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<!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" />
<meta name="author" content="Jonathan J. Borrelli" />
<title>Appendix - Selection against instability: stable subgraphs are most frequent in empirical food webs</title>
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xaXpygKB5dWVlFrb5mQOydwB7i0J6ubFjh7npdh1XXdKUdEAmoj3W5Db4m4QE1LVCapO1XgH2D%2FkB08JF83SNM9ZhZf5I9%2B7Rz8J%2FI3IIfrMb5LHcjByu%2BUvGUKxQ%2FkcaLYdZ40f8JWOkw%2BA4iEBtlYSmddP1HFw%2FdKtShd1YQrncW61ZeqsIAcmYleEIEKAhx1ry8ND6aFh%2F8V9VHtiPdBPGObFcRVTzQgcz40RO7WEpW0ba3k2z3i6zBvlL9xO4ka%2F1EVnLTSa%2Buo%2BmkNzrwWDyPcz4lWOAxAp2%2BTrKORXoPGvm6d5aKpzt50u4573rAOfhP1CUXfpbjl36l4XWpysmXBCr6PbGqqsTnSRvReJFj4Xl9rvYfHFko%2FqPrb9YYEpV1CsKxTiSrXhisap%2F%2BC%2B6uu%2F8CZVz1iWlY7fGdnKxd2eM7WS2lcof2ANfjrBHRsoomvoE%2BuiF%2FpXpsCFnJYVZIVk7UsM85PYeLXYofPYf9H42YsMdtUq%2FMTd79Ho4bf2S7Gq9PVRxDC6lKG1VpVBV9cvFXGr6oVycSFZ%2FauXWquCnKooTpFvcfy0YiWVX%2BI%2FD8UOPXvp%2BE5%2Bom3JHt0IXP6MxS5U%2FAqovYd3l62%2BltAxkkq6q7T7LR3xT%2Bcz8gICtekEZU28Hq3d9JkEXhcfclufMmmZusgqh%2B5ww%2B7k3Vwcd9XbHh1JbiELt3Fu67QYbvmRs%2FCg5by%2Fr3TnRlZXhu7ijl5o6qlZ%2BrQrpkGp3PTVTZFKpwyqWabnH%2Fce5T6T%2Ba%2BNhiV5b7vOiQWG1XNvGNzngqewJWX%2BO7%2BPupIVbDas6n8HPju1ZMXmrvkcJ%2FhQ1Ya89RaqlV9P%2Bu0DacBdfrcx5rlPXMqW5%2B%2FVv8cfLHuP4t%2F6ZgDdhPFR8DGRmRoMk6R6Yc9MgU65TdN%2BKH32y1gyJruJn9x3%2BQ4%2B1zUvkZZYoyqq52HfJR1T3OUca8Ss9VrVhgoR1nngEaUXl%2BEwnEj%2B5Lg7fIsNx%2FsEWwXdT%2BI%2FD8UOO75zqXdKad2WS2XFS9L3XHH%2FH3m9r4nePnO%2F7Ys%2Fk6qErLYy0lJ6agZeeN%2FwwccYGT1QoEPwJqvCIveWiGhaw0jqw4olppFhqa8b%2FC%2BdTSMfJ8SlX%2Fp%2B918A8%2Bor5fxP%2FNTuvM3TtoeHe%2FThlVC9NKslFVNwNc6blq86mEHcyuYlSiOqOvmLPKAkLhPzbxCP6j62%2B9f0qwwjHOiiWI80kKVVktH0mD79lpNHuEPZ9yx6Q3iKpAKUiIS%2BdKK4ZmEpg0z1gZ%2FjhD12TDPydq2A6DMfTF%2FCCSlRZO0fLXPJsLM9o5%2FJ%2BS1UU8jHffrIaAVo2H93qXRX3g%2FV5fZeaqtAxwpeeqH3Trtr4z%2Boo5qyzjqus%2FuvixZ5JszVn3T9bAuDz2jM54qngC1XyGupJhFtiO%2BapVZZeFqvBG9bLT64cJ8zEW2juBk3sMRUbTMA9ggQX%2FxuNExVKRpvwrklXWFA5ZaUTl2d%2FRNOseP4pZYB18QoGHvnMyyNx5aXCbSf9x47s%2BV9Vv%2FQ2nBFacueFU%2BfxH298aemcj%2BAollosRz0QwI9ygM56qmBNbdKZpA5nYorobKAtV1yzEXc4xMjWQ2Xzu%2BE7FzK0BZnfYN3ezIOaa7cYL%2BL91Kw6%2BwooX2cJdqES1Yl3fwkumIJzZeGJX6gvVmzcdfOOV0JL6h1jjlZuVAa78e1Xd1scYiWP5mRhHlc9%2F9PFYhwhrwqz%2BfBOLKP8AaClJVcxhKRb%2FbHAgM5D5bBD67tR1UFX8XUSS8JcpqS8QN340V4kWuHQHNRnlvBhKfbH7Vr8H6fkKWPUwq6eGeuYgy1ZNqcPGOz6%2BR9SZ1V7of6CvfPi4Z0Y6zuSjamFa6bv2XhUpNzRDI2ruGXdyLNC1U%2FVs9fxHH4912DsxkOnMds9tPgd%2FPNEpvw99qvKrPL3r8FZaC3Vl26BE558ratV5h5brrxqrSjZWe2oL%2FbGSS62BPrSGWgP31eFR1ZYP7%2F23Jv5tWjqelgG%2BMe9VoU1C5X6i5fIfCh7GYRjtwIM65C%2FhnJc6S%2F9XnldPHdKgJoWtn6q6WQa0qq4yZuwG%2BY%2FxN2PGjBkzZsyYMWPGjBkzZsyYMWPGjBkzZsyYMWPGjBkzZsyYseVnpcgqGjNm7EYTNd1MEGK0kaUITo7BMiNUZj1D6RBgIRmWfxAO%2FFpHr1Vl6qOHh2WCxTJWwxWpzzycMW1rU6TJ5QMexTRpz5cqLpp7Tvw4WJlhBGp%2BBo7p79qA4m5Bmngs%2F5fXJWZFOsN86VmYRFb3agsKnuuswqLabGc2wig6q2t%2BjKX3TfZN4tc1P6Y0CV1XT7c%2Buvjor4tXpcgXo5daH5QVaUf8fJhRy0f8ShZltOdLW1lj1bW5cG1qRVxmL77HjjgmvE9R%2FzPNIBmL4pz2%2FS4zGXS56nQyJ70tVuA43%2FnhhXCDWLVTsHLHWSNKIav78VHwuOp%2FIIMipCx1YtdARq2zGvoUS986vnXcXu35aXmpqlsfXTwuQ3eviwCdg68rVx9cjSm%2F72K8qp0Ka69yLaEXBOWD7i5NogZ0pBfagNRNqJFxxsqEFfWPwLL%2B09uwHqe3jaYjJJ1eWCSe0SKcjaeJvbvxVmCVVIo0mRsZbeHSfvd3JVC1cDG3mnyFKyZVeNRZBYmKOKvFKsJysjg6o%2BzmrAAX9OBrN1HQg9KAVKq66wPik8r6uPCT1iQBH4jbAtCO9c7Gmb8KgVM%2BfqdTH%2Fyu9bWEasxz4a06Nd5xLnewJl9aLgT0WD2Vqon8Ot6IYncG62CUwRrSIF%2FgCGtkgnsnosow2zrYZMcO3HPU%2FiPwqxhxq40cvmkhMjI00%2FaV%2FG5xiVySOYQtkapLVRdU5HNTVb3sG3VWD28VlUA7vFWus3rbPl76oT28l06y2%2FaVj6ru%2BnC8vD4Cb%2FWFUMG%2FT4XH2hcKkKBASfsT6vpA4Buj1ydHk5BqNakbb68qVa4%2BFe7kXqsqkWWbd4sS5D7Nq8qnh9fhq6ASUbCGlDUMzYSvyueGPCTnI541tkrS2bvxqGrS9jZl7inw218N%2Fe75%2B2RdsdMygrCWQjrAh6pe8igqsjo4SsrB0VkV1VPprIau8tLvS92Xk%2BgMXVU0X8ZyaqQIe9z14TWS14fjYceRL%2B1585dWnQL%2FP5PsR790%2F%2BRHvwQRrA%2FU9YliQHhQVZ%2FkNwJPM6d8qumNqgkP%2F0mw8lE1zh7dUfyzR3fECSoZKDuzd6IZZrcwKtdQ8FVVjzwQWaTGlIj%2F8bZ2hrK8%2FmKhznTC9jV7MiHrLH2pir3s0qaWj5Q6KQe3zmoyT2uZzqoVE5InEAzWijBJLnFcKMQlb2pRH8sWpuLEltWH42E86rbr1I2LlGV43EFndIv7J6NbZDvXuNsHHvmrqvpgcshjZLvsG56mlmoIoIpQuUZV3SSUF1VlSr1JNtlU%2FLPJJlp9qqruehS%2F3vUolXr3DHZmdah6zyC%2Fm3sGfdu%2F353R5d2ebHiTzlX1GloX7%2Bisiscu11nlsp9izM7nFX8lu4aOEJeoD253wLdAkNfHqb%2B4Uzne1nzFunMl2j7LFl%2F1byOn%2FJ452FykRVV%2B%2FwUv3dqB93QSKHKdW71RtRSqWnUDmQP7T287sJ%2FL6B3bIU1yVbtd284wVNPqYwVwRMWR1T8ALqz12mMbzupQde2xzeesGEaAsoCZ%2B7I7D5y8HqqKTF%2B5qaqrs4r5U97TYn24Ui%2BMSl%2FL5w4rGd%2FUaKUyJBf1YbWjaZALrVXVx6m%2FuFM5Pr%2BN0IR9NxOqNnLKB6m1enX53u354H7lm700rf1vxKgKMUqcrYAU0Qq1jF6xzJjjwH6jGB6jaR4AQ964gTXA%2FzUUPFDv2r6dcu8vxEe%2BHv9Z62vgq7WUlzWibUsKgIsTMuWnqp7OqjUswt%2FeP%2FExJx8CD9Nqw5NRlPrAcBdU67668PbGCiq8837RST9I1ded8qspOrT6urVcqfn5%2B%2Bj4So%2BqOjPn0bQXVUcVbylY8MQuzMOLvLHqKgJ%2Faotc974YP33f44mOxUd%2BQXtZI8ZXERIvM6rq6ay2vyHKvOOP%2BD3f70P2ZwTFdQkq1P71dV%2F18N6uK6tRZeuDNcJ3rzr4ys9V6Ybqy0upij9VnFeLGzFqXMfGUzUvHTyrAXo3UF7W8PeqPBMsU6QUvxVqiFVVOPzcEKrq6Kx2LIoyh1%2FG74dfFt%2F7adrru4qu7qseXp%2BqpdYHE1IDGTUeXnak9k5sPkfXuV36Z4X%2B9Xf2vHMO%2BW4LelR1Tz2KPy8Pk9Pb%2FXrGsmM%2B2v4Gzp8YYrYjN9a7Y2eS5mu%2F%2Ft6bVJ1VlwJqkPepKi1UPRVd3fro43V1fa%2BjPt2o2k7QrQ3Z%2BA4dnVsNXeKUBzolL1%2BbDK7rU%2Fd6XTZELtRtroeDrMTsRDdVxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjBeb6o%2By0Pt5KEzRo61BQha4rq6dBmzsnnUdfrlhLodptTKuFmDVJLn0sd0ZGdafebSRTli2lRY0tO8OVCkMzSS0VYAfPQuvfUp3VeDG%2BiNKTVLFK3ZU7aM6KnDijC0TqWfiqSo2CGxdvO7TnwP7e2RBZwpo1jB9Nss3n5Eu3rMmwTX%2BdtTuaqr4lULqUjgBkOUvuaJT4gG7ntEQYW3qvxWdWaOgsrn8SpSdDAxm6CnAhXk3WKLNXSzKqWKU%2BVVGCxCXi9rBegxCbcDgJy73WXiOQzpbYhBUUKy5Al9TxZ%2BpD6nolyZQaBC1QcgsKloK4S79Y%2F4gKvIWCpm7TwRa3Pr271z2L1ZTe0ajwxWVTFnZSl9cVo5JMl3qq8r3WNSU5VVFTIKKhAlyMV5HVq9nKS9X2J9xomXApF8O0Ckq3lHKYaKHfDZ7unU0wykYMos4oZh1fpFI18QcvyS8vpwJH7%2BQrGPOqi%2FX%2Bo7EOtngJHDEi6L%2F%2Bs6hlU%2FD6CzWFkAqt1jpU9fZmf77wPSuKNxTJURXJp6cCXIyXk7WyVEWioaCnc%2FzgvKzvcsbf3lmuczj6G5UcJoZr7ez5%2B7b%2FraojcFPVijWdBE3gs1SqYquqRNyKW05noTVR0lxzxxrtADVQQkBb8QA4yaiRVjGqFKqipK%2BsJvamNFdzeR5bmse%2BCp930lWAvfEyslaWqrbu7DcFwcI3lIBq78TU0NTQ3olkXn5ZZrftQ6mrX4LAaDthLszH6iaGTa4KaZ0gHqcWFMJVlqq6Gha6AapXcHpzA2A%2B9y%2FWIqTUJ0%2FySZ324drbsueLHBt5BYmKm4AEFqw6G89CemT1w%2FuTtfJUjRf0n3HCo%2B%2BdPdC5iq1iBzqFgrAi%2FL26%2BW2rL74B0S0vUNwd91fBRFHzx7TNkOL%2FNcnu%2Fh83n6q6Ghb6qhf6AW3lAmD0F0j9pR0lQZ3a81a10iHJSLzUm9e%2FpRIXtfdACCJRo7YAeuPFHN6LfOvfklTWB7%2F%2BLe%2BzKk9V%2FV66%2B9KmNvy6qa37EiHI7otDd4QCa9F8aKImBUhkNY5MRVngeRKRjifZxqM3n6olvSrTPEMnQK1sAIyEG5liIXcATLtXVxooBCX40ttDEN%2FmjzQUr4MXg4Hm%2B6O5M1y7%2BhSTD4SzpPvQeOGt9Pq3vM8qjaq9s6e3UUa80qgahTzx6W2nt4UfjhK6g9DfgxxnP9%2BJzB7D%2B6ikuB8SXrEPKUSKfYZ731WOqtaYHXyNUQitm8%2FVPUMnQK18AIwZdXcATLvXglGwRa89kT%2F%2BeCvWeKUNIr7b%2Fpdn%2Fd3kUxHVC%2B9P1NKoauvk14gNLtTBZnFqW%2F3om1ngo8BHzaT9Q8Ps4eeEk20%2BB3vo%2FD0prRSwxlqvJdmdv6dQCbuMB%2FoqR9Xm3F3rB8CVyAAvlwC4OANMFwHUzQB3gbokPzh%2F%2FPFNuSlcxK%2BrEeSjELUYLyOqN1WHZmQ3Jza0EBtcEGgx7wp2AkmSGGaURUlymJjHPZB%2FvTH4d%2FbcXPJXS9YenlZaBcRIEBNL%2FJxn%2FlqJg82hnSQGbaTkeLeLydIgJQWcyw1%2F3Rlgan3UVHVUHIGB9lFKWq%2FoKkg%2BKlHdeGtMRlS%2FEMAf7955hpNV1RTFfwKhLYYpkcO0DmK%2BrmlBqNnzfHFgwb9GrQUbJ8GfH9QrCZjh5zReUbZ5C7R4i85IKZIe7iPEdF6tlT9AXV4ZYEHVUupTiqpxGahqZ55COsVyPGjMhsoZUhVuEYUC1cp61BaU31DOpsspEafyWxUrlW4L6tJN2VgB%2Fkghh6a0uX8w5o3nSQ%2F3gYmUcgacyw2v73NLz6HVpxRV41Iy8MtUCVj9ZwDGtNqzRf0TY8aMGTNmzJgxY8aMGTNmzJgxY8aMGTNmzJgxY8aMGTNmzJgxY8ZujsFqucCyqMe0eRbGjEmI2nhR%2FHG6FDdmTYPuyzRFFsxGn7Euw%2FqXMzQ8LucGaZThkjub4WXQkmmasrIxYyU5%2Bbrm7ksJ6coR7obNoDIUgX%2FNSo1DlOxuxtV32QT8D%2FgMRcKk%2BWOQRvmKgrSGoRNgjuA1djarJcu%2FXfgzuKpUq%2Fx57MRgjX6dmqhhorKyW1sW20ofqz5LDw%2F327dsPDLvLTS%2FWYrnS%2BJoZ1GwrvZM08R4nFand95Qtux%2B0ckDH00N9c6mvpCPkbgwbCAzmsaF1mHFiklUiBnIgGh3SqwTbbyorOjBqK2ZFHhJTaTVuaW4fJ2rVTd4y4ZTvbN%2BMp0C35UdP4prB1cxaw%2Bl%2FL0TQzNd2eM7Wa2VblPeAZe60pFBF%2B0fZbpYyll6%2BDgsJ4J4iTwNEms3SxV4kZ2D3sJd1vkks6V4viSOdhYF67RnmFQjd%2FuTO2%2FwH8n98sJACwjIeqFfVtDa923hbnyiHUjWte%2FLaB3l2FpnLV5UQW6rry2HDCmD4JavQB40nVsq1Dl4S%2BPFxovn1sGysmoFPsUaISwHAaxWdMs6Zfmw1A%2BXwnESbjglb2gUssrpU4QoMuhcUYfLXulhaWfp4fEa7bhGl7gzgLN2s1RVRBlWuGySUcjqhaesV6Vj3e0ZJZJV4OWqZY5xqTSf0p3Cui%2FtvlW%2BEA2lJIZf5p9RFSHC5LQ%2BvLX4EcnVdNd86SDXLMibAkc8FnTfQ%2FelwVvUeFRYbWZ87AO3PKnET9qhr01U2QJ8KHc6zNzjX1jaFQik0%2F5qN3ewtLN08bzlEyC7CkFY382mqnDZJIkaXnhaq1Kx7vakkdXB62qseJTuFObWYPAzFD0R4l6xD%2FEcf2xssSvLl2W7H1HiG9k4HGc4VguHkSv%2BOU3L7wHrL6OqwAeejwCWb%2BgxNHNunWIUmwyhHut0WNncjRfbc4r9yfzXdkXAbCtAXIySZbgcLOUst2PRruI8pyiGwmn1SFZZqnKXpVHDC08VN6Nh3e1JqZE%2BUSVk1SNqVdWGs3w7DEiv2FtiyMLB7rnOrMcjysrG4aEZHKvzAixX6XM3TlQZMQR%2B3dTpbRAmx7uyeycgXK2W45%2B%2BtwuSYu1CS0oSvm845SW3IQ%2BYhYAklapRl5uoz2o6qYcvplJYKSRTeaoW3rN%2FDOSNp%2BsQUrCFRFVnX0T7g%2Bi7psZKz1zR%2FeoStapq306uqNaWU1U7frc%2FtvdPibxomHNz%2FRdk4fXGo32TDjbOKFQNPBbN1V%2BeNMnv3BJiNfj11BbWIKNeTguq9vhOjCU4UWVqRrw3dG%2FnpO5NedvTqepgKWedW6eHL6bS0MzH99x8qrrvwT8G8sbTqUrB5uV13Eenuv3jTO%2FlnZWOF94vfz2jQ1TcoGhkymlmSLrU%2BGPHnoH55tniRzT2jCy87vjz4fWOsmCSRNWew3sneP2jykdfcC81%2BOKJQG0gK9ckalbUSKi8ijPVYQ8ihZAqxakcLOUsoftIv0rSta8PyLiFVF5ReaqibyZJw4kXnkpVGlZ3Vx%2Bn%2FcNM52VNuPh%2BA4%2Fx1zN0oqK9kxCPHLK7QanjNvTO2sFyzN13yaTKNpyNstW%2F7b8g0PKdXDBIwEwlTKoaWDXqkmOoocbnk0CgSEjDgwRai7p8Tlbcyys3V02rwx57%2FK2mqB4XY2ln6eKF4Cq8zuqkyLhVmqrcN2nDiReeGqvQsXqKiPpk9SAqzAw%2FFa9ndOTHWPWR7Tju9cydT6mwWM0I7rA67%2FRdMvzJjV3ZcF6wuCsr8sc%2BwfgTuEGU6NtW2ptF7Xvi5uELkwK0REIuyCaoHi%2FF0s7Sw%2BM1Np%2BDqUHjcnhZI9yVFvd54Sn0o2NLURR0yKrzsqbgfq0AzvC2%2F63q9YzHxSEg7Jk7tkN9HsqD7p0YyHRme%2BY2n4MkTqf8HFZzagv%2BuQF3dXCYWil6xYH9fPotlHcP7Gcrbh7eTVZqxi8fZCtVj72wlLMEyn7Nr8Tb6sUdsmmNl%2FM6X2l4mqMLd7XqaHGfg3I%2Bqemngy3NeKvrvKwput%2Fdt9p50MZSBD0hIOyW08gdBsOsOgX4DopKL2zMFMpJa4fUDsNWQLlu5d0VNxfvNDc14%2Bc4q1r12AtL0UrmKP6cVXiaevGNMXedKV7qoFyf1KOeBvZ6yKrzsqaoY4IGqKkyZszYjeh2qiuHNmbMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmLEym65O7%2FcNb59Dlp1cnvWvuA8FoEYxnda02A2oVVr3SlbMmlyuNM3p9MYZTaf3%2B4YXZ3EZMXp7JrOdWZ36VAp%2FoyzwEUhYfkStC3XBXMGdZ%2FT3fXj%2BPr0rWbHAAuhkTt7Mrobvb5ETbA24WrRYK0al01sani9qw%2F8rU34yL2pW7vK5OPNKG7tyXq3b7%2Bges9SJXQMZSn1Kxe%2BdoOkq2488o%2B0yGtSwJqNK3aPrpWoUBU%2B19k1A4tGvBCMw4BPgpU%2FfW4n6U4nK97ewh4ZY00JeBg11evllhR6QXKfXwbudXYXvnf1kE67f%2FGQTLrClly%2BEoNR4WEUKomYndtHrT7tftKaTHYtIiiR76CUQO5VrGOd0jzfegd9tvIPFkXzy%2BgidZHthoQbeirVeo9QfhcebFqLajkWnhjUcyoum0UJyXVe3%2Bqw9qF%2B5mtHDU0G8E7uGZij4MAggIB6F2W8eVdc1xxdxfwssH%2BsfX1zXbP8CdXqdy6p1eh28%2B5Dju7K49g7Xb%2BKaPRxZaeX3zn58D6eICg8SMCusPVaM1fK19pTyhQCoSpfYqguz3S%2ByBpvejQ%2B91HpN1tBc9xh6QxTlTMP%2FscNbVfUROhd8awUqXjgitpBcV9maXA0uqO9YVGpYgTULzlNrvUYZi3VcHZQx54MgrZ6XcSeO9m2%2FEsSjL%2FEHUb%2BdlFXYlaMqq0HJvUROWteuP1%2BoGlsUI4wNy400%2Fjq9Dl4canzCFRY1nUwQykf5rYEMEnx8AKmtwsO4wkJXezZbdVFGqb%2B4A7UuMYq0JHFGyA7tObTHAodJSGcpXPeY1Q7N4J41sOofPkPDfyPHw3X2WAHcWqHpJBGfIyo8yAYZHgPfkKtzUsl2uTFUagQ%2BSri6bRgRPiqnq%2BPGI4miKK7pCsnpW0amaMRz16n1NfUc1SpqUcq8liaahugm1%2F0mUOqI47vniptMrtNbGt5RlOGqMSr81BCrhyCvmjukGp%2B0FY9YfdNJlc6wwFsFUYQ%2F3nEQqFG9Wg1I6B7z%2B%2BT33ZmV1Qfx1p5WtopFc0KSBLxD1Fo5vulKVEu2ywurogaX23R1gZ2KGXChq8u3uuoLL6lP7%2ByxHbQsLmuhEFVkiXODT0hNZx0RND0tKe8r2L%2Fo%2FZNoMsF%2FuU6vg3f3L3J8V9ZRbj23DkdJVfkBO5OYJ6oSjweEaiys1Bl28O5m8cez%2Fs8G7Zlwv2WPrKj6JBP14LrHVgxHVBxZ8XNCWh%2FET4cxcOdqOgT8mJuocvyxHY4ibqlUVVNDZ5ycGnILx3Zlp4akQezbmLEYmcKYRugSQyvVliOLW0qWuPJUZf0ndjkt1DMHCUTubajTu9R1%2FXV6Hbz7kOMTtpg%2Fzt0wu5UglG%2FL%2F%2FcJotLq4w5o1XgR8Kt1iVn10AwmkxC37qcdi7tflDU01z1mtdDAMDeH%2F2vXnFXVB%2FAwh7ddEEQ61PjmguSHHM9qsWR30C8XHiue2lCooUdVVvPkU47nPPmUXDKoHXWmu2F0tGMa1V4IelncUrLEhW1D1CvU0je0Arz%2BvCOL4wYsfPqBOr3FaRaZTq%2BDd%2Fe6KnwUXnPg3G3lfJRYPu6WktCqj1793TGBXJcYI4HB0825lAkmmKSPJad7LDLAuFWIqj6ID92OLghjMAGPNYF62COqCm%2FrZ4X2TuCj108rqalRyuyTrRCS7yCCrhCVA6IG8xHFLM7My5fFLSVLXPm00u5bU19g%2FXmKqyub%2BmL3rblfOYrrNJ3e0vAio1Wp8iuH586OYXCSfbJJrbjo6B5b800sQqqPLt5OdBHxnODHd6oFSJcE2wRqlOa8rIUH%2FKxFiQy675z6EoWeTNLNEt%2BADDBEWCipa4%2Fatae2uJQLhU5vF1Wn93uGF2dxdXoKUuged2vVp1J4JxDWdRpa4Fua8x7Z3jMnn6V63Xl5srjXkyWuPFWFjmhOW7mm6K71dHq%2Ff3gx4yBjl2P9q%2FVdRgvdr9VCqCJdAWFbSha3mKz6RNW9W2PGjBkzZsyYMWPGjBkzZsyYMWPGjBkzZsyYMWPGjBkzZsyYMWPGjBkzVgaDZXN7TCsYM1ZICw1dWVC6QQmPPvtzn72m%2F6DGlfrg%2FDNqWUZc2dpzuOL3PW0xqhwm1PqMVtkZlcJBHsm8P2tcK13GNnkOD%2B%2FvvpO%2BHbsxisPqZ3TdT0lXFzf2Ye9sfDEIq%2BytySDoqfXOxj4kXWUMnTfI2tidv1evSQi8FGU%2F3qbRAUwjleD%2FPh18x%2F%2B98wrtj9KtsQi0Dl3a0gpwsU01Ta0CVY1kSfqyoDYx7f3UoPtlHse8f1m9R%2FDw%2Fu67aO1PoG6H1DPn1a1SOl4QFddrXydZdXVxI%2Bzh53D1IwoQ4kq%2Fh5%2BLqB0y1nilmfHrbD7X%2F09qqq4F2cz1D9hjWZ2y6aaDrJ0hldqhK%2FBzWi%2F87eze1wtEkX3P4TKeoAZBHINZDW2ZlK4AiHASrmMPI8Y8J3i7z1NLeJafYOWmKldbLGV8kY824rdC%2F0gp47aka2qVyNlwmbtEvlUoMnF6eIeoOenV0skqdHFhmS8s6hEKDBIdWlu%2Frwkwzz797NOop9acFxXzf4yBhXhOKWbvxIP7w0Bx1aiHzdH%2BRlXVnb%2BXdxwYKLcXuGE7y4scE%2FAPPtJ8VIYXY3wC1HcHMqDG9xK1ZWlUXSrmIV9clVcFBBkPR3sKjw2n6F2BrF7Q2wWdBd2F38laNczU7bh0fJGPNs5vWUjIzsjr339h6b0Ov6zb%2Fv5PQL897auEuMQLbXleYWvkvxO6uPFF%2FC6%2BqNLFdfSL7nrgrgccXSPZpbmgaFd2%2FCjr7jrULJUd4zYeyfVBk%2BvfiUrnwo3vRmGcFuLeXAsI4oJ3qfhX1%2FSmZXg%2BdqE85%2Bs%2FfP2HttQmaV8WvnGGeusMz%2FCUyV0LZbJSX8Q3CKkRfCYgYxoqj2sV1oA0ZtTxyCxKIKtVl%2FjcGV%2FEaJP4XDEWQaSE7u7oGvmVv%2Fm1pfe6dVy3%2FS2JTFzPnF7n6n4S1FC5aHLDySp0cWEwr4NmVOriOg%2FfTVX5xTsWcdQ%2BtWV0i3W5TdnPWcPWQRE%2BhhiOgOGr%2FikuFCz5oDvJpu9DAtpiHXfbakUHKfjUV7DivsUfzw2FxkbTq0D%2BczSNomUUojZe5LVROW9JfTTIeDz7k9Uu1UI%2FopZC1cLfq%2BsjiJokkRXlSHjsBi54OSyVzGEhrlIIVOhwZxRkNbr%2FiaX3%2BnhCt%2F1lio6P%2FAKyLkw3A0ClKu%2BeChVBc2R1dHQDjwUeU%2BviVlVh4IsHUlV8lo9JCXgYR7YH34MkVK78w%2Bv98a2frJvCG%2BudFSNfnPlJRvdNwoz2X1j1QGb1b%2FfZwlGwSUTN%2Bn9Jsr5JP3z3JY6%2F96Uk23Icf%2BqPFwmlnrkZe5yfifTMRdTbTsS43Bt33pXzsnEYHXHpP9UD7eniRJ3YvX2tfQdvlS9g06OqQ1SxaQmdrPE8Uf1Se1x5WcfpxweK7xRGwZryURVKa2j7yvuc7a9eP1VzOtlFh%2F18HV3c1vxWA%2FIAFSlafEjdanNX9uHnAguRfOlIJ3981O5vkYL78j1kfIPfvGoggyPi%2BVTn%2Fw7aJZ9P4cgJVwj64SGgTiMex3fMMVtpf7xIKL3wU1a9%2Bdzmc6z6hZ%2FaWz3UyYiKgakY4zefs%2BeVMf8HyLO%2Bhf9UXUEgR9Tmj5vssv0zwJWlqkNUGNe7%2BWxSvd2VQ1Y5Uf0cXFYj3Jug8E4H3tOPavzLhzG1L%2B5zjmwAolKVz8kLJV5zMZOujm5V1WrGD6So%2BCy9eH3%2FhWaXtH9X9nxKdUvYGHf%2Bnq1wlO390OdTvbNtLPA8nII3Fg881gaP3%2F8KiIcEyLuv%2FxCdhdVbB8NSPCaUgKJw%2FQf3P7gf7wbJJ9vvLLDQmQWJ745czTsO7O%2FMBhbKNapiSCTkM8cjuBFRkzQDXOy44hn4X4HvpwcZ1z7IL6d5d%2BNPug2nckQNOakf7wSXF1lVRF3q4JgJzonD%2BqSiQHPK5ehd2cG%2FKydVYUx92%2FsMaIOacsxVsRXd3%2BcnN7o6urpzVXxrGylI%2BoBAp%2FThiPFo306%2BcR2eI3%2Fom8%2B1wTiM73mty63gWLLHz8WxI%2Fa2E3f92Qq0MSGV7Z2JxhdSJzfi52bIdePXkxu7sjCK%2Bb6%2F3XAWpCFXiLrDllcrTm3ZcLZco6qgmi2HaW9EJM8Ao%2BPyZ%2FrZoMuFJZ0l77zDkPhtyu1WgF2UzLGcmXLhdyqyylrefb%2F5eZsrE0y7Ck6%2B5G%2FndalqBdp9znh0h%2FSVk6KDKWxTn%2B90dXH1qNp4sfvS6W2gTgd5S8xVqgWgT25EYoNoZn3ra7w%2BzjYa3g%2BddcBmVO8l%2FpD4w8B7h%2FYUpiA88ZCuuAeS%2BtsObWoDvKRGzR9jwm1VvhvDr6vsCKH5Y9%2FyO7B3FYrtOJ6CQGRHuUZVQbX8Jo%2BpgiDJ5xrq0cs9bvBx1TVdaVC8iAj5fad6Duo6uWvivLaR3S28xMqTuwnOmmwqJ1Wbj3rjYXirV4W11A5G1mRaurh6VO2%2BBE5Sk3Mrkogjq%2Fn4HiB3A87AemdpOrewTUIHhMBx%2BL%2BedI36TdAN%2FGwjkKhe1idHmd%2BjjCpe2nTbe42c2NU9p3JF%2FbnqUpO6bp0OUfkkYWRKbMQwMiWfrlTail6KhNTdATzTfmenP9ZP82YqVdde88Y%2F%2FJw6rL1OooqelK4rm2%2B2W%2BBQvlXSc5J851GTu1InXedW8xotTClIDZ1Lv%2BSQng1tWcvVbrVcsb80fVmp61bTRL0LzmjJzfhS8Km66jtnogXVLan7JxCFM2HXoeZNqAxErWijfQcftDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxoz9%2F2u4KsiaNO1gTOYkgWLZCarynNZV6uyy6zRcFwRkdJzX1iee%2F64%2BhRBIyIR81S6W3CtZKy%2BHR53neZrO8zLFT0NXdhn%2BH9PyuTN2Gx0sqydraWHlz8rYyAyt9KVXs7%2BJjBQLTzbfr0X0PUh2BQokTLBsuXhJvoED6LqNFxsvhph9BYoOXl3o2vjRBNN4jJlcMxzU6Azmya41r%2BcgsAakBv9R0VQdJkfnOUHUeV6O%2BLav%2Bv9p5JV9T9zzWzXescZ3caU0LHMMSkrX1kkubXlF1F7rEyWIzRaWJ1YI8UJ%2BvWSB16%2BJzg594yoW%2Fmr3rSqHCX6ZyHUDwY9U5a5rhvWhGVxmhkvQrMwqtq5ZXZvA853ZX3YnSRLZ1suo5rrhFOt%2F9umRqTbSWAaaCJdv%2F%2Bcnn2omdQbN7Mmnbv9nGAX66FQFXZ1v7QXyhNqM%2FsY5lA6rqfNcKr53VkjTlr98EMwJxT6M%2FjryNUUQRvgnSgQNv4nLHP3JnWDutsQDqSHr8kGmr5jYw%2BquIMkKxNnnZX7Ax187qszwETXn17HPiqka%2B4zguOmVi21fJv5P97%2FGGatWadrF3es8FX0iq%2BmdjbrwsGhXOdZYsTb20EsYH1DGow1HhS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2Fy8vL6%2Bvqfn5%2Ft7e339%2Ff29vbo6Ojz8%2FP6%2Bvr19fX19fWmpqbLy8v6%2Bvr4%2BPjT09Pr6%2Bv6%2Bvrr6%2Buqqqrz8%2FPt7e2ioqLPz8%2Fa2trW1taioqLr6%2Bvi4uL5%2BflVVVXNzc3%2F%2F%2F%2FW1tbj4%2BPh4eHq6ur8%2FPz%2F%2F%2F%2F29vb7%2B%2Fvz8%2FP09PTMzMz%2F%2F%2F%2F%2F%2F%2F%2F5%2Bfn19fX%2F%2F%2F%2Fy8vL9%2Ff0AAADZ2dn8%2FPz7%2B%2Fv8%2FPzp6em%2Fv7%2F7%2B%2Fvq6urp6en%2B%2Fv7%2F%2F%2F%2F4ck%2FmAAAA8nRSTlMAGgDUzwIP8SMQ759fCgUvqfDGFeIYA78fbxNTt98%2FhsV%2FBhdD4Q1rRI%2Bvwo3ATxJTD18IoKWasozTETbQ4D40IX5hC6dAMR7RXydvEsRuotKLkZCATYahkzOxQlFqmbZwJiUhFWy1wyJYcXI7gB2XIEFbgjxgiWFtfTSFMy8wSYgEqFBDTSE2KCpnSyZZUaZHRFAsDuWBYJJ7AVZQpC0Z6njBKWjdN4dlMV30iN8bV7%2BzJJeHMRiDYsR6U9yVYxdP2c1dj8CKFZZVFjtaaTxOI9cMKQk4NnBW4PKUOmiNI%2FkwWoQYUdQOSk6GvkUURFSM3n71h14AAB4tSURBVHhe7J2HfyPHmaa%2FYicCDTQCQRAkQWgABpMcDSkOw3CGM5o8Gk2QRjlZOVjBsizbcs5pndb22r7d23ybc7zbdDnnnHPO%2Bd6%2F4FjdIGu6vmp280CtbF%2B%2Fkkn%2Fnip%2BaPSDDqA%2BFOm7J3ncIoDi0NAQkY3d2IaJSws2NNZZnCouduhAsrgf7o4BYy59O4fvn3ROJQKoREkBGKqYytAJCCEQWh220I81TPFIozLaNiCMH4PJr47WIooL1C1isUUsFSwpkMqPAMARDUIFjLcYpj5tGbmqw%2BP6bhz49jZwbZ9S9k8Kd20QQLDdzFbdIz%2FJJ0OFyJFaI6mOcZ6HGOzAGxdi0tN8JL063CmJwi9FviX34m4FUrlxl0PgaBgIbrXJJfVp08yTrbq2tt99bINtCj9p%2F2TiZMMigCzYGa0WxwBgrEjxCBUici56obyLjsF%2B%2Fez8KGLwUdxVJuq9HZcpljX16lgjlaeg8hTpmUVNqubcUjzNKnBbGIBbJS6pT8nMo5ilAms3kxsAbElvsP0DqP2Ttt9KsEYIoBELpWxWDyHMocSDdUiCYMYDvJmAl5sUE%2BcDgiaiLMd6FrTJUmskFaTyEah8JPZsiru8WGL8ouLpx2rfqshkVQix%2Bz%2FOoyRIte64GalXsb5%2FJFX7J4UfxsVI3EUcMyrVrbqAtbVVB1x96q39f4Yo0goYpBJ6EmhWa31nx3WrUmskFaTyJah8iVSofNrqY2umHOeNsyIQ457ksUTnlP0dq4NfVyuLrpTKLlHy0sUp1UASq%2F2Txr2ASAiiwJvNYrVzBLjUbJ4BjlS0qbdE%2F%2FStUgAExAMyWG2jI2EFDd3qujNsWcPOesxquY6d1OOSmiMbId4YCTT%2BBEq0xDjRKACM8mO1HwF2mYm%2BDnRdrRRht5hUmRPHAeD4CdL3jwBEBQ3OheC84VE%2FXi2L1Q9fB14kOgFc%2F%2BzeVgmgJKuVTnzsPSh2iFoncY82uVrw14aH1%2FxCNVbszO4heYa0vDPk30uc%2F%2BOxv2LgBAAGdjSM8R548OvqoxHiUl0bYWyX7R8h1P5J22%2BHUIlAxXSl5FYDeZS67hHgTO%2F%2F2aoPbWy12r9JqFVifFsqsLYGbGtlJyq%2BV2TuBRrA3WTgs%2FAY70S30519XFebg19X3520%2BbakctBO2j%2BZ%2BNt23qsdwduyWCWnjjB1h%2FZvdWkqhPxKVhi3gMamh2Ilhn304xeIaTVJpVlsTp9FLRt3F9DPgvtmX1czbf4FSeXghcT9k4WXLYxtg8oYrLJRKZNTC7XWa7R%2Fq1RDCDfq7RltpDwixPTcjIdii1R87MYnptUktdKYn6Pz89ZSJj6l6k8NcA%2Bc9bqavvmF6jbdHqwW0vYP5%2Fq9dLGo7qVTrY5OXKnXr0yM7m3V%2BFzIAs4S0crEckCmBDOedY1UCmI3%2BtN0LjUucan0yDOycjD8PZk4VJDCB3%2B%2FqmmtSqlc68g2dUYKlLJ%2FUrgzMl73Gu3xESfFqorzwO0OsXiI4kmrCe%2FSRoQ4T3slOK2ea0qa001Tgci0E2TiQkVk5tHooO9XnYJDWcP3TzovT4xOL5dJixDqXz29gHhGRZTRIRogzT2l5mk6b8F%2BG5KhtyB5%2Fj%2B2mie3mie3mlvNk1vNk1vNk1vNk1vNrZbouy65VR8%2BsST3UJbGpopjJYZdoNsFXGOptDrpfAn9LGWvU5xaLJFvmr9Ycu3kzstYuiHrUuaUFsfGFg%2FyQOFa%2BHaCIAeHMNTnPgA%2FwSrnrg3UPPD%2B1R8AHnwQ%2BIEUq7xONv4w%2Brk7ex2vBhRhng9ks%2BoyGAXU6XYrROTzXnTg4PrRW3EAIQQI8tueVn3I%2BGarnNuoz4%2BOztdZ%2F%2Bpl4KWXgMspVnmdbHwWIgxm91XHA7JxiJ1A64jHvJg0WS0CmBqzWf3NLSG2NmGTnopCOm8l8RZKpNsDSbG0l1UfUXyjVcZLqE8EoGCirj1cC%2F20Eq3yOgjrML6wwHgLFoWxUGHzicx1iB4CQJy7Iee7S4biAw4QUM9k1XhodzE%2B1yRqzo2zk3YXkPZaZODoEJl48avVU5pVQQjFJltVUgHfZJX9N%2FDDuJ3Cerdr%2FasvA5icBPByolVeB6yO5B2go%2FOXdzpJLuAVVseuGOv0%2F2M%2Bce6EnO0uIRO3elPbciars9UyhSlXZ%2FkJvoVSCS3OaeNRCTi%2F59j7UGFc0J7XVSWVad2hpv5VEO9fPQXgwx8GcMr4CRybTHWg6ijungJOuRo%2Fhp%2BgMD%2BBw4Y6Xb3OrOSG1BTPdKxCJZNVfJn6%2BbKhTnMcGG9yTv%2B5Zrb6CQT4LLtQEAkBIRKtFgR2IgpZrDa8aEzvX60AQBAAQIVi6bdzEa9jA7aso3FnGph2NA58ncJ8HTBsz5%2FQ69QkD1OM9TmNju7yYsqxmtFqI46fo36eg8HSzwM%2Fb7L3fR6RkYPwfTdzQVBtOklWuT1ulfevCiH0%2FtV7sZt7zd1ovM5F4KKqozgBpHMA6BB1AIDNb0yuGOvIVPAk8YT1BztW3fq5rXMb9fZjcexEEwEHpjPw%2BLjxDPwH2xHgvIIPMy5EBqtCiBSr6f2rswAaQjQAzCbsFVYn2NwMVB3FCWD1AeC9RO8FADb%2FmZ6az7fzcf15%2BWr7BzhWnYnV5irr1gPtWCX9swSbQHOrXN5qck61ByTgfPY9DzUC%2Fs6GICfsbVXCFKtp%2FatL%2FY9pHQKAJUOZyUnwOnNzYR3GhWAcKmDzHbU9GfpsvfcpPsh11ZhNZXVTG5qbt6hJ8l%2FOT%2FeITPyjX6l9kG8mqe0cwGp6%2F%2BrdAHCd6Lr%2BewKopNbh3Gx1kDoET%2FHBrqvGzCmrc6QlGFFA480k3jxdZpsJEoCgeE8lhfdQQ2JocjKj1fT%2B1RoAvJ%2Fo%2FQBQS7fK63CeZjW9TsOrM14dHW%2Br%2Ban6vF3qZbJKyurBpGnQQpicNDY0E4aAXnQC73%2BNh3XZsv5V1ow6RzQnv4%2FyMjJZ6nDO64jMdaZHJxgvUHnZND%2Bh%2FuguHdXmU0KEUF8PPpES0esZG5pJDAkxdDPOk%2FdC5Mmt5smt5smt5smt5lbz5Fbz5Fbz5Fbz5FZzq%2BYGw13usyHXNjcHKKrHZwuvpKWLinmDsECGlAwdND5R2vIg39VWq0atfV5Y14fs2ryIktVqjbUepmUW9zI2CUyes9AlnvJZtEfiaAEL%2B7OabBqJQ619rSnT4jwKiCHaRaD08MdFvVDnWhVXWpm9jFYrEf5AwoYQz1INNQZ7QG91GJfJkH%2BGBzSyghWyJoUAhJi0SIXRAaw292W1eSBWE4uI3YAIGAOYVsWl1sGsvhLhY3FahN6SqXLs0xZKxud5QurmeQee0xGIRnrRD%2FVGFE6iJKIQj0gdYsjI1RCzKhErnWrVj3Hy0Y3OwCDaqx2Ya92%2FVeBYhK8DbLplAbcC7MT2vh%2FEMZPVyhraZAjgMGRe9S2RQiWJg519D%2BoMnPi4e1n1oReZJXLHKtJqNUFrNaZ1EKuzIswstzp%2B6dK44Vm%2B3Ah%2BCmiZ9%2FsDxFNBnX6%2FrTYVHuwMvJBmdcFs1YdmtYp7yLVRdEFUSNBaiGsdwKqKxq0vAF%2BwuNVTn%2B68buH7uQqxdRYnXWL5XXxtYKtChfHEgcHPwKEeSixPJO3BZHVdt1oQc64NwEZM3zqpxPn6%2Bpth9fiLwIvHmdUOwswaVDTPb%2BB%2BYnkYP3dwx2rmu6XWQZyBhdgogHj5XYTChhCm%2BoWqZtXttn4EYW7Wpy%2Beqbi%2FXshk1dqy9mMVH9ja%2BgCY1YcsIcQW0DGp%2BGkcJpYbeGlfVktAaXCrzYM5A6%2FQ3lZpJWE7C9UYr0wBP4kwSh%2BTKrmSmsWqNdwctrhV0Q%2B3ipMnway6eF7usjYe4lZbpRpeIBbge%2FZlVZnI0nyXOjD4PTCHu8hk26tvh6gQ5ypKH5MacSWVW63G9VnDTriYLnNRhEyLdWSaWzLX8AU5%2Fkn98zpXwW6X1Mj%2F0NkCFhKOym0emVgYbKXag74HNtchGGyPTmyH2VbZ1adLVbykpGpW41xKJalV34qd30KwjkxjS2YX4WLXFfY%2BFmEakz3SYpt%2BH7lSXWFHJVud%2BvfXanNAqzxpj1vQpSpeLmQ7VUmpUivrTw9EmDJlyty25SD6oVHD404zqTQiMaOF3R%2FS%2BIboZ6Mw4PrDB3UGFpRchxTkSX3cwePQd0ZW2P8ZNHkvRJ7cap7cap7cam41T241T241T241T241t%2Bq2aOAs0rdVcquuXawYFrpdTF6%2Fl6eDJUqOu0SDxvdpH8mtus8eR9HUnQ3ftK4vANslPSdxisOlKcjZ8uc6jI9Ryzy%2FWKEuq%2BUn9KOHW5VA%2BVASn%2BrQAcR2wy%2FJvAWwoYjyuD4vFDnwTdi33ZhV1z55ybJYx0B9sw2UDOvrRqK0dAHcZ16C2xp2T1ywntO4d3aCcJXPH696M4EPm0s1aQWkISRQPpTEgcUWGQKAkLknBtIRlFbGm6yUokyeHDJyGLT6QKRVTcPJS8P6Wq%2F1ibnlNg4b1tcFwHR3jOunn8KmEGLkhG3fMeJofPR8yQcWXX1%2BuTAa%2BMAFTWpBAKLAtALSEBIoH0riAIrdwa1KEVA2OAfMQyZ5csjM14llHX2tahqOX2PLSr0%2F6kkwrK9r6ts%2BFcKaq1eZix7h%2BAnG%2B4uZr%2Bl8oUK%2B3p3hLiJURVhkjyANgQzUOJTEIWN3BrUqRSgbBs5KKcrlySHOE1tXIq1qGl8V1MPh0KJlWF%2FX0AVYQjuk9xuvb7CGTzB%2BP6w6UL1D4wsoLrLttrEbW7cRjpGR8iFXcaMl3x3UKmxlw8BZKUWZPF6IS%2BVauVSVNjDWHQMu8PWBI6u1%2BEFc%2FaTBNQE7Um3Gf3RrZMIbLzgaf6cHKTV%2Bgr%2BgrF4w2iAj5UNrGmeWpga2GmXNzHkpjbKXsc22v5HUutIAsDbEpao8gCg%2FxtcHJsn19XV%2F7kGE4VafkvVtMF5oEp0ul3QezHhSKvTXYfSpJ%2FY6BSylSKd86A7FjZaqzwxsNXqEOxI4K2WmI2InI3z7fTLGDx93KHxLY5ZKvQ3IbDYN6wMDgLa%2Brnf5i16C1Y%2BMb9cHGJdp%2BpwHMxsFAkjTGg3qUgkYlo7MlA85ihssWZMFZ1Cr1rA6TgycWzVTFcP2%2B4lSh50hoqfkWxopleddFoD6nGl9YAD6%2BrptrB2SuE6xNNClubLjdtFgfDtmHqworrRG72x0qQSEokzUOJTEw7daI71B75akTyXVwFkpTrlVrjVZ6hDRZZy8ZJZKzkUPjTNkWh%2FYsJL%2BxzzIeLfH8Z3YyZ0D8eS2ZSAUlUD5UBIH2qfPD%2F7ORvpUUg2clTJTocK33%2FzOpi91iFqwfvCaQ%2BYEM43H1FjKerzN01UPqJ4O4nj1XAMyjXOrA%2FHktmUgFJVE%2BZBELueNyeVmQk8mZW7dJ2nI5VIljwaZP0Z5uFZzU34kdYiubY2cdygpwbRylLoeb7MwKkSB7ZjVaSEzvToYT25bFkK1IXPKh0LkcD7dowNIVNkx8ugLO%2FY4TddqbsqPpA6R06TvvORxEnDeCzFo8l6IPLnVPLnVPLnV3Gqe3Gqe3Gqe3Gqe3Gpu1dzf%2B5Zx1ShxcPUHT2uqktR9uN%2F4ST9UWThIq65taI95S7gaAsyddTWPzc%2FCB85JnHT3ZdVuUULel2C1UsTCYK8at0XAUMsNrdqm9pi9uQd4%2B5kPq569Prk%2BgOISkaEPeXS%2BDns%2FfJzXJ2oplMnGAoC1fVlV28%2FkGVX529x750BW5YcvgEox7EYrAYAQrL835ICJW09Xq09b5vkNGPi5kYl5jbPHVVmrjQMfqpWI9SE%2FQvTIRB0lnQdEgZlXarw%2BLRVBaTZ4o3opu9XOVQALCVK9%2BaqxkjcTDGT12RqKQBG1Z4eIDgMAEevvlVyGc2%2FYKRScYc8033pmHIxbq1crgZWxPrm4qwyc%2F1CN9D7kCnwfldtxTOPRRxc4j3biuOLqyKOEmGy0apCptTJa7RYRxnTc3yvlFYxWpdRBrDZnPIQvjuYQUQ0QgkgIredTchnOo5PRGufWZH3Y%2BVmPceDUZ12Ac1ld5zt%2FBF1G60MOqkA1CLxZjdPVlo01zkOpM%2BU4b9kpa5oxGyf7%2FGQ2qz5UCyrLyoaSp1V6KKVtKfvirkNEDWCH1khlL74u8Trnl3oTTqXIOXBnbw0mTgSdQ6bXg4zeh7wePrZX0%2FjVsF%2BS8UhqoPEppFhlNkaEAKA3cJJtvi3oYCfWY4a73BUu1Q%2Bri8JBWj0UjbP%2BXsllOPfCRtc7PJ3L%2B8RKMXsd8%2BOKKzgngMmqJ4TWh1xBtSq%2FHtL4j1uyC4vxUiRV449ZKVa5DfNBecmDjHcpjh9FYyM81VSHg5S7XHZXPJBVMe9J2JgXQ0Rvi8ZZf2%2FIARO3Xd93bc5hd4rmOkIYuSASOienWisBf7J2F%2Bl9yMF8oTAfHNHrHHGGq8MOMY5Qqs6D4SqApHUDlY1Uq803IPNGM46xOb3S60F9JIHd5Wa7K%2B5vjcj8B%2Bdbxei9SbE1FPb3yrD%2B3r14ESgmzR%2BUE93xaQC1u8q8D1neA4%2FxOmO%2FUHAqBo67AmKcnMK4B0qIspFqlVY3AGysanRzTgJrppx2l8vvige7W7pmeTPAjGddG%2Br394L19751nJzCFeDpsrEPucjmZ%2BdK%2BIxFhjAbKVZpxYK1osO56MGDlLtcdlc8sFVn%2BHQABKdl735Cf%2B9bwtUQwOBB1g%2BGiYfZSLVKFxuXyBwn5S6X3RUPbpWcJgkx1JS9%2Bwn9vW8lZ82xB1%2BfiU4ZEOYNCqablDXqLlfXGuz1M3kvRJ7vZKt5cqu51Ty51Ty51Ty51Ty51Ty51dxqntyqe5W%2BrZP3A3dhd4g6NrpkSqc7BibV%2FgjtM4twDXRsjIyxYXMI9dUcn7Lk1VdfVd%2FexFSAA18nOXs%2F8GGrhoUF1KzDxOyVbAAvMKv34RNkSGdxbGyxY%2Bb%2F%2Bs84xFKCefnoFoCUngEebT3LoppfjM265ZZb1Lc3Ma94IgbcItsUxlPWSWZWk%2Fty8fyMBXgzzzN5lSkAaH%2BNDdTwx2jM1aC7iDCLrpE%2F0XLZ86kBNZd4mvuwiv5f%2FAwt2sb5yGrV9d3kA8b3GfUN9Yus0YdvTzrn6ySbrZYAWEJYAEqs6tGjkDG8iBrjj8Mj1oh1N71g8xZ6dTLg%2FHvvk1w75Ot13JexOUCoMNvFViQVFzJYnZubU9%2F44svmAyb6ptNCFWHM%2FVvvT9p%2BkdFqtE4y36DIqi%2BtHo6a%2FGp6X64AgNtuAwBBsawB3tnpf6e%2F6Ih%2BE8DCC9p1%2BAjaaABAFUdM%2FE%2F9Zcm1C8%2FHPw5UiMUF4GY8VoWY96zXZfuIQLWQwSoA9S198WX3BqRAH8AN7TBadAv8L36%2Fhp28lO1YbTDbKuaO1cgq%2FKFIJ1yXrwGrrLLzrHX661PsRbfUbQKsTBfWu%2FHRNoAfs9Dl%2FI87KxZ7HWwCm8o1270Zr6vB6T8ddRkqqZmtmhdf5qsJTmktOoVJQCw7hl3%2F09jJV7JZ%2FWAJKsUUq%2FrfgG4AwFNP8fV%2Bj27nttvkV%2F1Qsi4egcwXY%2FzyjxKssFqLVB7Edae%2B9gBQb17Hgzfz49v8d%2FAXiUKuUkLjV4FfbaBkasYDipUYhdj9h7T8QhHe2%2F820TrtzyqX2kjSyhYX7QHmXf%2Bz6KfRzGS1UT4FlXtSra6ryevJ%2Fbp0224ols96zxchU9c3bwrX7wSA10llro7umXcA9TNd1Odi3Jf8E%2BTHOLk1fMZpt53PoObqUtsA2kpryrFakVJPFivqHjijVSa1Ol2VWolpZVKJkqwGHqI8SZmsfrADFXzRZJWvnyyDaoH166afgXuHEMY7wzfvhVUA6N2Mz1i4f0KIiadgndH4kY9b6HU1fh%2FaPXr8ceq1tcWwi965ZQDL57xilmM1%2BszJb9b023sPO9Hu9uqA36n4QDum7gLkbipUgQvEtTKpBCTcqI6KMN4ns1ktPwqVapNb5Vqj62q1wPqB0626dv%2Fm52mHLeiOBypyRHvqbUwtLEyhPezEeRXAn22hGuMdeB%2BLtvpjHjqx%2BqdXZfXK6ul20rHK%2B2%2FDjxTFhIwKwLoiZEbJ2Nb%2BOFvnVH3TtUYbzy35ScveVvCJbFZbUMGXs7yzKURWC0OsHzjdqn18a1rMzwvWDP2xBsZ7D7GVyclZnnzyHe94cnLZ0Xhh8vfwR1%2FU1s4%2BiSj880rLTYrelzeXsxyr0lpAFIyyNd1hXuS6XEeYepmvc6q%2B6c%2BBVYLSKqVyTc9ls3ofVKxeyjrJrBeC9c2mWD0%2B3CQKAmJpPrNVJlisDlFveWJiuUfE%2BGv4B804ryCWCsXSmBfzjf3%2Fbiku1Y2k8pzZ8ABv4wwNFBGlwF4HTYFtDuFks1qDyvNp6yRzq6pvlm%2Fe6ip7uzTs7NFlTGKkTNmzIgKNBCIWbXg6oGA6bclrngJbG9gYZ2VUiNEVh96sCCmdwYQnMCpUmJtC4YB7IRz67kneC5Ent5ont5ont5ont5pbzZNbzZNbzZNbzZNbXZhaiIPcagtRii5ljQsYJy%2B4rnn3dlGkNzH4KFomHIbz0liR9T8fKF%2BcmlqUnMcdA7qUKXt0xNqAbZgeWu3%2FwFfRz4%2BQKa2rLUOTAYoV0%2FK0tg1qceFu7SzMi58i4Ul2i6a9VUzYIWiimdnqm7%2Fu8amv3XPna5LzHEFjck6C9P7kvZrRhICBhVZFNPYw%2BnmYWNzSGH7lGjR6yrhW47OwJbfxLOm53%2FspZhX4w8AFcXTDcJh1pn7jDRAL3viNqY7RK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<div id="header">
<h1 class="title">Appendix - Selection against instability: stable subgraphs are most frequent in empirical food webs</h1>
<h4 class="author"><em>Jonathan J. Borrelli</em></h4>
<h4 class="date"><em>Wednesday, July 23, 2014</em></h4>
</div>
<div id="TOC">
<ul>
<li><a href="#definitions"><span class="toc-section-number">1</span> Definitions</a><ul>
<li><a href="#subgraph-library"><span class="toc-section-number">1.1</span> Subgraph Library</a></li>
<li><a href="#define-required-functions"><span class="toc-section-number">1.2</span> Define required functions</a><ul>
<li><a href="#functions-for-counting-motifs"><span class="toc-section-number">1.2.1</span> Functions for counting motifs</a></li>
<li><a href="#functions-for-determining-quasi-sign-stability"><span class="toc-section-number">1.2.2</span> Functions for determining quasi sign-stability</a></li>
</ul></li>
</ul></li>
<li><a href="#analysis"><span class="toc-section-number">2</span> Analysis</a><ul>
<li><a href="#determining-motif-frequency"><span class="toc-section-number">2.1</span> Determining motif frequency</a></li>
<li><a href="#determining-quasi-sign-stability"><span class="toc-section-number">2.2</span> Determining Quasi Sign-Stability</a><ul>
<li><a href="#correlation"><span class="toc-section-number">2.2.1</span> Correlation</a></li>
</ul></li>
</ul></li>
<li><a href="#code-for-the-figures"><span class="toc-section-number">3</span> Code for the figures</a></li>
</ul>
</div>
<p><a href="https://github.com/jjborrelli/Subgraph-Stability">The code provided here can also be obtained from GitHub by clicking this link</a></p>
<div id="definitions" class="section level1">
<h1><span class="header-section-number">1</span> Definitions</h1>
<div id="subgraph-library" class="section level2">
<h2><span class="header-section-number">1.1</span> Subgraph Library</h2>
<p>The following code defines the sign matrix for each of the thirteen possible three-node subgraphs. Here, the “s” in the object name indicates that only single links are used, while a “d” indicates the presence of double links.</p>
<pre class="sourceCode r"><code class="sourceCode r">s1<-<span class="kw">matrix</span>(<span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">0</span>,-<span class="dv">1</span>,<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">0</span>,-<span class="dv">1</span>,<span class="dv">0</span>),<span class="dt">nrow=</span><span class="dv">3</span>,<span class="dt">ncol=</span><span class="dv">3</span>)
s2<-<span class="kw">matrix</span>(<span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">1</span>,-<span class="dv">1</span>,<span class="dv">0</span>,<span class="dv">1</span>,-<span class="dv">1</span>,-<span class="dv">1</span>,<span class="dv">0</span>),<span class="dt">nrow=</span><span class="dv">3</span>,<span class="dt">ncol=</span><span class="dv">3</span>)
s3<-<span class="kw">matrix</span>(<span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">1</span>,-<span class="dv">1</span>,-<span class="dv">1</span>,<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">1</span>,-<span class="dv">1</span>,<span class="dv">0</span>),<span class="dt">nrow=</span><span class="dv">3</span>,<span class="dt">ncol=</span><span class="dv">3</span>)
s4<-<span class="kw">matrix</span>(<span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">1</span>,-<span class="dv">1</span>,<span class="dv">0</span>,<span class="dv">0</span>,-<span class="dv">1</span>,<span class="dv">0</span>,<span class="dv">0</span>),<span class="dt">nrow=</span><span class="dv">3</span>,<span class="dt">ncol=</span><span class="dv">3</span>)
s5<-<span class="kw">matrix</span>(<span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">1</span>,-<span class="dv">1</span>,-<span class="dv">1</span>,<span class="dv">0</span>),<span class="dt">nrow=</span><span class="dv">3</span>,<span class="dt">ncol=</span><span class="dv">3</span>)
d1<-<span class="kw">matrix</span>(<span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">1</span>,-<span class="dv">1</span>,<span class="dv">0</span>,<span class="dv">1</span>,-<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">0</span>),<span class="dt">nrow=</span><span class="dv">3</span>,<span class="dt">ncol=</span><span class="dv">3</span>)
d2<-<span class="kw">matrix</span>(<span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">0</span>,<span class="dv">1</span>,-<span class="dv">1</span>,-<span class="dv">1</span>,<span class="dv">0</span>),<span class="dt">nrow=</span><span class="dv">3</span>,<span class="dt">ncol=</span><span class="dv">3</span>)
d3<-<span class="kw">matrix</span>(<span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">1</span>,-<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">0</span>,<span class="dv">0</span>),<span class="dt">nrow=</span><span class="dv">3</span>,<span class="dt">ncol=</span><span class="dv">3</span>)
d4<-<span class="kw">matrix</span>(<span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">1</span>,-<span class="dv">1</span>,<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">0</span>,<span class="dv">0</span>),<span class="dt">nrow=</span><span class="dv">3</span>,<span class="dt">ncol=</span><span class="dv">3</span>)
d5<-<span class="kw">matrix</span>(<span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">1</span>,-<span class="dv">1</span>,<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">1</span>,-<span class="dv">1</span>,<span class="dv">0</span>),<span class="dt">nrow=</span><span class="dv">3</span>,<span class="dt">ncol=</span><span class="dv">3</span>)
d6<-<span class="kw">matrix</span>(<span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">0</span>),<span class="dt">nrow=</span><span class="dv">3</span>,<span class="dt">ncol=</span><span class="dv">3</span>)
d7<-<span class="kw">matrix</span>(<span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">1</span>,-<span class="dv">1</span>,<span class="dv">0</span>),<span class="dt">nrow=</span><span class="dv">3</span>,<span class="dt">ncol=</span><span class="dv">3</span>)
d8<-<span class="kw">matrix</span>(<span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">0</span>,<span class="dv">0</span>),<span class="dt">nrow=</span><span class="dv">3</span>,<span class="dt">ncol=</span><span class="dv">3</span>)
mot.lst <-<span class="st"> </span><span class="kw">list</span>(s1, s2, s3, s4, s5, d1, d2, d3, d4, d5, d6, d7, d8)
<span class="kw">names</span>(mot.lst) <-<span class="st"> </span><span class="kw">c</span>(<span class="st">"s1"</span>, <span class="st">"s2"</span>, <span class="st">"s3"</span>, <span class="st">"s4"</span>, <span class="st">"s5"</span>, <span class="st">"d1"</span>, <span class="st">"d2"</span>, <span class="st">"d3"</span>, <span class="st">"d4"</span>, <span class="st">"d5"</span>, <span class="st">"d6"</span>, <span class="st">"d7"</span>, <span class="st">"d8"</span>)</code></pre>
</div>
<div id="define-required-functions" class="section level2">
<h2><span class="header-section-number">1.2</span> Define required functions</h2>
<div id="functions-for-counting-motifs" class="section level3">
<h3><span class="header-section-number">1.2.1</span> Functions for counting motifs</h3>
<p>The <code>motif_counter</code> function takes in a list of graph objects and applies <code>triad.census</code> to each. It returns a data frame of the frequency of each connected three-node digraph.</p>
<pre class="sourceCode r"><code class="sourceCode r">motif_counter <-<span class="st"> </span>function(graph.lists){
<span class="kw">require</span>(igraph)
if(!<span class="kw">is.list</span>(graph.lists)){
<span class="kw">stop</span>(<span class="st">"The input should be a list of graph objects"</span>)
}
triad.count <-<span class="st"> </span><span class="kw">lapply</span>(graph.lists, triad.census)
triad.matrix <-<span class="st"> </span><span class="kw">matrix</span>(<span class="kw">unlist</span>(triad.count), <span class="dt">nrow =</span> <span class="kw">length</span>(graph.lists), <span class="dt">ncol =</span> <span class="dv">16</span>, <span class="dt">byrow =</span> T)
<span class="kw">colnames</span>(triad.matrix) <-<span class="st"> </span><span class="kw">c</span>(<span class="st">"empty"</span>, <span class="st">"single"</span>, <span class="st">"mutual"</span>, <span class="st">"s5"</span>, <span class="st">"s4"</span>, <span class="st">"s1"</span>, <span class="st">"d4"</span>,
<span class="st">"d3"</span>, <span class="st">"s2"</span>, <span class="st">"s3"</span>,<span class="st">"d8"</span>, <span class="st">"d2"</span>, <span class="st">"d1"</span>, <span class="st">"d5"</span>, <span class="st">"d7"</span>, <span class="st">"d6"</span>)
triad.df <-<span class="st"> </span><span class="kw">as.data.frame</span>(triad.matrix)
motif.data.frame <-<span class="st"> </span><span class="kw">data.frame</span>(<span class="dt">s1 =</span> triad.df$s1, <span class="dt">s2 =</span> triad.df$s2, <span class="dt">s3 =</span> triad.df$s3, <span class="dt">s4 =</span> triad.df$s4,
<span class="dt">s5 =</span> triad.df$s5, <span class="dt">d1 =</span> triad.df$d1, <span class="dt">d2 =</span> triad.df$d2, <span class="dt">d3 =</span> triad.df$d3, <span class="dt">d4 =</span> triad.df$d4,
<span class="dt">d5 =</span> triad.df$d5, <span class="dt">d6 =</span> triad.df$d6, <span class="dt">d7 =</span> triad.df$d7, <span class="dt">d8 =</span> triad.df$d8)
<span class="kw">rownames</span>(motif.data.frame) <-<span class="st"> </span><span class="kw">names</span>(graph.lists)
<span class="kw">return</span>(motif.data.frame)
}</code></pre>
<p>The <code>permutes_rc</code> function is a null model that generates <code>iter</code> number of permuted matrices from the input matrix (<code>mat</code>). Each permuted matrix is created by randomly sampling 2x2 submatrices matching the pattern</p>
<pre><code> [,1] [,2]
[1,] 0 1
[2,] 1 0</code></pre>
<p>or</p>
<pre><code> [,1] [,2]
[1,] 1 0
[2,] 0 1</code></pre>
<p>and swapping the 0s and 1s. This null model preserves the number of prey and predators of each species (the degree distribution).</p>
<pre class="sourceCode r"><code class="sourceCode r">permutes_rc <-<span class="st"> </span>function(mat, <span class="dt">iter =</span> <span class="dv">100</span>){
pattern1 <-<span class="st"> </span><span class="kw">matrix</span>(<span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">0</span>), <span class="dt">nrow =</span> <span class="dv">2</span>, <span class="dt">ncol =</span> <span class="dv">2</span>)
pattern2 <-<span class="st"> </span><span class="kw">matrix</span>(<span class="kw">c</span>(<span class="dv">1</span>,<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">1</span>), <span class="dt">nrow =</span> <span class="dv">2</span>, <span class="dt">ncol =</span> <span class="dv">2</span>)
count <-<span class="st"> </span><span class="dv">0</span>
mat.list <-<span class="st"> </span><span class="kw">list</span>()
for(i in <span class="dv">1</span>:iter){
mat.list[[i]] <-<span class="st"> </span><span class="kw">matrix</span>(<span class="dv">0</span>, <span class="dt">nrow =</span> <span class="kw">nrow</span>(mat), <span class="dt">ncol =</span> <span class="kw">ncol</span>(mat))
}
while(count <<span class="st"> </span>iter){
srow <-<span class="st"> </span><span class="kw">sample</span>(<span class="dv">1</span>:<span class="kw">nrow</span>(mat), <span class="dv">2</span>)
scol <-<span class="st"> </span><span class="kw">sample</span>(<span class="dv">1</span>:<span class="kw">ncol</span>(mat), <span class="dv">2</span>)
test <-<span class="st"> </span>mat[srow, scol]
if(<span class="kw">sum</span>(test ==<span class="st"> </span>pattern1) ==<span class="st"> </span><span class="dv">4</span>){
count <-<span class="st"> </span>count +<span class="st"> </span><span class="dv">1</span>
mat[srow, scol] <-<span class="st"> </span>pattern2
mat.list[[count]] <-<span class="st"> </span>mat
next
} else if(<span class="kw">sum</span>(test ==<span class="st"> </span>pattern2) ==<span class="st"> </span><span class="dv">4</span>){
count <-<span class="st"> </span>count +<span class="st"> </span><span class="dv">1</span>
mat[srow, scol] <-<span class="st"> </span>pattern1
mat.list[[count]] <-<span class="st"> </span>mat
next
} else {next}
}
matrices <-<span class="st"> </span><span class="kw">lapply</span>(mat.list, as.matrix)
<span class="kw">return</span>(<span class="dt">permuted.matrices =</span> matrices)
}</code></pre>
</div>
<div id="functions-for-determining-quasi-sign-stability" class="section level3">
<h3><span class="header-section-number">1.2.2</span> Functions for determining quasi sign-stability</h3>
<p>There are two main functions for determining quasi sign-stability, and a third that wraps them together to generate the desired number of iterations.</p>
<p>The function <code>ran.unif</code> takes an input of a signed matrix. It will then check each cell to see if there is a 1 or -1. Each 1 will be replaced by a value drawn from the random uniform distribution between 0 and 10, while each -1 is replaced by a value from the random uniform distribution between -1 and 0. The <code>ran.unif</code> function also assigns values to the diagonal from a random uniform distribition between -1 and 0. The resulting randomly sample matrix is returned.</p>
<pre class="sourceCode r"><code class="sourceCode r">ran.unif <-<span class="st"> </span>function(motmat){
newmat <-<span class="st"> </span><span class="kw">apply</span>(motmat, <span class="kw">c</span>(<span class="dv">1</span>,<span class="dv">2</span>), function(x){
if(x==<span class="dv">1</span>){<span class="kw">runif</span>(<span class="dv">1</span>, <span class="dv">0</span>, <span class="dv">10</span>)}else if(x==-<span class="dv">1</span>){<span class="kw">runif</span>(<span class="dv">1</span>, -<span class="dv">1</span>, <span class="dv">0</span>)} else{<span class="dv">0</span>}
})
<span class="kw">diag</span>(newmat) <-<span class="st"> </span><span class="kw">runif</span>(<span class="dv">3</span>, -<span class="dv">1</span>, <span class="dv">0</span>)
<span class="kw">return</span>(newmat)
}</code></pre>
<p>Given the input matrix <code>maxRE</code> will compute the eigenvalues and return the largest real part.</p>
<pre class="sourceCode r"><code class="sourceCode r">maxRE <-<span class="st"> </span>function(rmat){
lam.max <-<span class="st"> </span><span class="kw">max</span>(<span class="kw">Re</span>(<span class="kw">eigen</span>(rmat)$values))
<span class="kw">return</span>(lam.max)
}</code></pre>
<p>The above two functions are combined in <code>eig.analysis</code>. Given the number of desired sampling iterations, <code>n</code>, and a list of sign matrices to analyze, <code>matrices</code>, the <code>eig.analysis</code> function will return an <code>n</code> by <code>length(matrices)</code> matrix of eigenvalues. Specifically it is returning the <span class="math">\(max(Re(\lambda))\)</span> for each sampled matrix. From this matrix quasi sign-stability can be calculated as the proportion of values in each column that are negative.</p>
<pre class="sourceCode r"><code class="sourceCode r">eig.analysis <-<span class="st"> </span>function(n, matrices){
cols <-<span class="st"> </span><span class="kw">length</span>(matrices)
rows <-<span class="st"> </span>n
eigenMATRIX <-<span class="st"> </span><span class="kw">matrix</span>(<span class="dv">0</span>, <span class="dt">nrow =</span> rows, <span class="dt">ncol =</span> cols)
for(i in <span class="dv">1</span>:n){
ranmat <-<span class="st"> </span><span class="kw">lapply</span>(matrices, ran.unif)
eigs <-<span class="st"> </span><span class="kw">sapply</span>(ranmat, maxRE)
eigenMATRIX[i,] <-<span class="st"> </span>eigs
}
<span class="kw">return</span>(eigenMATRIX)
}</code></pre>
</div>
</div>
</div>
<div id="analysis" class="section level1">
<h1><span class="header-section-number">2</span> Analysis</h1>
<p>Load required packages</p>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(igraph)
<span class="kw">library</span>(ggplot2)
<span class="kw">library</span>(reshape2)</code></pre>
<div id="determining-motif-frequency" class="section level2">
<h2><span class="header-section-number">2.1</span> Determining motif frequency</h2>
<p>Load in web data from GitHub. <a href="https://github.com/jjborrelli/Subgraph-Stability/blob/master/webGRAPHS.Rdata?raw=true">Click here to download the .Rdata file</a>. This file is a list of igraph graph objects for each of the 50 webs used in the analysis. Once you have downloaded the file into your working directory:</p>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">load</span>(<span class="kw">paste</span>(<span class="kw">getwd</span>(), <span class="st">"webGRAPHS.Rdata"</span>, <span class="dt">sep =</span> <span class="st">"/"</span>))</code></pre>
<p>The frequencies of each of the different subgraphs can now be determined easily with <code>motif_counter</code>.</p>
<pre class="sourceCode r"><code class="sourceCode r">motfreq <-<span class="st"> </span><span class="kw">motif_counter</span>(web.graphs)
<span class="kw">kable</span>(motfreq, <span class="dt">format =</span> <span class="st">"pandoc"</span>)</code></pre>
<pre><code>
s1 s2 s3 s4 s5 d1 d2 d3 d4 d5 d6 d7 d8
-------------- ------ ------ --- ------ ------ ---- ----- ----- ----- ---- ---- ---- ----
akatorea 115 14 0 789 1466 0 0 0 0 0 0 0 0
akatoreb 63 18 0 338 497 0 0 0 0 0 0 0 0
benguela 269 445 0 464 391 19 48 8 24 0 1 1 0
berwick 132 14 0 855 1553 0 0 0 0 0 0 0 0
blackrock 407 71 0 2507 1976 0 0 0 0 0 0 0 0
bridgebrook 1931 629 0 6338 1539 30 111 0 21 0 4 0 0
broad 641 16 0 5087 4151 0 0 0 0 0 0 0 0
broom 527 358 0 275 3292 0 0 0 0 0 0 0 0
bsq 5742 1202 0 10011 5736 0 0 0 0 0 0 0 0
canton 717 116 0 6561 5976 0 0 0 0 0 0 0 0
catlins 59 9 0 186 721 0 0 0 0 0 0 0 0
caymen fw 22330 5965 0 64365 53833 0 0 0 0 0 0 0 0
chesapeake 86 21 0 58 130 0 0 0 0 0 0 0 0
coachella 311 638 0 424 317 103 139 96 91 11 24 39 7
coweeta1 68 36 0 266 551 0 0 0 0 0 0 0 0
coweeta17 86 26 0 421 822 0 0 0 0 0 0 0 0
csm 4540 944 0 5545 5327 0 0 0 0 0 0 0 0
cuban fw 23615 6220 0 65677 56327 0 0 0 0 0 0 0 0
dempstersau 539 28 0 3215 2255 0 0 0 0 0 0 0 0
dempsterssp 723 28 0 4054 4145 0 0 0 0 0 0 0 0
dempsterssu 2464 567 0 10208 8210 0 0 0 0 0 0 0 0
elverde 8571 2824 26 11485 10558 183 179 1170 2668 174 13 112 382
epb 10931 1730 0 16385 11214 0 0 0 0 0 0 0 0
flensburg 1653 571 0 3763 2712 0 0 0 0 0 0 0 0
german 494 87 0 1876 2057 0 0 0 0 0 0 0 0
grass 82 30 0 193 152 0 0 0 0 0 0 0 0
healy 1108 267 0 5119 4929 0 0 0 0 0 0 0 0
jamaican fw 24879 6989 0 73176 61667 0 0 0 0 0 0 0 0
kyeburn 657 213 0 6381 4470 0 0 0 0 0 0 0 0
lilkyeburn 654 35 0 2116 2026 0 0 0 0 0 0 0 0
littlerock 12210 9148 0 39239 11325 383 1039 63 1061 30 40 27 21
martins 498 114 0 1257 2195 0 0 0 0 0 0 0 0
narrowdale 83 27 0 357 1208 0 0 0 0 0 0 0 0
northcol 278 50 0 710 1731 0 0 0 0 0 0 0 0
otago 5920 1950 0 10779 9177 182 211 272 634 0 16 22 36
powder 270 38 0 945 1894 0 0 0 0 0 0 0 0
quick 2990 3059 2 6332 1873 419 1219 297 660 38 123 195 53
reef 1448 1694 9 2001 1103 147 219 147 354 56 17 55 16
shelf 5978 11211 2 11458 7760 130 132 33 79 13 0 4 1
skipwith 330 1169 0 1985 559 54 314 1 45 0 20 0 0
stmarks 617 223 0 442 569 0 0 0 0 0 0 0 0
stmartin 538 278 0 712 482 0 0 0 0 0 0 0 0
stony 1035 124 0 8929 8208 0 0 0 0 0 0 0 0
suttonau 206 16 0 2570 1554 0 0 0 0 0 0 0 0
suttonsp 220 4 0 3467 2067 0 0 0 0 0 0 0 0
suttonsu 312 6 0 6445 1728 0 0 0 0 0 0 0 0
sylt 4489 1654 0 6938 7989 45 67 50 75 0 0 1 2
troy 186 20 0 507 794 0 0 0 0 0 0 0 0
venlaw 186 17 0 638 932 0 0 0 0 0 0 0 0
ythan_nopar96 1247 362 0 1905 2551 13 4 21 8 0 0 0 0</code></pre>
<p>The following code runs the null model analysis for the 50 food webs. First, each of the fifty webs are converted into binary adjacency matrices (<code>web.matrices</code>). Because the null model is a stochastic process the <code>set.seed(10)</code> allows for reproducible results. The code then loops through the list of adjacency matrices, generating 1000 permuted versions. The subgraphs are counted in each permuted matrix, and stored in a list (<code>p.mot</code>).</p>
<pre class="sourceCode r"><code class="sourceCode r">web.matrices <-<span class="st"> </span><span class="kw">lapply</span>(web.graphs, get.adjacency, <span class="dt">sparse =</span> F)
<span class="kw">set.seed</span>(<span class="dv">10</span>)
pmot <-<span class="st"> </span><span class="kw">list</span>()
for(i in <span class="dv">1</span>:<span class="kw">length</span>(web.matrices)){
p <-<span class="st"> </span><span class="kw">permutes_rc</span>(web.matrices[[i]], <span class="dv">1000</span>)
g <-<span class="st"> </span><span class="kw">lapply</span>(p, graph.adjacency)
pmot[[i]] <-<span class="st"> </span><span class="kw">motif_counter</span>(g)
<span class="kw">print</span>(i)
}</code></pre>
<p>Once subgraph counts have been obtained, the mean and standard deviation for each subgraph are computed. Z-scores are then computed as described in the methods section:<br /><span class="math">\[
z_i = \frac{x_i - \overline{x}}{\sigma}
\]</span> In cases where there were no occurences of a subgraph (standard deviation = 0) <code>NaN</code> is produced following the appllication of the above formula. In these cases I have replaced the <code>NaN</code> with 0. The normalized profile was then computed (as desribed in the methods):<br /><span class="math">\[
n_i = \frac{z_i}{\sqrt{\sum{z_j^2}}}
\]</span></p>
<pre class="sourceCode r"><code class="sourceCode r">mus <-<span class="st"> </span><span class="kw">t</span>(<span class="kw">sapply</span>(pmot, function(x){<span class="kw">colMeans</span>(x)}))
sig <-<span class="st"> </span><span class="kw">t</span>(<span class="kw">sapply</span>(pmot, function(x){<span class="kw">apply</span>(x, <span class="dv">2</span>, sd)}))</code></pre>
<pre class="sourceCode r"><code class="sourceCode r">z <-<span class="st"> </span>(motfreq -<span class="st"> </span>mus)/sig
zmat <-<span class="st"> </span><span class="kw">as.matrix</span>(z)
zmat[<span class="kw">is.nan</span>(zmat)] <-<span class="st"> </span><span class="dv">0</span>
profile <-<span class="st"> </span><span class="kw">apply</span>(zmat, <span class="dv">2</span>, function(x){x/<span class="kw">sqrt</span>(<span class="kw">rowSums</span>(zmat^<span class="dv">2</span>))})</code></pre>
<p><strong>Figure 1a</strong> is then just a boxplot of the above object <code>profile</code>, reordered according to decreasing quasi sign-stability (see below).</p>
</div>
<div id="determining-quasi-sign-stability" class="section level2">
<h2><span class="header-section-number">2.2</span> Determining Quasi Sign-Stability</h2>
<p>The first step to get quasi sign stability is to get the largest eigenvalues from a series of randomly parameterized sign matrices. In the following code I generate 10000 random parameterizations for each of the 13 subgraphs’s sign matrices (<code>mot.lst</code>). The <code>eig.analysis</code> function will return a matrix where each column is a different subgraph and each row is the largest eigenvalue of a particular randomization.</p>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">set.seed</span>(<span class="dv">5</span>)
n <-<span class="st"> </span><span class="dv">10000</span>
mot.stab<-<span class="st"> </span><span class="kw">eig.analysis</span>(n, mot.lst)
<span class="kw">colnames</span>(mot.stab) <-<span class="st"> </span><span class="kw">names</span>(mot.lst)</code></pre>
<p>From that matrix, quasi sign-stability is calculated as the proportion of rows with a negative value. In other words, how many random parameterizations of the sign matrix were locally stable?</p>
<pre class="sourceCode r"><code class="sourceCode r">mot.qss <-<span class="st"> </span><span class="kw">apply</span>(mot.stab, <span class="dv">2</span>, function(x){<span class="kw">sum</span>(x<<span class="dv">0</span>)/n})
sorted <-<span class="st"> </span><span class="kw">sort</span>(mot.qss, <span class="dt">decreasing =</span> T)
sorted</code></pre>
<pre><code> s1 s4 s5 s2 d3 d4 s3 d2 d1 d5
1.0000 1.0000 1.0000 0.5345 0.0891 0.0866 0.0561 0.0428 0.0370 0.0101
d7 d6 d8
0.0021 0.0000 0.0000 </code></pre>
<div id="correlation" class="section level3">
<h3><span class="header-section-number">2.2.1</span> Correlation</h3>
<p>Compute the correlation between QSS and median z-score</p>
<pre class="sourceCode r"><code class="sourceCode r">med.z <-<span class="st"> </span><span class="kw">apply</span>(zmat[,<span class="kw">names</span>(sorted)], <span class="dv">2</span>, median)
<span class="kw">cor.test</span>(sorted, med.z)</code></pre>
<pre><code>
Pearson's product-moment correlation
data: sorted and med.z
t = 3.527, df = 11, p-value = 0.004737
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.2966 0.9130
sample estimates:
cor
0.7285 </code></pre>
</div>
</div>
</div>
<div id="code-for-the-figures" class="section level1">
<h1><span class="header-section-number">3</span> Code for the figures</h1>
<pre class="sourceCode r"><code class="sourceCode r">plot.df <-<span class="st"> </span><span class="kw">melt</span>(profile[,<span class="kw">names</span>(sorted)])
fplot <-<span class="st"> </span><span class="kw">ggplot</span>(plot.df, <span class="kw">aes</span>(<span class="dt">x =</span> Var2, <span class="dt">y =</span> value)) +<span class="st"> </span><span class="kw">geom_boxplot</span>()
fplot <-<span class="st"> </span>fplot +<span class="st"> </span><span class="kw">geom_hline</span>(<span class="kw">aes</span>(<span class="dt">yintercept =</span> <span class="dv">0</span>), <span class="dt">lty =</span> <span class="dv">2</span>, <span class="dt">col =</span> <span class="st">"red"</span>)
fplot <-<span class="st"> </span>fplot +<span class="st"> </span><span class="kw">theme_bw</span>()
fplot +<span class="st"> </span><span class="kw">xlab</span>(<span class="st">"Subgraph"</span>) +<span class="st"> </span><span class="kw">ylab</span>(<span class="st">"Normalized Z-score"</span>)</code></pre>
<p><img src="data:image/png;base64,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" title="plot of chunk unnamed-chunk-12" alt="plot of chunk unnamed-chunk-12" width="672" /></p>
<pre class="sourceCode r"><code class="sourceCode r">sort.df <-<span class="st"> </span><span class="kw">melt</span>(sorted)
qssplot <-<span class="st"> </span><span class="kw">ggplot</span>(sort.df, <span class="kw">aes</span>(<span class="dt">x =</span> <span class="dv">1</span>:<span class="dv">13</span>, <span class="dt">y =</span> value)) +<span class="st"> </span><span class="kw">geom_point</span>(<span class="dt">shape =</span> <span class="dv">19</span>, <span class="dt">size =</span> <span class="dv">3</span>) +<span class="st"> </span><span class="kw">theme_bw</span>()
qssplot +<span class="st"> </span><span class="kw">xlab</span>(<span class="st">"Subgraph"</span>) +<span class="st"> </span><span class="kw">ylab</span>(<span class="st">"Quasi Sign-Stability"</span>) +<span class="st"> </span><span class="kw">scale_x_discrete</span>(<span class="dt">limits=</span><span class="kw">names</span>(sorted))</code></pre>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAABUAAAAPACAMAAADDuCPrAAAAgVBMVEUAAAAAADoAAGYAOjoAOmYAOpAAZmYAZpAAZrY6AAA6OgA6OpA6ZmY6kJA6kLY6kNtmAABmAGZmOgBmOpBmZgBmkJBmtrZmtv9/f3+QOgCQOmaQ2/+2ZgC225C2/7a2/9u2///bkDrbtmbb///l5eX6+vr/tmb/25D//7b//9v///83InJSAAAACXBIWXMAAB2HAAAdhwGP5fFlAAAgAElEQVR4nO3d7WLbaHedYY6Taa0krZS0ieIM+3bYmZeSdf4HWAIESICEPPbGfrawvO71xxZFXd4Dc5bxjd0bIYSQUHYfPQAhhKiGAiWEkGAoUEIICYYCJYSQYChQQggJhgIlhJBgKFBCCAmGAiWEkGAoUEIICYYCJYSQYChQQggJhgIlhJBgKFBCCAmGAiWEkGAoUEIICYYCJYSQYChQQggJhgIlhJBgKFBCCAmGAiWEkGAoUEIICYYCJYSQYChQQggJhgIlhJBgKFBCCAmGAiWEkGAoUEIICYYCJYSQYChQQggJhgIlhJBgKFBCCAmGAiWEkGAoUEIICYYCJYSQYChQQggJhgIlhJBgKFBCCAlmAwX6n4QQsrF8X3ttoUAjP/Rn9hTAwB8AC47sAVOgwQADF8KCI3vAFGgwwMCFsODIHjAFGgwwcCEsOLIHTIEGAwxcCAuO7AFToMEAAxfCgiN7wBRoMMDAhbDgyB4wBRoMMHAhLDiyB0yBBgMMXAgLjuwBU6DBAAMXwoIje8AUaDDAwIWw4MgeMAUaDDBwISw4sgdMgQYDDFwIC47sAVOgwQADF8KCI3vAFGgwwMCFsODIHjAFGgwwcCEsOLIHTIEGAwxcCAuO7AFToMEAAxfCgiN7wBRoMMDAhbDgyB4wBRoMMHAhLDiyB0yBBgMMXAgLjuwBU6DBAAMXwoIje8AUaDDAwIWw4MgeMAUaDDBwISw4sgdMgQYDDFwIC47sAVOgwQADF8KCI3vAFGgwwMCFsODIHjAFGgwwcCEsOLIHXFugx93j3SunfF7+6iY/XKC7MT/6gz8f3GVTnzvgrcjAq+DSAn19ui3Q/bkvPv2+8NVtfrRAd7tGfaQH99nU5w54KzLwKriyQE/9eVOgh/6Fl4fdr3/cfXWXHyzQ3a5RH+nB52zqcwe8FRl4FVxYoKdmvCnQcY309J3n26/u82MFuts16iM9eMimPnfAW5GBV8F1BXraPv/Hf5sX6PG67f759qv7UKDrsqnPHfBWZOBVcFmBntYrH79+mRfoftxYP3TdOf/qPj9UoLvbBMf+CeAxm/rcAW9FBl4F1xXoP//xdlOgpy+HVc3j7pff5l8tCBToumzqcwe8FRl4FVx6FP6+QIcvXx76Ap18Nf6xk1Cg67Kpzx3wVmTgVfBHFuj1rKauMudfjX/stED//P7ctdHuB37454IJIc2ylQLdPc+/Wvhp1kDXZVP/cANvRQZeBW+lQN9ZA52GAl2XTX3ugLciA6+CN74PdBoKdF029bkD3ooMvAr+4AK9HHf/9Pv8q4Wf5jzQddnU5w54KzLwKvgjC3R65ufpN/Ov7kOBrsumPnfAW5GBV8EfWqAtr0QSvGS9bX9u63MHvBUZeBX8oQXa8lp4xZsmNe3PbX3ugLciA6+CP7RAm96NSfG2nS37c1ufO+CtyMCr4I8p0NNvziXZ8n6gfTa1sIGBNycDr4I/uECb3pG+y6YWNjDw5mTgVTDPRAoGGLgQFhzZA6ZAgwEGLoQFR/aAKdBggIELYcGRPWAKNBhg4EJYcGQPmAINBhi4EBYc2QOmQIMBBi6EBUf2gCnQYICBC2HBkT1gCjQYYOBCWHBkD5gCDQYYuBAWHNkDpkCDAQYuhAVH9oAp0GCAgQthwZE9YAo0GGDgQlhwZA+YAg0GGLgQFhzZA6ZAgwEGLoQFR/aAKdBggIELYcGRPWAKNBhg4EJYcGQPmAINBhi4EBYc2QOmQIMBBi6EBUf2gCnQYICBC2HBkT1gCjQYYOBCWHBkD5gCDQYYuBAWHNkDpkCDAQYuhAVH9oAp0GCAgQthwZE9YAo0GGDgQlhwZA+YAg0GGLgQFhzZA6ZAgwEGLoQFR/aAKdBggIELYcGRPWAKNBhg4EJYcGQPmAINBhi4EBYc2QOmQIMBBi6EBUf2gCnQYICBC2HBkT1gCjQYYOBCWHBkD5gCDQYYuBAWHNkDpkCDAQYuhAVH9oAp0GCAgQthwZE9YAo0GGDgQlhwZA+YAg0GGLgQFhzZA6ZAgwEGLoQFR/aAKdBggIELYcGRPWAKNBhg4EJYcGQPmAINBhi4EBYc2QOmQIMBBi6EBUf2gCnQYICBC2HBkT1gCjQYYOBCWHBkD5gCDQYYuBAWHNkDpkCDAQYuhAVH9oAp0GCAgQthwZE9YAo0GGDgQlhwZA+YAg0GGLgQFhzZA6ZAgwEGLoQFR/aAKdBggIELYcGRPWAKNBhg4EJYcGQPmAINBhi4EBYc2QOmQIMBBi6EBUf2gCnQYICBC2HBkT1gCjQYYOBCWHBkD5gCDQYYuBAWHNkDpkCDAQYuhAVH9oAp0GCAgQthwZE9YAo0GGDgQlhwZA+YAg0GGLgQFhzZA6ZAgwEGLoQFR/aAKdBggIELYcGRPWAKNBhg4EJYcGQPmAINBhi4EBYc2QOmQIMBBi6EBUf2gCnQYICBC2HBkT1gCjQYYOBCWHBkD5gCDQYYuBAWHNkDpkCDAQYuhAVH9oAp0GCAgQthwZE9YAo0GGDgQlhwZA+YAg0GGLgQFhzZA6ZAgwEGLoQFR/aAKdBggIELYcGRPWAKNBhg4EJYcGQPmAINBhi4EBYc2QOmQIMBBi6EBUf2gCnQYICBC2HBkT1gCjQYYOBCWHBkD5gCDQYYuBAWHNkDVirQvwfyZ+SHgIE3BguO7AFToMEAAxfCgiN7wEoFGvmhTa3uAwNvTgZeBVOgwQADF8KCI3vAFGgwwMCFsODIHjAFGgwwcCEsOLIHTIEGAwxcCAuO7AFToMEAAxfCgiN7wBRoMMDAhbDgyB4wBRoMMHAhLDiyB0yBBgMMXAgLjuwBU6DBAAMXwoIje8AUaDDAwIWw4MgeMAUaDDBwISw4sgdMgQYDDFwIC47sAVOgwQADF8KCI3vAFGgwwMCFsODIHjAFGgwwcCEsOLIHTIEGAwxcCAuO7AFToMEAAxfCgiN7wBRoMMDAhbDgyB4wBRoMMHAhLDiyB0yBBgMMXAgLjuwBU6DBAAMXwoIje8AUaDDAwIWw4MgeMAUaDDBwISw4sgdMgQYDDFwIC47sAVOgwQADF8KCI3vAFGgwwMCFsODIHjAFGgwwcCEsOLIHTIEGAwxcCAuO7AFToMEAAxfCgiN7wBRoMMDAhbDgyB4wBRoMMHAhLDiyB0yBBgMMXAgLjuwBU6DBAAMXwoIje8AUaDDAwIWw4MgeMAUaDDBwISw4sgdMgQYDDFwIC47sAVOgwQADF8KCI3vAFGgwwMCFsODIHjAFGgwwcCEsOLIHTIEGAwxcCAuO7AFToMEAAxfCgiN7wBRoMMDAhbDgyB4wBRoMMHAhLDiyB0yBBgMMXAgLjuwBU6DBAAMXwoIje8AUaDDAwIWw4MgeMAUaDDBwISw4sgdMgQYDDFwIC47sAVOgwQADF8KCI3vAFGgwwMCFsODIHjAFGgwwcCEsOLIHTIEGAwxcCAuO7AFToMEAAxfCgiN7wBRoMMDAhbDgyB4wBRoMMHAhLDiyB0yBBgMMXAgLjuwBU6DBAAMXwoIje8AUaDDAwIWw4MgeMAUaDDBwISw4sgdMgQYDDFwIC47sAVOgwQADF8KCI3vAFGgwwMCFsODIHjAFGgwwcCEsOLIHTIEGAwxcCAuO7AFToMEAAxfCgiN7wBRoMMDAhbDgyB4wBRoMMHAhLDiyB0yBBgMMXAgLjuwBU6DBAAMXwoIje8AUaDDAwIWw4MgeMAUaDDBwISw4sgdMgQYDDFwIC47sAVOgwQADF8KCI3vAFGgwwMCFsODIHjAFGgwwcCEsOLIHTIEGAwxcCAuO7AFToMEAAxfCgiN7wBRoMMDAhbDgyB4wBRoMMHAhLDiyB0yBBgMMXAgLjuwBU6DBAAMXwoIje8AUaDDAwIWw4MgeMAUaDDBwISw4sgdMgQYDDFwIC47sARcW6HF3yufJC1+/7C759Y/J190XC6NG/tBNLWxg4M3JwKvgugLdn8vx0++XV24L9PWJAgUGrpWBV8FlBXrY7R7f3l4eltrxsPvlt7fum8vNOYQCBbaFBUf2gKsK9LR2+dj9emrQ59vvnV7rv3ecbeDfhQIFtoUFR/aAqwr0OG677+9bcj+slR7OPfpeKFBgW1hwZA+4qkDHkjy15GQvaJ/jblgp3fcb8u+GAgW2hQVH9oCLCvTrl3HF87i7qcnTt87d+vr06W9PNwfqp6FAgW1hwZE94LoCHTbPXx5uCvSyAvrysLs7UL+bhAIFtoUFR/aAiwp0PIa0UKCXjfvjcP7SfnKgflagfxJCyJbyAQU6Pwx//XrcO3paW707UN+FNVBgW1hwZA/4w9dA7w8qLR2o70KBAtvCgiN7wB+9D/R6dOmaw/KlSBQosC0sOLIH/AFH4WdrnKdV07vtdQoUGLhKBl4Ff8B5oLN2PN5vwVOgwMBlMvAq+KOvRLqW5XUrf798RRIFCmwLC47sAX/0tfCTPj1cTqhfviKJAgW2hQVH9oA/+G5M19XO/nuf35YPK/WhQIFtYcGRPeCPuR/o5PLNyQrpcThj/p1rOSlQYFtYcGQP+GPuSL9coMMdlhfPon+jQIGNYcGRPWCeiRQMMHAhLDiyB0yBBgMMXAgLjuwBU6DBAAMXwoIje8AUaDDAwIWw4MgeMAUaDDBwISw4sgdMgQYDDFwIC47sAVOgwQADF8KCI3vAFGgwwMCFsODIHjAFGgwwcCEsOLIHTIEGAwxcCAuO7AFToMEAAxfCgiN7wBRoMMDAhbDgyB4wBRoMMHAhLDiyB0yBBgMMXAgLjuwBU6DBAAMXwoIje8AUaDDAwIWw4MgeMAUaDDBwISw4sgdMgQYDDFwIC47sAVOgwQADF8KCI3vAFGgwwMCFsODIHjAFGgwwcCEsOLIHTIEGAwxcCAuO7AFToMEAAxfCgiN7wBRoMMDAhbDgyB4wBRoMMHAhLDiyB0yBBgMMXAgLjuwBU6DBAAMXwoIje8AUaDDAwIWw4MgeMAUaDDBwISw4sgdMgQYDDFwIC47sAVOgwQADF8KCI3vAFGgwwMCFsODIHjAFGgwwcCEsOLIHTIEGAwxcCAuO7AFToMEAAxfCgiN7wBRoMMDAhbDgyB5wZoG+/q8/AhN8dyhQYFtYcGQPOLVAn3a7z4EZvjMUKLAtLDiyB5xdoKc8Bsb4nlCgwLaw4MgecO4+0MPunOfAJH8ZChTYFhYc2QNOP4i0P1fop98Dw3w7FCiwLSw4sgfc4Cj81y/nDv01+ZASBQpsCwuO7AG3OY1p2Buae0iJAgW2hQVH9oCbnQc6rIf+8tuP/uC7oUCBbWHBkT3gRgU6Hk3KXAulQIFtYcGRPeAWBXq4HEfqV0OzTmuiQIFtYcGRPeD0Ar05k+n1Ke2APAUKbAsLjuwBtzkPdLLSuadAgYG3KwOvghtciTQ7fem0EZ91OhMFCmwLC47sAWcXaOJR99tQoMC2sODIHnBugTa5hHMMBQpsCwuO7AFzP9BggIELYcGRPeDcNdDZBvw++WJOChTYFhYc2QNuWqC5dxShQIFtYcGRPeB2BZp4Bug5FCiwLSw4sgecVKCTSzcnYRMeGHjjMvAqOKlAx9svzZN7b3oKFNgWFhzZA87ahD82708KFNgXFhzZA254ECk7FCiwLSw4sgdMgQYDDFwIC47sAXMifTDAwIWw4MgeMAUaDDBwISw4sgecU6DdQfjn+0PxnAcKDLxxGXgVTIEGAwxcCAuO7AFToMEAAxfCgiN7wOwDDQYYuBAWHNkDpkCDAQYuhAVH9oAp0GCAgQthwZE9YAo0GGDgQlhwZA847yDSQjiIBAy8cRl4FUyBBgMMXAgLjuwBU6DBAAMXwoIje8DsAw0GGLgQFhzZA6ZAgwEGLoQFR/aAKdBggIELYcGRPWAKNBhg4EJYcGQPmGvhgwEGLoQFR/aAKdBggIELYcGRPWAKNBhg4EJYcGQPmH2gwQADF8KCI3vAFGgwwMCFsODIHrBSgf49kD8jPwQMvDFYcGQPmAINBhi4EBYc2QNOL9CXhwbHj/qwCQ9sCwuO7AEnF+jxegj+l98C43wrFCiwLSw4sgecW6CH2VlMz4F5vhEKFNgWFhzZA04t0G7zfdh2n/w2KxQosC0sOLIHnFqg++la52lt9HNgoPdDgQLbwoIje8CZBfr1y6wy97tf/whM9G4oUGBbWHBkDzizQF+fZrs9j1zKCQy8dRl4FUyBBgMMXAgLjuwBJ+8D/fzuV+tDgQLbwoIje8DZR+EfL18cs88EpUCBbWHBkT3g3PNAj5fz50+b89ln0lOgwLaw4MgeMI81DgYYuBAWHNkDpkCDAQYuhAVH9oAp0GCAgQthwZE9YKXb2UV+aFMLGxh4czLwKpgCDQYYuBAWHNkDpkCDAQYuhAVH9oBbFujrv7IPFBh42zLwKrjdDZU5iAQMvH0ZeBWcW6B7jsIDA0vJwKvg9Bsqt7slPQUKbAsLjuwBZ99Q+XN3J+XPbzc3V04JBQpsCwuO7AEn31C5u4XycBu7A4/0AAbevAy8Ck6+H2h3M6aXh/42Iqc6ZRMeGHjjMvAquMENlcf7Kh+4Hygw8NZl4FVwgwI9rXr2dwV9eeCZSMDAG5eBV8EtHukx3Ir+5YHTmICBNy4Dr4KTDyL1q56H8+M4eSYSMPDmZeBVcOppTMOB9+FhHgceawwMvHUZeBWcfSJ9V52nX07VedxxEAkYeOsy8Co4/1LOx+sVnZzGBAy8cRl4FZxboF+/9K053KA+dwWUAgX2hQVH9oCzb2d3PD+Lc1gVTQ0FCmwLC47sAXND5WCAgQthwZE9YAo0GGDgQlhwZA8490T68/b7kD2nMQEDb10GXgU3LVBOpAcG3rgMvApuV6CvTxQoMPDWZeBVcFKBHnZLYRMeGHjjMvAqOKlAhzM/b5J7IhMFCmwLC47sAWdtwh+b9ycFCuwLC47sATc8iJQdChTYFhYc2QOmQIMBBi6EBUf2gDmRPhhg4EJYcGQPmAINBhi4EBYc2QNuUaD9IfnkWzG9UaDAxrDgyB5wYoGOl26OB+Rz7wZKgQIbw4Ije8BpBdrVZn/l0cvDrk2DUqDAtrDgyB5w6nmgXYF291Q+/dr9knshEgUK7AsLjuwBJ16JdL7yfXgu0nhz+sRQoMC2sODIHnBSgV6fIHcYf3dqUh4qBwy8cRl4FZxUoPvdcA79acXz+jtuJgIMvHEZeBWcU6DXsjytd443seN+oMDAm5eBV8E5Bfr6NG6uT54GT4ECA29eBl4FZxfo/nroiAIFBt68DLwKTivQ8yb8dRfo9bWsUKDAtrDgyB5w2j7Qy0lMY2tyFB4YePsy8Co475Ee/Zb7/nob5T13pAcG3rwMvApOKtDu+s3n/hDSuAV/2CXvAqVAV+TylIAWuNai0IQFR/aAsy7l3M+f49HfkIlHemwFnjxnpYEutShEYcGRPeC0m4nsJw/iPN9PJPuGdhRoNLMnVeXzSotCFRYc2QPOu51d35rP19+m3xCUAg3m5ll/6b7QopCFBUf2gJvckT79AHwfCjQYClQfFhzZA+aRHsHowHePm87+A3QWhS4sOLIHTIEGowNToD8BLDiyB9yiQA+7Jo83pkBjoUB/AlhwZA+YAg1GBr7rTwpUEBYc2QOmQIPRgSnQnwAWHNkDpkCD0YEp0J8AFhzZA6ZAg9GBKdCfABYc2QOmQIMRgjkPVB8WHNkDpkCDEYIpUH1YcGQPmAINRglu259Si0IVFhzZA6ZAg5GCm/an1qIQhQVH9oC5EikYLbhlf4otCk1YcGQPmAINBhi4EBYc2QOmQIMBBi6EBUf2gJML9Hwr5TE81hgYeOMy8Co4t0AP8xNmKFBg4I3LwKvg1AI97ihQYGApGXgVnFqg+/QncU5DgQLbwoIje8CZBfr1S8v+pECBfWHBkT3gzAJ9fcp+kvEsFCiwLSw4sgdMgQYDDFwIC47sASdvwn+rQPtDTPOndZ5+4pz+cfKLb7mGAgW2hQVH9oBTDyIdxiJcyn7hyPxpnXVaoEtvmYz6fZPOs6mFDQy8ORl4FZxaoN/ahj/suu+9PMw69uVh+tXiWyajft+k82xqYQMDb04GXgXnnkj/bvlduvX0jufrq8fp9vryWyajft+k82xqYQMDb04GXgUnH0R690T64/jFftqZh+ka6/JbJqN+36TzbGphAwNvTgZeBVcV6H5cNT3MXp3eOHT5LZNRv2/SeTa1sIGBNycDr4KLCvTrl3Gt8ji52/Lr06e/PY3H3ZffMh31+yadZ1MLGxh4czLwKrjodnbXM5xeHq7teLl3U9e0i2+Z1jEFCmwLC47sARcV6PX4/LRAj8P5S/3G++JbZgX6JyGEbCkfUKDXY+zjzs7TyufzO2+ZhDVQYFtYcGQP+EPXQC/pjrv/xVsoUGBjWHBkD/hD94Fe0l3C9BdvoUCBjWHBkT3gpkfhL9e4zw6xL5yjNBTot95CgQIbw4Ije8CNC/Rya5DJSZ4L1yr1L377LRQosDEsOLIH3LxAhwZduszoutG+737DlUjAwOUy8Co4/Vr4YfdlV6aPkxcWL3QfVzVfn7o3cS08MHC5DLwKTi3QU/Vdr20/X090asXz6uTSrZZOX3XfHPd+cjcmYOBqGXgVnPxQuc93X112aE5v9nmqzP7V4+2OUu4HCgxcKgOvgpP3gU63vc/7NK+H1Ce3mx8LdLgl/fP1R3bckR4YuFAGXgUXFujaUKDAtrDgyB5w8jOR5pvw3VomBQoMvGEZeBWcvA90dhCpr9P9t56T9EOhQIFtYcGRPeDso/Dj+mZ3GlN3FP6wS3vUMQUKbAsLjuwB554HepidQv/cN+ride2RUKDAtrDgyB5w8s1ELrdIPhdnd1Q9awWUAgX2hQVH9oDT78Y0XM953pJ/5+EcsVCgwLaw4MgecNHt7DJCgQLbwoIje8AUaDDAwIWw4MgeMAUaDDBwISw4sgecU6Ddjs/nbz4XPiEUKLAtLDiyB0yBBgMMXAgLjuwBU6DBAAMXwoIje8DsAw0GGLgQFhzZA6ZAgwEGLoQFR/aAKdBggIELYcGRPWAKNBhg4EJYcGQPuEWB9geT3ruvfDwUKLAtLDiyB5xYoOOdP8cHHS0+WnNFKFBgW1hwZA84rUCP42lL1xsyJTcoBQpsCwuO7AFnFehxPO+ze0zc6dful6xb0Q+hQIFtYcGRPeCkAu12e55Pmz+tgPa3sOsaNHcVlAIFtoUFR/aAkwr0eDlqdBh/d2rS3ANJFCiwLSw4sgecVKD78c7JpxXP6+9yt+EpUGBbWHBkDzinQK9leVrvHK+A33MtPDDw1mXgVXDazUSGzfXrtjwFCgy8fRl4FZxdoPvroSMKFBh48zLwKjitQM+b8NddoNfXskKBAtvCgiN7wGn7QC8nMY2tyVF4YODty8Cr4KSj8Idhy31/fQ78PvGR8H0oUGBbWHBkDzipQLvrN5/7Q0jjFvwh+4b0FCiwLyw4sgecdSnnfrwA/rzW2d+QKXcFlAIF9oUFR/aA024mMjRovwf0fD+R7BvaUaDAtrDgyB5w3u3s+tZ8vv42/YagFCiwLSw4sgfc5I706Qfg+1CgwLaw4MgeMI/0CAYYuBAWHNkDpkCDAQYuhAVH9oAp0GCAgQthwZE9YAo0GGDgQlhwZA+YAg0GGLgQFhzZA6ZAgwEGLoQFR/aAKdBggIELYcGRPWAKNBhg4EJYcGQPmAINBhi4EBYc2QOmQIMBBi6EBUf2gCnQYICBC2HBkT1gCjQYYOBCWHBkDzjtmUi75/NNQKfhoXLAwBuXgVfBFGgwwMCFsODIHjAFGgwwcCEsOLIHzD7QYICBC2HBkT1gCjQYYOBCWHBkD5gCDQYYuBAWHNkDblOg3UOR+sfLZYYCBbaFBUf2gJML9PWp683zUznHJ8RnhQIFtoUFR/aAcwv02B95//qlxUF4ChTYFxYc2QNOLdBuzfO03nn65dSdh93uMTDQ+6FAgW1hwZE94NQCPZyfBj9U5z752cYUKLAtLDiyB5xZoKdN924P6OmXfvfnkRPpgYG3LgOvgjML9PVp93z+pW9OChQYePMy8Cq4QYEezxvyFCgw8PZl4FVwgwLd7/pf3g7Jp4JSoMC2sODIHnDyPtDH6y7QU51yEAkYeOMy8Co49Sj8vqvOw/kipO6UpufAQO+HAgW2hQVH9oDTzwPt8txvx2dfzEmBAtvCgiN7wLlXIh36/uyK85B+IRIFCuwLC47sASdfC3/cXQ7B526/v1GgwMaw4MgeMLezCwYYuBAWHNkDpkCDAQYuhAVH9oBbFujrv3IiPTDwtmXgVXCDfaA8VA4YWEYGXgXnFuiep3ICA0vJwKvgJueBjuFEemDgjcvAq+DkK5G6c5gO/YlM++z+pECBfWHBkT3gBvcDHe7CdOCRHsDAm5eBV8HJd2Pq7kT/8tDfTORUp2zCAwNvXAZeBbe5ofJwOzvuxgQMvHEZeBXcoEDPd7Xr1kS5Hygw8MZl4FVwgwIdnyb38sBpTMDAG5eBV8H5N1S+3IqeR3oAA29eBl4FJz/WeHiaXH8UiUd6AANvXgZeBWefSN9V5+mXU3WOz5ZLy3/+PZA/Iz8EDLwxWHBkDzj/Us7H6xWdyacxVS0TYOCtwYIje8C5Bfr1S9+ar099f+augLIJD+wLC47sAWffzu7Y7/4cV0VTQ4EC28KCI3vA3FA5GGDgQlhwZA+YAg0GGLgQFhzZA6ZAgwEGLoQFR/aAk69E4obKwMBSMvAqmAINBhi4EBYc2QOmQIMBBi6EBUf2gFvtAx1urpwZChTYFhYc2QNudxAp+1J4ChTYFxYc2QNuV6DckR4YePsy8Cq44WlM3I0JGHjzMvAquGmBchAJGHjjMvAqmAINBhi4EBYc2QNuV6CvT2zCAwNvXQZeBTcr0O6kUJ7KCQy8cRl4FdzyRPrzne3SQoEC28KCI3vALQs0+YagFCiwLZVMOUIAABtwSURBVCw4sgfcrkBzjyC9UaDAxrDgyB4wt7MLBhi4EBYc2QOmQIMBBi6EBUf2gCnQYICBC2HBkT3glgX69b84kR4YeNsy8Co4t0CPswfCH3OfDE+BAtvCgiN7wIkF2j0U/pLP/depR+IpUGBbWHBkDzivQI+7WX757Zh8KRIFCmwLC47sAacV6HFy7ud4QmjupUgUKLAtLDiyB5xVoC8Ps1Pnz5vzuZciUaDAtrDgyB5wVoHud/N7L3UNmnwtEgUKbAsLjuwBJxXoaQV0XpfdGimP9AAG3roMvApOKtDDbVvuh0PxiaFAgW1hwZE94JwCvTtj6bQC+h/cUBkYePMy8Co4p0Dv7j5/2H36v8mngVKgwL6w4MgecFqB3myu7z+ftuIpUGDgjcvAq+BWBfr2RoECA29fBl4Fp+0DvdvfufTaqlCgwLaw4MgecKODSG/vrJWuCQUKbAsLjuwBtzqNqb+2kyuRgIE3LgOvgludSN+tgPJUTmDgrcvAq+DESzk/f/uF1aFAgW1hwZE94MybiUyOGTW4FJ4CBfaFBUf2gHNvZzdUaH87u+QNeAoU2BgWHNkDzruhcn/7kOkNlQPTfDMUKLAtLDiyB5z5TKT9/JEe2aFAgW1hwZE94NyHyg1roflrn10oUGBbWHBkD5jnwgcDDFwIC47sAVOgwQADF8KCI3vAFGgwwMCFsODIHjAFGgwwcCEsOLIHTIEGAwxcCAuO7AFToMEAAxfCgiN7wBRoMMDAhbDgyB4wBRoMMHAhLDiyB0yBBgMMXAgLjuwBU6DBAAMXwoIje8AUaDDAwIWw4MgeMAUaDDBwISw4sgdMgQYDDFwIC47sAVOgwQADF8KCI3vAFGgwwMCFsODIHjAFGgwwcCEsOLIHTIEGAwxcCAuO7AFToMEAAxfCgiN7wBRoMMDAhbDgyB4wBRoMMHAhLDiyB0yBBgMMXAgLjuwBU6DBAAMXwoIje8AUaDDAwIWw4MgeMAUaDDBwISw4sgdMgQYDDFwIC47sAVOgwQADF8KCI3vAFGgwwMCFsODIHjAFGgwwcCEsOLIHTIEGAwxcCAuO7AFToMEAAxfCgiN7wBRoMMDAhbDgyB4wBRoMMHAhLDiyB0yBBgMMXAgLjuwBU6DBAAMXwoIje8AUaDDAwIWw4MgeMAUaDDBwISw4sgdMgQYDDFwIC47sAVOgwQADF8KCI3vAFGgwwMCFsODIHnBhgR53p3y+efEwefHrl905v/6x9PMUKLAtLDiyB1xXoPtzOX76ffLa69P5xV9+m35FgQIDV8nAq+CyAj2taj6+vb08TNvxtMrZVef44svDcnMOoUCBbWHBkT3gqgI9rV0+dr+eyvL58uJxWPUcXjzebeDPQoEC28KCI3vAVQV6HLfd95OW3A+ro6c10e7Fw7lj3wsFCmwLC47sAVcV6NiVp5a87gW9lOn5N/vz+uh7oUCBbWHBkT3gogId1jHfrpvt05y371+fPv3taeFA/RgKFNgWFhzZA64r0GHz/OXhvkCP47GkuwP1u0koUGBbWHBkD7ioQMdjSIsFevpmt31/HM5f2k8O1M8K9E9CCNlSPqBAJ4fhx+/165zj3tHT2urNO85hDRTYFhYc2QP++DXQ07duXtkv7walQIFtYcGRPeAP3wfaXX50s8J5WL4UiQIFtoUFR/aAP+Ao/OxiztMW/d0+UQoUGLhKBl4Ff8B5oNN2XOpPChQYuEwGXgV/6JVIXX9e1kevW/n75SuSKFBgW1hwZA/4Q6+FH4+/nzOueL4+LV+RRIEC28KCI3vAH3o3psNs+/30vW7l9Lq79CYUKLAtLDiyB/wx9wM9leSpRy/3/xyu3zxOfr80auRP3dTCBgbenAy8Cv6YO9KfC/Ry7eb4+vmW9Itn0b9RoMDGsODIHjDPRAoGGLgQFhzZA6ZAgwEGLoQFR/aAKdBggIELYcGRPWAKNBhg4EJYcGQPmAINBhi4EBYc2QOmQIMBBi6EBUf2gCnQYICBC2HBkT1gCjQYYOBCWHBkD5gCDQYYuBAWHNkDpkCDAQYuhAVH9oAp0GCAgQthwZE9YAo0GGDgQlhwZA+YAg0GGLgQFhzZA6ZAgwEGLoQFR/aAKdBggIELYcGRPWAKNBhg4EJYcGQPmAINBhi4EBYc2QOmQIMBBi6EBUf2gCnQYICBC2HBkT1gCjQYYOBCWHBkD5gCDQYYuBAWHNkDpkCDAQYuhAVH9oAp0GCAgQthwZE9YAo0GGDgQlhwZA+YAg0GGLgQFhzZA6ZAgwEGLoQFR/aAKdBggIELYcGRPWAKNBhg4EJYcGQPmAINBhi4EBYc2QOmQIMBBi6EBUf2gCnQYICBC2HBkT1gCjQYYOBCWHBkD5gCDQYYuBAWHNkDpkCDAQYuhAVH9oAp0GCAgQthwZE9YAo0GGDgQlhwZA+YAg0GGLgQFhzZA6ZAgwEGLoQFR/aAKdBggIELYcGRPWAKNBhg4EJYcGQPmAINBhi4EBYc2QOmQIMBBi6EBUf2gCnQYICBC2HBkT1gCjQYYOBCWHBkD5gCDQYYuBAWHNkDpkCDAQYuhAVH9oAp0GCAgQthwZE9YAo0GGDgQlhwZA+YAg0GGLgQFhzZA6ZAgwEGLoQFR/aAKdBggIELYcGRPWAKNBhg4EJYcGQPmAINBhi4EBYc2QOmQIMBBi6EBUf2gCnQYICBC2HBkT1gCjQYYOBCWHBkD5gCDQYYuBAWHNkDpkCDAQYuhAVH9oAp0GCAgQthwZE9YAo0GGDgQlhwZA+YAg0GGLgQFhzZA6ZAgwEGLoQFR/aAKdBggIELYcGRPWAKNBhg4EJYcGQPmAINBhi4EBYc2QOmQIMBBi6EBUf2gCnQYICBC2HBkT1gCjQYYOBCWHBkD5gCDQYYuBAWHNkDpkCDAQYuhAVH9oAp0GCAgQthwZE9YAo0GGDgQlhwZA+YAg0GGLgQFhzZA6ZAgwEGLoQFR/aAKdBggIELYcGRPWAKNBhg4EJYcGQPmAINBhi4EBYc2QOmQIMBBi6EBUf2gCnQYICBC2HBkT1gCjQYYOBCWHBkD5gCDQYYuBAWHNkDpkCDAQYuhAVH9oCVCvTvgfwZ+SFg4I3BgiN7wBRoMMDAhbDgyB6wUoFGfmhTq/vAwJuTgVfBFGgwwMCFsODIHjAFGgwwcCEsOLIHTIEGAwxcCAuO7AFToMEAAxfCgiN7wBRoMMDAhbDgyB4wBRoMMHAhLDiyB0yBBgMMXAgLjuwBU6DBAAMXwoIje8AUaDDAwIWw4MgeMAUaDDBwISw4sgdMgQYDDFwIC47sAVOgwQADF8KCI3vAFGgwwMCFsODIHjAFGgwwcCEsOLIHTIEGAwxcCAuO7AFToMEAAxfCgiN7wBRoMMB9dmNa4FqLoiksOLIHTIEGA9xlt2vZoFKLoi0sOLIHTIEGA/w268/sBmXVtkgGXgVToMEA3/RnbtWxalslA6+CKdBggFsWaMNV2y5Cy7i5DLwKpkCDAb7tz8Sma7hq20dnGbeXgVfBFGgwwBRoISw4sgdMgQYD3K5A2zXzEJ1l3F4GXgVToMEA39UcBUqB2sEUaDDArIEWwoIje8AUaDDAzXqu3artGJ1l3F4GXgVToMEAswZaCAuO7AFToMEAtztYToEWysCrYAo0GGAKtBAWHNkDpkCDAX5rd8FQ4/6UWsatZeBVMAUaDHCXRi1HgdbJwKtgCjQY4D6NSq5tf4ot47Yy8CqYAg0GuCnctD+1FkVjGXgVTIEGA9wWbtmfYouirQy8CqZAgwEGLoQFR/aAKdBggIELYcGRPWAKNBhg4EJYcGQPmAINBhi4EBYc2QOmQIMBBi6EBUf2gCnQYICBC2HBkT1gCjQYYFFY8/wosYXsA1OgwQBrwqJn6GstZCOYAg0GWBJWvUZUaiE7wRRoMMCKsOxdSpQWshVMgQYDrAhToMC5MAUaDLAgvLtN9h9AgbrBFGgwwIIwBQqcDFOgwQALwhQocDJMgQYDrAff9ScFCrwSpkCDARaEKVDgZJgCDQZYEG5aoA1PL31TWsheMAUaDLAg3LJAW54d9aa0kL1gCjQYYEW4pD+1LhIFXgVToMEAK8LNCrTxvlWphWwFU6DBAEvCJSugzR7ynMueo/S3t0GYAg0GWBMu6c9GR6fYN7A9mAINBlgUbt1xantXtf72NgdToMEAA1/TsEBb713VWcibhCnQYICBL7nrTwrUBaZAgwEGvqZdgbbcOdBHZyFvEqZAgwEGvoYCdYUp0GCAga+hQF1hCjQYYOBJyvqTAt0WTIEGAww8SbOWo0C3DVOgwQADT9Oq5CjQbcMUaDDAwLM06jgKdNswBRoMMPA8jSqucX+KLeTNwRRoMMDAJTAFummYAg0GGLgGbtufWstiezAFGgwwcBHctD/FlsXmYAo0GGDgKrhlf6oti63BFGgwwMCFsODIHjAFGgwwcCEsOLIHTIEGAwxcCAuO7AFToMEAAxfCUqeunqO3kCnQ+2xqYQMDb0nm8P56mAINBhi4EG5+in4+r7eQKdD7bGphAwNvR+YSpwyYAg0GGLgQpkA3ClOgwQADF8L5Mrd5SoEp0GCAgQthsQL1ObxPgQYDDFwIaxWo0eH9wgI9dsvz8zdfXHzLGAoU2BZOl+/6s9VjSPLYGZ3LxuG6At2f5/v0+/svLr7lEgoU2BZWWgOt2DXQ8LbVP/aDZQV62O0e395eHna//vHei4tvmYwa+WP1/lcBBq6QFQu0oph/EK4q0Nenrhz7enx+58XFt0xHjfy5ev+rAANXyM0KVLCZV8BVBXq8bqZ/fufFxbdMQoEC28JC54FSoIt/RGSuSfbjdvlhsotz/uLiWyahQIFtYQp0o3BRgX79Mq5VHne//Lb44uJbpqFAgW1hnWvh79poEz3XDK4r0Mfz714epgU6eXHxLdP/KgoU2BZuIrfoz432XDO4qEDHA0Szdpy/uPiWWYH+SQhJzOX/rSZoMn7nbgL+gAK9HGOfv7j4lmlYAwW2hYVG3uSKYjN442ug01CgwLaw0siNas66QKP7QKehQIFtYaWRKdClPyM02SXTQ+yXc5TmLy6+ZRoKFNgWlhq5TX9yHmj/m8PkQs35i4tvmYQCBbaFtUZu05/WBcqVSMDAW5SbwE36k2vh37gWHhh4W7IU3Kg/uRvTu5H6eAADl8tacKP+VLsf6NcvQ0lyP1Bg4A+VgVfBH3NH+kuBckd6YOAPlYFXwTwTKRhg4EJYcGQPmAINBhi4EBYc2QOmQIMBBi6EBUf2gCnQYICBC2HBkT1gCjQYYOBCWHBkD5gCDQYYuBAWHNkDpkCDAQYuhAVH9oAp0GCAgQthwZE9YAo0GGDgQlhwZA+YAg0GGLgQFhzZA6ZAgwEGLoQFR/aAKdBggIELYcGRPWAKNBhg4EJYcGQPmAINBhi4EBYc2QOmQIMBBi6EBUf2gCnQYICBC2HBkT1gCjQYYOBCWHBkD5gCDQYYuBAWHNkDpkCDAQYuhAVH9oAp0GCAgQthwZE9YAo0GGDgQlhwZA+YAg0GGLgQFhzZA6ZAgwEGLoQFR/aAKdBggIELYcGRPWAKNBhg4EJYcGQPWKlACSFkY/m+9hIt0N0ue3EBA9fDgiPbwN/XXhso0Eh2reYGBi6EBUcGnuMN7YbRW9jAwJUycHu4xxvaDaO3sIGBK2Xg9nCPN7QbRm9hAwNXysDt4R5vaDeM3sIGBq6UgdvDPd7Qbhi9hQ0MXCkDt4d7vKHdMHoLGxi4UgZuD/d4Q7th9BY2MHClDNwe7vGGdsPoLWxg4EoZuD3c4w3thtFb2MDAlTJwe7jHG9oNo7ewgYErZeD2cI83tAkh5KcOBUoIIcFQoIQQEgwFSgghwVCghBASDAVKCCHBUKCEEBIMBUoIIcFQoIQQEox2gR53j43kw+5zNvn1y+6cX//Ipg8dmznwy8Mvv/W/2Z/gT783gLs0WMjpA18nbreQ35I/yQOc/4Hr4QubKF8WxctD7kK+wMfsv70h0gX6+tSqQE9/j+kL+zRtmwId4Uk1rc3wuRvlvKU8LY0GCzl/4NtFkb+Q396yP8k3IwsV6P7M5v0LePNvSeLf3hDlAu0+IG0KtFve6QX68pC/6tnlNGz3uTjVUZ5//tyd5O6jfFr1es6F+zRYyA0Gvi6KRgu5S/IneYDzP3Cz7YfTYk7rowHepy/kAT70yzf1b2+IcIH2a/ttCvTQYnX/2GILonfPn+PT8kjuuVHe500++V+wwUJuMPDNoshfyG/5n+QBzv/AzQr0NHXazGd4XLjH7GYeV/Az//aG6BboaW3/H/+tTYG+Pn363/ltd2jU9vvhn9XTSlJyz409dEhfI3hrs5AbDHxZFK0WcoNP8mW1K/sDNyvQffpCPlwXctbkYzOf506Ex0gV6GGyG6P79y9teRzm+0f2u+ekdZgpvM/cATOBL6OmzHzo3dtttYT/VW7htIV8uN+5lVOg04kbLuTMT/IMzvzA3X8sjjn7SSZwbr1NJ6ZAu1x2Xvef4Jd//iNreczh86ZPyv8nM/i0xvW3p6St1tuJ+2QciBiPO/zLtEAz1rru4KyFvLQoUlYTFxdFi4Wc90mew4kfuIVlcZo44R+pGXz6Im0D+3ZRsAl/2Wc92UGSVKA38OvT6dekFY0J3O/oSjrEeL8o7r4KpWuj5/On72oNR2Zy4bSFvLAoMgZeXhTNFnLKJ/kGzvvALU2csgI6h7v1xP7fw5x/VqcTnw8inb50Poh0/79bUoHewPsOTSnQGXIcTvrI2HW0NF3Gp+P6b8jl/5Rjyskqd3DaQr4zcgZeWhRvzRZyzif5Bs77wC1NnLIHdA4fd5/+z0PO2UZ3Ex/vt9hyIlWgt/+UphXoFD72n4ykAp3Ah+GL09Cr/+m+XxTdR2X9atflv/owK9D1H+hbOG8h3y2KnIGXFkW7hZzzSb6B8z5wCxPnbAzP4ePwF5ewBXE7MeeBvg3/Z8w+ZkkFOoO/fhnOSEso0PuJ33Loe3i+ohTMdXnODyLt19q3cOJCXlzGqwdeXhTtFnLGJ/m9v73Vi3kJPmTsibqBj+PehtU7mm8nHv7ihg371AgV6Plw63Q1PPPY5QgPlxcmHiC+3XDIOER8C3c7e1J2ST2P3vR/wdUHZW7hzIW8tIzXH0VaWhQNF3JSgS7+7a3+wC3AOWdz3cDHy7+E2RNf6j7z1KtzlAp03JORfRBpCr88nBd11qnYNxN3yTnHZgafNqgyNk6q/hdMXsgtlvHComi5kNUKNOeA+d3HYvwyeeJ3180TolWgb+fVgHHppp7WdYaH9Zk+Sf9YTSfuknaW9wVO+l/7/Q9awgd6Cucv5PRlfL8omi7kppvwyX97XY4pl6vfwNdWTp74uksg80ypc+QKdPqXl3xebAc3KNAzfJ11nzf0eVGc/tdOuvvCZQunP4p5HXn1bZPmcIuFPF/G6+/zNJ+43UI+J+kg0vLf3uoP3P3ESSsBdxNnXa3wHuy8Bnr5QGQX6AKcs3U5h8fP3M321Xo45dDwOeNG1HDrjEPWTv1beEjCQr5dxlkD307cbiG/Db9f/0m++9vL+sDdT5y08+UGnpx8tHI98Z0P8tLpKyujU6DjPXYm9zBIO5H+Fs47vnGFh5u3pex+n8GJN8XpLsuenH98+nUYefX6xn7ptPScE+kniyJx4JuJ2y3kPjmf5P3tifRZH7jbidM2/ebwcP5S/udtPH1in3/3IaECvb8/bPalnJO/ttxLOXt4OJc3G77c9TGDHuF/v1ym3Sfnwp4JfE7qpZzj3uCkgecTt1zIw0s521JTOO8Ddztx2q7EG3hczOmft8tVWen38xEq0PETcf2rS/uH8BZOPkA8wOe/1JxP3hW+fDZyuvl8NvPsjvQ5I9/AZzxjIc//8vIGnk7cdiHnfZLncOIHbg4nHou5WRTLp04nwIekf1dvI1WghBCypVCghBASDAVKCCHBUKCEEBIMBUoIIcFQoIQQEgwFSgghwVCghBASDAVKCCHBUKCEEBIMBUoIIcFQoGRLGS46/8bdeIabDGVlfoM9Qn4sFCjZTo7XW3a8e98HCpRsKBQo2Uwm/fn+E2gpULKhUKBkK5ncYvjw/mY8BUo2FAqUbCWHyb02u32hy7ecpEDJhkKBkq1kP62yw3t3LqZAyYZCgZKtZFag1yf6jC+eXum26vtv9M9+uPZo/+Wn30+/9Nv93TMZj5fdqPvpLtW7nz7/Ace/OPRPyHIoULKVLK10LhfocLLT+J3xMcn/41qg/2/8/vURyuNDk+Y/3f8B++Etyc8MJz9/KFCylXTFdrs5vVig/218xNv5W9OD90OB/sPD8PSi6SPoH8/If/8y/enuD/invzx3ipDlUKBkM9nfn8C0WKDnnjwO2+HdBnnXfMdJge4uz0QfHlHW/eby0+O7h30Ew6rnIetxZsQoFCjZTq7ri+O64HKBfh5fGDbSz23ZfWcs0GF/5vGyV+D0zc68vGf86a5Ahz/s3eNWhLwXCpRsKftLhZ5rbrFAx1f2/Srj/rLv8nAt0LtVydMq6FCg85/uCvRx9gcQ8v2hQMnGcpyuhC4W6Fhz/frl0IyTd0wqdUy/oT4U6OynF/4AQr4/FCjZYA676y7KpdOYLq/0BTrW3vU0pslu1ONst8DtT1OgZFUoULLJHHbjLspvFuivf0xqb6FAh1OW3inQ07spULImFCjZSl4ephve5+3wlWugr09jd173gbIGSvJCgZKN5DA/9HN4v0D/eh/o5BT74ZvXAmUfKMkLBUo2kuP8RPahBWdlOBTo+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