7u%2Frz%2B7hbzAVbz8%2F6qa41XzI7%2BpgG2AUQBEqCg%2Fu7%2BvP7uoKACX%2F6q8%2FMBVvP%2BI41XzY7%2BpwAAAAMABAAEBKwErAALABMAGwBGALAKL7AWzbARL7AEzQGwHC%2BwAdawDM2wDBCxGQErsAfNsR0BK7EZDBEStQQJCgMPFCQXOQCxERYRErUBBgcADhskFzkwMRIQEiQgBBIQAgQgJBMUFwEmIyIGExYzMjY1NCcEoAESAUQBEqCg%2Fu7%2BvP7uFj4COGR0q%2FPNYXCr8zsBtgFEARKgoP7u%2Frz%2B7qCgAbRzZAI3PvP98jvzq3BhAAAAAAEAAABjBLAD6AAGABoAsAUvsALNAbAHL7EIASsAsQIFERKwADkwMREBESERIRECWAJY%2FagCIwHF%2FtT%2B1P7TAAABAAAAYwSwA%2BgABgAaALAAL7ABzQGwBy%2BxCAErALEBABESsAQ5MDEZASERCQERAlgCWP2oAZABLAEs%2Fjv%2BQAEtAAAAAAEAzAAABEoEsAAGAB8AsgUAACsBsAcvsAXWsATNsQgBK7EEBRESsAE5ADAxEwkBIREhEcwBwgG8%2Ftb%2B1AJYAlj9qP2oAlgAAAEAaAAAA%2BYEsAAGAB8AsgYAACsBsAcvsAHWsATNsQgBK7EEARESsAY5ADAxEyERIREhAWgBKAEsASr%2BPwJYAlj9qP2oAAAAAAEAAADHBLAETAANAAA1PgM3EQkBEQ4DBkaJ55wCWP2oX7CkgsiE1a1nCAEP%2Fjv%2BQAEtAiREdQAAAgAAAAAEsASwAAYADQARALIAAAArAbAOL7EPASsAMDExERcBFwEXExcBFxEhF4EBJo7%2B2oHrjgEmgf5wgQGQgQEmjv7agQMJjgEmgQGQgQACACIAIwSOBI4ABgANAAA3ASchEScJAREXARcBFyIBJ4EBkIH%2B2QGogQEnjv7ZgbABJ4H%2BcIL%2B2QI1AZCBASeN%2FtmCAAMAFwAXBJkEmQAPAB8AIwBPALANL7AgzbAjL7AUzbAdL7AFzQGwJC%2BwAdawEM2wEBCxGQErsAnNsSUBK7EZEBEStQUMDQQhIyQXOQCxFCMRErEJADk5sB0RsQgBOTkwMRI0PgIyHgIUDgIiLgEBEx4BOwEyNjcTNiYrASIGEzM1Ixdbm9Xs1ZtbW5vV7NWbAVY6BCMUNhQjBDoEGBTPFRgwyMgB4uzVm1tbm9Xs1ZtbW5sCRv7SFB0dFAEuFB0d%2FcVkAAAFAAAAAASwBLAAJgAqADAANAA7ADQAsicAACuwMTOwKs2wMjIBsDwvsDHWsAUysDTNsAcysT0BK7E0MREStAsMEzU6JBc5ADAxETMVIREzESE1MzUjNjQmLwEuASMiDwEGByYvASYjIgYPAQ4BFBUjEyERIRMiNj8BFxMRIREBNx4DI2QBkMgBkGRvAQMCIgs9JyAd7xYSExXuIR0nPQojAgJvZAGQ%2FnBkAyITEtXbAZD%2Bj8oFDiASAgMgyAEs%2FtTIZAELEwisJzARkA0WGAyQEi4msQgUCgH8fAGQAfRgMC%2B%2F%2FHwBkP5wA4TFDClXOQACAAD%2F6gSvBLAAGwAyABcAsgAAACsBsDMvsCfWsA%2FNsTQBKwAwMRU1Ny4CPgE3PgU3FAIOBC4CIwc2Fjc2JT4DNz4BJyYiBgcOAQ8BBAfYCQgDFTguL2llmonoaCxKaHGDeHtcUw9jEidDNwE4RmFrWykWBAgHFCERI509Pf6PWRaPwTU8gGKCOzxVMy0eOR69%2FszQm1UzCQYTDzd%2FDVNCqCY%2FX4BUMhQJBR0ZM3MgIMXMAAABAG8ADAREBOcASAAjAAGwSS%2BwAdawRc2wRRCxPAErsUoBK7E8RRESsTo2OTkAMDESFBceARcWPgM3PgEnHgEHDgEHDgQeAT4BNz4ENzYCJxYXFicmJy4CNw4EFx4DDgQHBi4CNw4BbwUJRkYfQjo4KA8gDhRPVhEFHxYKCQ8DAwgOGSQYOURrQ0APJqWkFhUnRw8ST1MFMw0qZ0ouDwIMBAgBAQsQGhImOhcHDjQ%2FAblCHjh%2FLRUKJT49HkLtJ1CoZCFJLBMUIA8XCAsBBAYUHD1DbkOsAVNtLFWfBQIHIYbZlQgfZm2nUww7GzQbKBcZEAQKLk1WIC5uAAAD%2F8MAfQTtBDMAIQA%2FAEcAQwCwGi%2BwKc2wOi%2BwCc0BsEgvsDzWsDfNsUkBK7E3PBESQAoJGRoIKSg1PkBDJBc5ALEJOhEStwARJC41PkJHJBc5MDEDNz4GMh4FHwEHDgYiLgUnNx4FMj4ENy4EJxYVFAYiJjU0NwYXFhc3LgEvAT0aBhxGT3N2k5CTdnNPRhwGGhoGHEZPc3aTkJN2c09GHAabB0MtW1R6gHdSWSxICwE3HTo5HjGw%2BLAuZoUxaWklTBMUAlgoCihXVGBHLy9HYFRXKAooKAooV1RgRy8vR2BUVygKKApgPV44KygzXDtoDgFJJUU6GUpZfLCwfFVJV3N8Q2kYYCQkAAAABP%2FDAAAE7QSwABYAIAApAEEAoQCyDwAAK7AOMwGwQi%2BxQwErsDYauj3v790AFSsKsA8uDrAMwAWxDgH5DrANwLAPELMLDwwTK7MQDwwTK7MZDwwTK7MaDwwTK7MkDwwTK7MlDwwTK7IQDwwgiiCKIwYOERI5sBk5sBo5sCQ5sCU5sAs5ALcLDA0QGRokJS4uLi4uLi4uAUAKCwwNDg8QGRokJS4uLi4uLi4uLi6wQBoBADAxAzc%2BBjMyFzczASM3LgQnNxIXNy4BNTQ3BhcWFz8BLgEvAQE3PgY3Jic3HgIfAQcOBD0aBhxGT3N2k0g9PCWU%2FsaUJVKmcmknCpvStyVrjy5mhTFpLxceOg8OASgmFi0vIjATLwFhKydDgS4NGhoHJVplkwJYKAooV1RgRy8RjvtQjxVlZ3k4Dyj%2B5jaNEqduVUlXc3xDL1ccUhsa%2FaeRDyYyJj8YQAJ%2FMJI2j0AUKCgMNGtiZgAAAAP%2FngAABRIErAALABIAFwAAJhYzITI2JwEuAQcBNwkBITUjFREbATUjbxslBQ4lGxX9fhQ4FP1%2B9QG9Ab3%2Bp8hkZMhEREcgBCAiBSD71mQC0%2F0tZGQBkP7UASxkAAAAAAEAZAAVBLAEsAApAEgAsB4vsAnNAbAqL7Al1rAFMrAWzbALMrIWJQors0AWGAkrsiUWCiuzQCUjCSuxKwErsRYlERKxHR45OQCxCR4RErEWJTk5MDETNTQ2NwERNDYyFhURAR4BHQEUBiclERYdARQGLwEjBwYmPQE0NxEFBiZkFg8Ba1h8WAFrDxYYEf6ZZBoTXt5eExpk%2FpkRGAEGKRQxDgFFAVM%2BWFg%2B%2Fq3%2Buw4xFCkUDQz5%2FvlbFkAUEQlOTgkRFEAWWwEH%2BQwNABEAAAAABEwEsAAJABsAHwAjACcAKwAvADMANwA7AD8AQwBHAEsATwBTAFcAADUUFjMhMjY1ESE1ITU0JisBNSMVITUjFSMiBhUTNTMVJzUzFSc1MxUTNTMVJzUzFSc1MxUTNTMVJzUzFSc1MxUTNTMVJzUzFSc1MxUTNTMVJzUzFSc1MxUdFQPoFR37tARMHRWWZP4MZJYVHWRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZDIUHh4UAu5klhUdZGRkZB0V%2FEpkZMhkZMhkZP5wZGTIZGTIZGT%2BcGRkyGRkyGRk%2FnBkZMhkZMhkZP5wZGTIZGTIZGQAAAMAAAADBXgErgAKABAAGQBBALAAL7AYM7ABzbATMrALL7AIM7AQzbADMgGwGi%2BxGwErALEBABESsREWOTmwCxGzBw0SFSQXObAQErEGDjk5MDE9ASEBMzUJATUjCQEhFzcnIQE3FzM1CQE1IwEDAljxASz%2B1J%2F9qP6rAQN6jbX%2BqwKmjXqfASz%2B1PHIyAJYxv7Z%2FtTF%2FagCWHqOtP2VjnvG%2Ftn%2B1MUAAAEAAAAABLAETAASABoAsg4AACuwEC%2BwDDOwBM0BsBMvsRQBKwAwMRkBNDYzITIWFREUBiMhAREjIiY7KQPoKTs7Kf2s%2FtBkKTsBkAJYKTs7Kf2oKTv%2B1AEsOwAAAwBkAAAETASwACUAKQAtAGAAsh8AACuwCc2yCR8KK7NACQEJK7AVMrAmL7AqM7AnzbArMgGwLi%2BwANawJjKwA82wKDKwAxCxEgErsCoysBfNsCwysS8BK7EDABESsCQ5sBIRsR4fOTmwFxKwGTkAMDETNSEVFBcWFxYzMj4GJzQ9ASEVFA4FIi4FGQEhESERIRFkASwGEVUnNSU7KR8RCwMCAQEsBhgnTWWdwJ1lTScYBgEsAZABLAJYyPpxIFwZCwsUHCMoLC4YEQj6yCpSfmpxUDMzUHFqflIBVgEs%2FtQBLP7UAAAAAAH%2F4gC4BGgD3gAFAAADFwkBNwEe4wFgAWHi%2Fb4Bm%2BMBYf6f4wJDAAABAEYA2gTMBAAABQAAEwkBJwkBRgJEAkLi%2Fp%2F%2BoAMd%2Fb0CQ%2BP%2BnwFhAAAAAAL%2FOgBkBXYD6AAIABEAKACwBy%2BwBM0BsBIvsAfWsATNsRMBK7EEBxESsAE5ALEEBxESsA45MDEDCQEjESEXIREBFyERIwkBIxHGASsBLMsBgdf84AGU1wF9xgErASvIArwBG%2F7l%2FnDIAlgBLMj%2BcP7lARsCWAAAAAEAEgAABKoEsAAyAEYAsiIAACuwGTOwLM2wLBCwJs2xFR0yMrAvL7AEzbAQL7AJzQGwMy%2BwJNawH82wHxCxHAErsBfNsTQBK7EXHBESsC05ADAxEyY3NjMhNz4BOwEyFhQGKwEDDgIrARUUBiImPQEhFRQGIiY9ASMiJjU0NjMhNyEiJicSBQ8OGQOAJgUbEV4UHh4UNskCCB4SHx0qHf7UHSodMhUdHRUCFzD9hyAtBQOrGBITohEVHSod%2FD8EDRYyFB4eFDIyFB4eFDIeFBUdyCoWAAAAAAIAAAAABLAETAADAA8AIACyAAAAK7ABzbAEL7AFzbANMrAJzQGwEC%2BxEQErADAxMREhEQE1MzQ2MyEyFhUhFQSw%2B1DIOykBLCk7AfQDIPzgA4RkKTs7KWQAAAAAAgABAAAF3QRMAAMAEAAoALIAAAArsAHNsA8vsA3NsAUysAnNAbARL7ESASsAsQEAERKwBDkwMTMBIQkBETM0NjMhMhYVIRUhAQEsBLD%2B1PtQyDspASwpOwH0%2FBgCvP1EAZACWCk7OynIAAAAAQEuAAADggSwAAkAIQCyCQAAKwGwCi%2BwAdawB82xCwErsQcBERKxBAk5OQAwMQEzESMJASMRMwEBLsbGASoBKsbG%2FtYBLAJYASz%2B1P2o%2FtQAAAAAAQAAAS8EsAOCAAkAHACwCC%2BwAs0BsAovsQsBKwCxAggRErEABTk5MDERARUhNQkBNSEVASwCWAEs%2FtT9qAJYASrGxv7W%2FtfFxQAAAAQAAAAABLAEsAAPABkAHQAhAEkAsgwAACuwGs2wHjKwHS%2BwIDOwBc2wEC%2BwFM0BsCIvsBvWsB7NsB4QsR8BK7AJzbIfCQors0AfAAkrsSMBK7EJHxESsBk5ADAxPQE0NjMhMhYdARQGIyEiJhsBPgEzITIWFxMBMzUjFzM1IzspA%2BgpOzsp%2FBgpOx%2BsBSQUAqATJQWs%2Fo9kZMhkZGRkKTs7KWQpOzsBVQLjFictF%2F0k%2FtRkZGQAAAAD%2F5sAZASwBEwACwApADcAJgABsDgvsADWsAbNsAYQsSoBK7AyzbE5ASuxKgYRErEMGjk5ADAxAzU0Nj8BFS4EFzU8Az4FOwElESUjExYOASMiKwEiJicCARE0NjMyFhURFAYjIiZlMhkZBA4iGhbJAQICBAUHBMgCo%2F1dJi8CCgwPBQNTFB0ENwPoHRUUHh4UFR0CWDIYMg0N%2BgIHFRYhVfoCDAQKBAcDBQIB%2BvyuyP7sDAsBHBUBUf7iA1IVHR0V%2FK4UHh4AAAIASgAABGYEsAArADMANQCyLwAAK7AzzbApL7AfM7ADzbAYMrIpAwors0ApJQkrAbA0L7E1ASsAsSkzERKxLDE5OTAxEzQ2OwE3Ez4BNycmNjsBMhYHBhUeARcTFzMyFhUUBgcOBCMiJi8BLgEFHgEyNjcGIkobFBJ1Pw96UxIGEhReFBIGElN6Dz92ERQbGhIIHmRqn0998To6EhoBpww4RjgLMGwBXhUdrQFHTX4UIBMaFRMkARN%2FTf65rR0VFCgHAwsdFRIpFBQHKdwxPT0xBgAAAQAVABUEnAScABcAABMXBzcXNxc3Fyc3JzcnNwcnBycHJxcHFxXpTuAtm5st4E7qtLTqTuAtm5st4E7pswG9LeBO6bOz6U7gLZucLOFO6bS06U7hLJwAAAMAAABkBLAEsAADACIALgAaAAGwLy%2BwKNawFs2xMAErsRYoERKwFDkAMDE1MxEjARQ7ARY7ATI3EzY9ATQmIyE2PQE0JisBIgYPAgYVExE%2FATMVByEVAyMnyMgBLGQ9fA%2F6LiXuHT0n%2FrgcPScyGzAOYJEUZJZkMjIBwvrWiMgCWP3zS2Q5AVgfK2QsUXYHlixRKBzGxBol%2FokBd9XUr%2BF9%2FolkAAAAAAMAAAAABLAETAADACIALgBwALIcAAArsCXNsBUvsAAzsCjNsC4vsAfNsAEysCwvsArNAbAvL7AA1rADzbADELEEASuwI82wIxCxJgErsBjNsBgQsSkBK7ARzbEwASuxJiMRErIIKCw5OTmwGBGwFTmwKRKwKzkAsS4cERKwKjkwMRkBMxE3ETQ7ATY7ATIXExYdARQGIyEWHQEUBisBIiYvAiY3HwEzNSchNQMjByPIZGQ9fA%2F6LiXuHT0n%2FrgcPScyGzAOYJEUZJZkMjIBwvrWiGQBkAJY%2Fah9AZBLZDn%2BqB8rZCxRdgeWLFEoHMbEGiXU1a%2FhfQF3ZAAAAAMACABkBRUEVQADACIAQQB5ALAgL7AkzbAbL7ApzbAxL7AUzbABMrIxFAors0AxAAkrAbBCL7AA1rADzbADELEEASuwI82wIxCxLQErsBjNsi0YCiuzQC08CSuxQwErsS0jERK0DBEbFD8kFzkAsRskERKwIzmwKRGwGDmxFDERErIXPEE5OTkwMTcRMxE3ETQ2PwElNjMyHwEWFRQPASEyFhQGKwEDDgEjISImNxchEz4BOwEyNjU0JiMhKgIuBCcmNTQ%2FAScFCMhkHA4OAWoOCxEMbQ4LVQEuVWttVGuCBxsP%2FqsHpmRkASWDBhsPyxASEhD%2BNwELBAkDBwQEAgUKk1b%2BrcgCWP2oSwINESUKCeYGDHAOFBIOeUyQTv6tFieiG1kBUxUoHhUUHQEBAgMFAwwIDg23U%2BwAAAAD%2F5sAZQSwBFYAHgA4ADwAeQCwGC%2BwJM2wHS%2BwH82wOC%2BwA82wOjKyOAMKK7NAODkJKwGwPS%2BwAdawH82yHwEKK7NAHywJK7AfELEmASuwFM2wFBCxOQErsDzNsT4BK7EmHxEStAcMHAQpJBc5ALEdJBESsCY5sB8RsAA5sQM4ERKyAScsOTk5MDECNDYzBScmNTQ%2FATYzMhcFHgIVERQGIyEiJicDIyInMzIWFxMhNxElBxcWFRQHDgUqASMhAREzEWVsVQEuVQsObQ0QCw4BbQcUIawI%2FqsQGwaCa1QK3g8bBoMBJWv%2BqVeRCgUBBQMHBAkECwH%2BJAPpyAJDkEwBeRAQFQ1xDAbmBA0nEf3yDaEoFQFTZCkU%2Fq1ZAfbtU7gLDwsJAwUDAgEB%2FgwCWP2oAAAAAAMAYQAABEwFDgAbADYAOgBHALI3AAArsDjNAbA7L7AV1rA3MrApzbIpFQors0ApOgkrsDMysCkQsS8BK7AOzbE8ASuxKRURErESNjk5sQ4vERKwETkAMDEbAR4CMyEyNjURNCYnJTU0JiIGFREnJgYPAQYXNxcWNz4FPAE1ETQ2Fh0BFBYXBREHIQM1IRVh5gQNJxECDQ2iKBX%2BrU6QTHkPJQ5wFltTtxYZAwUDAgEBMjIoFQFTWf4JCAJYAs%2F%2BlQYTH6YHAVYPGwaDalRua1X%2B0lQMAQ1uFgtWkhINAQUDBwQJBAsBAcgWEhMVyhAbBoL%2B2mT%2BcMjIAAAAAAMAAgAKA%2B0FGAAdADQAOABFALA1L7A2zQGwOS%2BwCtawNTKwK82yKwoKK7NAKzgJK7AhMrArELEnASuwD82xOgErsSsKERKxDB85ObEPJxESsA05ADAxEwYfAR4BPwEUBhUUFjI2PQElPgE1ETQmIyEiBg8BAxMhFxEFDgEdARQGJjURPAEuAScmDwETNSEVAhAWcA0mD3kBTZBOAVMUKaIN%2FfMRJQoKmuwB91n%2BrBQoMjIDBwYYFriSAlgCSR8Wbg0BC1UzzS5UbG5UaoMGGw8BVgemHA4P%2FoIBU2T%2B2oIGHA%2FKFhISFgHICwcQCAMNEpICccjIAAAAAgAFAAAEsASrAA4AFQA6ALIMAAArsBDNsA8vsAXNAbAWL7AA1rAQzbEXASsAsRAMERKxCRI5ObAPEbEAEzk5sAUSsQgUOTkwMRM0PgIzMgQSEAIEICQCARchBwkBFQVfoN16ogEToKD%2B7f68%2FuygASUCASwCAZL%2BbgJVet2gX6D%2B7P68%2Fu2goAETAQrJwgEmASrFAAIAAAAABKsEqwAQABcAOACyDgAAK7AUzbAWL7AFzQGwGC%2BwFNawCs2xGQErALEUDhESsBI5sBYRsgoAETk5ObAFErAXOTAxETQ%2BAjMyHgIVFAIEICQCNwEnITchNV%2Bg3Xl63aBfoP7s%2Frz%2B7aDIAZICASwC%2FtQCVXrdoF9foN16ov7toKABE6X%2B2sLJxQAAAAIABQAABLAEqwAOABUAPgCyDAAAK7ARzQGwFi%2BwANawEc2wERCxEgErsAnNsRcBK7ERABESsQwPOTmwEhGxBRU5ObAJErELFDk5ADAxEzQ%2BAjMyBBIQAgQgJAIlMxEzETMBBV%2Bg3XqiAROgoP7t%2Frz%2B7KABJ8jIyP7UAlV63aBfoP7s%2Frz%2B7aCgAROl%2FtQBLAGQAAACAAUAAASwBKsADgAVAE0AsgwAACuwFC%2BwBc0BsBYvsADWsBXNsBUQsRIBK7AJzbEXASuxFQARErEMDzk5sBIRsQUQOTmwCRKxCxE5OQCxFAwRErIIABA5OTkwMRM0PgIzMgQSEAIEICQCJQkBIxEjEQVfoN16ogEToKD%2B7f68%2FuygAScBLAEsyMgCVXrdoF%2Bg%2Fuz%2BvP7toKABE6X%2BcAGQASz%2B1AAAAAAEAAUAAASwBKsAEACIAJgAmgB8ALIOAAArsCrNsE8vsIwvAbCbL7AA1rAUzbAUELFYASuwCs2xnAErsRQAERKwEjmwWBFADg4FEyEjJDxKVXiEhYmUJBc5sAoSQAoNIiYwO1pndpmaJBc5ALFPKhEStxYwNjxGSFVXJBc5sIwRQAkKABRYbIWNjpQkFzkwMRM0PgIzMh4CFRQCBCAkAhMGFgcUFgcyHgEXFhceAjcWBhcWFxQOARcWNz4CNy4BJy4BJyIOAgcGJyY2NS4BJzYuAQcGJyY3NjceAhceAR8BNDYnJjY3PgM3JjcyFjI2Ny4DJzYnHgE%2FATYuAScGJw4DBwYmBw4BBwYWBw4BJT4BNxYyPgE3FBYVLgM3MwVfoN16ed2gX6D%2B7f68%2Fuyg%2BQgbBiIBDBYYCBhUFj45HQguAyotBgEFaHUeIiMDDi4NDkYRCT0gLhAyEAQBBikEAggZGhcTEwsGEAYoGwYMKA4OEwQEJQQFCgcYFgYQCB8SFwkKKSM%2FDAsJHzYMCwcvUg8TEg8rGj4IDz0PFT4DAxMBAzEBAwMaAwoRCxIHIgksHCSiAQJVet2gX1%2Bg3Xqi%2Fu2goAETAVkhdxwJRhkLEwQMHggvHgQSShRHCQYTCgwDcx0kPh8JAQcHEAsBAgsLIxcCLwINCAMWJhIdGR0cHhAGAQEHChMlCQgDSRUXKwoOKhQZCRITAwkLFycVIAcnBQ0DBQQkIxYMAwMMEgYKAQMHBgcnDwsXByJxcQwkBwoMEQQYVQECBgQMXwAAAAABAAAAAgSvBIUAFAAAPAE3ASY2NzYXBRc3FgcGJwEGIi8BDwJYIU5gpI7%2B%2FZH7DaR7gv2sDysPb48rEAJXZck2XGWK6H6vXEYv%2FawQEG4AAAYAAABgBLAErAAPAB8ALwAzADcAOwBQALAML7A0zbA3L7AFzbAcL7AwzbAzL7AVzbAsL7A4zbA7L7AlzQGwPC%2BwNdaxMTkyMrAJzbEYKDIysjUJCiuzQDUACSuxECAyMrE9ASsAMDE9ATQ2MyEyFh0BFAYjISImETU0NjMhMhYdARQGIyEiJhE1NDYzITIWHQEUBiMhIiYBITUhEyE1IRMzNSM7KQPoKTs7KfwYKTs7KQPoKTs7KfwYKTs7KQPoKTs7KfwYKTsCWAH0%2FgzIASz%2B1GTIyMRkKTs7KWQpOzsBuWQpOzspZCk7OwG5ZCk7OylkKTs7%2Fplk%2FgxkArxkAAACAGQAAARMBLAAAwAJACUAsggAACuwAC%2BwAc0BsAovsAjWsAfNsQsBKwCxAAgRErAEOTAxEzUhFQUhAREHEWQD6PxKA4T%2BosgETGRkZP4M%2FtTIAfQAAAAAAwAAAGQEsASwAAkAIQAlAGAAsAcvsAHNsAovsB0zsA7NsRgiMjKwJS%2BwE80BsCYvsA%2FWsCLNsCAysg8iCiuzQA8LCSuwADKwIhCxIwErsB4ysBjNshgjCiuzQBgcCSuwAjKxJwErALEOChESsB85MDE9ASEVFAYjISImGQE0NjMhNTQ2OwEyFh0BITIWFREhNSMVETM1IwSwOyn8GCk7OykBLDspyCk7ASwpO%2F4MyMjIyMjIKTs7AVUBkCk7ZCk7OylkOyn%2BcGRkAfRkAAAAAAQAAAAABLAEsAAGAA0AFAAbABQAsgAAACuwEjMBsBwvsR0BKwAwMTERFzcXBxcBNxc3JzchATcXNxEhNwM3JyERJweByI7Igf5wgciOyIH%2BcALZjsiB%2FnCByMiBAZCByAGQgciOyIEDIIHIjsiB%2FJmOyIH%2BcIEC5siB%2FnCByAAABgAAAAAEqASoAAsAFQAfACkAQgBMANIAsgoAACuwD82wHi%2BwSjOwGc2wRTKwKC%2BwOTOwI82wNDKyKCMKK7NAKEEJK7AUL7AEzQGwTS%2BwAdawDM2wDBCxFwErsBvNsBsQsSELK7AmzbAmELEqASuwPs2wPhCxQwErsEjNszdIQwgrsDHNsDEvsDfNsEgQsREBK7AHzbFOASuxJhsRErMKDhQDJBc5sT4qERKxLTw5ObE3MREStQkPEwQvOyQXOQCxHg8RErMHAAwRJBc5sBkRsyotPD4kFzmwKBKxBgE5ObAjEbEvOzk5MDEYARIkIAQSEAIEICQTFBYgNjU0JiAGFjQ2MhYVFAYjIjY0NjMyFhQGIyIXNDY%2FAiY1NDYzMhYUBiMiJwcWFRQGIiYlNDYyFhQGIyImoAESAUQBEqCg%2Fu7%2BvP7uFvMBVvPz%2FqrzbR8uICAXFk0gFxYgIBYXUikfegEJIBcWICAWDg83ETNIMwEeIC4fIBYXIAGyAUQBEqCg%2Fu7%2BvP7uoKABtKzy8qyr8%2FOHLh8gFhcg5CwhIC4guiAxBX4BDg4WISAuIAqRFh0kMzNSFiAfLiAgAAAAAf%2FYADsEugSwAE8AOgCwBS%2BwJ82wIC%2BwFc2wNi%2BwSs0BsFAvsVEBKwCxJwURErA%2FObAgEbQLDxobMSQXObAVErEyMzk5MDECBhceATMyNz4CNzY3AT4BJyYnJiMiBgcBBxcBNjc2MzIXFgcBBiMiJicmPgI3NjcBPgIzMhceAQcGDwEDHwEBPgEnLgEnJiMiBwYHARsaMCN2Rj84IUApJygRAYojGA8bWhQJLkEj%2FnsHRQF5FBMXGyYPECT93TRJN1oJBQ8wJCYYFAFcND1rNhkXX3YIB1v8%2FQdFAgVDOBEQZk9FU2taKEf%2BAAHWvk45QBwQMSorLBEBiiNiL1cRAiEj%2FnQHQwF1FhAXJCck%2Fd00Qj8jPkAkJBUUAVw0NzUEEZtiZVv5%2FwAHPAH%2FQ7RdV4YkITcYR%2F4AAAAAAAIAUAA2BMMEWAAbADUAPQCwMy%2BwLTOwA82wBzIBsDYvsADWsBzNsBwQsSoBK7AKzbE3ASuxKhwRErMDBw8YJBc5ALEDMxESsAU5MDETNDYzMhc2MzIWFRQOAgcGDwEnLgInLgM3FB4BHwEWFzY%2FAT4CNTQmIyIPAScmIyIGUMWEj2Jnj4HCI1dDR8VgERArckZCR0NXI6o9PkAWXWFScQxAQz5gOUo6dnIzSDxjAxCDxYGBxYMuWmxHRr%2BDFxc6gUZBRkdsWi4bVkE%2BFlpvXG8MPkZYHEdhU6uuUGMAAAAAAgA5%2F%2FIEdwS%2BABgAMwAAExQfARYzMjcBNjQvASYnBxcBJzcnJicHBhMUHwEWFzcnARcHFxYXNz4BNTQvASYjIgcBBjlCjURbXUIBG0JCjQgLadT%2Be%2FdfEi4dN0LUQo0HDGnUAYX3XxIvHh0jN0KNQl1fQP7lQgFhX0COQkIBG0K6Qo0JCGnU%2Fnv4XxItODdCAQRdQo0HCmnUAYX3YBExMx0jaitdQo1CQv7lQAAAAAADAMgAAAPoBLAAEQAVAB0ARQCyDwAAK7AZzbAdL7ASzbAVL7AGzQGwHi%2BwANawEs2wEhCxEwErsAvNsAsQsBvNsBsvsR8BK7EbEhESsgYFFjk5OQAwMTcRND4CMh4CFREUBiMhIiY3IREhEhQWMjY0JiLIPGacqppkOjsp%2FagpO2QCWP2oxD1WPT1WZAO5FTIuHh4uMhX8Ryk7O%2FECvPzZVj09Vj0AAAABAAAAAASwBLAAGAARALIAAAArAbAZL7EaASsAMDExATcnIQEnJjQ3NjIXARYUBwYiLwEBEScHAS%2FP0gEsAQsjDw8OKg4BGw8PDioOJP7p1NABfNDUARckDioODw%2F%2B5g8qDg8PI%2F71%2FtTSzwADAScAEgQJBOEAMQA9AEMAlwCwLS%2BwKjOwBM2wPjKyLQQKK7NALSwJK7A7L7AfM7ASzbISOwors0ASEwkrAbBEL7AO1rAAMrAyzbABzbAyELEsASuyBBI6MjIysCvNshQfPjIyMrArELFAASuwJ82wHCDWEbAbzbFFASuxMgERErACObAsEbAJOQCxBC0RErApObA7EbYADhsnOkBDJBc5sBISsBU5MDEBMx4BFxEuASMuBDU0PgE3NTMVHgQXIy4BJxEXHgQVFAYHFSM1JicuARMUHgMXFhcRDgETNjU0JicBJ4sFV0oGEwIuQk4vIViCT2QmRVI8KwOfCDZKQCI8UDcosptkmFUoGagQESoUHAcEPUnqqlhSAbFNYw8BTwEGDhkvOVg3XIdDB05PBBMsP2lCSEsN%2Fs0OBxMsPGU%2Bi6oLTU4RVyhrAh4dLBgVBgcCAQESCDv9KxKFQEcZAAAAAQBkAGYDlAStAEMAjQCwMS%2BwKs2wAC%2BwHjOwAc2wHDKwEy%2BwC82yEwsKK7NAEw4JKwGwRC%2BwB9awOTKwGM2wJDKyGAcKK7NAGB4JK7IHGAors0AHAAkrsBgQsQ8BK7AOzbFFASuxGAcRErMCOEJDJBc5sA8RtQsfICoxMyQXObAOErAsOQCxKjERErEtOTk5sAARsSw8OTkwMRM1MyYnLgE%2BATc2MzIWFSM0LgEjIgYHBhUUHgEXMxUjFgYHBgc%2BATM2FjMyNxcOAiMiJgcOAQ8BJz4FNz4BJ2SmGBQKCQMvLWGmgcqZRFAkJVQUKSEXHvHFCBUVKTojYhUhjCFMPDIpTycqF9IyJ1YXGDcGFQoRDBEJMAwkAlhkMTcaO1ZeKFiydzRLHB0VLDkcUyozZDKCHTs2Cw4BIh6TGRcDQgQEGgwLkQQOBg0LEQo3j0cAAgACAAAErgSwAAYADQAfALIMAAArAbAOL7AM1rALzbEPASuxCwwRErAIOQAwMRMJASMRIxEJAiMRIxECASoBKsbIAZIBKgEqxsgBLP7UASwDhPx8AlgBLP7U%2FHwDhAAABQACAAAD6ASwAAYADAAWAB4AIgCmALIHAAArsAYzsArNsgcAACuwCM2wEy%2BwFM2xAAQyMrANL7AOzbAdL7AfzbIdHwors0AdFwkrsBoysCIvsBjNsAIyAbAjL7AB1rAEzbAEELEIASuxDRcyMrAKzbEdHzIysAoQsRUBK7EbIDIysBDNsQsZMjKzEhAVCCuwE82wEy%2BwEs2xJAErsQQBERKwBjmwCBGwBTkAsRQIERKwEDmwDRGwETkwMRMzETMRMwEhNTMVMxUBNSEVIxUjNTM1AxEhESM1IxU3MzUjAsbIxv7WAZBkyP7UASxjZGPIASxkZAFkZAEsA4T8fP7UyGRkAZBkyGRkZAEsAfT%2BDGRkyMgABQACAAAD6ASwAAYADgAUAB4AIgCgALIGAAArsQcKMzOwDS%2BwH82wIi%2BwCM2wDy%2BwEs2wEM2wGy%2BwHM2wFS%2BwFs2wAjIBsCMvsAHWsATNsAQQsQcBK7EPFTIysA7NsREfMjKwDhCxCwErsR0gMjKwCs2xExcyMrMaCgsIK7AbzbAbL7AazbEkASuxBAERErAGObAHEbAFOQCxIh8RErMBBAUAJBc5sRwQERKwGDmwFRGwGTkwMRMzETMRMwEhESERIzUjFQM1MxUzFQE1IRUjFSM1MzUDMzUjAsbIxv7WAZABLGRkZGTI%2FtQBLGNkY2NkZAEsA4T8fP7UAfT%2BDGRkArzIZGQBkGTIZGRk%2FHzIAAAEAAIAAARMBLAABgAMABIAFgBrALILAAArsAwvsBPNsBYvsAjNsA0vsA7Nsg0OCiuzQA0RCSsBsBcvsBHWsBDNsxMQEQgrsAfNsAcvsA0zsBPNsBAQsRQLK7ALMrAKzbEYASsAsQgLERK0AAIDBgEkFzmxDg0RErEFBDk5MDETCQEjESMRBREhESM1AzUzESMREzM1IwIBKgEqxsgCWAEsZMjIZAFkZAEs%2FtQBLAOE%2FHzIAZD%2BDGQD6GT%2BDAGQ%2FHzIAAAABAACAAAETASwAAYADAASABYAawCyCwAAK7AHL7AIzbASL7ATzbISEwors0ASEAkrsBYvsA7NAbAXL7AL1rAKzbMTCgsIK7ANzbANL7AHM7ATzbAKELEUCyuwETKwEM2xGAErALETCxEStAACAwYBJBc5sQ4WERKxBQQ5OTAxEwkBIxEjESU1MxEjEQMRIREjNSczNSMCASoBKsbIAljIZGQBLGRjZGQBLP7UASwDhPx8ZGT%2BDAGQAZABkP4MZGTIAAAAAAUAAgAABLAEsAAGAAoADgASABYAUgCwBy%2BwCM2wCy%2BwDM2wDy%2BwEM2wEy%2BwFM0BsBcvsA%2FWsgcLEzIyMrASzbAWzbIWDwors0AWCgkrs0AWDgkrsRgBKwCxCwgRErMCAwYAJBc5MDETCQEjESMRBTUhFQE1IRUBNSEVATUzFQIBKgEqxsgB9AH0%2FgwBkP5wASz%2B1MgBLP7UASwDhPx8yMjIASzIyAEsyMgBLMjIAAAABQACAAAEsASwAAYACgAOABIAFgBSALAHL7AIzbALL7AMzbAPL7AQzbATL7AUzQGwFy%2BwC9ayBw8TMjIysA7NsArNsgoLCiuzQAoSCSuzQAoWCSuxGAErALELCBESswIDBgAkFzkwMRMJASMRIxEFNTMVAzUhFQE1IRUBNSEVAgEqASrGyAH0yMgBLP7UAZD%2BcAH0ASz%2B1AEsA4T8fMjIyAEsyMgBLMjIASzIyAAAAAACAAAAAARMBEwADwAfACoAsg0AACuwE82wHC%2BwBM0BsCAvsADWsBDNsBAQsRcBK7AJzbEhASsAMDEZATQ2MyEyFhURFAYjISImNxQWMyEyNjURNCYjISIGFeulASyi7u2j%2FtSl68g7KQH0KTs7Kf4MKTsBkAEspevto%2F7UpevrQSk7OykB9Ck7OykAAAMAAAAABEwETAAPAB8AIgA%2BALINAAArsBPNsBwvsATNAbAjL7AA1rAQzbAQELEXASuwCc2xJAErsRcQERKxICE5OQCxHBMRErEgIjk5MDEZATQ2MyEyFhURFAYjISImNxQWMyEyNjURNCYjISIGFRMtAe6iASyl6%2Bul%2FtSj7cg7KQH0KTs7Kf4MKTvIAU3%2BswGQASyj7eul%2FtSl6%2BtBKTs7KQH0KTs7Kf4M%2BvoAAAAAAwAAAAAETARMAA8AHwAiAD4Asg0AACuwE82wHC%2BwBM0BsCMvsADWsBDNsBAQsRcBK7AJzbEkASuxFxARErEgIjk5ALEcExESsSAhOTkwMRkBNDYzITIWFREUBiMhIiY3FBYzITI2NRE0JiMhIgYVFxsB66UBLKPt66X%2B1KXryDspAfQpOzsp%2FgwpO2T6%2BgGQASyj7e6i%2FtSl6%2BtBKTs7KQH0KTs7KWT%2BswFNAAMAAAAABEwETAAPAB8AIgA%2BALINAAArsBPNsBwvsATNAbAjL7AA1rAQzbAQELEXASuwCc2xJAErsRcQERKxICE5OQCxHBMRErEgIjk5MDEZATQ2MyEyFhURFAYjISImNxQWMyEyNjURNCYjISIGFRMhA%2BulASyl6%2B2j%2FtSl68g7KQH0KTs7Kf4MKTtkAfT6AZABLKXr66X%2B1KLu7T8pOzspAfQpOzsp%2FnABTQACAAAAAAUUBEwABgAaADwAsgcAACuwCM2wAC%2BwAc2wES%2BwEs0BsBsvsAzWsBfNsRwBKwCxCAcRErAFObEBABESsAQ5sBERsAM5MDEZASE1CQE1EzUhMjY1ETQmIyE1ITIWFREUBiMBLAGQ%2FnDIAfQpOzsp%2FgwBkKXr66UBkAEsyP6i%2FqLI%2FnDIOykB9Ck7yOul%2FtSl6wAAAAEA2QACA9YEngAhACgAsA4vsBPNAbAiL7Ac1rAWzbEjASuxFhwRErAZOQCxEw4RErAPOTAxExYzIQIHBh8BMzI3NgAzNicmIwU2Ejc2LwEjIgcOAQAHBtkIFwEumwUFCQkJDgwLAg8BDgkIF%2F7TAZoCAgcJCQ8KBLz%2B80sQAgcT%2FkoUFQsIDw0CaRMREQEEAa8MDwwJEAbT%2FtFWEwAAAAACAAAAAAUUBEwAGAAfAD8AsgMAACuwCM2wCBCwBs2wGS%2BwGs2wEC%2BwEs2wFM0BsCAvsADWsAvNsSEBKwCxGgMRErEdHjk5sBARsBw5MDERFBYzITI3NSEiJjURNDYzITUuAS8BIgYVAREhNQkBNeulASwvNf4MKTs7KQH0DshdXaXrAlgBLAGQ%2FnABkKXrD7k7KQH0KTu5BAcCAuul%2FtQBLMj%2Bov6iyAACAAAAAASwBLAAHQAkAFQAsgMAACuwD82wFi%2BwGs0BsCUvsADWsBLNsBIQsQsBK7AHzbEmASuxCxIRErUYGR4fICQkFzmwBxGwIzkAsRYPERK1CAkeIiMkJBc5sBoRsB85MDERFBYzITI2PQEnBxUUBiMhIiY1ETQ2OwE3JyMiBhUlASchEScB66UBLKPtTno7Kf4MKTs7KZx2SmSl6wHwAWGVAfSV%2FqoBkKXr66ViSXuUKTs7KQH0KTt6TuulCQFWlf4Mlf6fAAMABAAEBKwErAALABMAGwBaALAKL7APzbAbL7AXzbATL7AEzQGwHC%2BwAdawDc2wDRCxFQErsBnNsBkQsREBK7AHzbEdASuxGRURErcECQoODxITAyQXOQCxFxsRErcBBgcMDRARACQXOTAxEhASJCAEEhACBCAkEhAWIDYQJiACNDYyFhQGIgSgARIBRAESoKD%2B7v68%2Fu4W8wFW8%2FP%2BqhdyoHJyoAG2AUQBEqCg%2Fu7%2BvP7uoKACX%2F6q8%2FMBVvP%2BEqBycqByAAAAAwAAAAAETASwAAkAEAAUAC4AsgkAACuwEc2wFC%2BwBc2wCzIBsBUvsBLWsAjNshIICiuzQBIACSuxFgErADAxMRE0NjMhMhYVEQkCIREhEQEzNSMOCwQYCxD8GAG9AcL%2B2f7UAfRkZAETCw4PCv7tAyD%2BDAH0AZD%2BcP12MgAAAAADAAAAAARMBLAACQAQABQAKwCyCQAAK7ARzbAUL7AFzQGwFS%2BwEtawCM2yEggKK7NAEgAJK7EWASsAMDExETQ2MyEyFhURASERIREhCQEzNSMOCwQYCxD8GAEsASwBJ%2F5DAV5kZAETCw4PCv7tArz%2B1AEsAfT75jIAAAAAAwAAAAAETAR%2FAAkADwATAC4AsgkAACuwEM2wEy%2BwBc0BsBQvsBHWsAwysAjNshEICiuzQBEACSuxFQErADAxMRE0NjMhMhYVEQkCJwEnATM1Iw4LBBgLEPwYATECVJr%2BRpYChWRkARMLDg8K%2Fu0Cwf7PAlSb%2FkaX%2FToyAAQAAAAABEwEsAAJAA0AFAAYACsAsgkAACuwFc2wGC%2BwBc0BsBkvsBbWsAjNshYICiuzQBYACSuxGgErADAxMRE0NjMhMhYVEQEXNycDJRMHJwcXATM1Iw4LBBgLEPwYYdRhcAK5A%2FqV1JUBzmRkARMLDg8K%2Fu0D3GLVYfzgAQK775XUlf4NMgAEAAAAAARMBLAACQANABQAGAAuALIJAAArsBXNsBgvsAXNAbAZL7AW1rATMrAIzbIWCAors0AWAAkrsRoBKwAwMTERNDYzITIWFREBFzcnExcHFzcXCwEzNSMOCwQYCxD8fNRi1QPvldSV%2BQFjZGQBEwsODwr%2B7QJk1GHUAev6ldSU7QK5%2B%2BkyAAAAAAIAF%2F%2F%2FBLAErwAFAAgAFwCyBAAAKwGwCS%2BwBdawBs2xCgErADAxEwERCQERFwkBFwSZ%2FiX%2Byk8CoP1gAZ8DEPvJARD%2BdwGgzQOq%2FTgAAAAAAgAAAGQETASwABUAGQBNALARL7AGzbIRBgors0AREwkrsA4ysgYRCiuzQAYECSuwCDIBsBovsADWsBLNsAbNsBIQsQ8BK7ALzbEbASuxDwYRErIJFhc5OTkAMDE1ETQ2OwERIREzFxEUBisBESERIyImATM1Ix0V%2BgH0ZMgeFJb9RJYVHQJYZGSWA%2BgUHv7UASzI%2FK4VHQGQ%2FnAdA2fIAAMAAAA%2BBRQEsAATABkAHQBAALAPL7AGzbIPBgors0APEQkrsgYPCiuzQAYECSuwCDIBsB4vsADWsBDNsAbNsR8BKwCxBg8RErILFxg5OTkwMTURNDY7AREhETMXFQEnByERIyImJTcXARcBAzM1Ix0V%2BgH0ZMj%2B7Hh%2B%2FoaWFR0CRXt4AWF7%2FiXhZGSWA%2BgUHv7UASzI2v7teH%2F%2BcB2xe3gBYHv%2BJAOqyAAAAAADAAAABgUOBLAAEwAXACMAFQABsCQvsADWsBDNsAbNsSUBKwAwMTURNDY7AREhETMXEQcnASERIyImATM1IxM3JzcXNxcHFwcnBx0V%2BgH0ZMhnqv7W%2FreWFR0CWGRkZKqqf6qqf6qqf6qqlgPoFB7%2B1AEsyP7zZ6r%2B1v5wHQNnyPvVqqp%2FqqqAqap%2FqqoAAAADAAAAAASwBLAAEgAZAB0AbACwDi%2BwBs2yDgYKK7NADhAJK7AGELAMzbAaL7AbzbEECDIyAbAeL7AA1rAPzbIPAAors0APCwkrsAAQsAbNsA8QsRoBK7AdzbAMMrEfASuxGgYRErATOQCxDA4RErEXGDk5sRoGERKwCjkwMTURNDY7AREhETMXESEVIREjIiYlCQEjESMRAzUzFR0V%2BgH0ZMj%2BcP4MlhUdAlgBLAEsyMjIZJYD6BQe%2FtQBLMj%2B1Mj%2BcB2r%2FtQBLAEs%2FtQCvMjIAAAAAAMAAAAABLAEsAASABkAHQBbALAOL7AGzbIOBgors0AOEAkrsBovsBvNsQQIMjIBsB4vsADWsA%2FNsAbNsA8QsRoBK7AdzbEfASuxGgYRErATObAdEbANOQCxBg4RErILDBk5OTmwGhGwCjkwMTURNDY7AREhETMXEScBIREjIiYlMxEzETMJATUzFR0V%2BgH0ZMjI%2Ftb%2BbpYVHQJYyMjI%2FtT%2B1GSWA%2BgUHv7UASzI%2Fm7I%2Ftb%2BcB2r%2FtQBLAEsAZDIyAAAAAADAAAAyASwBEwACQATABcAADUUFjMhMjY1ESE1ITU0JiMhIgYVEzUhFR0VBEwVHftQBLAdFfu0FR1kAZD6FR0dFQImZJYVHR0V%2FRLIyAAAAAYAAABmBLAErgAGAAoADgAVABkAHQCBALAFL7EWGjMzsALNsRccMjKwBy%2BxCw8zM7AIzbEMEDIyAbAeL7AH1rAKzbAKELELASuwDs2wDhCxFgErsBnNsR8BK7ELChESswIFBgEkFzmxFg4RErMEAw8QJBc5sBkRsxIUFREkFzkAsQIFERKwADmwBxGxARQ5ObAIErATOTAxEQEVIRUhFQM1MxUzNTMVMzUhNQkBNQM1MxU7ATUjASwBkP5wyGRkZGQBkAEs%2FtRkZGRkZAGQASrGyMYCusjIyMjIxv7W%2FtbG%2FgzIyMgAAAACAGQAAASwBLAAGAAvADoAshQAACsBsDAvsADWsATNsAQQsRcLK7AQzbMJEBcIK7AFzbAFL7AJzbAQELEKCyuwDs2xMQErADAxExE3FxEzETcXETMRNxcRBxEUBisBIiY1ESUUHgIfAREUFjsBMjY1ETQmBwUOARVkMjJkMjJkMjJkHRXIFR0CWBUdHQsKHRXIFR0kGv7sGSUCvAGQZGT%2B1AEsZGT%2B1AEsZGT%2BcMv%2BQRUdHRUBv2QdNSEYBgX%2BcxUdHRUEUh8TEXQRRR8AAAAAAQBkAAAEsARMADMAOACyAAAAK7AMM7AzzbICCw4yMjKwKC%2ByGBwlMzMzsCfNsBoyAbA0L7E1ASsAsSgzERKxBiA5OTAxMyE1IiY1ESERFAYjFSE1Ii4DNRE0Nj8BNSEVMhYVESERNDYzNSEVMh4DFREUBg8BZAGQSxkB9BlLAZAEDiIaFjIZGf5wSxn%2BDBlL%2FnAEDiIaFjIZGTgMJgGK%2FnYmDDg4AQUJFQ4DeBYZAQI4OAwm%2FnYBiiYMODgBBQkVDvyIFhkBAgAGAAAAAARMBEwADwAYABwAIAAqAC4AMgCyGAAAK7AQzbAWL7ASzbISFgors0ASFAkrAbAvL7EwASsAsRIQERKzBAMZHCQXOTAxERQWMyEyNjURNCYjISIGFRMhNzMlESEHIQM1IRUBNSEVASEXFSUzNSEnIQE1JRU7KQEsKTs7Kf7UKTtkAZDIaQEn%2Fldk%2FolkASz%2B1AEs%2FtQBkMgBJ2n%2BV2T%2BiQH0AZABLCk7OykB9Ck7Oyn9RMhi%2FtZkASzIyAEsyMgBkMhiYshk%2FUajhaMAAQAQABAEnwSfACAAABIeAxceAzM%2FATYmLwEmBg8BLgEnNz4BLwEuAQ8BEAEfPpJmZ9GXex8foxEHE8ATNBB2jvxldhEGDosOLRKiA%2BQriY%2FUZmeSPSEBohIuDogOBBF2ZfyOdhExFMITBhGiAAAAAAIAAAAABLAETAAdAEAALwCyGwAAK7AMzbAoL7A4zQGwQS%2BxQgErALEMGxESsSAvOTmwKBGzJikyQCQXOTAxPQE0NjcBNTQ%2BAzIeAh8BFQEeAR0BFAYjISImERQWPwE%2BAT0BNiAXFRQWHwEWNj0BLgQjIg4EDwEVDgFtAhYmUnBSJhYBAQFtDhUdFfu0FB4dFMoUHY0BPo0dFMoUHQYaZHzaflymdWQ%2FLAkJMtQUMw4BLzIEDSAZFRQbHAoKMv7RDjMU1BUdHQKrFRkEIQQiFZIYGJIVIgQhBBkVyAgZQTEpFSEoKCELCgACAGQAAASwBEwAAwAZABQAsgAAACuwAc0BsBovsRsBKwAwMTM1IRUlISc1NxEjFSM1IxUjNSMVIzUjERcVZARM%2B%2F8Dtn1kZGTIZMhkZGRkZMiW%2BmQBkMjIyMjIyP5wZPoAAAAAAwBkAAAEsARMAAkAEwAdACQAsgoAACuwFDMBsB4vsArWsBPNsBMQsRQBK7AdzbEfASsAMDEzIRE0JisBIgYVARE0NjsBMhYVETMRNDY7ATIWFRFkASw7KWQpOwGQOylkKTtkOylkKTsBkCk7Oyn%2BcAPoKTs7KfwYArwpOzsp%2FUQAAAAABf%2BcAAAEsARMAA8AEwAfACcAKwBIALINAAArsBDNsBMvsATNAbAsL7AA1rAQzbAQELERASuwCc2xLQErsREQERK1FBUgIygqJBc5ALETEBEStRQaICYoKSQXOTAxAxE0NjMhMhYVERQGIyEiJjchESETIREjNTM1IREzFSMFMzUzESM1IxMRMxFksHwCvHywsHz9RHywyAOE%2FHxkASzIyP7UyMgBkMhkZMhkZAEsAfR8sLB8%2Fgx8sLAYArz9qAEsZGT%2B1GRkZAEsZP5wASz%2B1AAAAAAF%2F5wAAASwBEwADwATAB8AJwArAEgAsg0AACuwEM2wEy%2BwBM0BsCwvsADWsBDNsBAQsREBK7AJzbEtASuxERARErUUGSAjKCokFzkAsRMQERK1FBogJigpJBc5MDEDETQ2MyEyFhURFAYjISImNyERIRMzNTMVMxEjFSM1IwEzNTMRIzUjExEzEWSwfAK8fLCwfP1EfLDIA4T8fGRkZGRkZGQBkMhkZMhkZAEsAfR8sLB8%2Fgx8sLAYArz9qMjIAfTIyP4MZAEsZP5wASz%2B1AAABP%2BcAAAEsARMAA8AEwAbACMARACyDQAAK7AQzbATL7AEzQGwJC%2BwANawEM2wEBCxEQErsAnNsSUBK7EREBESsxQVHB0kFzkAsRMQERKzFBocIiQXOTAxAxE0NjMhMhYVERQGIyEiJjchESETITUjETM1IQEhNSMRMzUhZLB8Arx8sLB8%2FUR8sMgDhPx8ZAEsyMj%2B1AGQASzIyP7UASwB9HywsHz%2BDHywsBgCvP2oZAEsZP4MZAEsZAAAAAAE%2F5wAAASwBEwADwATABYAGQBEALINAAArsBDNsBMvsATNAbAaL7AA1rAQzbAQELERASuwCc2xGwErsREQERKzFBUXGCQXOQCxExARErMVFhcZJBc5MDEDETQ2MyEyFhURFAYjISImNyERIRMFERMtAWSwfAK8fLCwfP1EfLDIA4T8fGQBLGQBLP7UASwB9HywsHz%2BDHywsBgCvP6ilgEs%2FtSWlgAAAAAF%2F5wAAASwBEwADwATABcAHwAnAFoAsg0AACuwEM2wFC%2BwGM2wIzKwHy%2BwJTOwFc2wEy%2BwBM0BsCgvsADWsBDNsBAQsRQBK7AYzbAYELEcASuwIc2wIRCxJAErsBfNsBcQsREBK7AJzbEpASsAMDEDETQ2MyEyFhURFAYjISImNyERIRMRIRElMzI2NCYrAQQUFjsBESMiZLB8Arx8sLB8%2FUR8sMgDhPx8ZAK8%2FaiCKTY5JoIBEzYpgoImASwB9HywsHz%2BDHywsBgCvP2oAfT%2BDGRUglZWglQBLAAABf%2BcAAAEsARMAA8AEwAfACMAKQBIALINAAArsBDNsBMvsATNAbAqL7AA1rAQzbAQELERASuwCc2xKwErsREQERK1FBUgISQnJBc5ALETEBEStRQaICImKCQXOTAxAxE0NjMhMhYVERQGIyEiJjchESETIREjNTM1IREzFSMFMzUjEzMRMxEjZLB8Arx8sLB8%2FUR8sMgDhPx8ZAEsyMj%2B1MjIAZFkZGNkZMgBLAH0fLCwfP4MfLCwGAK8%2FagBLGRk%2FtRkZGQBLP5wAfQABv%2BcAAAEsARMAA8AEwAZAB0AIQAnAEwAsg0AACuwEM2wEy%2BwBM0BsCgvsADWsBDNsBAQsREBK7AJzbEpASuxERARErcUFRocHh8iJSQXOQCxExARErcUGBobHiAkJiQXOTAxAxE0NjMhMhYVERQGIyEiJjchESETIREjNSMTNTMVFzM1IxMzETMRI2SwfAK8fLCwfP1EfLDIA4T8fGQBLMhkZWTIZGRjZGTIASwB9HywsHz%2BDHywsBgCvP2oAZBk%2FnDIyGRkASz%2BcAH0AAAAAAb%2FnAAABLAETAAPABMAHQAhACUAKwCbALINAAArsBDNsB4vsSIpMzOwH82wIzKwGi%2BwG82wFC%2BwJjOwFc2wJzKwEy%2BwBM0BsCwvsADWsBDNsBAQsR4BK7AUMrAhzbAhELEcASuwF82zGRccCCuwGs2wGi%2BwGc2wFxCxIgErsCXNsCUQsSoBK7ApzbApELAmzbAmL7ApELERASuwCc2xLQErALEbHxESsBc5sBQRsBg5MDEDETQ2MyEyFhURFAYjISImNyERIRc1IREjFSM1MzUDNTMVITUzFQM1MxEjEWSwfAK8fLCwfP1EfLDIA4T8fGQBLGNkY8dkASxkAchkASwB9HywsHz%2BDHywsBgCvMhk%2FtRkZMj%2BcGRkZGQBkGT%2BDAGQAAADAAQABASsBKwACwATAB0AeQCwCi%2BwD82wHS%2BwGs2wGS%2BwFs2wEy%2BwBM0BsB4vsAHWsA3NsA0QsRQBK7AazbAaELERASuwB82xHwErsRoUERK1Cg4TAxYdJBc5sBERtQkPBBIXGyQXOQCxGh0RErQHDRAAFCQXObAZEbAVObAWErMGDBEBJBc5MDESEBIkIAQSEAIEICQSEBYgNhAmIAM1NyEVIRUhFSEEoAESAUQBEqCg%2Fu7%2BvP7uFvMBVvPz%2FqodZAEs%2FtQBLP7UAbYBRAESoKD%2B7v68%2Fu6goAJf%2Fqrz8wFW8%2F3%2ByGRkyGQAAAQAAAAEBKgErAALABMAIAAkAKAAsAovsA%2FNsCEvsBQzsCLNsBsvsBXNsBMvsATNAbAlL7AB1rANzbANELEUASuwIM2wGzKyIBQKK7NAIB4JK7AgELEhASuwGTKwJM2wFzKwJBCxEQErsAfNsSYBK7EgFBESswoOEwMkFzmwIRGwFjmwJBKzCQ8SBCQXOQCxIiERErQHDRAAHiQXObAbEbIXGB85OTmwFRKzBgwRASQXOTAxGAESJCAEEhACBCAkEhAWIDYQJiADESEXFSM1IxUzFSMVMzUzFaABEgFEARKgoP7u%2Frz%2B7hbzAVbz8%2F6qGQEsZGTIyMjIZAG2AUQBEqCg%2Fu7%2BvP7uoKACX%2F6q8%2FMBVvP9mgGQZGRkZGRkZGQA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%2F4WwAY0AS7AIUFixAQGOWbFGBitYIbAQWUuwFFJYIbCAWR2wBitcWFmwFCsAAAABUuZYrgAA%29%20format%28%27truetype%27%29%2Curl%28data%3Aimage%2Fsvg%2Bxml%3Bbase64%2CPD94bWwgdmVyc2lvbj0iMS4wIiBzdGFuZGFsb25lPSJubyI%2FPgo8IURPQ1RZUEUgc3ZnIFBVQkxJQyAiLS8vVzNDLy9EVEQgU1ZHIDEuMS8vRU4iICJodHRwOi8vd3d3LnczLm9yZy9HcmFwaGljcy9TVkcvMS4xL0RURC9zdmcxMS5kdGQiID4KPHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPgo8bWV0YWRhdGE%2BPC9tZXRhZGF0YT4KPGRlZnM%2BCjxmb250IGlkPSJnbHlwaGljb25zX2hhbGZsaW5nc3JlZ3VsYXIiIGhvcml6LWFkdi14PSIxMjAwIiA%2BCjxmb250LWZhY2UgdW5pdHMtcGVyLWVtPSIxMjAwIiBhc2NlbnQ9Ijk2MCIgZGVzY2VudD0iLTI0MCIgLz4KPG1pc3NpbmctZ2x5cGggaG9yaXotYWR2LXg9IjUwMCIgLz4KPGdseXBoIC8%2BCjxnbHlwaCAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZDsiIC8%2BCjxnbHlwaCB1bmljb2RlPSIgIiAvPgo8Z2x5cGggdW5pY29kZT0iKiIgZD0iTTEwMCA1MDB2MjAwaDI1OWwtMTgzIDE4M2wxNDEgMTQxbDE4MyAtMTgzdjI1OWgyMDB2LTI1OWwxODMgMTgzbDE0MSAtMTQxbC0xODMgLTE4M2gyNTl2LTIwMGgtMjU5bDE4MyAtMTgzbC0xNDEgLTE0MWwtMTgzIDE4M3YtMjU5aC0yMDB2MjU5bC0xODMgLTE4M2wtMTQxIDE0MWwxODMgMTgzaC0yNTl6IiAvPgo8Z2x5cGggdW5pY29kZT0iKyIgZD0iTTAgNDAwdjMwMGg0MDB2NDAwaDMwMHYtNDAwaDQwMHYtMzAwaC00MDB2LTQwMGgtMzAwdjQwMGgtNDAweiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGEwOyIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeDIwMDA7IiBob3Jpei1hZHYteD0iNjUyIiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4MjAwMTsiIGhvcml6LWFkdi14PSIxMzA0IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4MjAwMjsiIGhvcml6LWFkdi14PSI2NTIiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3gyMDAzOyIgaG9yaXotYWR2LXg9IjEzMDQiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3gyMDA0OyIgaG9yaXotYWR2LXg9IjQzNCIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeDIwMDU7IiBob3Jpei1hZHYteD0iMzI2IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4MjAwNjsiIGhvcml6LWFkdi14PSIyMTciIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3gyMDA3OyIgaG9yaXotYWR2LXg9IjIxNyIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeDIwMDg7IiBob3Jpei1hZHYteD0iMTYzIiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4MjAwOTsiIGhvcml6LWFkdi14PSIyNjAiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3gyMDBhOyIgaG9yaXotYWR2LXg9IjcyIiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4MjAyZjsiIGhvcml6LWFkdi14PSIyNjAiIC8%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%2BCjxnbHlwaCB1bmljb2RlPSImI3gyMjEyOyIgZD0iTTIwMCA0MDBoOTAwdjMwMGgtOTAwdi0zMDB6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4MjVmYzsiIGhvcml6LWFkdi14PSI1MDAiIGQ9Ik0wIDB6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4MjYwMTsiIGQ9Ik0tMTQgNDk0cTAgLTgwIDU2LjUgLTEzN3QxMzUuNSAtNTdoNzUwcTEyMCAwIDIwNSA4Ni41dDg1IDIwNy41dC04NSAyMDd0LTIwNSA4NnEtNDYgMCAtOTAgLTE0cS00NCA5NyAtMTM0LjUgMTU2LjV0LTIwMC41IDU5LjVxLTE1MiAwIC0yNjAgLTEwNy41dC0xMDggLTI2MC41cTAgLTI1IDIgLTM3cS02NiAtMTQgLTEwOC41IC02Ny41dC00Mi41IC0xMjIuNXoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3gyNzA5OyIgZD0iTTAgMTAwbDQwMCA0MDBsMjAwIC0yMDBsMjAwIDIwMGw0MDAgLTQwMGgtMTIwMHpNMCAzMDB2NjAwbDMwMCAtMzAwek0wIDExMDBsNjAwIC02MDNsNjAwIDYwM2gtMTIwMHpNOTAwIDYwMGwzMDAgMzAwdi02MDB6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4MjcwZjsiIGQ9Ik0tMTMgLTEzbDMzMyAxMTJsLTIyMyAyMjN6TTE4NyA0MDNsMjE0IC0yMTRsNjE0IDYxNGwtMjE0IDIxNHpNODg3IDExMDNsMjE0IC0yMTRsOTkgOTJxMTMgMTMgMTMgMzIuNXQtMTMgMzMuNWwtMTUzIDE1M3EtMTUgMTMgLTMzIDEzdC0zMyAtMTN6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTAwMTsiIGQ9Ik0wIDEyMDBoMTIwMGwtNTAwIC01NTB2LTU1MGgzMDB2LTEwMGgtODAwdjEwMGgzMDB2NTUweiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUwMDI7IiBkPSJNMTQgODRxMTggLTU1IDg2IC03NS41dDE0NyA1LjVxNjUgMjEgMTA5IDY5dDQ0IDkwdjYwNmw2MDAgMTU1di01MjFxLTY0IDE2IC0xMzggLTdxLTc5IC0yNiAtMTIyLjUgLTgzdC0yNS41IC0xMTFxMTggLTU1IDg2IC03NS41dDE0NyA0LjVxNzAgMjMgMTExLjUgNjMuNXQ0MS41IDk1LjV2ODgxcTAgMTAgLTcgMTUuNXQtMTcgMi41bC03NTIgLTE5M3EtMTAgLTMgLTE3IC0xMi41dC03IC0xOS41di02ODlxLTY0IDE3IC0xMzggLTcgcS03OSAtMjUgLTEyMi41IC04MnQtMjUuNSAtMTEyeiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUwMDM7IiBkPSJNMjMgNjkzcTAgMjAwIDE0MiAzNDJ0MzQyIDE0MnQzNDIgLTE0MnQxNDIgLTM0MnEwIC0xNDIgLTc4IC0yNjFsMzAwIC0zMDBxNyAtOCA3IC0xOHQtNyAtMThsLTEwOSAtMTA5cS04IC03IC0xOCAtN3QtMTggN2wtMzAwIDMwMHEtMTE5IC03OCAtMjYxIC03OHEtMjAwIDAgLTM0MiAxNDJ0LTE0MiAzNDJ6TTE3NiA2OTNxMCAtMTM2IDk3IC0yMzN0MjM0IC05N3QyMzMuNSA5Ni41dDk2LjUgMjMzLjV0LTk2LjUgMjMzLjV0LTIzMy41IDk2LjUgdC0yMzQgLTk3dC05NyAtMjMzeiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUwMDU7IiBkPSJNMTAwIDc4NHEwIDY0IDI4IDEyM3Q3MyAxMDAuNXQxMDQuNSA2NHQxMTkgMjAuNXQxMjAgLTM4LjV0MTA0LjUgLTEwNC41cTQ4IDY5IDEwOS41IDEwNXQxMjEuNSAzOHQxMTguNSAtMjAuNXQxMDIuNSAtNjR0NzEgLTEwMC41dDI3IC0xMjNxMCAtNTcgLTMzLjUgLTExNy41dC05NCAtMTI0LjV0LTEyNi41IC0xMjcuNXQtMTUwIC0xNTIuNXQtMTQ2IC0xNzRxLTYyIDg1IC0xNDUuNSAxNzR0LTE0OS41IDE1Mi41dC0xMjYuNSAxMjcuNSB0LTk0IDEyNC41dC0zMy41IDExNy41eiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUwMDY7IiBkPSJNLTcyIDgwMGg0NzlsMTQ2IDQwMGgybDE0NiAtNDAwaDQ3MmwtMzgyIC0yNzhsMTQ1IC00NDlsLTM4NCAyNzVsLTM4MiAtMjc1bDE0NiA0NDd6TTE2OCA3MWwyIDF6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTAwNzsiIGQ9Ik0tNzIgODAwaDQ3OWwxNDYgNDAwaDJsMTQ2IC00MDBoNDcybC0zODIgLTI3OGwxNDUgLTQ0OWwtMzg0IDI3NWwtMzgyIC0yNzVsMTQ2IDQ0N3pNMTY4IDcxbDIgMXpNMjM3IDcwMGwxOTYgLTE0MmwtNzMgLTIyNmwxOTIgMTQwbDE5NSAtMTQxbC03NCAyMjlsMTkzIDE0MGgtMjM1bC03NyAyMTFsLTc4IC0yMTFoLTIzOXoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDA4OyIgZD0iTTAgMHYxNDNsNDAwIDI1N3YxMDBxLTM3IDAgLTY4LjUgNzQuNXQtMzEuNSAxMjUuNXYyMDBxMCAxMjQgODggMjEydDIxMiA4OHQyMTIgLTg4dDg4IC0yMTJ2LTIwMHEwIC01MSAtMzEuNSAtMTI1LjV0LTY4LjUgLTc0LjV2LTEwMGw0MDAgLTI1N3YtMTQzaC0xMjAweiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUwMDk7IiBkPSJNMCAwdjExMDBoMTIwMHYtMTEwMGgtMTIwMHpNMTAwIDEwMGgxMDB2MTAwaC0xMDB2LTEwMHpNMTAwIDMwMGgxMDB2MTAwaC0xMDB2LTEwMHpNMTAwIDUwMGgxMDB2MTAwaC0xMDB2LTEwMHpNMTAwIDcwMGgxMDB2MTAwaC0xMDB2LTEwMHpNMTAwIDkwMGgxMDB2MTAwaC0xMDB2LTEwMHpNMzAwIDEwMGg2MDB2NDAwaC02MDB2LTQwMHpNMzAwIDYwMGg2MDB2NDAwaC02MDB2LTQwMHpNMTAwMCAxMDBoMTAwdjEwMGgtMTAwdi0xMDB6IE0xMDAwIDMwMGgxMDB2MTAwaC0xMDB2LTEwMHpNMTAwMCA1MDBoMTAwdjEwMGgtMTAwdi0xMDB6TTEwMDAgNzAwaDEwMHYxMDBoLTEwMHYtMTAwek0xMDAwIDkwMGgxMDB2MTAwaC0xMDB2LTEwMHoiIC8%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDEzOyIgZD0iTTI5IDQ1NGw0MTkgLTQyMGw4MTggODIwbC0yMTIgMjEybC02MDcgLTYwN2wtMjA2IDIwN3oiIC8%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%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDI3OyIgZD0iTTQgNjAwcTAgMTYyIDgwIDI5OXQyMTcgMjE3dDI5OSA4MHQyOTkgLTgwdDIxNyAtMjE3dDgwIC0yOTl0LTgwIC0yOTl0LTIxNyAtMjE3dC0yOTkgLTgwdC0yOTkgODB0LTIxNyAyMTd0LTgwIDI5OXpNMTg2IDYwMHEwIC0xNzEgMTIxLjUgLTI5Mi41dDI5Mi41IC0xMjEuNXQyOTIuNSAxMjEuNXQxMjEuNSAyOTIuNXQtMTIxLjUgMjkyLjV0LTI5Mi41IDEyMS41dC0yOTIuNSAtMTIxLjV0LTEyMS41IC0yOTIuNXpNMzUwIDYwMGwyNTAgMzAwIGwyNTAgLTMwMGgtMTUwdi0zMDBoLTIwMHYzMDBoLTE1MHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDI4OyIgZD0iTTAgMjV2NDc1bDIwMCA3MDBoODAwbDE5OSAtNzAwbDEgLTQ3NXEwIC0xMSAtNyAtMTh0LTE4IC03aC0xMTUwcS0xMSAwIC0xOCA3dC03IDE4ek0yMDAgNTAwaDIwMGw1MCAtMjAwaDMwMGw1MCAyMDBoMjAwbC05NyA1MDBoLTYwNnoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDI5OyIgZD0iTTQgNjAwcTAgMTYyIDgwIDI5OXQyMTcgMjE3dDI5OSA4MHQyOTkgLTgwdDIxNyAtMjE3dDgwIC0yOTl0LTgwIC0yOTl0LTIxNyAtMjE3dC0yOTkgLTgwdC0yOTkgODB0LTIxNyAyMTd0LTgwIDI5OXpNMTg2IDYwMHEwIC0xNzIgMTIxLjUgLTI5M3QyOTIuNSAtMTIxdDI5Mi41IDEyMXQxMjEuNSAyOTNxMCAxNzEgLTEyMS41IDI5Mi41dC0yOTIuNSAxMjEuNXQtMjkyLjUgLTEyMS41dC0xMjEuNSAtMjkyLjV6TTUwMCAzOTd2NDAxIGwyOTcgLTIwMHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDMwOyIgZD0iTTIzIDYwMHEwIC0xMTggNDUuNSAtMjI0LjV0MTIzIC0xODR0MTg0IC0xMjN0MjI0LjUgLTQ1LjV0MjI0LjUgNDUuNXQxODQgMTIzdDEyMyAxODR0NDUuNSAyMjQuNWgtMTUwcTAgLTE3NyAtMTI1IC0zMDJ0LTMwMiAtMTI1dC0zMDIgMTI1dC0xMjUgMzAydDEyNSAzMDJ0MzAyIDEyNXExMzYgMCAyNDYgLTgxbC0xNDYgLTE0Nmg0MDB2NDAwbC0xNDUgLTE0NXEtMTU3IDEyMiAtMzU1IDEyMnEtMTE4IDAgLTIyNC41IC00NS41dC0xODQgLTEyMyB0LTEyMyAtMTg0dC00NS41IC0yMjQuNXoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDMxOyIgZD0iTTIzIDYwMHEwIDExOCA0NS41IDIyNC41dDEyMyAxODR0MTg0IDEyM3QyMjQuNSA0NS41cTE5OCAwIDM1NSAtMTIybDE0NSAxNDV2LTQwMGgtNDAwbDE0NyAxNDdxLTExMiA4MCAtMjQ3IDgwcS0xNzcgMCAtMzAyIC0xMjV0LTEyNSAtMzAyaC0xNTB6TTEwMCAwdjQwMGg0MDBsLTE0NyAtMTQ3cTExMiAtODAgMjQ3IC04MHExNzcgMCAzMDIgMTI1dDEyNSAzMDJoMTUwcTAgLTExOCAtNDUuNSAtMjI0LjV0LTEyMyAtMTg0dC0xODQgLTEyMyB0LTIyNC41IC00NS41cS0xOTggMCAtMzU1IDEyMnoiIC8%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%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%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%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%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%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDU5OyIgZD0iTTAgMjc1djY1MHEwIDMxIDIyIDUzdDUzIDIyaDc1MHEzMSAwIDUzIC0yMnQyMiAtNTN2LTY1MHEwIC0zMSAtMjIgLTUzdC01MyAtMjJoLTc1MHEtMzEgMCAtNTMgMjJ0LTIyIDUzek05MDAgNjAwbDMwMCAzMDB2LTYwMHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDYwOyIgZD0iTTAgNDR2MTAxMnEwIDE4IDEzIDMxdDMxIDEzaDExMTJxMTkgMCAzMS41IC0xM3QxMi41IC0zMXYtMTAxMnEwIC0xOCAtMTIuNSAtMzF0LTMxLjUgLTEzaC0xMTEycS0xOCAwIC0zMSAxM3QtMTMgMzF6TTEwMCAyNjNsMjQ3IDE4MmwyOTggLTEzMWwtNzQgMTU2bDI5MyAzMThsMjM2IC0yODh2NTAwaC0xMDAwdi03Mzd6TTIwOCA3NTBxMCA1NiAzOSA5NXQ5NSAzOXQ5NSAtMzl0MzkgLTk1dC0zOSAtOTV0LTk1IC0zOXQtOTUgMzl0LTM5IDk1eiAiIC8%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDcxOyIgZD0iTTEzNiA1NTBsNTY0IDU1MHYtNDg3bDUwMCA0ODd2LTExMDBsLTUwMCA0ODh2LTQ4OHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDcyOyIgZD0iTTIwMCAwbDkwMCA1NTBsLTkwMCA1NTB2LTExMDB6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTA3MzsiIGQ9Ik0yMDAgMTUwcTAgLTIxIDE0LjUgLTM1LjV0MzUuNSAtMTQuNWgyMDBxMjEgMCAzNS41IDE0LjV0MTQuNSAzNS41djgwMHEwIDIxIC0xNC41IDM1LjV0LTM1LjUgMTQuNWgtMjAwcS0yMSAwIC0zNS41IC0xNC41dC0xNC41IC0zNS41di04MDB6TTYwMCAxNTBxMCAtMjEgMTQuNSAtMzUuNXQzNS41IC0xNC41aDIwMHEyMSAwIDM1LjUgMTQuNXQxNC41IDM1LjV2ODAwcTAgMjEgLTE0LjUgMzUuNXQtMzUuNSAxNC41aC0yMDAgcS0yMSAwIC0zNS41IC0xNC41dC0xNC41IC0zNS41di04MDB6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTA3NDsiIGQ9Ik0yMDAgMTUwcTAgLTIwIDE0LjUgLTM1dDM1LjUgLTE1aDgwMHEyMSAwIDM1LjUgMTV0MTQuNSAzNXY4MDBxMCAyMSAtMTQuNSAzNS41dC0zNS41IDE0LjVoLTgwMHEtMjEgMCAtMzUuNSAtMTQuNXQtMTQuNSAtMzUuNXYtODAweiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUwNzU7IiBkPSJNMCAwdjExMDBsNTAwIC00ODd2NDg3bDU2NCAtNTUwbC01NjQgLTU1MHY0ODh6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTA3NjsiIGQ9Ik0wIDB2MTEwMGw1MDAgLTQ4N3Y0ODdsNTAwIC00ODd2NDM3cTAgMjEgMTQuNSAzNS41dDM1LjUgMTQuNWgxMDBxMjEgMCAzNS41IC0xNC41dDE0LjUgLTM1LjV2LTEwMDBxMCAtMjEgLTE0LjUgLTM1LjV0LTM1LjUgLTE0LjVoLTEwMHEtMjEgMCAtMzUuNSAxNC41dC0xNC41IDM1LjV2NDM4bC01MDAgLTQ4OHY0ODh6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTA3NzsiIGQ9Ik0zMDAgMHYxMTAwbDUwMCAtNDg3djQzN3EwIDIxIDE0LjUgMzUuNXQzNS41IDE0LjVoMTAwcTIxIDAgMzUuNSAtMTQuNXQxNC41IC0zNS41di0xMDAwcTAgLTIxIC0xNC41IC0zNS41dC0zNS41IC0xNC41aC0xMDBxLTIxIDAgLTM1LjUgMTQuNXQtMTQuNSAzNS41djQzOHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDc4OyIgZD0iTTEwMCAyNTB2MTAwcTAgMjEgMTQuNSAzNS41dDM1LjUgMTQuNWgxMDAwcTIxIDAgMzUuNSAtMTQuNXQxNC41IC0zNS41di0xMDBxMCAtMjEgLTE0LjUgLTM1LjV0LTM1LjUgLTE0LjVoLTEwMDBxLTIxIDAgLTM1LjUgMTQuNXQtMTQuNSAzNS41ek0xMDAgNTAwaDExMDBsLTU1MCA1NjR6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTA3OTsiIGQ9Ik0xODUgNTk5bDU5MiAtNTkybDI0MCAyNDBsLTM1MyAzNTNsMzUzIDM1M2wtMjQwIDI0MHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDgwOyIgZD0iTTI3MiAxOTRsMzUzIDM1M2wtMzUzIDM1M2wyNDEgMjQwbDU3MiAtNTcxbDIxIC0yMmwtMSAtMXYtMWwtNTkyIC01OTF6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTA4MTsiIGQ9Ik0zIDYwMHEwIDE2MiA4MCAyOTkuNXQyMTcuNSAyMTcuNXQyOTkuNSA4MHQyOTkuNSAtODB0MjE3LjUgLTIxNy41dDgwIC0yOTkuNXQtODAgLTI5OS41dC0yMTcuNSAtMjE3LjV0LTI5OS41IC04MHQtMjk5LjUgODB0LTIxNy41IDIxNy41dC04MCAyOTkuNXpNMzAwIDUwMGgyMDB2LTIwMGgyMDB2MjAwaDIwMHYyMDBoLTIwMHYyMDBoLTIwMHYtMjAwaC0yMDB2LTIwMHoiIC8%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDkxOyIgZD0iTTAgNTQ3bDYwMCA0NTN2LTMwMGg2MDB2LTMwMGgtNjAwdi0zMDF6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTA5MjsiIGQ9Ik0wIDQwMHYzMDBoNjAwdjMwMGw2MDAgLTQ1M2wtNjAwIC00NDh2MzAxaC02MDB6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTA5MzsiIGQ9Ik0yMDQgNjAwbDQ1MCA2MDBsNDQ0IC02MDBoLTI5OHYtNjAwaC0zMDB2NjAwaC0yOTZ6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTA5NDsiIGQ9Ik0xMDQgNjAwaDI5NnY2MDBoMzAwdi02MDBoMjk4bC00NDkgLTYwMHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDk1OyIgZD0iTTAgMjAwcTYgMTMyIDQxIDIzOC41dDEwMy41IDE5M3QxODQgMTM4dDI3MS41IDU5LjV2MjcxbDYwMCAtNDUzbC02MDAgLTQ0OHYzMDFxLTk1IC0yIC0xODMgLTIwdC0xNzAgLTUydC0xNDcgLTkyLjV0LTEwMCAtMTM1LjV6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTA5NjsiIGQ9Ik0wIDB2NDAwbDEyOSAtMTI5bDI5NCAyOTRsMTQyIC0xNDJsLTI5NCAtMjk0bDEyOSAtMTI5aC00MDB6TTYzNSA3NzdsMTQyIC0xNDJsMjk0IDI5NGwxMjkgLTEyOXY0MDBoLTQwMGwxMjkgLTEyOXoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDk3OyIgZD0iTTM0IDE3NmwyOTUgMjk1bC0xMjkgMTI5aDQwMHYtNDAwbC0xMjkgMTMwbC0yOTUgLTI5NXpNNjAwIDYwMHY0MDBsMTI5IC0xMjlsMjk1IDI5NWwxNDIgLTE0MWwtMjk1IC0yOTVsMTI5IC0xMzBoLTQwMHoiIC8%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%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%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%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%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%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%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%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTUwOyIgZD0iTTIgMzAwbDI5OCAtMzAwbDI5OCAzMDBoLTE5OHY5MDBoLTIwMHYtOTAwaC0xOTh6TTYwMiA5MDBsMjk4IDMwMGwyOTggLTMwMGgtMTk4di05MDBoLTIwMHY5MDBoLTE5OHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTUxOyIgZD0iTTIgMzAwaDE5OHY5MDBoMjAwdi05MDBoMTk4bC0yOTggLTMwMHpNNzAwIDB2MjAwaDEwMHYtMTAwaDIwMHYtMTAwaC0zMDB6TTcwMCA0MDB2MTAwaDMwMHYtMjAwaC05OXYtMTAwaC0xMDB2MTAwaDk5djEwMGgtMjAwek03MDAgNzAwdjUwMGgzMDB2LTUwMGgtMTAwdjEwMGgtMTAwdi0xMDBoLTEwMHpNODAxIDkwMGgxMDB2MjAwaC0xMDB2LTIwMHoiIC8%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTU0OyIgZD0iTTIgMzAwbDI5OCAtMzAwbDI5OCAzMDBoLTE5OHY5MDBoLTIwMHYtOTAwaC0xOTh6TTgwMCA0MDB2MTAwaDIwMHYtNTAwaC0xMDB2NDAwaC0xMDB6TTgwMCA4MDB2NDAwaDMwMHYtNTAwaC0xMDB2MTAwaC0yMDB6TTkwMSA5MDBoMTAwdjIwMGgtMTAwdi0yMDB6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTE1NTsiIGQ9Ik0yIDMwMGwyOTggLTMwMGwyOTggMzAwaC0xOTh2OTAwaC0yMDB2LTkwMGgtMTk4ek03MDAgMTAwdjIwMGg1MDB2LTIwMGgtNTAwek03MDAgNDAwdjIwMGg0MDB2LTIwMGgtNDAwek03MDAgNzAwdjIwMGgzMDB2LTIwMGgtMzAwek03MDAgMTAwMHYyMDBoMjAwdi0yMDBoLTIwMHoiIC8%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTY3OyIgZD0iTTAgMHYyNzVxMCAxMSA3IDE4dDE4IDdoMTA0OHExMSAwIDE5IC03LjV0OCAtMTcuNXYtMjc1aC0xMTAwek0xMDAgNzAwaDMwMHYtMzAwaDMwMHYzMDBoMjk1bC00NDUgNTAwek05MDAgMTUwaDEwMHY1MGgtMTAwdi01MHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTY4OyIgZD0iTTAgMHYyNzVxMCAxMSA3IDE4dDE4IDdoMTA0OHExMSAwIDE5IC03LjV0OCAtMTcuNXYtMjc1aC0xMTAwek0xMDAgNzA1bDMwNSAtMzA1bDU5NiA1OTZsLTE1NCAxNTVsLTQ0MiAtNDQybC0xNTAgMTUxek05MDAgMTUwaDEwMHY1MGgtMTAwdi01MHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTY5OyIgZD0iTTAgMHYyNzVxMCAxMSA3IDE4dDE4IDdoMTA0OHExMSAwIDE5IC03LjV0OCAtMTcuNXYtMjc1aC0xMTAwek0xMDAgOTg4bDk3IC05OGwyMTIgMjEzbC05NyA5N3pNMjAwIDQwMGw2OTcgMWwzIDY5OWwtMjUwIC0yMzlsLTE0OSAxNDlsLTIxMiAtMjEybDE0OSAtMTQ5ek05MDAgMTUwaDEwMHY1MGgtMTAwdi01MHoiIC8%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTczOyIgZD0iTTAgMTUwdjEwMDBxMCAyMCAxNC41IDM1dDM1LjUgMTVoMjUwdi0zMDBoNTAwdjMwMGgxMDBsMjAwIC0yMDB2LTIxOGwtMjc2IC0yNzVsLTEyMCAxMjBsLTEyNiAtMTI3aC0zNzh2LTQwMGgtMTUwcS0yMSAwIC0zNS41IDE0LjV0LTE0LjUgMzUuNXpNNTgxIDMwNmwxMjMgMTIzbDEyMCAtMTIwbDM1MyAzNTJsMTIzIC0xMjNsLTQ3NSAtNDc2ek02MDAgMTAwMGgxMDB2MjAwaC0xMDB2LTIwMHoiIC8%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTg0OyIgZD0iTTEwMCAwdjEwMGgxMTAwdi0xMDBoLTExMDB6TTE3NSAyMDBoOTUwbC0xMjUgMTUwdjI1MGwxMDAgMTAwdjQwMGgtMTAwdi0yMDBoLTEwMHYyMDBoLTIwMHYtMjAwaC0xMDB2MjAwaC0yMDB2LTIwMGgtMTAwdjIwMGgtMTAwdi00MDBsMTAwIC0xMDB2LTI1MHoiIC8%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTg4OyIgZD0iTS0xMDAgMzAwdjUwMHEwIDEyNCA4OCAyMTJ0MjEyIDg4aDcwMHExMjQgMCAyMTIgLTg4dDg4IC0yMTJ2LTUwMHEwIC0xMjQgLTg4IC0yMTJ0LTIxMiAtODhoLTcwMHEtMTI0IDAgLTIxMiA4OHQtODggMjEyek0xMDAgMjAwaDkwMHY3MDBoLTkwMHYtNzAwek0yMDAgMzAwaDMwMHYxMDBoLTIwMHYzMDBoMjAwdjEwMGgtMzAwdi01MDB6TTYwMCAzMDBoMzAwdjEwMGgtMjAwdjMwMGgyMDB2MTAwaC0zMDB2LTUwMHoiIC8%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%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type="text/css"> pre:not([class]) { background-color: white; } </style><script type="text/javascript">if (window.hljs && document.readyState && document.readyState === "complete") { window.setTimeout(function() { hljs.initHighlighting(); }, 0); } </script> </head> <body> <style type="text/css">.main-container { max-width: 940px; margin-left: auto; margin-right: auto; } code { color: inherit; background-color: rgba(0, 0, 0, 0.04); } img { max-width:100%; height: auto; } </style><div class="container-fluid main-container"> <p>As the 2016 Rio Olympics draw to a close, much of the <a href="http://www.bbc.co.uk/sport/olympics/37085511">media coverage</a> here in the UK focuses on how many medals Team GB has won, and how this <a href="https://www.theguardian.com/sport/2016/aug/21/great-britain-team-gb-second-rio-2016-olympic-medal-table">compares to other countries and to previous Olympics</a>. Team GB has done particularly well this year, rising to 2nd in the medal table (as of Sunday afternoon) and increasing the number of medals won compared to London - the first time a host country has improved its medal haul in the subsequent Olympics.</p><p>The medal table has become an increasingly prominent feature of the Olympics (at least in the UK). Many people have pointed out an simple flaw in looking at a country’s position in the table as a measure of its sporting ‘quality’ (whatever that means): larger countries win more medals, simply by having more people. The USA, China and in the past the Soviet Union have been large countries dominating the upper echelons of the table. The obvious way to compare countries ‘fairly’ is to look at a per capita medal table. <a href="http://www.medalspercapita.com">One website</a> that has done this places the Bahamas at the top of its list of per capita gold medals. On the one hand correcting for population size in this way seems like a sensible thing to do if you want to know whether a country performed well for its size or not. But I can’t help noticing that of the top 10 countries in this list, none has a population onf more than 10m people, and two have populations below 1m. A single gold medal in the Bahamas puts them top of the list. This suggests to me that places at the top of the per capita table are likely to be the result of statistical noise - whichever of the many small countries compteting manages to win one gold tops the table.</p><p>A more robust solution is to treat the medal table as a statistical sample that is generated from the underlying sporting quality of each country, and to try to infer this quality from the data that we observe. To do this we can use <a href="https://en.wikipedia.org/wiki/Bayesian_inference">Bayesian inference</a>. Let the quality of a country in Olympic sport be represented by a single number, <span class="math">\(q\)</span>, such that the expected number of gold medals that country will win is <span class="math">\(qN\)</span>, with <span class="math">\(N\)</span> being the population of the country (I’ll ignore complications about differing proportions of athlete-age population). Bayes’ rule tells us that our belief about the quality of a country should be represented by a probability distribution that combines our prior beliefs about <span class="math">\(q\)</span>, <span class="math">\(P(q)\)</span> and the likelihood of observing the medals we saw given a specific value of q, <span class="math">\(P(\textrm{# Golds = g} \mid q)\)</span>: <span class="math">\[ P(q \mid \textrm{# Golds = g}) \propto P(q)P(\textrm{# Golds = g} \mid q) \]</span> The likelihood is easy to define. Given that gaining a gold is a rare event, the number of golds won should follow a Poisson distribution. Therefore: <span class="math">\[ P(\textrm{# Golds = g} \mid q) = \frac{(qN)^g \exp(-qN)}{g!} \]</span> For the prior distribution of <span class="math">\(q\)</span> we can use the <a href="https://en.wikipedia.org/wiki/Principle_of_maximum_entropy">Principle of Maximum Entropy</a>: we use a distribution that has the most uncertainty given the facts that we know. We know what the mean number of golds per person over the whole world must be, since the total number of golds, <span class="math">\(G\)</span> and the world population, <span class="math">\(N_W\)</span> is fixed at the time of the Olympics. The maximum-entropy distribution defined over positive numbers and with a known mean is the exponential distribution: <span class="math">\[ P(q) = \frac{N_W}{G}\exp(-\frac{qN_W}{G}) \]</span> Putting this together and discarding constants we get <span class="math">\[ P(q \mid \textrm{# Golds = g}) \propto q^g \exp \left(-q\left(N + \frac{N_W}{G}\right) \right) \]</span> If we want a single number to represent this distribution we should use the mean value <span class="math">\(\bar{q} = \int_0^1 qP(q \mid \textrm{# Golds = g}) dq\)</span>, which we can calculate as below: <span class="math">\[ \bar{q} = \frac{\int_0^1 q^{g+1} \exp \left(-q\left(N + \frac{N_W}{G}\right)\right)dq}{\int_0^1q^{g} \exp \left(-q\left(N + \frac{N_W}{G}\right)\right)dq} \\ = \frac{g+1}{N + \frac{N_W}{G}}\frac{1-\exp(-(N + \frac{N_W}{G}))\sum_{i=0}^{g+1} \frac{(N + \frac{N_W}{G})^i}{i!}}{1-\exp(-(N + \frac{N_W}{G}))\sum_{i=0}^{g} \frac{(N + \frac{N_W}{G})^i}{i!}} \]</span> where the final step is done using repeated integration by parts. In practice the exponential terms in the final expression tend to be extremely small, so this can be approximated as <span class="math">\(\bar{q} = \frac{g+1}{N + N_W/G}\)</span>. This shows what effect the Bayesian prior has: the simple per capita estimate is just <span class="math">\(\frac{g}{N}\)</span>; using the prior effectively increases the medal count by 1 and the population count by <span class="math">\(N_W/G\)</span>, the worldwide number of people per medal, so it is as if the country got one more gold medal at the cost of having an additional population of the worldwide average needed to do this.</p><p>So I’m sure if you’ve slogged through the mathematics this far you’re dying to know what the Bayesian medal table actually looks like. Here is the R code used to do the above calculations, and then finally the medal table:</p><pre class="r"><code>library(knitr)<br /><br />#Read in data<br />medal_table = read.delim("medal_table.txt")<br />medal_table$Population = as.numeric(gsub(",", "", as.character(medal_table$Population)))<br /><br /><br />#Define prior distribution mean parameter<br />world_pop = 7.4e9<br />prior_mean = sum(medal_table$Gold)/world_pop<br /><br />#Define useful function for calculating posterior mean<br />myf <- function(n, k){<br /> s = rep(0, k)<br /> for (ii in 0:k){<br /> s[ii] = -n + ii*log(n) - lfactorial(ii)<br /> }<br /> <br /> y = 1 - sum(exp(s))<br /> return(y)<br />}<br /><br />#Loop over countries and calculate posterior mean <br />medal_table$Quality = rep(NA, dim(medal_table)[1])<br />for (i in 1:dim(medal_table)[1]){<br /> k = medal_table$Gold[i]<br /> n = medal_table$Population[i] + 1/prior_mean<br /> <br /> #Calculate mean of the posterior distribution<br /> medal_table$Quality[i] = ((k+1)/n)*myf(n, k+1)/myf(n, k)<br /> <br />}<br /><br />#Order results by quality and print<br />medal_table_print=medal_table[order(medal_table$Quality, decreasing=TRUE), c("Country", "Gold", "Population", "Quality")]<br />#Print only countries with quality higher than the prior<br />medal_table_print = medal_table_print[which(medal_table_print$Quality > prior_mean), ]<br />row.names(medal_table_print) <-NULL<br /><br />kable(medal_table_print, digits = 9)</code></pre><table><thead><tr class="header"><th align="left">Country</th><th align="right">Gold</th><th align="right">Population</th><th align="right">Quality</th></tr></thead><tbody><tr class="odd"><td align="left">Great Britain</td><td align="right">27</td><td align="right">65138232</td><td align="right">3.13e-07</td></tr><tr class="even"><td align="left">Hungary</td><td align="right">8</td><td align="right">9844686</td><td align="right">2.64e-07</td></tr><tr class="odd"><td align="left">Jamaica</td><td align="right">6</td><td align="right">2725941</td><td align="right">2.60e-07</td></tr><tr class="even"><td align="left">Netherlands</td><td align="right">8</td><td align="right">16936520</td><td align="right">2.19e-07</td></tr><tr class="odd"><td align="left">Croatia</td><td align="right">5</td><td align="right">4224404</td><td align="right">2.11e-07</td></tr><tr class="even"><td align="left">Australia</td><td align="right">8</td><td align="right">23781169</td><td align="right">1.88e-07</td></tr><tr class="odd"><td align="left">New Zealand</td><td align="right">4</td><td align="right">4595700</td><td align="right">1.74e-07</td></tr><tr class="even"><td align="left">Germany</td><td align="right">17</td><td align="right">81413145</td><td align="right">1.70e-07</td></tr><tr class="odd"><td align="left">Cuba</td><td align="right">5</td><td align="right">11389562</td><td align="right">1.69e-07</td></tr><tr class="even"><td align="left">United States</td><td align="right">46</td><td align="right">321418820</td><td align="right">1.36e-07</td></tr><tr class="odd"><td align="left">South Korea</td><td align="right">9</td><td align="right">50617045</td><td align="right">1.34e-07</td></tr><tr class="even"><td align="left">Switzerland</td><td align="right">3</td><td align="right">8286976</td><td align="right">1.23e-07</td></tr><tr class="odd"><td align="left">France</td><td align="right">10</td><td align="right">66808385</td><td align="right">1.21e-07</td></tr><tr class="even"><td align="left">Russian Federation</td><td align="right">19</td><td align="right">144096812</td><td align="right">1.19e-07</td></tr><tr class="odd"><td align="left">Greece</td><td align="right">3</td><td align="right">10823732</td><td align="right">1.14e-07</td></tr><tr class="even"><td align="left">Spain</td><td align="right">7</td><td align="right">46418269</td><td align="right">1.13e-07</td></tr><tr class="odd"><td align="left">Georgia</td><td align="right">2</td><td align="right">3679000</td><td align="right">1.08e-07</td></tr><tr class="even"><td align="left">Italy</td><td align="right">8</td><td align="right">60802085</td><td align="right">1.06e-07</td></tr><tr class="odd"><td align="left">Slovakia</td><td align="right">2</td><td align="right">5424050</td><td align="right">1.01e-07</td></tr><tr class="even"><td align="left">Denmark</td><td align="right">2</td><td align="right">5676002</td><td align="right">1.00e-07</td></tr><tr class="odd"><td align="left">Kenya</td><td align="right">6</td><td align="right">46050302</td><td align="right">1.00e-07</td></tr><tr class="even"><td align="left">Serbia</td><td align="right">2</td><td align="right">7098247</td><td align="right">9.60e-08</td></tr><tr class="odd"><td align="left">Kazakhstan</td><td align="right">3</td><td align="right">17544126</td><td align="right">9.60e-08</td></tr><tr class="even"><td align="left">Uzbekistan</td><td align="right">4</td><td align="right">31299500</td><td align="right">9.00e-08</td></tr><tr class="odd"><td align="left">Sweden</td><td align="right">2</td><td align="right">9798871</td><td align="right">8.80e-08</td></tr><tr class="even"><td align="left">Japan</td><td align="right">12</td><td align="right">126958472</td><td align="right">8.60e-08</td></tr><tr class="odd"><td align="left">Belgium</td><td align="right">2</td><td align="right">11285721</td><td align="right">8.50e-08</td></tr><tr class="even"><td align="left">Canada</td><td align="right">4</td><td align="right">35851774</td><td align="right">8.30e-08</td></tr><tr class="odd"><td align="left">Bahamas</td><td align="right">1</td><td align="right">388019</td><td align="right">8.10e-08</td></tr><tr class="even"><td align="left">Fiji</td><td align="right">1</td><td align="right">892145</td><td align="right">8.00e-08</td></tr><tr class="odd"><td align="left">Bahrain</td><td align="right">1</td><td align="right">1377237</td><td align="right">7.80e-08</td></tr><tr class="even"><td align="left">Kosovo</td><td align="right">1</td><td align="right">1859203</td><td align="right">7.70e-08</td></tr><tr class="odd"><td align="left">Slovenia</td><td align="right">1</td><td align="right">2063768</td><td align="right">7.60e-08</td></tr><tr class="even"><td align="left">Armenia</td><td align="right">1</td><td align="right">3017712</td><td align="right">7.40e-08</td></tr><tr class="odd"><td align="left">Puerto Rico</td><td align="right">1</td><td align="right">3474182</td><td align="right">7.20e-08</td></tr><tr class="even"><td align="left">Singapore</td><td align="right">1</td><td align="right">5535002</td><td align="right">6.70e-08</td></tr><tr class="odd"><td align="left">Jordan</td><td align="right">1</td><td align="right">7594547</td><td align="right">6.30e-08</td></tr><tr class="even"><td align="left">Tajikistan</td><td align="right">1</td><td align="right">8481855</td><td align="right">6.10e-08</td></tr><tr class="odd"><td align="left">North Korea</td><td align="right">2</td><td align="right">25155317</td><td align="right">6.10e-08</td></tr><tr class="even"><td align="left">Belarus</td><td align="right">1</td><td align="right">9513000</td><td align="right">5.90e-08</td></tr><tr class="odd"><td align="left">Argentina</td><td align="right">3</td><td align="right">43416755</td><td align="right">5.90e-08</td></tr><tr class="even"><td align="left">Azerbaijan</td><td align="right">1</td><td align="right">9651349</td><td align="right">5.90e-08</td></tr><tr class="odd"><td align="left">Czech Republic</td><td align="right">1</td><td align="right">10551219</td><td align="right">5.80e-08</td></tr><tr class="even"><td align="left">Colombia</td><td align="right">3</td><td align="right">48228704</td><td align="right">5.50e-08</td></tr><tr class="odd"><td align="left">Poland</td><td align="right">2</td><td align="right">37999494</td><td align="right">4.80e-08</td></tr><tr class="even"><td align="left">Romania</td><td align="right">1</td><td align="right">19832389</td><td align="right">4.50e-08</td></tr><tr class="odd"><td align="left">Ukraine</td><td align="right">2</td><td align="right">45198200</td><td align="right">4.30e-08</td></tr><tr class="even"><td align="left">Cote d’Ivoire</td><td align="right">1</td><td align="right">22701556</td><td align="right">4.30e-08</td></tr><tr class="odd"><td align="left">Taiwan</td><td align="right">1</td><td align="right">23510000</td><td align="right">4.20e-08</td></tr></tbody></table><p>Team GB tops the chart! Mathematically, this is because GB combines a large rate of medals per capita with a large population. Therefore it has the statistical weight to move the inferred value of <span class="math">\(q\)</span> away from the prior expectation. Smaller countries with several golds like Jamaica also do well, but tiny Bahamas is now much further down the list - 1 gold medal just isn’t enough information to tell you much about the underlying rate at which a country tends to win golds.</p><p>You could easily extend this analysis by aggregating the results of previous Olympics too. With data from more years there would be more evidence to move the quality of smaller countries away from the prior. In terms of predicting the future performance of countries you would need to decide on an appropriate weighting of past results, which you could in principle do by trying to make a predictive model for the 2016 results from 2012, 2008 etc. Data from Rio and previous Olympics is available <a href="http://http://www.medalspercapita.com/">here</a></p><p>Additional note: this is my first blog post written entirely in R Markdown.</p> </div> <script> // add bootstrap table styles to pandoc tables $(document).ready(function () { $('tr.header').parent('thead').parent('table').addClass('table table-condensed'); }); </script> <!-- dynamically load mathjax for compatibility with self-contained --><script> (function () { var script = document.createElement("script"); script.type = "text/javascript"; script.src = "https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"; document.getElementsByTagName("head")[0].appendChild(script); })(); </script> </body></html>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com0tag:blogger.com,1999:blog-1931373673946954854.post-50717061028634601322016-08-10T11:57:00.001+02:002016-08-10T12:15:18.794+02:00In defence of the Journal Impact Factor<div dir="ltr" style="text-align: left;" trbidi="on">With the possible exception of the BBC, academia must be the institution that spends the biggest percentage of its time criticising itself. The 'science of science' is an established field of research in its own right. Researcher's have rightly raised awareness of how <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1182327/">statistical methods are misused</a>, <a href="http://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.1001747">how career and funding incentives can be better aligned with good scientific practise</a> and the inappropriate use of performance metrics.<br /><br />Perhaps the most frequent target of criticism in this last category is the <a href="https://en.wikipedia.org/wiki/Impact_factor">Journal Impact Factor </a>(JIF). The JIF is a measure of how many citations papers in a specific journal tend to receive. Precisely, it is <a href="https://en.wikipedia.org/wiki/Impact_factor#Calculation">defined </a>as the mean number of citations received in the last year by articles published in the journal in the previous two years.<br /><br />A list of common complaints about the JIF would include:<br /><ol style="text-align: left;"><li>Citation distributions are skewed, with many papers receiving few citations and a few papers receiving many citations. As such the JIF is a poor representation of a 'typical' paper in the journal.</li><li>The JIF is a statistic of relevance to the journal, but is inappropriately used to judge individual papers or researchers, which are better judged by their own number of citations.</li><li>Journals' pursuit of higher JIF scores biases them towards eye-catching papers and positive results, rather than solid research, replication studies and negative results</li><li>Journals engage in dodgy practices in order to artificially inflate their JIF</li></ol><div>I don't hold any great admiration for the JIF, but my instinctive contrarianism has made me skeptical about these complaints. As an exercise in devil's advocacy, I'll try and give answers to each of them.</div><div><br /></div><div><b>1. </b>Citation distributions certainly are skewed. So are lots of things. People's salaries, for instance, are highly skewed. Take a look at this plot of household income from Wikipedia</div><div><div><a href="http://2.bp.blogspot.com/-3_UuuhdgsyQ/V6oP4cwM6WI/AAAAAAAAp5w/-Q8Ygti8UwI6sO4ZHpj_hl3ZsSFfdmdrACK4B/s1600/UK_Equivalised_Income_Distribution.png" imageanchor="1"><img border="0" height="285" src="https://2.bp.blogspot.com/-3_UuuhdgsyQ/V6oP4cwM6WI/AAAAAAAAp5w/-Q8Ygti8UwI6sO4ZHpj_hl3ZsSFfdmdrACK4B/s400/UK_Equivalised_Income_Distribution.png" width="400" /></a></div></div><div>That huge bar on the right hand side indicates a long tail of households with very high incomes. Because of this the mean income is about 20% higher than the median. This skew is more pronounced in some countries than others: The US and the UK have substantially more income inequality than most continental European countries for instance. As such one should treat differences in the mean income between countries with a little caution - the higher mean income in the US compared to most European countries is predominantly due to a small number of wealthy individuals. That being said, do we seriously doubt that there is a difference between a country with a mean income of $50,000 a year and one with $10,000 a year? Clearly mean incomes tell us <i>something</i> about the quality of life in different countries, the prospects of their citizens, their overall clout in the world. Compare the plot above with the distribution of citations to two journals, also from Wikipedia. They have the same basic features.<br /><br /><a href="http://1.bp.blogspot.com/-p74auu7pnH8/V6r3iYVb41I/AAAAAAAAp6A/IjaKtCapu7YpPQac7eYhmSasINHU-YwfQCK4B/s1600/Journal_impact_factor_Nature_Plos_One%2B%25281%2529.png" imageanchor="1"><img border="0" height="216" src="https://1.bp.blogspot.com/-p74auu7pnH8/V6r3iYVb41I/AAAAAAAAp6A/IjaKtCapu7YpPQac7eYhmSasINHU-YwfQCK4B/s400/Journal_impact_factor_Nature_Plos_One%2B%25281%2529.png" width="400" /></a></div><div><br /></div><div>Sure, it may be daft to claim that a journal with a JIF of 5 is substantially different to one with a JIF of 4.5. One should not fetishise irrelevant differences just because they are presented with apparently high precision. But the truth of the matter is that knowing that one paper was published in a high JIF journal and another in a low JIF journal gives you <i>some</i> information about the likely quality of each. There will be many exceptions where bad papers appear in good journals and vice versa. But as long as it provides some information people will continue to use it. Seeking to <a href="http://www.nature.com/news/beat-it-impact-factor-publishing-elite-turns-against-controversial-metric-1.20224">banish impact factors from discussion</a> will only make this use more opaque.<br /><br />The skewed nature of the distribution introduces a lot of uncertainty into the statistics of estimating a population mean. It is often stated that because citations follow an approximate power-law distribution the mean of the distribution has no descriptive value. This is untrue. <a href="http://www.pnas.org/content/107/37/16023.full">Estimates of the power-law coefficient are generally in excess of 3</a>, <a href="https://en.wikipedia.org/wiki/Pareto_distribution">meaning that both the mean and variance of the distribution are well defined</a>. As such the <a href="https://en.wikipedia.org/wiki/Law_of_large_numbers">Law of Large Numbers</a> and the <a href="https://en.wikipedia.org/wiki/Central_limit_theorem">Central Limit Theorem </a>apply and the sample mean converges to the underlying mean of the distribution, with normally distributed uncertainty. Therefore the JIF does what it says on the tin: gives a reasonable estimate of the expected number of citations a paper in that journal will receive.<br /><br />For describing what is likely to happen to a single paper, the median may have been a better measure to use than the mean. But few people are claiming that a switch from mean to median would fix their issues with the JIF. </div><div><br /></div><div><b>2.</b> This is the point I take most issue with. In <a href="http://biorxiv.org/content/biorxiv/early/2016/07/05/062109.full.pdf">a recent pre-print paper on Biorxiv.org relating to the use of JIFs</a>, the authors claim in their abstract that:</div><div><br /></div><div><i>Although there are differences among journals across the spectrum of JIFs, the citation distributions overlap extensively, demonstrating that the citation performance of individual papers cannot be inferred from the JIF.</i></div><div><i><br /></i></div><div>This obviously relates strongly to the discussion of point 1. To what extent can I predict how many citations a paper will receive, based on the JIF of the publishing journal?</div><div><br /></div><div><b>Overlapping distributions. </b>A simple reposte to the above quote is that just because distributions overlap does make them useless. <a href="http://genderedinnovations.stanford.edu/methods/sex.html">The distributions in height of men and women overlap a lot</a>. There are many men below 5ft 8' tall and many women taller than 5ft 10'. Nonetheless, the mean height of a man is significantly greater than the mean height of a woman, and knowing someone's gender gives you a lot of predictive power when estimating their height. Likewise there are plenty of people in developing countries who have incomes greater than the average British worker, but no one thinks the country someone lives in is irrelevant in determining their income. The case of JIFs is only different from this examples in the quantitative degree of overlap. Since JIFs are relatively stable over time, by definition the JIF must give accurate information about the expected number of citations a paper will receive. Indeed, <a href="https://figshare.com/articles/Does_Quality_Matter_for_Citedness_A_comparison_with_para_textual_factors_and_over_time/1269182">studies show that the JIF is a better predictor of the citations a paper will receive than subjective judgements about paper quality</a>. Unless the JIF was fluctuating wildly over time this simply has to be true. </div><div><br /></div><div><b>Journal level vs article-level metrics</b>. My major gripe about this point is not whether or not the JIF is a useful predictor of the number of citations a paper will get. It is the idea that the actual number of citations received is somehow a superior estimate of a paper's quality. New publication houses such as the <a href="https://www.plos.org/">Public Library of Science</a> like to champion<a href="https://www.plos.org/article-level-metrics"> 'article-level metrics' </a>over the JIF, arguing that the paper should be judged independently of the journal it is in. If we lived in a world where everyone took the trouble to read, consider and evaluate papers in their entirety, I'd be perfectly happy to get on the ditch-the-JIF bandwagon. But that simply isn't going to happen. If we stop looking at the journal metrics we are left looking at article-level metrics such as number of citations or social-media response. But the very arguments against JIFs are at least as valid against article-level metrics. The highly skewed distribution of citations is not necessarily due to a highly skewed distribution of article quality, but reflects the nature (or <a href="http://www.nature.com/">Nature?</a>) of the science citation game. The simplest explanation for this skew is that papers with many citations tend to be cited more in future. This could be because they are intrinsically better papers, but the effect tends to be exponential rather than linear in time, suggesting the appearance of the paper in references adds to its salience for future citers. Moreover, papers with famous authors, papers with lots of co-authors and papers in popular areas tend to receive more citations. Untangling quality effects from random noise is extremely difficult. Do I think citation metrics are useless? No. But are they a clean estimate of a single paper's quality relative to other work. Not at all. </div><div><br /></div><div><b>Citation-process noise reduction and new papers.</b> In fact, in my opinion the JIF <i>is superior to article-level citations in many instances</i>. Consider that if a paper is published in, say, PNAS, several referees have read the paper in detail (hopefully) and decided that it is a piece of work that meets the general standards of that journal. The JIF of PNAS (which is about 9) then does the useful statistical job of averaging over all papers that meet that standard, removing a lot of noise in the process, and telling us something about how good the average paper meeting those standards is. In science we usually favour statistics from large sample sizes rather than single data points. Why should you be punished because your excellent paper wasn't one of the few runaway citation successes? Is the JIF perfect? Of course not! Publication in leading journals is also biased towards established leading scientists and their proteges, to native English-speakers, etc. Using the median would probably be more informative about the prospects of a 'typical' paper. But is it better to use only the citations to a specific article? Absolutely not. For one thing, the journal a paper is published gives immediate information about the paper, whereas citations can take years to build up. For researchers with few previous papers (I refuse to use the term Early Career Researchers, which seems to apply to anyone below 50 now), this can make a serious difference.</div><div><br /></div><div><b>3.</b> Journal's want people to read them, or more importantly they want librarians to subscribe to them. As long as journals make their money from subscriptions they will always want eye-catching results, and forever neglect less glamorous work, especially in the journals that leading publication houses use as the eye-candy to get people to subscribe on-mass to their less read titles. Trying to increase their JIF scores is a much a symptom of this problem as it is a cause. </div><div><br /></div><div>Librarians simply are not going to look at the full distribution of citations from a journal when making subscription decisions. They want a few or ideally one number to use to make that choice. We could, for instance, redefine the JIF to be based on the median number of citations. This might stop top journals chasing a few geese that lay the golden eggs of mega-citations (which seem to be far more likely to later be proved flawed or even retracted). But ultimately journals will always want research that is more likely to be read and cited. I am more concerned with the <a href="http://www.straitstimes.com/opinion/prof-no-one-is-reading-you">mountains of academic research published at great expense and hardly ever read</a>. </div><div><br /></div><div>The only exception to this rule is journals that receive all their money from authors paying to publish. PLoS One charges about $1500 per article to authors for publication, and promises to publish anything that is technically correct. I will leave the reader to guess whether I think this is <a href="http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0085047">a good idea</a>. (I used to publish in PLoS One, but now I conveniently can't afford to do so anymore).<br /><br />Personally I'm broadly in favour of more open science (not capitalised), and the use of open repositories such as <a href="https://arxiv.org/">Arxiv</a> and <a href="http://biorxiv.org/">Biorxiv</a>. I'm interested in the possibilities of formalised <a href="http://blog.scienceopen.com/2016/02/pre-or-post-publication-peer-review/">post-publication review</a>. I think the amount of money spent on academic publishing is a disgrace. Everyone should learn to <a href="https://www.latex-project.org/">typeset their own papers properly</a> as is standard in computer science fields. I hear about and read most papers as a result of the Twitter grapevine rather than browsing particular journals, but this is process subject to a whole load of <a href="https://en.wikipedia.org/wiki/Filter_bubble">biases of its own</a>. </div><div><br /></div><div><b>4.</b> <a href="https://en.wikipedia.org/wiki/Goodhart%27s_law">Goodhart's law.</a> Whatever metric you choose as a proxy for quality will become corrupted if rewards accrue to those with higher scores. Gaming is all but inevitable. Perfectly reasonable standards of behaviour should be adopted, such as counting papers as being published when they first appear online rather than much later in print. The best way to ensure this is to shun journal's that obviously engage in dodgy practices. Almost no one is going to do this if the journal is a leader in their field. You already know a rough order of journal quality in your field, so gaming tactics that add a few points to the JIF should not unduly trouble you.</div><div><br /></div><div>Ultimately the best way to judge a paper is to read it. Within our respective fields we all know what a 'good' journal is, and what it takes to be published there. Anyone who judges a researcher or makes a hiring decision by simply adding up the JIFs of all their papers is a fool. So is someone making the same decision based on total citations or the h-index. <a href="http://biorxiv.org/content/biorxiv/early/2016/07/05/062109.full.pdf">The data is now accessible about the detailed citation distributions in various leading journals</a>. So if you want to find out which journal gives you the best chance of getting that h-index-improving <i>n </i>citations you can.<br /><br />The 'game' of a scientific career is noisy, prejudiced, unfair and no sure way to health, wealth and happiness. The same is true of almost any career. Do work you believe in and enjoy, make reasonable adjustments to adapt to the system and don't make becoming a professor at a top institution or publishing in Science or Nature your only goals in life. This much is obvious. But the JIF is no more flawed than any other reductionist metric of outputs, and getting rid of it will, in and of itself, solve absolutely nothing.</div><div><br /></div><div><br /></div><div><i><br /></i></div><div><i><br /></i></div><div><br /></div><div><br /></div><div><br /></div><br /><br /></div>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com0tag:blogger.com,1999:blog-1931373673946954854.post-40407206554828826732016-08-05T00:48:00.001+02:002016-08-05T00:51:07.046+02:00A few fascinating laws and paradoxes<div dir="ltr" style="text-align: left;" trbidi="on">I recently spent an evening discussing the time-reversibility in Newtonian mechanics through the medium of 140 character tweets, after being introduced to one of my favourite things: <a href="https://en.wikipedia.org/wiki/Norton%27s_dome">a new paradox</a> (hat tip to @MikeBenchCapon). This reminded me that there can be no excuse to be bored in this day and age when you can spend happy hours perusing the lists of <a href="https://en.wikipedia.org/wiki/List_of_eponymous_laws">eponymous laws</a> and of <a href="https://en.wikipedia.org/wiki/List_of_paradoxes">paradoxes</a> on Wikipedia. Here are a few of my favourites eponymous laws from those lists and elsewhere:<br /><br /><a href="https://en.wikipedia.org/wiki/Benford%27s_law">Benford's law</a>: on the power-law distribution of specific digits in naturally occurring statistics. The most commonly quoted part of the law is that about 30% of all statistics will start with the digit 1, compared to a naive expectation of around 11%. This law was used to show that Iran had been fabricating data relating to its nuclear program, since the digits in the data did not follow Benford's law. My favourite aspect of the law is that it can be derived from the assumption that if there <i>does</i> exist a distribution for the digits, it must be independent of the numerical basis used to represent the statistics.<br /><br /><a href="https://en.wikipedia.org/wiki/Baumol%27s_cost_disease">Baumol's cost disease</a>: why the cost of doctors, teachers and other service professionals increases over time. The efficiency of manufacturing has historically progressed faster than service sector occupations such as health care and education, through mechanisation. Instead of raising the salaries of manufacturing workers faster than service workers, all salaries tend to grow at roughly the same rate. As a result, labour-intensive industries become more costly over time relative to the price of manufactured goods. Expect tuition fees to carry on rising.<br /><br /><a href="https://en.wikipedia.org/wiki/Goodhart%27s_law">Goodhart's law</a>: why you can't measure how well an intelligent system performs if you reward it for that performance (see also <a href="https://en.wikipedia.org/wiki/Campbell%27s_law">Campbell's law</a>). Academics will be familiar with the gaming of league tables and the UK Research Excellence Framework by their institutions. When a body such as the government decides on metrics as a proxy to measure performance, and then rewards those who perform well by these measures, individuals choose to target the measures rather than genuinely improving overall performance. Hence we get teachers teaching-to-test, universities gaming the REF, scientists prioritising citations over true advances, and hospitals playing games with patient waiting times.<br /><br />And of course <a href="https://en.wikipedia.org/wiki/Stigler%27s_law_of_eponymy">Stigler's law of eponymy</a>, which states that these laws were probably not named after the people who discovered them first. Stigler was, of course, not the first to propose this.<br /><br />Here are a few of my favourites paradoxes, along with a rating for how genuinely paradoxical they seem to me:<br /><br /><a href="https://en.wikipedia.org/wiki/Berkson%27s_paradox">Berkson's paradox</a>: why the best-looking people you date have the worst personalities. While beautiful people may be no more or less pleasant in the population as a whole, you will let a bad personality slide for a beautiful mate, or date someone below your usual standards of physical beauty if they have a sparkling wit. As a result, in the group of people you date there will be an inverse correlation between beauty and personality. <b>Paradox rating 1/10</b><br /><br /><a href="https://en.wikipedia.org/wiki/Friendship_paradox">The friendship paradox</a>: why your friends probably are more successful and have more friends than you do. It is a simple result of networkm theory that you are most likely to be friends with people who have lots of friends, since they have more friendship links available. This means that a typical person is connected to people who have more friends than they do (while a few individuals are connected to lots of people with fewer friends). A simple corrolary is that if more successful people have more friends, then your friends will, on average, be more successful than you. In science, this selection effect is why everyone you know seems to be doing better than you are - the better they are doing, the more likely you are to be aware of them. <b>Paradox rating 3/10</b><br /><br /><a href="https://en.wikipedia.org/wiki/Two_envelopes_problem">The envelope paradox</a>: how a simple game tests the bounds of probability theory. A game show host offers you two envelopes and tells you that one contains twice as much money as the other. You open one envelope and find it contains £10. The other must contain either £5 or £20, with an average of £12.5. When the host offers to let you switch it seems that you should. But that choice would have been the same if you had never opened the envelope. The next time you don't even bother to open the envelope before switching, but now the same logic applies to the new envelope, making you switch back and forth forever. What has gone wrong? <b>Paradox rating 7/10</b><br /><br /><a href="https://en.wikipedia.org/wiki/Norton%27s_dome">Norton's dome</a>: Theoretical departure from causality in Newtonian physics. A point mass sits atop a radially-symmetric, frictionless dome, with no force acting on it. After some arbitrary amount of time it begins to move spontaneously and rolls down the side of the dome. Its motion nonetheless obeys Newton's laws at all times, despite there being no way to predict, or even place probabilities on, the time elapsed before it starts to roll. <b>Paradox rating 9/10</b><br /><br /></div>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com0tag:blogger.com,1999:blog-1931373673946954854.post-72976962489264155722016-07-18T16:38:00.000+02:002016-08-22T12:24:14.110+02:00Will your job be automated? A critique of the predictions of Frey and Osborne<div dir="ltr" style="text-align: left;" trbidi="on">You cannot have failed to encounter the current hype and/or panic about job automation. The basic story is compelling. Drawing on the availability of Big Data, artificial intelligence is progressing at a breakneck speed, solving problems that once seemed like science fiction: driverless cars, recognising people in photos, giving eerily accurate suggestions about which films we might want to watch or even what email replies we might want to give. More mundane tasks that were once the preserve of highly-trained professionals are also at risk, such as legal research. A computer can scan millions of legal texts for relevant information while a lawyer is still finding the reference for the text they need.<br /><br />All of this has led to a widespread belief that many people face the loss of their job in the near future. Of course, automation has been with us since the industrial revolution, and in some areas even before then. <a href="https://en.wikipedia.org/wiki/Luddite">Resistance to, and despair about automation is as old as automation itself</a>. But the new panic is about the possible scale of job losses, and the lack of useful employment opportunities for those displaced. An oft-quoted figure is that 47% of U.S. jobs are at risk of automation.<br /><br />The figure of 47% originates<a href="http://www.oxfordmartin.ox.ac.uk/downloads/academic/The_Future_of_Employment.pdf"> in the work of Carl Frey and Michael Osborne</a>, of Oxford University. Frey and Osborne persuasively argue that the progress in data collection, data analytics and artificial intelligence puts many tasks that were previously thought to be out of reach for computers and robots within touching distance of being automated. They contend that advances in pattern recognition mean that computers, which previously had been used to automate routine tasks, such as performing repeated calculations or fitting parts together in factories, will increasingly be able to tackle non-routine tasks. For example, <a href="https://en.wikipedia.org/wiki/Siri">Siri </a>and similar artificial personal assistants take in unstructured voice requests and determine what the user wants, where to seek the required information and how to present it to them. With enough data, they suggest, almost any task can be automated by looking for patterns in the data that inform the task at hand:<br /><br /><i>"...we argue that it is largely already technologically possible to automate almost any task, provided that sufficient amounts of data are gathered for pattern recognition."</i> [F&O]<br /><br />These arguments are persuasive, and there is no doubt that modern machine-learning research has made great strides - it is worth trying to recall how outlandish some of today's AI technologies would have seemed just 10 years ago. Nonetheless, others such as Neil Lawrence, of Sheffield University, have <a href="http://inverseprobability.com/2016/03/04/deep-learning-and-uncertainty">argued</a> that relying on huge data sets in this way is not the same thing as true artificial intelligence. Only a few organisations in the world such as Google and Facebook have access to truly vast amounts of data about our daily behaviours, and a great deal of their research is dedicated to targeting adverts at us with increasing precision. Moreover, if a computer needs a vast data set to learn what it should do, how readily can it adapt to new tasks? Will there always be a big enough relevant data set that has, or even could be collected? What about tasks where the computer may not have access to 'the grid' and the vast centres where data is stored? These are big questions that drive significant bodies of research in AI. Given these uncertainties, it is worth considering how F&O arrive at the rather precise number of 47% for the proportion of jobs at risk.<br /><br />Fittingly enough, F&O use machine-learning itself to determine whether a job is automatable. They use a tool called <a href="http://www.gaussianprocess.org/">Gaussian process</a> classification (GPC) to predict whether a job is automatable, based on the characteristics of that job, as defined and measured in a <a href="https://www.onetonline.org/">data set called O*NET</a>, collected by the US Department of Labor. O*NET lists the skills and knowledge required to perform each job. To use GPC to make predictions requires two things, a set of predictors (in this case the O*NET data) and a matching set of known outputs on which to train the classifier. In plain terms, they require not only the job characteristics, but also, for some of these jobs, a known risk of automation. Where does this second part come from? In short, they make an educated guess (or more precisely, they ask a group of well-informed people to make such a guess). In the paper they describe this process:<br /><br /><i>"First, together with a group of ML researchers, we subjectively hand-labelled 70 occupations, assigning 1 if automatable, and 0 if not. For our subjective assessments, we draw upon a workshop held at the Oxford University Engineering Sciences Department, examining the automatability of a wide range of tasks. Our label assignments were based on eyeballing the O∗NET tasks and job description of each occupation. This information is particular to each occupation, as opposed to standardised across different jobs. The hand-labelling of the occupations was made by answering the question “Can the tasks of this job be sufficiently specified, conditional on the availability of big data, to be performed by state of the art computer-controlled equipment”</i>. [F&O]<br /><br />To make the process plain, they took 70 of the jobs in the data set about which they were most confident, and made their best guess as to whether these were going to be automated. They then use the GPC to translate these subjective opinions about 70 jobs into predictions on the other 600 or so in the data set. Essentially they train the GPC to learn what it is about certain jobs that makes <i>them</i> believe they will be automated. Ultimately then, the GPC propagates this subjective opinion to all the other jobs, and determines that 47% are predicted to be automated.<br /><br />As a side effect, the GPC is also able to identify the factors that seemed to influence whether the workshop participants thought a job would be automated. The factors identified seem reasonable: jobs requiring high social perceptiveness have a low risk for example. But we should perhaps treat these findings with care - the very fact that they seem reasonable to us suggests that they also seemed reasonable to the people making the predictions - no wonder then that they labelled jobs requiring high social perceptiveness as less likely to be automated. Moreover, while the participants of a workshop at the Oxford University Engineering Sciences Department no doubt have greater expertise than the average person in determining the capabilities of machines, we should also be aware that such groups are somewhat selective to technological optimism - few people choose to become researchers in artificial intelligence if they do not believe it is important, any more than you would become a teacher if you didn't think education made a difference. Any biases or blind spots these individuals might have will be translated into the final figure of 47%, as well as the characteristics chosen as most important.<br /><br />There is a danger when reading the paper (if one does, no doubt many news sources do not), that one can be impressed by the mathematical sophistication of the GPC prediction machinery. It is an impressive piece of technical work. But the GPC can only work with what is is given - it generalises from known examples in the data. The old saying about computer science: 'garbage in, garbage out' is overly pejorative here - the predictions the GPC has been trained on are not garbage, but the best educated guesses of well informed people. They are internally consistent - the GPC can predict well the predictions made by workshop participants for unseen examples. But the GPC cannot predict more accurately than the individuals themselves. It is important to realise that the trained-GPC is effective a machine for making the predictions these same individuals would have made themselves if they were asked. With all the uncertainties involved in a still nascent and quickly changing field, making precise predictions is extremely speculative. Just imagine how different many of these predictions would have been if people had been asked 10 years ago. What might they look like in 10 years time?<br /><br />All of this makes me very skeptical about the now ubiquitous assumption that masses job losses are inevitable. In many ways I hope they are - we should hope that more of the tasks we only do out of necessity will be automated, as long as the economic gains can be spread equitably (a whole other ball game!). But a narrative of huge disruption feeds into the rather millennial milieu in which we find ourselves, plagued with doubts about our economic system, possible catastrophic climate change, antibiotic resistance etc. It is very tempting to believe that disruptive, destructive change is now a permanent feature of our lives. F&O, to their credit, do not take this line - I have seen Michael Osborne <a href="https://prawnsandprobability.blogspot.co.uk/2014/05/this-is-blog-post-i-wrote-about-our.html">present his work previously</a> and he speaks to all great possibilities automation creates. It is also worth noting that many tasks that can be automated take an amazingly long time to be so. I recently took a trip to the <a href="https://www.ncm.org.uk/">National Coal Mining Museum</a>, where I was amazed to learn that very few mines had any serious machinery involved in the actual hacking off of coal until nationalisation and unionisation drove up labour costs and pushed efficiency up the agenda after the war. I'm perpetually amazed, as a renter, how many people think dishwashers are optional! As Frey & Osborne note, but few news outlets pick up on, automation will only happen if the cost of labour is sufficiently high - many government policies are directed explicitly at lowering the cost of labour to the employer.<br /><br />We shall no doubt see feats of automation in our lifetimes that would stagger us today, just as the household appliances created in the 20th century would amaze our ancestors. But exactly which jobs will disappear, when they will do so and how many people will become unemployed? I would not want to guess.<br /><br />Reference: <a href="http://www.oxfordmartin.ox.ac.uk/downloads/academic/The_Future_of_Employment.pdf">[F&O] <i>The future of employment: How susceptible are jobs to computerisation?</i> Carl Benedikt Frey and Michael A. Osborne</a><br /> </div>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com1tag:blogger.com,1999:blog-1931373673946954854.post-83536938505646781732016-07-13T16:39:00.000+02:002016-08-04T10:25:26.237+02:00Brexit: a statistical demographic analysis<div dir="ltr" style="text-align: left;" trbidi="on">Britain voted for Brexit, defying <a href="https://prawnsandprobability.blogspot.co.uk/2016/06/predicting-brexit-vote-from-betting.html">the predictions from Betfair's prediction market.</a> I was in the US at the time, giving me the dubious privilege of watching the votes come in without having to stay up all night. As a (relatively) young, (relatively) affluent graduate and resident of a major UK city you will be completely unsurprised to learn that I voted to remain.<br /><div><br /></div><div>There has been a lot of discussion in the press since the vote regarding different demographic splits between remain and leave voters. We are told that city-dwellers, graduates, the young and the affluent tended to vote remain, while poorer voters, those in small towns and villages, those without higher education and older voters tended to vote leave. The Scottish and the Irish voted in, the English and the Welsh voted out. The Guardian provides <a href="http://www.theguardian.com/politics/ng-interactive/2016/jun/23/eu-referendum-live-results-and-analysis">a breakdown of these trends</a>, which appear to show a nation divided. I assume the data they use comes from the 2011 UK Census.</div><div><br /></div><div>In an effort to channel my increasing angst in a positive direction I set out to do a more thorough statistical analysis of the data The Guardian presented to identify which demographic factors were most important in determining how people voted. After scraping the data from the Guardian website I first reproduced the graphs <a href="http://www.theguardian.com/politics/ng-interactive/2016/jun/23/eu-referendum-live-results-and-analysis">The Guardian had displayed </a>(see end for scraping details. NB: I could have aggregated data from the UK Census directly, but this was quicker and ensured I was using exactly the same measures as the Guardian). My demographic data are all in arbitrary units since I had to scrape the values in pixel units from the webpage, but since this won't affect the statistics I wish to do - in fact, scaling each demographic variable to lie between 0 and 1 helps us to compare the magnitude of effects. On each subplot I have given the correlation coefficient between the demographic indicator and the proportion of leave voters.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-LDUu0IzCS2s/V4Usxrqny2I/AAAAAAAApnM/BCcZ0QCIULMZkihMr6lJyWDbU4ycQaxRACLcB/s1600/guardian_plot.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="428" src="https://4.bp.blogspot.com/-LDUu0IzCS2s/V4Usxrqny2I/AAAAAAAApnM/BCcZ0QCIULMZkihMr6lJyWDbU4ycQaxRACLcB/s640/guardian_plot.jpg" width="640" /></a></div><div><br /></div><div> In short these plots (working left to right and top to bottom) seem to indicate that:</div><div><ol style="text-align: left;"><li>Voters with degrees tend to vote remain</li><li>Voters with no formal qualifications tend to vote leave</li><li>Voters with higher incomes tend to vote remain</li><li>Voters in the ABC1 classes tend to vote remain</li><li>Older voters tend to vote leave</li><li>Voters in areas with more non-UK born residents tend to vote remain</li></ol><div>So far, so much in agreement with the general terms of discussion. How do these perceptions hold up when we actually do some statistics on the data?</div><div><br /></div><div>The tool I used for this analysis is the Generalised Linear Mixed Effects Model. I specified the model as:</div></div><div><br /></div><div><b><span style="font-family: "courier new" , "courier" , monospace; font-size: x-small;">proportion voting leave ~ (1 | Region) + proportion with higher education. + proportion with no formal qualifications + median income + proportion in ABC1 social classes + median age + proportion not born in UK</span></b></div><div><br /></div><div>This model states that the proportion of leave voters in an electoral area is determined by the demographic characteristics plotted above, but with regional variations specified by the random effect (1 | Region). We know that each nation of the UK had distinctly different voting patterns, quite separate from their different demographics, e.g. older voters in Scotland didn't necessarily vote the same way as similarly-aged voters in England. We'd better account for this in the analysis if we want to identify the real underlying effects.</div><div><br /></div><div>Running this model in R (lme4::glmer, scaling the independent variables to have zero mean and unit standard deviation) we infer estimated effect sizes for each of the demographic variables. Below I've listed these and plotted the effect sizes with 95% confidence intervals for visual comparison. Points plotted to the left of the vertical grey line indicate a negative affect on the leave vote, those on the right a positive effect.</div><div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-0a_ADbin-q8/V4ZWzqqywCI/AAAAAAAApoY/zL4hJB09q4ckMK9SCgTejagQ5vYOdgJKgCLcB/s1600/glmm.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="258" src="https://2.bp.blogspot.com/-0a_ADbin-q8/V4ZWzqqywCI/AAAAAAAApoY/zL4hJB09q4ckMK9SCgTejagQ5vYOdgJKgCLcB/s640/glmm.jpeg" width="640" /></a></div><br /></div><div class="separator" style="clear: both; text-align: center;"></div><div>Some of the initial impressions from the data are born out in this analysis. The intercept is weakly positive, indicating that overall the nation voted to leave (albeit by such a slim margin that the intercept is not significantly greater than zero! - worth noting by those claiming an uncontestable mandate). By far the most important predictor of how an individual will vote is whether or not they have had any higher education. Older voters do tend to vote leave in greater numbers (in fact this tendency is shown more strongly here than we saw in the first set of plots). But some of the other results are surprising. The proportion of residents who are not born in the UK has a negligible effect on how that area will vote. Class has a relatively weak effect despite showing one of the strongest correlations. Voters with higher incomes are <i>more </i>likely to vote leave (all other things being equal). Perhaps most surprising, areas where more people have no formal qualifications are substantially <i>less</i> likely to vote leave (again, all other things being equal). The strong positive correlation seen between proportion with no formal qualification and leave vote seen in the first figure appears to be a side effect of the strong anti-correlation between the proportion with no formal qualification and the proportion with higher education. </div><div><br /></div><div>Of course, that caveat <i>all other things being equal</i> is doing a lot of work. Its rare to find someone with a high income, but with no higher education and who would not be classified as being in the ABC1 social classes. Likewise there are not many areas where there are simultaneously a large number of graduates and a large number of people without formal qualifications. Nonetheless, the differences between the statistical results and the original impression from the data plots should make us pause before reading too much into the apparent demographic trends.</div><div><br /></div><div>This analysis was a simple effort with a readily available model - hopefully some more sophisticated analysis will reveal a clearer picture. In particular, including interactions between these different indicators may give better predictions. As usual in such analyses, we should be aware of all the caveats surrounding <a href="https://en.wikipedia.org/wiki/Ecological_regression">ecological regression</a> - data based on individual characteristics would be preferable, but that may be a pipedream.</div><div><br /></div><div><b>How I got the data: scraping, xml and awk</b></div><div><br /></div><div>The Guardian is one of the best newspapers in the world for presenting real data and analysis to the public. That it is free to access is an amazing privilege for those of us who are interested in the real evidence behind the headlines. It regularly presents beautiful summaries of important data in an easily understood format. </div><div><br /></div><div>However, on <a href="http://www.theguardian.com/politics/ng-interactive/2016/jun/23/eu-referendum-live-results-and-analysis">this page </a>where the demographic data is plotted, there is no information on how one might view the original data is numerical form. That is the newspaper's prerogative, and may be due to worries that other publications would piggyback on the hard work Guardian journalists do in finding the information. It does however make <a href="http://www.collective-behavior.com/open-science-2-0/">Open Science</a> difficult.</div><div><br /></div><div>To get the data I needed I first inspected the elements comprising the interactive plot (in Chrome, right click: inspect)</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-319x4-eEqHY/V4U10zvDvRI/AAAAAAAApno/ssWTzO1S69QL1OuT0nzqa8FrKwZydSRQgCLcB/s1600/inpsect.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://2.bp.blogspot.com/-319x4-eEqHY/V4U10zvDvRI/AAAAAAAApno/ssWTzO1S69QL1OuT0nzqa8FrKwZydSRQgCLcB/s400/inpsect.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">Then I found the xml entries that gave the screen coordinates for each circle plotted on each graph</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-FOSHAoUSIfg/V4U2h3Aip1I/AAAAAAAApns/9AtF769MzSMOt9q8Mi4cxb7vY3IPodGwACLcB/s1600/xml.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="218" src="https://2.bp.blogspot.com/-FOSHAoUSIfg/V4U2h3Aip1I/AAAAAAAApns/9AtF769MzSMOt9q8Mi4cxb7vY3IPodGwACLcB/s400/xml.jpg" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">I copied this element, which specifies the location of each circle and, thankfully, a code for the electoral area, into a text file, getting text that looks like this:</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-839RP8T8apo/V4U4ElrkAUI/AAAAAAAApoA/e8sVXzOcvXIZqzK9izfjmQe1S7eymEqKgCK4B/s1600/Screen%2BShot%2B2016-07-12%2Bat%2B19.33.41.png" imageanchor="1"><img border="0" height="214" src="https://2.bp.blogspot.com/-839RP8T8apo/V4U4ElrkAUI/AAAAAAAApoA/e8sVXzOcvXIZqzK9izfjmQe1S7eymEqKgCK4B/s640/Screen%2BShot%2B2016-07-12%2Bat%2B19.33.41.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">To get the raw x, y positions for each circle I processed this text file using an awk script (credit for awk-ing goes to <a href="http://www.cse.wustl.edu/~garnett/">Roman Garnett</a>). Using an xml processing tool may be more efficient (or at least more sensible).</div><div class="separator" style="clear: both; text-align: left;"><span style="font-family: "courier new" , "courier" , monospace;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"></div><div class="p1"><span class="s1"><span style="font-family: "courier new" , "courier" , monospace; font-size: x-small;"><b>awk 'BEGIN {RS="<"} /^circle/ {gsub("[[:punct:]]", " "); gsub("data id", "dataid"); for (i = 1; i <= NF; i++) {if ($i ~ "cx" || $i ~ "cy" || $i ~ "dataid") {printf "%s ", $(i + 1)}} printf "\n"}' input_file >> output_file</b></span></span></div><div class="p1"><br /></div><div class="p1"><span style="font-family: inherit;">I rescaled these data so that every demographic indicator lies between 0 and 1, and then matched these data with far more easily obtainable data on how each electoral area voted from <a href="http://www.electoralcommission.org.uk/find-information-by-subject/elections-and-referendums/upcoming-elections-and-referendums/eu-referendum/electorate-and-count-information">The Electoral </a></span><a href="http://www.electoralcommission.org.uk/find-information-by-subject/elections-and-referendums/upcoming-elections-and-referendums/eu-referendum/electorate-and-count-information">Commission</a>. (NB: the raw numbers are inverted in scale when collected from the website, because they indicate pixel positions from the top of the graph element.)</div><div class="p1"><br />I am a little uncertain on whether one should make this data openly accessible. On the one hand the raw numbers I used are all publicly accessible on The Guardian's webpage (with a bit of work!), and could in principle be retrieved from the <a href="http://infuse.ukdataservice.ac.uk/">UK Census</a>. On the other hand The Guardian didn't publish the numerical data, and so I will respect that and not do so here. These instructions should be sufficient to allow you to get the data yourself should you wish, and I would suggest contacting The Guardian if you want to do anything remotely commercial with them.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div><br /></div></div>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com4tag:blogger.com,1999:blog-1931373673946954854.post-81260404273863605022016-06-19T14:00:00.000+02:002016-08-04T10:25:43.266+02:00Predicting the Brexit vote from the betting market with R<div dir="ltr" style="text-align: left;" trbidi="on">There is currently an intriguing (one might say terrifying) mismatch between the many opinion polls on the coming EU referendum and the betting markets. The poll analysis website <a href="http://whatukthinks.org/eu/">http://whatukthinksthinks.org /eu</a> presents a 'poll of polls' that puts Remain and Leave neck and neck at 50%-50%, but on betfair.com the implied probability of a remain vote is (as of 12pm on June 19) 70%.<br /><br />Tight polls don't necessarily mean the outcome is uncertain. If every poll gave Remain 51% and Leave 49% then we could be quite confident that Remain would win - they only need 50% + 1 vote. When the vote arrives, if 51% say Remain then we can be 100% sure that Remain has won.<br /><br />But how to compare directly what the polls and betting markets think? The <a href="https://www.betfair.com/exchange/plus/#/politics/market/1.118739911">main betting market </a>indicates the probability that Remain or Leave will win, not their respective vote shares. But in <a href="https://www.betfair.com/exchange/plus/#/politics/market/1.122981377">a sub-market</a> one can bet on the vote shares themselves, generally in 5% intervals. Using the odds on this market we can find out what the betting market thinks (on average) the Remain vote share will be.<br /><br />At the moment this sub-market looks like this:<br /><br /><a href="http://2.bp.blogspot.com/-wA2yZDT0_i0/V2aE7q6nOaI/AAAAAAAAph0/PXvyGRWzSms6fZE_v_TyI8byofo-QD9NQCK4B/s1600/betfair.jpg" imageanchor="1"><img border="0" height="306" src="https://2.bp.blogspot.com/-wA2yZDT0_i0/V2aE7q6nOaI/AAAAAAAAph0/PXvyGRWzSms6fZE_v_TyI8byofo-QD9NQCK4B/s640/betfair.jpg" width="640" /></a><br /><br />We can take the average of the blue and pink numbers for each percentile as estimates of the reciprocal of the cumulative distribution function (CDF) of the vote share. These are quite coarsely spread at 5% intervals, so to get a better idea what the true CDF looks like we can fit a Beta Distribution to these numbers. A <a href="https://en.wikipedia.org/wiki/Beta_distribution">Beta Distribution</a> is a general distribution for describing quantities that can take values between 0 and 1, just like the vote share. In R:<br /><span style="font-size: x-small;"><br /></span><br /><div class="p1"><span style="font-family: "courier new" , "courier" , monospace; font-size: x-small;">x = c(seq(0.4, 0.7, 0.05), 1)#voting percentiles from betfair</span></div><div class="p2"><span style="font-family: "courier new" , "courier" , monospace; font-size: x-small;">iy = c(28.5, 17.5, 5.05, 2.95, 3.83, 11.5, 52.5, 92.5)#betfair odds for each segment</span></div><div class="p2"><span style="font-family: "courier new" , "courier" , monospace; font-size: x-small;">y = 1/iy #Get estimated PDF points from odds</span></div><div class="p2"><span style="font-family: "courier new" , "courier" , monospace; font-size: x-small;">Y = cumsum(y)#get CDF points from PDF</span></div><div class="p2"><span style="font-family: "courier new" , "courier" , monospace; font-size: x-small;">objective_fn <- function(parameters) sum((Y-pbeta(x, parameters[1], parameters[2]))^2) #Create a sqaure error objective to minimise</span></div><div class="p2"><span style="font-family: "courier new" , "courier" , monospace; font-size: x-small;">best_parameters = optim(par=c(1,1), fn = objective_fn) #Get minimising parameters</span></div><div class="p2"><span style="font-family: "courier new" , "courier" , monospace; font-size: x-small;">plot(x, Y, xlab="x", ylab="P(Vote share < x)")</span></div><div class="p2"><span style="font-family: "courier new" , "courier" , monospace; font-size: x-small;">z = seq(0,1, length.out=100)</span></div><div class="p2"><span style="font-family: "courier new" , "courier" , monospace; font-size: x-small;">lines(z, pbeta(z, best_parameters$par[1], best_parameters$par[2]))</span></div><div class="p2"><span style="font-family: "courier new" , "courier" , monospace; font-size: x-small;">print(paste(c("Expected Remain vote: ", best_parameters$par[1]/(best_parameters$par[1]+best_parameters$par[2]) )))</span></div><div class="p2"><br /></div><div class="p2">Which gives us an output of <b>Expected Remain vote: 0.53</b>, and the figure below:</div><div class="p2"><a href="http://1.bp.blogspot.com/-66FCfaG2ZVg/V2aFyQkzPCI/AAAAAAAApiA/1yyJI4gy9LIVdyBwbOSR1iVaxxYlkGbSgCK4B/s1600/voting.jpeg" imageanchor="1"><img border="0" height="468" src="https://1.bp.blogspot.com/-66FCfaG2ZVg/V2aFyQkzPCI/AAAAAAAApiA/1yyJI4gy9LIVdyBwbOSR1iVaxxYlkGbSgCK4B/s640/voting.jpeg" width="640" /></a></div><div class="p2">We can also plot the probability density function to see how likely any given vote share is:</div><div class="p2"><br /></div><div class="p2"><span style="font-size: x-small;"><br class="Apple-interchange-newline" /></span><span style="font-family: "courier new" , "courier" , monospace; font-size: x-small;">plot(z, dbeta(z, best_parameters$par[1], best_parameters$par[2]), type="n", xlab="x", ylab="p(Vote=x)")</span></div><div class="p2"><span style="font-family: "courier new" , "courier" , monospace; font-size: x-small;">lines(z, dbeta(z, best_parameters$par[1], best_parameters$par[2]))</span></div><div class="p2"><br /></div><div class="p2">to give the figure below, which shows that the predicted Remain vote share is peaked around 0.53, and pretty much symmetrically distributed on either side. </div><div class="p2"><br /></div><div class="p2"><a href="http://1.bp.blogspot.com/-1v3crBxvKUc/V2aHSZvzcPI/AAAAAAAApiM/im1i2x-7dTIt9wsXd6MXI9jIcwry_S2QACK4B/s1600/voting2.jpeg" imageanchor="1"><img border="0" height="293" src="https://1.bp.blogspot.com/-1v3crBxvKUc/V2aHSZvzcPI/AAAAAAAApiM/im1i2x-7dTIt9wsXd6MXI9jIcwry_S2QACK4B/s400/voting2.jpeg" width="400" /></a></div><div class="p2"><b>So the betting market predicts that the vote share for Remain will be 53%, compared to the polls which put it at 50%.</b> Fitting a Beta Distribution to the data from the market allows us to see what probability the market assigns to any given vote share. We will see in a few days whether the market or the polls are more accurate...<br /><br />Update 8pm BST June 20. Things have picked up somewhat for the Remain campaign, though uncertainty is still very high. The market currently looks like below, giving a prediction for Remain of: 53.8%± 10.7% (95% CI)<br /><br /><a href="http://2.bp.blogspot.com/-aPnqIj0JbBA/V2g9d9JId_I/AAAAAAAApi4/400v7FnjfLE6vnMLHHTdQo79z1ppilHDACK4B/s1600/Screen%2BShot%2B2016-06-20%2Bat%2B19.59.42.png" imageanchor="1"><img border="0" height="294" src="https://2.bp.blogspot.com/-aPnqIj0JbBA/V2g9d9JId_I/AAAAAAAApi4/400v7FnjfLE6vnMLHHTdQo79z1ppilHDACK4B/s640/Screen%2BShot%2B2016-06-20%2Bat%2B19.59.42.png" width="640" /></a></div><br /><b>Update 2pm BST June 23. With the polls now open and all opinion polls in there has been a lot of movement on the betting exchanges. Betfair currently give Remain over an 85% chance of victory. With the market looking as below, the expected Remain vote is: 55.5% ± 8.7% (95% CI).</b><br /><br /><a href="http://4.bp.blogspot.com/-JlHK-2sLoZU/V2vhRLa6IqI/AAAAAAAApjI/sdYXifksa6QzwTvWDUqPA_qZ6qD6yn-sgCK4B/s1600/Screen%2BShot%2B2016-06-23%2Bat%2B08.11.36.png" imageanchor="1"><img border="0" height="292" src="https://4.bp.blogspot.com/-JlHK-2sLoZU/V2vhRLa6IqI/AAAAAAAApjI/sdYXifksa6QzwTvWDUqPA_qZ6qD6yn-sgCK4B/s640/Screen%2BShot%2B2016-06-23%2Bat%2B08.11.36.png" width="640" /></a></div>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com5tag:blogger.com,1999:blog-1931373673946954854.post-23119738667533967482016-02-05T12:37:00.001+01:002016-02-05T12:37:54.233+01:00Some thoughts on academic funding<div dir="ltr" style="text-align: left;" trbidi="on"><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;">Research costs money, whether it be for buying equipment, compensating drug test subjects or simply to pay the salaries of researchers. Much of the money that funds academic research comes in the form of competitive research grants from a variety of national and supra-national research councils (e.g. EPSRC in the UK, the European Research Council, or the National Science Foudation in the USA), or private foundations (e.g. the Wellcome Trust). </span></span><br /><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><br /></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;">Funding from these bodies is allocated by a competitive process where researchers submit grant applications to the relevant body, describing the project they wish to carry out and justifying the cost. Panels of experts then decide which grants to fund. As well as deciding which research gets done, this also has a profound impact on the academic's career progression as universities depend on the money from these grants to maintain their operations. </span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><br /></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;">Because of the high importance of these grant awards, many academics in research positions will spend a great deal of time and effort on preparing applications. Universities may support them by allocating them dedicated time for preparation, or by giving them smaller amounts of money to perform preliminary studies which make the full application stronger. Each applicant knows that competing researchers from other universities will be working hard on their applications too, so they must go the extra mile to succeed.</span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><br /></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;">I wondered about the 'deadweight costs' of this process. Time and money spent on applications is time and money that cannot be spent on the research itself. Ultimately we want a system that produces as much excellent research as we can get. Competition may spur academics to do better research, but it is also costing resources that could be devoted to research alone.</span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><br /></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;">We can model this mathematically. Imagine there are two research teams vying to obtain a grant of size <i>G </i>(a typical grant may be a few hundred thousand pounds). Each team can increase its probability of winning the grant by devoting more initial resources to preparation, either in time, salaries, experiments etc. Call the investment of team 1, <i>A</i> and the investment of team 2 <i>B</i>.</span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><br /></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;">A simple model might suggest that the probability of winning the grant is proportional to the initial investment. In that case, for team 1 the probability to win is:</span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><br /></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><i>P = A / (A + B) </i></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><br /></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;">The expected <i>reward, R, </i>for team 1 is the probability of winning, multiplied by the grant amount, <i>minus </i> the amount invested</span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><br /></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><i>R = GP - A</i></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><i>R = GA / (A + B) - A</i></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><br /></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;">Now, in order to work out how much team 1 will invest we need to introduce two ideas. The first is a Nash equilibrium. This is a situation where both teams have decided on investments<i> A </i>and <i>B </i>and neither wants to change, i.e. neither can increase their reward by changing. This implies that</span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><br /></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><i>dR/dA = 0</i></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><br /></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;">which implies that</span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><br /></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><i>0 = G/(A+B) - GA/(A+B)<sup>2</sup> - 1</i></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><i>0 = GB - (A+B)<sup>2</sup></i></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><br /></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;">the second idea is symmetry. Since in this simple model both teams are identical, they should come to the same conclusion about how much to spend, so when both teams are 'happy' (at the Nash equilibrium)<i> A = B = X </i>so:</span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><i><br /></i></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><i>0 = GX - 4X<sup>2</sup></i></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><i>0 = G - 4X</i></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><i>X = G/4</i></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><br /></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;">so eventually each team will invest one quarter of the grant value into its preparation. One team will be lucky and end up <i>3G/4</i> better off, while the other will be <i>G/4 </i>poorer than before.</span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><br /></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;">With two identical teams then the deadweight cost is <i>G/2.</i> This much must be invested by both teams together to decide who gets the final grant. Nothing is produced from this investment, and each team still ends up with a 50% chance of winning the grant.</span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><br /></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;">With more teams one can perform a similar analysis to find that when there are N teams, each will invest <i>G(N-1)/N^2</i> in the process. So as <i>N </i>becomes large (as it is in most cases), the total deadweight cost will become <i>G(N-1)/N ~ G</i>. In other words, the deadweight costs reach the value of the grant itself. For every £1m the government or private trusts puts on the table to be fought over, another £1m will be wasted in application preparation.</span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><br /></span></span></div><div><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;">But what if this model isn't correct. Maybe the team that puts in the best application always wins. Maybe it really is worth spending another week, another month of research time on preparation? Well in this case the situation is even worse. The resulting incentives look a lot like a famous hypothetical game called a 'Dollar Auction' (<a href="https://en.wikipedia.org/wiki/Dollar_auction">https://en.wikipedia.org/wiki/Dollar_auction</a>). In this game players bid against each other to win a single dollar, with the caveat that everyone must pay their highest bid (just like everyone must pay the cost of their application). Initially bids are low, since bidding a few cents for a dollar seems like a good deal. But once the bids grow over a dollar something strange happens. Players with bids lower than the highest still want to increase their bid, even if it is now more than a dollar, because if they don't win they will lose even more. In such a game the only way to win is not to play!</span></span><br /><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><br /></span></span><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;">These are very simple models and reality will be a lot more complex. Applications can be improved and resubmitted. Reviewing applications filters out poorly thought out ideas. But when we consider the effects of competition in science, we should not only see the positive incentive to produce better research, but also the damaging waste that competition over a fixed pool of resources can produce.</span></span><br /><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><br /></span></span><span style="font-family: "arial";"><span style="font-size: 14.6667px; white-space: pre-wrap;"><br /></span></span></div></div>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com2tag:blogger.com,1999:blog-1931373673946954854.post-38087256605877690892015-01-07T19:50:00.000+01:002016-07-18T23:51:15.895+02:00What we do when we do regressions in social science<div dir="ltr" style="text-align: left;" trbidi="on">The Nobel prize is the most prestigious award a scientist, economist (not really a Nobel prize says every scientist simultaneously), writer or statesman (dubious) can win. As well as conferring enormous status on the recipient, these awards also carry substantial monetary value, both directly and in terms of future earnings. As with any prestigious and lucrative award, we'd like to think that the prizes are given on a purely meritocratic basis. But as we've seen in <a href="http://prawnsandprobability.blogspot.ch/2014/09/is-number-of-female-royal-society.html" target="_blank">previous</a> <a href="http://prawnsandprobability.blogspot.ch/2014/09/more-remarks-on-gender-and-selection.html" target="_blank">posts</a>, academic selections are rarely free from the suspicion of bias.<br /><div><br /></div><div>Is anyone surprised that a disproportionate number of previous winners have been Swedish? After all, the prizes (except for the peace prize) are awarded by a committee from the Swedish Royal Academy of Science. More glaringly, an <a href="http://io9.com/this-map-of-nobel-prize-winners-shows-a-disturbing-leve-1446346273" target="_blank">overwhelming majority of winners have come from western nations </a>which are culturally similar to Sweden.</div><div><br /></div><div>So are the Swedes culturally biased? I thought this question would be a good way to demonstrate the basic techniques used to answer such questions in empirical social science, as well as to discuss the problems with these approaches. So here we go...</div><div><br /></div><div>Lets start by clarifying the hypothesis: The Nobel committee is biased towards awarding prizes to individuals from nations culturally similar to Sweden.</div><div><br /></div><div>How do we measure cultural similarity? Thankfully the Swedish-founded <a href="http://www.worldvaluessurvey.org/" target="_blank">World Value Survey</a> has toured the world, asking people a series of questions about their values to try and answer this exact question. Their results are broken down into two main axes of values, survival versus self expressive values, and traditional versus secular/rational values (keen observers may note that these terms are somewhat value loaded in themselves!). The results for many countries are shown in the plot below</div><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><img height="553" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/79/Inglehart_Values_Map2.svg/2000px-Inglehart_Values_Map2.svg.png" style="-webkit-user-select: none;" width="640" /></div><br /><br /></div><div>Conveniently Sweden is placed in the top right of the graph (everyone gasps in surprise). We can approximate the cultural distance between any country and Sweden by the distance separating them on this plot.</div><div><br /></div><div>I collected data on per-capita Nobel prize awards by nation (<a href="http://en.wikipedia.org/wiki/List_of_countries_by_Nobel_laureates_per_capita" target="_blank">data source</a>) for 41 countries, along with their cultural distance from Sweden. The plot below shows that more culturally distant countries are definitely awarded fewer prizes.</div><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-5URYR-39cbU/VK10DPaXInI/AAAAAAAAloA/rlsIjsDNMVc/s1600/prizes_v_culture.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="239" src="https://4.bp.blogspot.com/-5URYR-39cbU/VK10DPaXInI/AAAAAAAAloA/rlsIjsDNMVc/s1600/prizes_v_culture.jpg" width="320" /></a></div><span id="goog_1279548707"></span><span id="goog_1279548708"></span><br /></div><div><br /></div><div>So are the Swedes biased then? Not so fast! Of course cultural separation might not be the only force at play here. Western nations are rich and spend a significant proportion of their income on research and development. We'd expect this to yield more and better science, and thus to win more prizes. Sure enough, we see in the plot below that countries with higher research spending do tend to win more prizes (<a href="http://en.wikipedia.org/wiki/List_of_countries_by_research_and_development_spending" target="_blank">data source</a>).<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/--sMRv4mDi8A/VK10PEoJLAI/AAAAAAAAloI/_OScwE5FD8A/s1600/prizes_v_spending.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="298" src="https://2.bp.blogspot.com/--sMRv4mDi8A/VK10PEoJLAI/AAAAAAAAloI/_OScwE5FD8A/s400/prizes_v_spending.jpg" width="400" /></a></div><br /></div><div><br /></div><div>So what a good paid-up social scientist would do next is to 'control' for research spending before judging if any bias exists. For this we need to do a bit of regression. Lets say that the rate, <b>R</b>, at which individuals from a nation are awarded Nobel prizes is partly due to cultural distance, <b>C</b>, and partly due to spending, <b>S</b><br /><br /><b>R = aC + bS </b><br /><br />where <b>a </b>and <b>b</b> are coefficients that express how strong each influence is. Technically what we're going to do is use a <a href="http://en.wikipedia.org/wiki/Generalized_linear_model" target="_blank">Generalized Linear Model</a> with a Poisson distribution to model the number of prizes per 10 million citizens each country receives. With the <b>S</b> factor there, if only research spending is to blame for the disparity of prizes we should find that a is close to zero and statistically not significant. Carrying out a regression like this tells us how likely the correlation of <b>R </b>with <b>C </b>is to be due to random chance, given that <b>R </b>is also correlated with <b>S</b>.<b> </b>When we carry this out in Matlab, (not R stats!), we get highly significant effects for both culture and spending. So a social scientist would say that there is a significant effect of cultural distance on number of prizes, <i>after controlling for research spending</i>.<br /><br />p-values: (culture: p = 1e-12, spending: p = 0.2e-8)<br /><br />Everyone knows however that<a href="http://prawnsandprobability.blogspot.ch/2012/04/why-model-selection-bayes-and-biased.html" target="_blank"> p-values suck</a>. A better way to test whether both culture and spending have effects is to do <a href="http://prawnsandprobability.blogspot.ch/2012/04/why-model-selection-bayes-and-biased.html" target="_blank">model selection</a>. That is, to see if a model including only culture, only spending or both is best at predicting the data we see. I calculated approximate values of the marginal likelihood of the data for all these 3 models - i.e. the probability of the data, based on each model. Comparing these to a simple null model that prizes are given at the same rate to all countries, we get the results below, again showing that including both effects gives a better prediction than either alone (marginal likelihoods shown in log values).<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-TwF5zqodZbo/VK13WOnsJmI/AAAAAAAAloU/C_Accl_c1eM/s1600/prizes_marglik.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="298" src="https://2.bp.blogspot.com/-TwF5zqodZbo/VK13WOnsJmI/AAAAAAAAloU/C_Accl_c1eM/s400/prizes_marglik.jpg" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">So surely now we can conclude that the Swedes are biased? Well conclude away...but be prepared to be wrong. Or right. Who knows? Because although this basic procedure (with a little more tweaking and a few more control variables) is ubiquitous in social science, where the <a href="http://en.wikipedia.org/wiki/Observational_study" target="_blank">observational study</a> is king, it rarely tells us anything conclusively.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">On the simplest level, there may well be an additional factor which we haven't controlled for that causes all these apparent effects. Maybe its really cultural distance to the USA that matters. Maybe (God forbid!) Sweden really does produce unusually excellent research. In estimating bias we often assume that fundamentally all nations, genders or whatever category are genuinely equal before any bias kicks in (for example in this <a href="http://is%20the%20number%20of%20female%20royal%20society%20fellowships%20a%20red%20herring/?" target="_blank">previous post</a>). This may be the enlightened thing to do, but it is certainly a strong assumption that we should be aware of.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">But beyond these simple problems, there lie deeper issues. What we have just done is a case of <a href="http://en.wikipedia.org/wiki/Ecological_regression" target="_blank">Ecological Regression</a>, which, though widely used, is essentially a precise codification of the <a href="http://en.wikipedia.org/wiki/Ecological_fallacy" target="_blank">Ecological Fallacy</a>. For instance, if developing an academic culture, producing highly quality research and winning international science prizes tended to make a country more liberal, richer and more secular and self-expressive, then we'd see exactly the same results, without any need for a bias on the part of the ever fair and impartial Swedish Academy. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">So what can we conclude then? Generally, to be very cautious about over-interpreting correlations, or even significant regression coefficients after controlling for other factors. Causation is a slippery beast, and Ecological Regression won't pin it down for you, no matter how many stories the Daily Mail runs saying that <a href="http://www.anorak.co.uk/288298/scare-stories/the-daily-mails-list-of-things-that-give-you-cancer-from-a-to-z.html/" target="_blank">X <i>causes</i> cancer</a>. Is the Swedish Academy biased towards western scientists? I genuinely don't know, and this data won't tell me. I wouldn't be surprised if they were, any more than I'd be surprised if grant awarding agencies were biased in favour of men. But unless someone can do a double blind randomised test, you can continue believing whatever you like about the meritocratic value of our most prestigious prize.</div><br /></div></div>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com0tag:blogger.com,1999:blog-1931373673946954854.post-432382854709255302014-09-25T10:31:00.001+02:002016-07-18T23:55:29.231+02:00Is the number of female Royal Society Fellowships a red herring?<div dir="ltr" style="text-align: left;" trbidi="on">Personally I'm in no doubt that conscious and unconscious, personal and systematic biases hinder women's progress in science on many levels. However, the recent outcry over the number of women selected by the Royal Society for university fellowships is (probably) a red herring.<br /><br />Lets break it down statistically. We'll be looking for significant statistical deviation, at the 0.05 level, and doing 1-tailed tests (only looking at whether women are under-represented, I doubt if anyone including myself much cares about the possibility of men being under-represented)<br /><br />Here is the table of application and acceptance rates since 2010 from the <a class="g-profile" href="https://plus.google.com/105620501225599197603" target="_blank">+The Royal Society</a><br /><img src="https://pbs.twimg.com/media/ByTumTXCYAE9rqv.jpg:large" style="-webkit-user-select: none;" /><br /><img src="https://pbs.twimg.com/media/ByTumTXCYAE9rqv.jpg:large" style="-webkit-user-select: none;" /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-qiT2AjyTbTU/V41QSNuVMkI/AAAAAAAAppE/cATb0TQH-BUpQlu17kMQpzkL2i8IIyMBwCLcB/s1600/rs.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="412" src="https://4.bp.blogspot.com/-qiT2AjyTbTU/V41QSNuVMkI/AAAAAAAAppE/cATb0TQH-BUpQlu17kMQpzkL2i8IIyMBwCLcB/s640/rs.jpg" width="640" /></a></div><br />The key ingredients here, in assessing whether the Royal Society shows any bias, are the number of women accepted, <i>and the percentage of female applicants.</i><br /><br />Doing a 1-tailed binomial significance test for the number of women accepted each year, based on the number expected give the percentage of applicants, we get the following (I've used the numbers above, though other sources give 43 for the number of awards in 2014 - I don't know why that discrepancy exists):<br /><br />P_2014 = 0.0164<br />P_2013 = 0.437<br />P_2012 = 0.533<br />P_2011 = 0.440<br />P_2010 = 0.972<br /><br />(p values calculated using http://graphpad.com/quickcalcs/binomial1.cfm)<br /><br />Clearly 2014 is very different from the other years, where the number of awards to female scientists was pretty much as expected (in fact we almost saw a significant over-representation in 2010, but as I said before, who cares? I think we can live with that!)<br /><br />So it looks like 2014 saw a sudden emergence of bias in the Royal Society's selections. But we need to consider the fact that we're performing this significance test 5 times. If you look at anything for long enough it's going to do something 'odd', and no doubt generate Twitter outrage. The standard way to account for this in statistics is a correction for multiple hypothesis testing. The best standard method is probably the <a href="http://en.wikipedia.org/wiki/Holm%E2%80%93Bonferroni_method" target="_blank">Holm-Bonferroni method</a>, which says that to find any significant results here we need to take the p-value we deem to be significant (0.05) and divide it by the number of tests (5). So we're left with a new significance level of 0.01, just below what we see in 2014. I'd say the best interpretation of this years acceptance rate then is that it's suspicious, but not sufficiently low to be definite evidence of bias.<br /><br />Of course, we should be asking questions about why only 20% of applicants were female in the first place. The Royal Society, like almost every scientific body, could probably be doing more to encourage female applicants. But given the applications we saw, there is no firm statistical evidence of biased selection. Of course, if we saw the same sort of results next year that would change everything - but given the outcry I think we can rest assured that that won't be allowed to happen. I'm also a little concerned about that 40/43 discrepancy which might make this result just significant - thats the absurd binary nature of significance tests for you. If you want to do and compare a Bayesian analysis then please do and I'll happily post the results.<br /><br /><b>Update 1: Luca Borger points out that accepting so few women applicants this time is unlikely to mean more apply next year. And Ben Sheldon points to the fact that fewer women were selected at every stage of the process. The problem with assessing bias against women in science is that the overall effect, which is undoubtably large, comes from many cumulative and feedback effects like this, so the outcry against the Royal Society may be useful in combating this, even if </b><b>in isolation their selection does not appear statistically biased.</b><br /><b><br /></b><b>Update 2: David Sumpter <a href="http://www.collective-behavior.com/?p=525" target="_blank">shows</a> how the cumulative effect of many individually non-significant biases can lead to huge system-wide imbalances.</b><br /><br /></div>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com0tag:blogger.com,1999:blog-1931373673946954854.post-6646566438213007092014-05-18T20:37:00.002+02:002016-08-22T12:24:30.665+02:00<div dir="ltr" style="text-align: left;" trbidi="on"><div style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt; text-align: left;">This is a blog post I wrote about our seminar speaker at IFFS on Friday May 16, mainly for <a href="http://collective-behavior.blogspot.se/" target="_blank">David Sumpter's blog</a> and the <a href="http://www.iffs.se/" target="_blank">IFFS website</a>, but it won't do any harm to post it here as well. I and the speaker, Michael Osborne, did our PhDs together, and now he's one of Oxford's foremost experts on Machine Learning. In this presentation he described how Machine Learning will change everyone's employment in the coming century...</div><div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: 'Trebuchet MS'; font-size: 28px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div><div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: 'Trebuchet MS'; font-size: 28px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The future of automation</span></div><b id="docs-internal-guid-db0e0b95-1098-6b74-8358-68fed55edd4f" style="font-weight: normal;"><br /></b><br /><div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Depending on your perspective, technological development has been saving us from drudgery, or destroying our livelihoods, for centuries. From the very first domestication of animals we’ve been finding ways to perform tasks with less human action since civilisation began.</span></div><b style="font-weight: normal;"><br /></b><br /><div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Last week </span><a href="http://www.robots.ox.ac.uk/~mosb/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">Dr. Michael Osborne</span></a><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> from the University of Oxford gave a presentation at the Institute for Futures Studies showing his predictions about which of us will be losing our jobs in the century to come. Michael, as an expert in Machine Learning, is interested in which jobs will be automated as a result of increasing artificial intelligence in the Big Data era. He and his colleagues have been impressed at the rapid pace with which tasks that were seen as impossible for computers to perform, such as driving a car or translating accurately between different languages have become almost routine.</span></div><b style="font-weight: normal;"><br /></b><br /><div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Machine Learning itself can be used to predict which tasks are ripe for automation. First they gathered data on the skills necessary to perform over 700 different jobs, such as social sensitivity, manual dexterity and creativity. A panel of experts was then asked to predict which of 70 specific jobs would be automatable in the near future. Using Gaussian process regression, Michael and his colleagues learned a relationship between the skills a job requires and the probability that a computer will be able to perform, and extrapolated this relationship to the 700 jobs the panel had not evaluated. </span><a href="http://www.oxfordmartin.ox.ac.uk/downloads/academic/The_Future_of_Employment.pdf" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">Their results</span></a><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> give us a view on which sectors of the economy will be most affected by the continued rise of artificial intelligence. The graph below shows, by sector, what proportion of jobs are at low, medium or high risk of being automated. In general, those jobs requiring the most </span><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: italic; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">necessary </span><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">social interactions and/or high level creativity appear to be safest from the coming tide of job losses, but none of us can rest too easy!</span></div><b style="font-weight: normal;"><br /></b><br /><div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;"><img alt="Inline images 1" class="GH" height="447.3812949640288" src="https://mail.google.com/mail/u/0/?ui=2&ik=ace58ae0e8&view=att&th=1460b5c945d5d7b2&attid=0.0.1&disp=emb&realattid=ii_1460b5bfa38983a1&zw&atsh=1" width="472" /></div><b style="font-weight: normal;"><br /></b><br /><div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">However, we shouldn’t be too distressed at this imminent redundancy. As Michael pointed out for example, while technological progress has reduced the workforce in agriculture from almost 40% of employment in 1900 to around 2% today, the total unemployment rate has barely changed. Technology has allowed society to move human labour to more productive areas. The results of Michael’s analysis also show that it is generally lower paid, lower skilled jobs that will be destroyed, giving hope that people will be able to move into better employment, if society provides them with the necessary skills.</span></div><div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div><img alt="Inline images 2" height="198.41481481481483" src="https://mail.google.com/mail/u/0/?ui=2&ik=ace58ae0e8&view=att&th=1460b5c945d5d7b2&attid=0.0.2&disp=emb&realattid=ii_1460b5c1f918dadf&zw&atsh=1" width="472" /><br /><br /><br /><span style="font-family: Arial; font-size: 15px; vertical-align: baseline; white-space: pre-wrap;">Nonetheless, Michael also showed examples of resistance to change, such as the guilds of Tudor England blocking the development of machines for making textiles in fear of their members livelihoods. The ever increasing rate of automation, and the subsequent need for people to continually adapt to new careers and find new skills presents society with a powerful challenge, that may require new social contracts, such as a guaranteed citizen’s income and much more investment in public education to solve. It will be exciting to see where this process takes us!</span></div>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com1tag:blogger.com,1999:blog-1931373673946954854.post-15610495023028439212013-06-28T17:55:00.001+02:002018-11-08T12:11:14.311+01:00Meta-contagion? The spread of people asking about the spread of clapping<div dir="ltr" style="text-align: left;" trbidi="on">At some point soon I mean to sit down and write a proper post about our <a href="http://rsif.royalsocietypublishing.org/content/10/85/20130466" target="_blank">recent work</a> analysing the spread of clapping behaviour in audiences. Before that though, a quick analysis about how media attention on the paper spread over time. The graph below shows the times I was first contacted by different media outlets over a period of about 2 weeks. Social contagion in papers about social contagion? Maybe there's a paper in that...<br /><br />And is there some evidence of a second wave, starting from when a press release was finally released in Swedish?<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-2MwYpL78Ym0/Uc24iOsRP3I/AAAAAAAAddc/bcBSnSrqKiA/s1600/contact_times.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="480" src="https://3.bp.blogspot.com/-2MwYpL78Ym0/Uc24iOsRP3I/AAAAAAAAddc/bcBSnSrqKiA/s640/contact_times.jpg" width="640" /></a></div><br /><div><br /></div><div class="separator" style="clear: both; text-align: center;"></div><div><br /></div><div class="separator" style="clear: both; text-align: center;"></div><div><br /></div></div>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com0tag:blogger.com,1999:blog-1931373673946954854.post-34993465904567895392013-03-08T14:16:00.002+01:002017-06-16T22:45:36.427+02:00Rethinking Retractions<div dir="ltr" style="text-align: left;" trbidi="on">This time last year I had to retract a<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002308" target="_blank"> paper I had recently published</a> as a result of a coding error that invalidated the analysis. Now, one year later, a revised version on the same paper is about to be re-published, complete with an analysis of <span style="color: red;"><b>ALL THE DATA</b></span>. Broadly speaking the results are the same as before, the methodology is still pretty novel, my career may just about have been salvaged from last years wreckage. With the whole episode (hopefully!) behind me, I wanted to write an article reflecting on the experience. While my view is obviously coloured by my own difficulties, I hope it will have some relevance to other scientists as well.<br /><br /><b>UPDATE: The relevant re-published paper is now available <a href="http://www.ploscompbiol.org/article/info%3Adoi%2F10.1371%2Fjournal.pcbi.1002961" target="_blank">here</a></b><br /><b><br /></b>--------------------<br /><br />Almost exactly one year ago I started this blog. I was also down in Australia, about to give a seminar entitled 'Prawns and Probability: Model Selection in Collective Behaviour'. The centre point of the presentation was going to be the work I had recently published on identifying interaction rules in groups of prawns. As the name of this blog suggests, it was also going to be the subject of one of the early posts here too. Having spent about 18 months on the research and writing before getting it published I was feeling pretty pleased with myself...<br /><br />Back in the UK my friend and colleague from my PhD days, <a href="http://www.robots.ox.ac.uk/~mosb/" target="_blank">Michael Osborne</a>, was also playing around with the prawn data, after I had passed it on to him as a nice example data set for him to test his numerical integration methods on. There was hope we might get a nice conference paper out of it. All was well with the world.<br /><br />One night while I was finishing up my presentation slides I had a message from Mike come up on the computer. The conversation that followed is still starred in my gmail:<br /><br /><span dir="ltr" style="background-color: white; color: #222222; font-family: "arial" , sans-serif; font-size: 13px; font-weight: bold;"> Michael</span><span style="background-color: white; color: #222222; font-family: "arial" , sans-serif; font-size: 13px;">: hey rich</span><br /><div style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"><span style="color: #888888; display: block; float: left;">11:45 </span><span style="display: block; padding-left: 6em;"><br /></span></div><div style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"><span style="color: #888888; display: block; float: left;"> </span><span style="display: block; padding-left: 6em;"><span dir="ltr" style="font-weight: bold;">Michael</span>: it's going ok, I hope</span></div><div style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"><span style="color: #888888; display: block; float: left;"> </span><span style="display: block; padding-left: 6em;">hey are you ready for some news</span></div><div style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"><span style="color: #888888; display: block; float: left;">11:46 </span><span style="display: block; padding-left: 6em;"><span dir="ltr" style="font-weight: bold;">me</span>: bring it</span></div><div style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"><span style="color: #888888; display: block; float: left;"> </span><span style="display: block; padding-left: 6em;"><span dir="ltr" style="font-weight: bold;">Michael</span>: dave reckons you only used 1/100th of the data in the .m files you sent us</span></div><div style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"><span style="color: #888888; display: block; float: left;"> </span><span style="display: block; padding-left: 6em;">rather than 1/2 as it seems you intended</span></div><div style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"><span style="color: #888888; display: block; float: left;"> </span><span style="display: block; padding-left: 6em;">basically just data from a single trial</span></div><div style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"><span style="color: #888888; display: block; float: left;"> </span><span style="display: block; padding-left: 6em;"><span dir="ltr" style="font-weight: bold;">me</span>: ...</span></div><div style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"><span style="color: #888888; display: block; float: left;"> </span><span style="display: block; padding-left: 6em;">.........</span></div><div style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"><span style="color: #888888; display: block; float: left;"> </span><span style="display: block; padding-left: 6em;">um, ok</span></div><div style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"><span style="color: #888888; display: block; float: left;">11:47 </span><span style="display: block; padding-left: 6em;">what leads you/him to this conclusion?</span></div><div style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"><span style="color: #888888; display: block; float: left;"> </span><span style="display: block; padding-left: 6em;"><span dir="ltr" style="font-weight: bold;">Michael</span>: well, looking at the code</span></div><div style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"><span style="color: #888888; display: block; float: left;"> </span><span style="display: block; padding-left: 6em;">our evidences approximately match yours on the 1/100th dataset</span></div><div style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"><span style="color: #888888; display: block; float: left;">11:48 </span><span style="display: block; padding-left: 6em;">it's actually good news for us, because running on the whole dataset is crazy slow</span></div><div style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"><span style="color: #888888; display: block; float: left;"> </span><span style="display: block; padding-left: 6em;">which allows us to make the argument that choosing samples is important</span></div><div style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"><span style="color: #888888; display: block; float: left;"> </span><span style="display: block; padding-left: 6em;"><span dir="ltr" style="font-weight: bold;">me</span>: ok, but how did i manage to only pull out 1/100th?</span></div><div style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"><span style="color: #888888; display: block; float: left;">11:49 </span><span style="display: block; padding-left: 6em;">is it just 1:100:end?</span></div><div style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"><span style="color: #888888; display: block; float: left;"> </span><span style="display: block; padding-left: 6em;">or are you only goijg on the evidences?</span></div><div style="background-color: white; text-align: left;"><span style="color: #888888; display: block; float: left; font-family: "arial" , sans-serif; font-size: 13px;">11:50 </span><span style="color: #222222; display: block; font-family: "arial" , sans-serif; font-size: 13px; padding-left: 6em;"><span dir="ltr" style="font-weight: bold;">Michael</span>: David: so there is something weird about the scripts we got<br /><br />it seems like there is a bug that means that only 1/100th of the data is used<br />14:32<br />instead of 1/2 like they meant<br /><br />me: ha<br /><br />David: lines 12-15 of<br /><br />logP_mc_...<br />14:33<br />so prawn_MC_results_script just hands it these cell arrays<br /><br />and then it divides them in half 100 times<br /><br />I think the code is supposed to just take every second row<br /><br />but it takes every second cell, and does this over and over</span><span style="color: #222222; display: block; font-family: "arial" , sans-serif; font-size: 13px; padding-left: 6em;"><br /></span><span style="color: #222222; display: block; font-family: "arial" , sans-serif; font-size: 13px; padding-left: 6em;">----------------------------------------------------</span><span style="color: #222222; display: block; font-family: "arial" , sans-serif; font-size: 13px; padding-left: 6em;"><br /></span><span style="color: #222222; display: block; font-family: "arial" , sans-serif; padding-left: 6em;"><br /></span></div><div dir="ltr" style="text-align: left;" trbidi="on">In the 5 minutes it took to have that conversation my mood went from buoyant to despairing. Mike and his colleague <a href="http://mlg.eng.cam.ac.uk/duvenaud/" target="_blank">David Duvenaud</a> had found an error in the code I had used to analyse the data in our paper which had in a stroke invalidated all our results. This had a number of extremely unpleasant repercussions.<br /><br /><br /><ul><li>I was now due to give an hour long seminar in ~3 days that focused on some completely false results.</li><li>The paper I had been writing with Mike and David was now floundering without a data set, and my contribution had been wiped out</li><li>The blog I had started had nowhere to go (hence the lack of posts over the last year!)</li><li><b>Worst of all</b>: I had to tell my co-authors on the original paper that our results were invalid, that we would have to retract the paper and that it was <span style="color: red;"><b>ALL MY FAULT</b> </span>for not checking the code well enough.</li></ul><div>I won't bore you with the exact details of the next few weeks. Suffice to say I had a very drunk Skype conversation with my boss who was very good about the whole thing, I somehow gave a successful seminar despite having "<span style="color: red;"><b>CAUTION, POSSIBLY INVALID</b></span>" over my most important results, and after crafting an extremely apologetic statement the paper was retracted. Mike and David found other data to play with. I wrote about some older topics in my blog. I didn't sleep very much for a few months.</div><div><br /></div><div>The general unpleasantness of the whole experience led me to reflect on the nature of retractions and mistakes in the scientific literature. My conclusions:</div><div><br /></div><div><ul style="text-align: left;"><li>Mistakes like this <b>must</b> be relatively common. I may not be the most thorough person in the world, but I am far from the most careless. I made a similar mistake during my PhD but caught it shortly before publication (another few sleepless months there...). Any work that involves a lot of involved computational analysis of data by one or a few people must have a small but significant chance of including a coding error. Many of these doubtless have little impact on the results, but some will.</li><li>My mistake was only caught because <b>I gave my code to someone else</b>. While this now makes it terrifying to do so every again, it also shows the value in journals insisting on code being made available. Given how involved some analysis of large data sets is becoming it is implausible to expect anyone to replicate your results without seeing your own code. The chances of peer-review catching this sort of error are somewhere between very small and non-existent.</li><li>The business of retracting a paper is <b>far too stigmatising. </b>To be fair to PLoS, who published the paper, they were extremely good about the retraction and certainly didn't accuse me of anything underhand. Nonetheless, most peoples' first reaction on hearing I was retracting a paper was similar to <a href="http://www.shoalgroup.org/" target="_blank">Andrew King</a>'s: "Retracted? What did you do?" (actually, Andrew was very nice about it too, but his was the only reaction I had in writing!). Many other people gave me a there-but-for-the-grace-of-God-go-I look and said how awful it must be. Most of the stigma I felt came from the wider community who did not know me personally, but knew of websites like <a href="http://retractionwatch.wordpress.com/" target="_blank">retraction watch</a>, which, while aiming to shame fraudulent scientists also gives all retractions a a bad name.</li></ul><div>Now I understand that retractions have often been associated with gross mispractice. Some successful scientists have been made a retract whole careers worth of publications after it was discovered they had been intentionally falsifying data. Of course this sort of thing needs to be stamped out as vigorously as possible.</div><div><br /></div><div><b>BUT....</b></div><div><b><br /></b></div><div>If mistakes are common (my assertion), and retracting a paper is awful (my experience), that seems like a recipe for encouraging cover ups and quietly ignored errors in the literature. I am not ashamed to say that the night I found out about my mistake I was initially tempted to ignore it. I'm glad now that I didn't, but a the time the little devil on my shoulder was trying to persuade me it wasn't worth the ensuing misery to correct an error in one paper among thousands, that the methodology was still sound, that it wasn't <b>that big a deal. </b>And therein lies the problem - a mistake in the literature seems like a small thing. In contrast, retracting a paper seems like a <b>huge</b> thing. Especially as it wiped from the record some of the work I was most proud of when my publication list was already a little sparse.</div></div><div><br /></div><div>In conclusion, based on my experience I think there should be an easier, less painful and less stigmatising way to admit to serious but non-fraudulent errors in published work. The type of mistake I made will, I believe, only become more common. It doesn't mean everything the authors did was wrong, nor does it necessarily imply that there was any foul play. We should also advocate for making data <b>and code </b>publicly available alongside published work so more mistakes can be picked up before they have a chance to become accepted results. More should be done to create a system for distinguishing between mistakes and fraud.</div><div><br /></div><div>Meanwhile, my advice to other scientists doing similar work to me is:</div><div><br /></div><div>a) Don't trust the results in papers as being revealed truth just because they are peer-reviewed. </div><div>b) I'm not going to tell you to 'do the right thing' if you find a mistake in your own (published) paper. Just be aware you might not be able to sleep until you do!</div><div>c) Go and check your code again now!</div><div><br /></div><div>Please get in touch if you have had any similar experience, or if you disagree about anything I've written here. I'd be glad to know how people in the scientific community feel about these issues.<br /><br /><b><a href="http://prawnsandprobability.blogspot.ch/2017/06/rethinking-retractions-rethought.html">Follow up post - Rethinking Retractions: Rethought</a> - details of everything that has happened since this post was first written</b></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><br /><br /><br /></div></div>Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com6tag:blogger.com,1999:blog-1931373673946954854.post-88530386805127855962012-05-27T19:57:00.000+02:002012-05-27T20:03:55.861+02:00Pigeon Navigation (4): Identifying LandmarksIn this last post on pigeon navigation we'll see how we can identify the most important or "information rich" parts of a pigeons flight paths, and then equate these to the landmarks the pigeon uses.<br /><br />Using the idea that a pigeon learns, and then attempts to follow a memorised `habitual route', we saw in the <a href="http://prawnsandprobability.blogspot.se/2012/05/pigeon-navigation-3-habitual-routes.html" target="_blank">last post</a> that we could use previously recorded flight paths to predict what future flights by the same pigeon, from the same release site would look like. We could assign a probability to any future path, thus deciding whether it was predictable or not after considering the past flights. The fact that paths typically became more predictable over successive flights was evidence that the pigeons were learning routes home and then sticking to them.<br /><br />But how does a pigeon learn a route home. It is unlikely that it imagines a perfect line on the ground below it, representing some kind of idealised route it wants to follow. Memorising a complete continuous path, which has an infinite number of locations along it, is <i>hard</i>. Instead, the generally accepted hypothesis is that a pigeon learns its route by memorising a small number of <i>landmarks</i> which act as waypoints. This idea, known as `pilotage', supposes that the bird reaches one landmark, then reorients itself to head for the next until it reaches home.<br /><br />Can we detect where these landmarks are, using the methodology we've developed so far? Of course we can!<br /><br />Recall that we <a href="http://prawnsandprobability.blogspot.se/2012/05/pigeon-navigation-3-habitual-routes.html" target="_blank">previously</a> assumed that a flight path always consisted of 100 recorded positions, starting at the release point and ending at the home loft. We predicted future flights by using these 100 points on each flight path to estimate a <i>habitual route </i> that the bird was trying to follow. We predict that future flights will also look like this habitual route, plus some variation that changes from flight to flight.<br /><br />In principle we can choose to ignore some of this data. We can, if we want, choose to estimate the habitual path using only a subset of the data we have. For example, we might choose 10 random points of the 100 we have of each flight, then try to estimate the habitual route from these.<br /><br />The first important point to understand for identifying landmarks is that <i>such an approach will have varying degrees of success, depending on which points are selected.</i> Consider the figure below<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-JybsGiGtJjk/T8JmoC3n0UI/AAAAAAAAVmg/s-5dj3i75xo/s1600/gausslandmark.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="252" src="http://3.bp.blogspot.com/-JybsGiGtJjk/T8JmoC3n0UI/AAAAAAAAVmg/s-5dj3i75xo/s640/gausslandmark.jpg" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">In each case the faint black line is the same simple bell curve. The black dots indicate 3 points on this curve that we are "allowed" to know in order to make a guess what the whole curve looks like. If we draw a smooth line through these three points we get the two red lines. Hopefully it should be clear that the red line on the left is a much better estimate of the bell curve than the very low red line on the right. Therefore, if I wanted to remember 3 points to try and remember the whole of the faint black line, I would better off choosing those on the left, rather than those on the left</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">But this is exactly what the pigeon has to do! It needs to remember a few landmarks so it can remember the whole of its route home. This suggests the second important point for identifying landmarks: <i>the points that allow best estimation of the habitual route are the same points as the pigeon's landmarks. </i>That means that we assume the pigeon does a good job of choosing the most efficient way to compress its habitual route into a few key points.</div><div class="separator" style="clear: both; text-align: left;"><i><br /></i></div><div class="separator" style="clear: both; text-align: left;">Since we can never measure exactly how well we have estimated the habitual route, we do the next best thing and test how well any set of possible landmarks allows us to predict future flights. If we call the subset of times that correspond to landmark locations at <b>t_<sub>lm</sub></b><i style="font-weight: bold;">, </i>and the full set of times as <b>t_<sub>full</sub></b>, then our task is to choose <b>t_<sub>lm</sub></b> to maximise <b>p(x_<sub>n+1</sub>(t_<sub>full</sub>) | x_<sub>1</sub>(t_<sub>lm</sub>), x_<sub>2</sub>(t_<sub>lm</sub>), ..., x_<sub>n</sub>(t_<sub>lm</sub>))</b></div><div class="separator" style="clear: both; text-align: left;"><b><br /></b></div><div class="separator" style="clear: both; text-align: left;">And when we do this, we find landmarks that correspond to recognisable features of both the paths and the landscape beneath, such as below (remember I promised to explain what those red dots were...?)</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-q2fIU0qn5IQ/S_kKfHYo2OI/AAAAAAAAR9I/bfjyKwD-VqE/s1600/1200dpi_mann_fig2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="390" src="http://1.bp.blogspot.com/-q2fIU0qn5IQ/S_kKfHYo2OI/AAAAAAAAR9I/bfjyKwD-VqE/s400/1200dpi_mann_fig2.jpg" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">The landmarks (the red dots) tend to be where the paths are very similar, since here the paths are a very good predictor of the habitual route, where the pigeon flies somewhere unexpected - the apex of the `C' shape - and where the path curves sharply. They also tend to be on the edge of forests and villages, above major roads and obvious features such as a church spire. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">[NB: Those with a machine learning background may see that this process is largely analogous to two other ideas. Active sampling, where we take data in an intelligent way to maximise our predictive power while minimising collection costs, and reduced rank Gaussian process approximations, where we use a subset of data points as `inducing points' to create a lower rank covariance matrix and speed up calculations.]</div><br />Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com0tag:blogger.com,1999:blog-1931373673946954854.post-21368862299021074472012-05-14T15:09:00.000+02:002012-05-14T15:17:10.411+02:00Pigeon Navigation (3): Habitual Routes<b>[NB: This post, and the rest of the pigeon posts will be quite mathsy. I've done my best to keep the maths as simple as possible - it should be possible to follow the argument without understanding all the working! On the other hand, if you do want to see the maths done properly, please <a href="http://171.66.127.193/content/8/55/210.abstract" target="_blank">read it properly formatted</a>!]</b><br /><b><br /></b><br /><b><br /></b><br /><br />Way back when this century was young, the <a href="http://oxnav.zoo.ox.ac.uk/" target="_blank">navigation group in Oxford</a> published a series of <a href="http://www.pnas.org/content/101/50/17440.long" target="_blank">papers</a> <a href="http://rspb.royalsocietypublishing.org/content/272/1558/17.short" target="_blank">demonstrating</a> <a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1863466/" target="_blank">that</a> pigeons, when repeatedly released from the same site, would learn to follow the same route back the home loft each time.<br /><br />If a pigeon is learning and following a route this ought to make its flight patterns <i>predictable</i>. If those flights are getting more and more predictable we should be able to observe that by using a model to predict the flights with increasing accuracy. In other words, we should have a model which gives the probability of a flight path, and that probability should get higher as our predictions get better.<br /><br />In the <a href="http://www.blogger.com/blogger.g?blogID=1931373673946954854#editor/target=post;postID=7399344935921665819" target="_blank">last post</a> we saw how to assign probabilities to individual flight paths using a Gaussian process (GP). The precise probability of a given flight path depended on the mean, <b>m</b>, and covariance, <b>S</b>, of that GP. I told you that the covariance dictated how likely the flight path was to be either smooth or wiggly, and we used the straight line between release point and home loft to create the mean. For convenience I'll write down the resulting probability as:<br /><br /><b>p(x| m, S) = GP(x; m, S)</b><br /><br />Now, the reason we chose the straight line path to be the mean was that if we only look at a single path, and we have never seen this particular bird fly before, there is no reason to assume it will fly either one side or the other from this most efficient route. We don't expect the flight path to be perfectly straight, but we don't know beforehand in which direction it will go.<br /><br />Imagine instead that we had already seen the flight paths below.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-kRErKHb_Ah4/S_kKl43B4GI/AAAAAAAAR9s/VJSMtxzA4es/s1600/example_habitual_route.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="315" src="http://2.bp.blogspot.com/-kRErKHb_Ah4/S_kKl43B4GI/AAAAAAAAR9s/VJSMtxzA4es/s400/example_habitual_route.jpg" width="400" /></a></div><br /><br /><br />Now we should have a very good idea where the next path is going to be, somewhere close to the paths we have already seen. It looks like the pigeon is following a particular route home every time, so its unlikely to suddenly fly directly south from the release point next time. Obviously it doesn't fly exactly the same path every time, but each new flight path is like an imperfect attempt to fly some memorised route.<br /><br />Lets imagine that we could look into the mind of the pigeon and retrieve exactly what its memorised route looks like. We can call this route <b>h </b>(for 'habitual'). Then we might replace the earlier straight line mean path with the one we now know the bird is trying to fly<br /><br /><b>p(x | h, S) = GP(x; h, S)</b><br /><b><br /></b><br />(I'm going to assume for simplicity that we know what <b>S </b>is, but in practice we would infer it from the data)<br /><br />Whats more, if we want to find the probability of several flight paths by the same bird, each an attempt to replicate <b>h</b>, we can simply multiply the probability of each path together, because each one is <i>independent</i> if we know <b>h</b>.<br /><br /><b>p(x<sub>1</sub>, x<sub>2</sub>, ...,x<sub>n</sub> | h, S) = GP(x<sub>1</sub>; h, S) x GP(x<sub>2</sub>; h, S) x ... x GP(x<sub>n</sub>; h, S)</b><br /><b><br /></b><br />Hang on! Surely those flight paths aren't really independent?! After all, they all look the same. Yes! But the reason they look the same is that they are all attempts to replicate <b>h</b>. They way each path varies around <b>h</b> <i>is </i>independent. All the shared structure in the paths is located in <b>h</b>.<br /><br />Ok, thats nice, but the problem is that we don't know what <b>h </b>is. All we can see are a few paths that look a bit like <b>h</b>. But never fear - Bayes is here...we can use those flight paths we have actually seen to infer what <b>h </b>is. Recall <a href="http://en.wikipedia.org/wiki/Bayes'_rule" target="_blank">Bayes' rule</a> which allows use to reverse the order of the conditional probability:<br /><br /><b>p(h | x<sub>1</sub>, x<sub>2</sub>, ...,x<sub>n</sub>, S)</b> = <b>p(x<sub>1</sub>, x<sub>2</sub>, ...,x<sub>n</sub>| h, S) x p(h | S) / p(x<sub>1</sub>, x<sub>2</sub>, ...,x<sub>n</sub>| S)</b><br /><b><br /></b><br />But we seem to be creating more trouble for ourselves. Now we need to know two more things, <b>p(h | S) </b>and <b>p(x<sub>1</sub>, x<sub>2</sub>, ...,x<sub>n</sub> | S)</b>. Are we digging a hole for ourselves?<br /><br />No! The first of these terms is a <i>prior</i> distribution. It's how likely we think any particular habitual route would be before we see any real paths. So we need to place a probability distribution over a path that could lie anywhere between the release point and the home loft. Thats exactly what we learned how to do in the <a href="http://www.blogger.com/blogger.g?blogID=1931373673946954854#editor/target=post;postID=7399344935921665819" target="_blank">last post</a>! Before we see any real paths theres no reason to expect the habitual path to be on either side of the straight line, so the probability of <b>h </b>is exactly like a single path on its own, with the straight line as a mean.<br /><br /><b>p(h | S) = GP(h; m, S)</b><br /><br />The second term is the joint probability of the real paths, if we don't know what <b>h</b> is. This can be calculated by integrating over all possible values of <b>h.</b><br /><b><br /></b><br /><b>∫ p(x<sub>1</sub>, x<sub>2</sub>, ...,x<sub>n</sub> | h, S) x p(h | S) dh</b><br /><b><br /></b><br />and this is where the theory of Gaussian processes really helps us. Integrals like this are really easy to do (using a few matrix rules...easy is a relative term!) when everything is Gaussian...<br /><b><br /></b><br /><b>∫ p(x<sub>1</sub>, x<sub>2</sub>, ...,x<sub>n</sub> | h, S) p(h | S) dh = </b><b>∫ </b><b>GP(x<sub>1</sub>; h, S) GP(x<sub>2</sub>; h, S) GP(x<sub>n</sub>; h, S) GP(h; m, S) dh</b><br /><b><br /></b><br /><b>= GP ([x<sub>1</sub>, x<sub>2</sub>, ...,x<sub>n</sub>], [m,m,...,m], Σ)</b><br /><b><br /></b><br />where those square brackets indicate that we're concatenating the n paths and n copies of the vector <b>m</b>. We have a big new covariance matrix, <b>Σ</b>, which is generated from <b>S. </b>If we want to mathematical details of how we do that I would suggest reading them in <a href="http://171.66.127.193/content/8/55/210.abstract" target="_blank">this paper</a> (Open access), where it's all properly formatted without the restrictions of html. Here we'll just assume we know the matrix rules for multiplying Gaussian distributions together - check out Appendix A of <a href="http://www.math.uu.se/~rmann/papers/thesis.pdf" target="_blank">my thesis</a> if you're interested.<br /><br />The upshot of all this is that we can calculate a probability distribution, <b>p(h | x<sub>1</sub>, x<sub>2</sub>, ...,x<sub>n</sub>, S)</b>, which tells us how likely any given habitual route <b>h</b> is, based on the flight paths we've already seen. Does it work? Well, look at the picture below, showing a set of flight paths from two birds, and the distribution (mean + variance) of the inferred habitual routes. The faint black lines are the flight paths, recorded from GPS. The thick black lines are the 'best guess' of the habitual routes, and the dashed red lines indicate how uncertain these are. The dashed black lines indicate where most future flight paths are expected to lie.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-3BTPIbLVgj8/S_kLM3NDAoI/AAAAAAAAR_4/q4rEkX8Qri4/s1600/2predictions.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="315" src="http://1.bp.blogspot.com/-3BTPIbLVgj8/S_kLM3NDAoI/AAAAAAAAR_4/q4rEkX8Qri4/s400/2predictions.jpg" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">If we can infer what the habitual route is, we should then be able to do exactly what I suggested at the top of this post, and make some predictions about where future flight paths will be, and see if these become more accurate as the birds learn their routes. In fact, we have already done everything we need. We calculated the joint probability of n paths, assuming that we didn't know the habitual route.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><span style="text-align: -webkit-auto;"> </span><b style="text-align: -webkit-auto;">p(</b><b style="text-align: -webkit-auto;">x<sub>1</sub>, x<sub>2</sub>, ...,x<sub>n</sub>| S) = </b><b>GP ([x<sub>1</sub>, x<sub>2</sub>, ...,x<sub>n</sub>], [m,m,...,m], Sigma)</b></div><div class="separator" style="clear: both; text-align: left;"><b><br /></b></div><div class="separator" style="clear: both; text-align: left;">if we want to calculate how probable path <b>x<sub>n</sub></b> is, based on the previous n-1 paths, we simply calculate the joint probability of <b> x<sub>1</sub>, x<sub>2</sub>, ...,x<sub>n</sub></b>and of <b>x<sub>1</sub>, x<sub>2</sub>, ...,x<sub>n-1</sub></b></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><b>p(x<sub>n</sub> | x<sub>1</sub>, x<sub>2</sub>, ...,x<sub>n-1</sub>| S ) =</b> <b>p(x<sub>1</sub>, x<sub>2</sub>, ...,x<sub>n</sub> | S) / </b><b>p(x<sub>1</sub>, x<sub>2</sub>, ...,x<sub>n-1</sub> | S)</b></div><div class="separator" style="clear: both; text-align: left;"><b><br /></b></div><div class="separator" style="clear: both; text-align: left;">So lets test it out. In the experiments done in Oxford the typical procedure was to release the same bird 20 times from the same spot. What happens if we calculate how likely each of these flight paths are, based on the previous 2 flights immediately before?</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-0_vwJ-kY9xk/S_kKjSyJOuI/AAAAAAAAR9g/f8z7agakcyk/s1600/300dpibigPredict.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="http://1.bp.blogspot.com/-0_vwJ-kY9xk/S_kKjSyJOuI/AAAAAAAAR9g/f8z7agakcyk/s400/300dpibigPredict.jpg" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">That graph shows the (log) probability of the next path becoming higher over time - the pigeons are becoming more predictable, just as we hoped! Where the y-axis is equal to zero is the point at which the paths are more predictable than if we just guessed wildly without seeing any other previous flights. Therefore we can say that after ~10 flights the birds are more predictable than random - they have learnt their routes. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">This demonstration of increasing predictability is a nice alternative way of seeing route learning that was previously shown by measuring the average distance between successive paths, but its not immediately clear why it should be any more useful. In the next post we'll see how we can see now only that the route is being learnt, but <i>where</i> it is being learnt, to identify where the landmarks the pigeons use to navigate are and what they might be. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><b><br /></b></div><div class="separator" style="clear: both; text-align: left;"><b><br /></b></div><br /><b><br /></b><br /><b><br /></b><br /><br />Richard Mannhttp://www.blogger.com/profile/13769786662205310175noreply@blogger.com0