{ "cells": [ { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## 例2" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "subslide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "今度考えるのは、自然な例として、発言者間の距離が定義されているようなものを考える。ここで言う\"距離\"とは、実際の発言者間の物理的な距離だけでなく、それぞれの間の関係性や声の大きさなどの概念を含んだ一般的な意味での距離である。実際には、そのように距離の計算に用いるパラメータが$b$(<$a$)個あるとして、そのパラメータによる元に対して距離を考える。" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_type": "subslide" }, "slideshow": { "slide_type": "subslide" } }, "source": [ "簡単な例として$b$次元ユークリッド距離を取ることを考える。すなわち$b$個の数の組み合わせによって表される集合$X$があった時、\n", "\n", "距離関数$d: X \\times X \\rightarrow R$が\n", "\n", "$$d(x, y) = \\sqrt{\\sum_{i=1}^{b}(x_{i}-y_{i})^{2}}\\ \\ ,\\ x,y\\in X$$\n", "\n", "と書けることを意味する。\n", "\n", "\n", "**NOTE:**実際の場合には、各データ同士の相関を考慮に入れたマハラノビス距離などのほうが適当な場合もあるかもしれないが、まずはイメージしやすいということでユークリッド距離を考えた。" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "source": [ "以下では、記述の簡単にするため、発言者$i$と発言者$j$の間の距離を$d_{ij}$と書くことにする。" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "subslide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "時刻$k$に$i$が発言を行い、その後時刻$k+1$に$j$が発言$x_{k+1}^{j}$を行う確率$p_{k}(i,j)$は、距離$d_{ij}$の関数として、次のようにできる。\n", "\n", "$$p_{k}(i,j) = \\frac{g_{k}(d_{ij})}{\\sum_{j} g_{k}(d_{ij})}$$\n", "\n", "この$g$の選び方によって、距離の大きさがどのように確率に重みを持たせるかということが決定される。一般に$g$は時刻$k$によって変化してもいいので、添字$k$をつけて時刻$k$における関数であることを表した。" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "subslide_end", "slideshow": { "slide_type": "subslide" } }, "source": [ "単純な例として$g_{k}(d) = const.,\\ ^{\\forall}k, d\\in R^{1}$とすると、距離に依らず発言者が選ばれるわけなので、例1の発言者の選び方と同じである。\n", "\n", "$g(d)$は$[0, +\\infty]$で定義される非負の有界な実関数である。\n", "\n", "ex)\n", "\n", "$$g(d) = \\frac{1}{d+1}$$\n", "\n", "$$g(d) = e^{-d}$$\n", "\n", "$$g(d) = \\left\\{ \\begin{array}{ll} c & (0\\le d \\le 1/c) \\\\\n", "1/d & (d>1/c) \\\\\n", "\\end{array}\\right., \\ \\ c>0$$" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "subslide" } }, "source": [ "しかし、ここで注意すべき点として、どの発言者が発言するにしても、例1で考えたように、どの発言者も$[0,1]$の一様乱数を取るなら、結局、意見について見た時の試行は同じことをしており、誰が発言したかは本質的な問題にはならないことが分かる。" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "以下に示すのは上に示すような簡単なことに気付かないまま色々機能をつけてしまったもの。\n", "\n", "はじめに人の配置をGUIで設定、その後startを押すと、[-1,1]ほどの領域にスケールし直され、その位置関係でシミュレーションが実行される。Notebook上ではインタラクティブに表示されないが、これを通常のプログラムとして走らせるとちゃんとインタラクティブに繋がれていく様子が分かる。その後は各発言者の発言回数とリンクのつながり方に関して、その重みを反映したグラフを表示する。また、各時刻においての発言に対して張られたリンクの数のグラフとその累積のグラフを生成する。" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "from Tkinter import *\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import collections\n", "import operator\n", "\n", "def accumulate(iterable, func=operator.add):\n", " 'Return running totals'\n", " # accumulate([1,2,3,4,5]) --> 1 3 6 10 15\n", " # accumulate([1,2,3,4,5], operator.mul) --> 1 2 6 24 120\n", " it = iter(iterable)\n", " total = next(it)\n", " yield total\n", " for element in it:\n", " total = func(total, element)\n", " yield total\n", "\n", "\n", "class Person(object):\n", "\n", " def __init__(self, ideas_num=10, place=(0., 0.), **kwargs):\n", " # 意見は0~1の間の値を一様に取りうる\n", " self.ideas = list(np.random.random(ideas_num))\n", " # 発言者の実際の位置が2次元の座標として表せる\n", " self.place = place\n", " # その他の特徴量\n", " for (k, v) in kwargs.items():\n", " setattr(self, k, v)\n", "\n", " def distance(self, p):\n", " # 人pと自分との間の距離(ユークリッド距離)\n", " d = np.sqrt((self.place[0]-p.place[0])**2 + (self.place[1]-p.place[1])**2)\n", " return d\n", "\n", "\n", "class meeting(object):\n", "\n", " def __init__(self, N):\n", " # 会議の参加人数\n", " self.N = N\n", " # 意見の時系列\n", " self.ideas = []\n", " # 発言者の時系列\n", " self.speaker = []\n", " # 時刻\n", " self.k = 0\n", " self.K = 100\n", " # 張られたリンク(時刻, 時刻)のタプルで表現する\n", " self.links = []\n", " # リンクの数(各時刻)\n", " self.l = [0]\n", " # リンクの数(累計)\n", " self.L = [0]\n", "\n", " def g(self, x):\n", " # 発言者の物理的距離に対する関数\n", " return np.exp(-x)\n", "\n", " def p(self, i):\n", "\n", " # 参加者の中で話せる人のみを対象に\n", " _N = []\n", " for k in range(1, self.N+1):\n", " if len(self.members[k].ideas):\n", " _N.append(k)\n", "\n", " # それらの人たちに対し、関数gによる重み付けの確率を付与\n", " w = []\n", " for n in _N:\n", " d = self.members[n].distance(i)\n", " w.append(self.g(d))\n", " w = np.array(w)\n", " sum_ = np.sum(w)\n", " _p = list(w/sum_)\n", " p = list(accumulate(_p))\n", " rn = np.random.rand()\n", " nm = 0\n", " while True:\n", " if p[nm] > rn:\n", " break\n", " else:\n", " nm += 1\n", " # その確率で選ばれた人の名前を返す\n", " j = _N[nm]\n", " return j\n", "\n", " def q(self, j):\n", " # 発言者jが選ばれた時、持っている意見から等確率で意見を取り出す\n", " x_j = self.members[j]\n", " return np.random.rand() #x_j.ideas.pop()\n", "\n", " def distance(self, x, y):\n", " # 意見の近さを絶対値で表現\n", " d = np.abs(x - y)\n", " if d == 0:\n", " return self.radius + 1\n", " else:\n", " return d\n", "\n", " def connect(self):\n", " l = 0\n", " for i, v in enumerate(self.ideas[:-1]):\n", " # k番目の意見と意見が近い時、それらノードの間にリンクを形成する\n", " if self.distance(v, self.ideas[self.k]) < self.radius:\n", " self.links.append((i, self.k))\n", " l += 1\n", " return l\n", "\n", " def check_agreement(self):\n", " # 合意チェック 参加人数Nによる関数\n", " def L(N):\n", " return N**2\n", " #if self.l[-1] > L(self.N):\n", " if self.k > self.K:\n", " return True\n", " else:\n", " return False\n", "\n", " def check_ideas(self):\n", " for k in range(1, self.N+1):\n", " if len(self.members[k].ideas):\n", " return True\n", " return False\n", "\n", " def f_L(self):\n", " # リンクから会議の評価\n", " # 単純に会議終了時に得られたリンクの数を返す\n", " return self.L[-1]\n", "\n", " def f_T(self):\n", " # 会議に必要な時間の評価\n", " # 単純に必要な時間kを返す\n", " return self.k\n", "\n", " def f(self):\n", " # f_Lとf_Tを使った評価関数f\n", " return self.f_L() - self.f_T()\n", "\n", " def end(self):\n", " # 会議の通常終了、各定義量の計算や受け渡しなどはここで\n", " plt.ioff()\n", " plt.show()\n", "\n", " # ネットワーク図を描画\n", " link_s = [(a, b) for a, b in zip(self.speaker[:-1], self.speaker[1:])]\n", " counter_links = collections.Counter(link_s)\n", " for link, lw in counter_links.items():\n", " ix = self.members[link[0]].place[0]\n", " iy = self.members[link[0]].place[1]\n", " jx = self.members[link[1]].place[0]\n", " jy = self.members[link[1]].place[1]\n", " _x, _y = ((ix+jx)/2, (iy+jy)/2)\n", " if link[0] == link[1]:\n", " continue\n", " elif link[0] < link[1]:\n", " color = 'black'\n", " va = 'bottom'\n", " else:\n", " color = 'red'\n", " va = 'top'\n", "\n", " plt.plot([ix, jx], [iy, jy], color=color, lw=lw*4/self.k+1)\n", " plt.text(_x, _y, '(%d,%d)' % (link[0], link[1]),\n", " color=color, va=va)\n", "\n", " counter = collections.Counter(self.speaker)\n", "\n", " for key, i in self.members.items():\n", " x = i.place[0]\n", " y = i.place[1]\n", " size = counter[key] * 30\n", " plt.scatter(x, y, s=size)\n", " plt.text(x, y, str(key), color='green')\n", " plt.show()\n", "\n", " # 各時刻に追加されたリンク数のグラフ\n", " r = self.radius\n", " k = np.arange(self.k + 1)\n", " y = (-r**2 + 2*r)*k\n", " delta = np.sqrt((-r**4 + 4*r**3 - 5*r**2 + 2*r)*k)\n", " y1 = y + delta\n", " y2 = y - delta\n", " plt.fill_between(k, y1, y2, facecolor='green', alpha=0.2)\n", " plt.plot(k, self.l)\n", " plt.plot(k, y)\n", " plt.xlabel(r\"Time: $k$\")\n", " plt.ylabel(r\"A number of edges for each time: $l$\")\n", " plt.show()\n", "\n", " # リンク数の累積グラフ\n", " plt.plot(k, self.L)\n", " plt.plot(k, (-self.radius**2 + 2*self.radius)*k**2/2.)\n", " plt.xlabel(r\"Time: $k$\")\n", " plt.ylabel(r\"A number of edges: $L$\")\n", " plt.show()\n", "\n", " # 時系列で発言者の表示\n", " # print 'self.speaker:', self.speaker\n", " \n", " # 評価関数を通した結果\n", " # print 'self.f', self.f()\n", "\n", " def end2(self):\n", " # 会議の異常終了(発言者が発言できなくなる)\n", " pass\n", "\n", " def init(self):\n", " x = [i.place[0] for i in self.members.values()]\n", " y = [i.place[1] for i in self.members.values()]\n", " plt.scatter(x, y)\n", " plt.ion()\n", " plt.draw()\n", "\n", " def callback(self):\n", " # print 'speaker:', self.speaker[-1]\n", " # print 'link:', self.l[-1]\n", " ix = self.members[self.speaker[-2]].place[0]\n", " iy = self.members[self.speaker[-2]].place[1]\n", " jx = self.members[self.speaker[-1]].place[0]\n", " jy = self.members[self.speaker[-1]].place[1]\n", " plt.plot([ix, jx], [iy, jy])\n", " plt.text((ix+jx)/2, (iy+jy)/2, '%d:(%d,%d)'\n", " % (self.k, self.speaker[-2], self.speaker[-1]))\n", " plt.draw()\n", "\n", " def progress(self):\n", " self.init()\n", " # はじめに1が発言するとする\n", " self.ideas.append(self.q(1))\n", " self.speaker.append(1)\n", " while True:\n", " j = self.p(self.members[self.speaker[-1]])\n", " self.ideas.append(self.q(j))\n", " self.speaker.append(j)\n", " self.k += 1\n", " self.l.append(self.connect())\n", " self.L.append(len(self.links))\n", " self.callback()\n", " if self.check_agreement():\n", " print \"\\nnormal end\"\n", " self.end()\n", " break\n", " if not self.check_ideas():\n", " print \"\\nno one can speak\"\n", " self.end2()\n", " break\n", "\n", " \n", "class Main:\n", "\n", " def __init__(self, radius=0.3):\n", " N = 6\n", " self.app = meeting(N)\n", " self.app.radius = radius\n", " window = Window(N, main=self.app)\n", " window.display()\n", "\n", "class Window(object):\n", "\n", " def __init__(self, N, main):\n", " self.root = Tk()\n", " self.main = main\n", " self.width = 640\n", " self.height = 480\n", " self.canvas = Canvas(self.root, width=self.width, height=self.height)\n", " self.var = StringVar()\n", " self.oval(self.canvas, N)\n", " self.canvas.bind('', self.pointer)\n", " self.canvas.pack()\n", " label = Label(self.root, textvariable=self.var, font='Ubuntu 9')\n", " label.pack(side='left')\n", " b1 = Button(self.root, text='start', command=self.b1_clicked)\n", " b1.pack(side='right')\n", " b2 = Button(self.root, text='save', command=self.b2_clicked)\n", " b2.pack(side='right')\n", "\n", " def oval(self, canvas, N=6):\n", " self.members = dict()\n", " deg = np.linspace(0., 360., N, endpoint=False)\n", " radius = 20\n", " self.r = int((min(self.height, self.width)/2-radius)*0.9)\n", " self.centerx = int(self.width/2)\n", " self.centery = int(self.height/2)\n", " for n in range(1, N+1):\n", " rad = np.radians(deg[n-1])\n", " self.members[n] = Oval(canvas, n,\n", " self.centerx+self.r*np.cos(rad),\n", " self.centery+self.r*np.sin(rad),\n", " radius, self.var)\n", "\n", " def pointer(self, event):\n", " self.var.set(\"(%d,%d)\" % (event.x, event.y))\n", "\n", " def b1_clicked(self):\n", " self.main.members = dict()\n", " for n in range(1, self.main.N+1):\n", " x = (self.members[n].x-self.centerx)/float(self.r)\n", " y = (self.members[n].y-self.centery)/float(self.r)\n", " self.main.members[n] = Person(place=(x, y))\n", " self.main.progress()\n", " self.root.destroy()\n", " \n", " def b2_clicked(self):\n", " import tkFileDialog\n", " import os\n", "\n", " fTyp = [('eps file', '*.eps'), ('all files', '*')]\n", " filename = tkFileDialog.asksaveasfilename(filetypes=fTyp,\n", " initialdir=os.getcwd(),\n", " initialfile='figure_1.eps')\n", "\n", " if filename is None:\n", " return\n", " try:\n", " self.canvas.postscript(file=filename)\n", " except TclError:\n", " print \"\"\"\n", " TclError: Cannot save the figure.\n", " Canvas Window must be alive for save.\"\"\"\n", " return 1\n", " \n", " def display(self):\n", " self.root.mainloop()\n", "\n", "\n", "class Oval:\n", "\n", " def __init__(self, canvas, id, x, y, r, var):\n", " self.c = canvas\n", " self.x = x\n", " self.y = y\n", " self.var = var\n", " self.tag = str(id)\n", " self.c.create_oval(x-r, y-r, x+r, y+r, outline='', fill='#069', tags=self.tag)\n", "\n", " self.c.tag_bind(self.tag, '', self.pressed)\n", " self.c.tag_bind(self.tag, '', self.dragging)\n", "\n", " def pressed(self, event):\n", " self.x = event.x\n", " self.y = event.y\n", "\n", " def dragging(self, event):\n", " self.c.move(self.tag, event.x - self.x, event.y - self.y)\n", " self.x = event.x\n", " self.y = event.y" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "subslide_end", "slideshow": { "slide_type": "slide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "normal end\n" ] }, { "data": { "image/png": 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Vzx5IlckeD6TK5YUHUmvWfOxrd3Ep9UCqv78/7t+/j8uXLz8znZGREVQq1XPlSaVSREVF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\nZxROlV/VbDj09k9QXizZ7sm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aiRWgWfHk5OVgx5UdCI8JR+SNSAS4BSDMJwzdaneDhVHp\nNms6fBgYNAgYMEBrJGRC5OIrATUaKKK349jEXZBeaYnGeeMgqZIPVUBDSEP6wLzDCIhNXssNuwpR\nHkYhsNMEJMvP48y6PXqV+zIIYwoGZuCQIEiRj60bjj43rW+Lc/gnyr0CtCqMMl+JbZe3YcDGAXCe\n44z/nfkfunl1Q/yH8dgathX96/UvtUEAgLZtgdOngZgYoE0bID6+/HQX0B8isRi/f/EvcMEfFv+r\nD4v4BGhmTgOogfjTKdDYWSLD3xFpX4ciJ3qHztUk8HwGD+qHOPejiD5zx9CqvNYYbO2QF2X9ATuO\ne2/mc9Nt3L+PED3kw9SUctcpT53HvVf3ctiWYbSZaUP/lf5cfHIx72fdf37mUqJWk3PmkPb25IaS\nl38SqCQs6/oN99v/zr82Fr/xfIkL+v08lsrbF4rN8yqij7WPiqPOYD926WL4/SYg7KdgeLLzLJCd\nf/O56UIDO8LIKB6TZ60pFz001OBw/GGM2TEGznOc8eXBL1HfsT7OjzmPw0MPY0yzMXAwd9BbeWIx\nMH48sHMn8OmnwLvvArklB7sIGJBlvaej5vHakM6vitahrYpNI3PyhNXIubBedwnGd1TQHNgDNGkE\nrNsAcZ26yKlthtS3myNj0yyos0uexf9fpXpSIBIsIw2tht4RjMJLkKM0g5Fl6SIPavgcw56N+pvk\nQhJ/3/4bH+35CNXmVcOHez5EDesaODHyBE6MPIFxLcbBRe6it/KKo1kzrTspORnw8wMuXSrX4gRe\nkOUDZ6FWlBfyplsiYEBAqfKIxGKY1u8I68/WwSrqLsQPs6FZMAcwNYP4629BextktrRD6mddkXN8\nneBqAvDBuEG45nYSew7EPT/xK4RgFF4ChcIUpjaZpUrbf4gpEq8FIC8v/6XLI4mz985i8oHJqLWg\nFoZsGQIrEyscGHwA/77zLya9MQm1bGq9tPyXwcoKCA8H3ntPO86wenWFFi9QAiuGz0OtXR7InipF\np7c7v7ScggX9bH48BIuzmcCtm9C88zZEN+K1C/pVkSKtW02kLRgF5Y3TenyCV4cuneqg1s0mmD/3\n9VoLSTAKL4EiywRmVs9e6qKAz8cMBWmMhWsjXricSw8v4atDX6Hu4rroEdEDALC532ZcfO8ivgr4\nCt723i8sU5+IRMDbbwNRUcD33wNvvQVkls5WCpQDq979CW4b3ZD6aR66f9hDr7KLLOh39BDQprVB\nF/SrDFRLC8Qt2wOGVkOvCEbhJcjJMIeZ5bNnNRcgk0nhWCMKK5eW7odyI/UGZv41Ew1/aYgOazog\nPTcdq95chesfXMeMwBlo6NSw0q07VK8e8M8/gJER0KSJdm9ogYrl14+XovpaFyS9n4Fek/uVe3km\n3v6w/vQ3gy3oV1n4cupbuFntHMLXnTW0Kq8lhh7ELzXjvuzBH9fX57Zt2wpG/nXHnDlzaGlpWeja\nGyFDaGJWNAIkNjaWAHj9wXXOOz6Pfsv8aDn0cd58dck7YBkZGREA16xZQ5Ls2rUrK8M7/P137X7Q\nCxZo94cWKH/++GwVI+Wb+NsnywytCkkyL/Uu03+fypQhDZnjZkSVlYhpwa5Mnf0WFZf+qnB9yiv6\nqICGfTsyMHhiuZbxLCBEHxkeRaoVTE1z4OTkhKpVq+L7779HaGgoAGD37t0wNTXF3LlzYWNjA5FI\nhFNREcjN8UHk38d1Mh5kP0DjZo0hkojQ5H9NcO7+OXwd8DWyVmuX5RaJRJCIi9/w5LPPPoNKVbj1\ntX37dgDAwoULy+ORS03//sDx49qVVkNDgZTXcyWASsPGGRFwWChHwqBEDJw90tDqAACk1k6Q9/8K\nNqvOwPSGEupTf4OdgiE6eBjiFm2gqG6EtEH1kfHrFOSn3Da0umWmuiIQCVVfHxeSYBReAiocYCbL\ngbu7O0xNTbFz5074+PgAAFxdXaFUKnHs2DG4u7tDKpVCpVLBqsphTJ15ECvPrETwb8HwXOgJZY4S\nAd0CcPfju1jx5grMGj0LJCF/zjZo06dPR9euXYtcl8lkmDjRcLOnC/DwAI4dA9zcgEaNtJ8F9M+2\neZthM0uG+N7xGLqocqzYWRz6WtCvsjJ7znAkOl7B4iXCP7q+MVj360X59vNl3BppSZJs1KhRIVdR\nZmYm69SpQw8PDxobGxMAxRIx7Xq8R9iGEQAjYiKYcDehkLsnMzOTADht2jTK5XKKRKJiy3Z2dtbd\nwxPuI5L08fGpFC6kJ9m2jXRwIKdP105+E9APu5fs4gGb9Vw24HtDq1Im8jOTmb5hOlNHNmW2pwnz\nLERMb1+VqdPDmHPuADV6+Kcpb/cRSTYJ7cp2wePKvZzigOA+MjxDRrwJM1EOvvx8OuLj4xEXF6cb\n/B01ahSkMilM7EygytO6eAhiZP+qQMovSLh3B319+mLDHxsKybS3t4dMJsNnn31WYrnHjx9HYmIi\ntp0YnrUAACAASURBVG3bprumVqt1nxs0aKDPx9QL3bppt/rctUu7oN79Z68jKFAKon6LgmxKJq63\nv4KRaz81tDplQmJhC3mvybBe9g/MriiguXAO7NUDOPkPJO2CoHQ1Rlo/b6T/72Pk3a+8S9G7sSNu\nVnt9l9M2FAaxsi+KUqnk++9P4OZIa9rbVaexsTFlMhklEgkhAsUyMUUWIkqMJQRAkUhEkUjE+/fv\n08TsKPu/P5skOXfu3EKtejw1YA2AYrG4UNndu3cvNt2CBQtIkv369at0PYUC8vLIzz8nq1Yl9+0z\ntDblg0KhYPPmzVm/fn0aGxvT3d2dJLlv3z7K5XIaGxtTLpczMjKy2Pzp6em0srKi+lHr2M7OjiKR\niA4ODro0f208yv32v3Npt28K5S0INLh69SpJcv369fT09CyPx6wwNGo1s09uYcqXPZj+hj3zzMCs\nuuZMebc1M3bMp1qRWSo5FdFTuH07lfIJ1vzuu4r/54aeewqViQp/mS/D6NEf0tS0I3/d68qWLYMJ\nMWjuYE6jVtpooHr+9Thw6EAaGxuzadOmlMlkbNq0KUnSp8VcVq25kiSZnJxcYgX+tPtILBbT2dm5\nSDo85T7y9vautEahgMhI0tmZnDxZayheN7KzszlnzhyGhYXR2tqaR44c+T975x1XVf3G8c+5E+5l\ngyxlqaACKg4cKIijJPdKc2SaVlppVqbVL9PKypmmZqbiaJi5B24BldwD9x64AFGWzDvg8/vj4o0r\nqCjjAvJ+vXi9OOd8x3POvff7nO/zfZ7nSxcXF7799tskyaFDh9LV1bXQukOGDGGnTp30xzNmzOCE\nCRP0SuHo9uPc5fAnF3WcZFDv0KFDtLW1pUQi0SsFkrS0tOTZs2dL+haNRk5mKh9umsWkkS2Z7q2g\nRgGmBtozeVJPZhzb/ERTU1koBZJs1r0324S8XyZ95QdV5iPjsmrVWmRl/Qrtb8lIFR8EcoGMhAyo\nD6gBAegQYoK/lv0FlUqFY8eOQaPR4MzZU/j3ym+wsV6PuBtDcSk2CiqRzo4ycNCAZ/aZm5sLd3f3\nZ5a7evUqTE3L93677drp4hhOnNBlX711y9gSlSxJSUnYunUrBg8eDJKwtrZGSkoKmjdvDgDw9/dH\ncnJyoXU3bdqE0aNH648//fRT2Njodkc7E3UOSW+fwS2fKxi+faJBvd69e2PBggUF2mvZsiW++eab\nkro1oyMytYB51zGwnn8AynMZ4LXL4JsDgHPnIe7cA2pHKVJ6eSJ1wSio714oc/lqK17BdfedZd5v\nSVOeoqDylF75pnr1OoiNXYKf2vWE3R3irSuH4dloDkZNPAuFWSaYmw3mZgFUA1BBoAYiqCGGFkKu\nBkO7ncXoca8juO0pvNGDUKuArTsBTS6gpgjaXBE0FCMHYuRAglxIMey1RCza7gYIMkAwgSAygUhk\nCrHYFGKxEhKRElKJEr2bLcDI8SHo+1ZHyKXmkEstoZBZw1RqCVO5NZRSa5jKrCASGf9dIDcXmDED\nmDkT+O03oEfJBuAajT59+uD06dO4c+cOnJ2dcfXqVVhaWsLCwgKCICA3NxdpaWlITU3FiRMnEBIS\ngoSEBKjVapiamhqsEQHA7NmzMfm7yfhLORXx7rfx1r5JBte//PJLbN++HSdOnIBUKsXFixdRq5Yu\nXftPP/2E2bNn41Zl07yFwNxcZJ/ZBVVYKITwKCiPxkPtbApVcH2c6n8Egf7JECutSlWG9AwV3L52\nwVDRQsyYXnZf6JLeT0FSUg29LEybNhHvvNMX2253xj+3l6Gp6zs4eeZzjOo+FvXr70BYWHe4uto9\nsf7/ai3Glh1v46cfRuH0qavw9PREs2b3oGEGstTJyFQnI0udgmztQ6g0D6HSpGLTiXRotOnQ5mRA\nk5OOnJxM5OZmQatJhloVC1CFORN0P/ymwUcRc/MgRNBCAi0kQg6kQi6kIkImIiQCoM4FNBSgyRWg\noRhavRKSIhdSELI8BSSHIMqvhBSQiBSQSJSQiM0gk5hDJjWHXGIOudQCplIrmEitoJBbQSG1glJu\nB7lUUehzEIl0mVaDgnSxDRERwPTpgFxeKh9bmRAWFgYHBwdcvnwZYWFhePPNNxEZGYnMzEwsW7YM\nPXv2xOrVqzFggG522LhxYyQk6CLdL1++DLG4YFxKUlwSclLUuO91BwMjJhhce/DgAebMmYOL+TIS\n5uZLVFe3bl0kvSSBIoJIBNOGHWHasCPwPyBXlYncPcuBrbr0MqxmjTQ/W2jbtoC8y2CYNu8DoYRf\njsyUctS5/AoO54QBqLhvOVVK4TkZOHAAnJwcsWHDFhzdL8fnNqfQK+YVTJ68Fd9/7wg3Ny08PZdg\n48aOqFevYLbSkN4ZWP5TawBA7dq1YTg78nhhuYa/WrRy2hw1MtUpyFQnI1OdhCx1CrLylE+2JhVq\nbRrU2nRotenQ5KRDq81ETq5OCalV8VAxG6AKoAoC1RCggRganRISciAVciARciETCHneGKfKRZ4C\nypsFUTcLyoEUhBRjplfD77NnwMvXBe/+7ys4uyVAJFJALFJAIlFAIlZCKjGHTKJTRHKpBUykVjCV\nWsBUZgVTqRWUclso5TYQi4z3lT5w4AA2bdqErVu3Ijs7GxkZGRg7dixyc3PRsmVLAECrVq0MBu6n\nEXs9HvGh55ErysUbUV9BIjFUGnv37kVmZiY8PHTfG61Wi3r16uHUqVPw8fEpcj+VkUcJ/dBxJLBH\n0CX0C/sVwo7NuoR+GW8gs5Ub8EoHmHYdCblH4xLp19shBFsU/4NKpYFcLkXv3r2xbt06gzL79u3D\niBEjcP78eYPzbm5u+P3339GnTx/cv38fANCuXTtERERArVZDKpUapLgRBAGFWFd+AjAawKMvyyoA\nj/KeLAPwZr5rhVJlPioGOyf0g/fcVbC5fg8KG92+BXPnRuCLLx4iI6MVXF23YN26NmjS5L/BPjEl\nGXbWxNpdx9GrwyvGEr3MUGkykalOQoY6CZmqFGRrUpCteYhsTQpU2jSoNWnQ5KRDrUnD9jUBWLO4\nL974YD5atN+UZ4rL1pniqIIANUTQQAwtxHlKSCLkQirkQiYiZCJAyzxTXK4IGooemwVJkJtvFvRo\nJiQWK/LNhJSQSswglZhBJjGDXGIBucwSJpJHCsgSCrktlHJrmEgsDExxDx48gEQigZWVFXbu3In+\n/ftj1apVGDBgAHr06IHffvsNw4cPx5YtWxAXF2fwnB43Hz2ITcLBtn9gdfoO7NAex718vrwtW7ZE\ncHAwfvzxR4M2HjcfzZw5Ez///PNLYT56GoVtx5l9YR+yNy+EEL4HikOx0NjJoA7yhiikB5SvjYDY\n4sX2IVGpNHAd546eqmlYsGAgJk6ciG+//RZSqRQODg64c+cOevXqhQ0bNsDR0RExMTGwsLBAdnY2\nIiMj4eHhgbVr12LFihU4d+4ccnNzIZVKkZ6uy3TQsmVLPHz4EOfPn0f//v0RHh7+aLb5aCz3BPAv\nAGsAUhgqBUC3KD0IwF9PuocqpVBMot1EuBHki15/nDY4//vvBzB69B2kpraHk9MWrFjhj+BgXVZT\nW6c18PK7gYPbPjOGyOWaU6eAfv2AFi2AefMAs+fYQjg3NxfZ2odIVyUiS5WMLE2qzhSnSYFKkwaV\n9iHU2nRotGnQaDOgzc1ATk6m3hynU0CqvD81RFBDBC3E0OhWePJMcTJRLqQi6E1x6rxZ0PXrAn6Z\nkQNSQFYmIZGJ8O1vjrhwKgfzv02AVkNIZSJ89H0DeDd2xu2rKkz95F8s3/0OpGIz9A+ejQkzhsK/\nSSOkDU5Gv/MTkE01SEIsFmPy5Mn4/PPP4eDggB9++AHDhg0zuP/HlUJISAgsLCywatWqkvyIKhzP\n2qOZWjUyov6CZusKSCKPwvR8KrJ8rKBt2wzSTgOhbP0GBImsyP217jwUFGmxf/MfmD9/Pj74QBdt\nPnnyZHz11VcIDAxEVFQUevXqhVmzZsHNzU0nR77xb+jQofjnn3+QlZWFMWPGYNasWf+137o19u/f\njxs3biAwMBB37twBDMfy0wB88849rhTSAagB2DxJ/iqlUEzWvlEHrkevwv9aTqHX168/jnfeuYTE\nxBDY2m7HkiX18MvKnTi4rSEeJoeUsbQVg/R04MMPgUOHgFWrgAYNjC1R4Whz1HkzoGRkaVJ0prh8\n60HqfDMhbU5GnikuA7m5WcjNyQaZDVA3ExKoxrLZyUi5n4OfTCdAyBUj+X/fQibTQioi5HkTElUO\n8EZvYMlqsX49KDefKY75ZkGje17Al3MbwqWmXZ4pTgmpWAmJfhZkqXdIMJVaQCGzganMCgqZtdFN\ncSXJs5TC42hT4pG5bQFydmyEyd7zkCRrkNmiBtihLUy6vguTOq2eWn/MJ2vxJz5AzHc3sWvnVn1e\ntEcEBATgQCG5X0jil19+wYcffoghQ4bgzz//hFarLWAiKoJSWA7gdQCmKKgU/gUQgKd4nlYphWKS\ncvc6suvVwoUvhqHtF4ufWC4i4jwGDjyO+PhOMDOPRHpaR1yKuQ8vt7LdHKci8ccfuu0/v/0WGDFC\nt39DZeZBQiJcnapjRa3vERQ1DDYOht4yKk0mMlQPkKlJQaYqBVnqZGRrU3UOCdo0qDW6mZA2Jx37\nd13EPwtP48ffm+tnQf/NhNT5THH5Z0E5kIoIqfCfKU6dK+jXg7QUQwtJnhmuoClOJDKFSGwKkcgU\nErFS/yeVmEEutfhvPUhiofOKk1nBVGZdqCmuJHlepfA42VePIjvsNwi7dsP0wC3kmEugCqoLUccu\nUHR+HxKbGgXq1PigFprHjUZa+hbs2rULUqkUAKDRaGBra4ukpCSYm5sjJycHmZmZIFlgplAMpfAj\ngBEArFBQKfwM3ZrDE39NleNVwIhYVa+JDU2tIF+/AniKUmjXzhtxcd44cuQaXn89Helpcvh63cFP\nM2Pw4YftylDiisObb+q2++zXDwgPBxYvBqxK16vQaKhVGuzu9CtW1ZyOpjv7FVAIACCXKiCXusIG\nrs9s7/XmwOyvXlye3NxcZKlTkKFJRpYqzytOkwqVJhUqTRqytanQaHTOCBptBrQ56cjJzUROThY0\nmkSoVXf1s6D/THGP1oPyHBJEuZAJhZviNBTlc0jQKSAKUgByQJBBEJkaesWJlZCIFXlrQeZ6BSSX\n6JJLXrn3LxQyKyhkVjAzsYNUbFLkZ2FS2x8mY/yBMQBztNAcWgtuWa5L6Pfej0j3MoembRNIO/WH\nos1gHDx6HO5X2+OOfD+O7IoAoFMGjxaJExMTAQDr169H9+7doVQqkZ6ejsTERNja2j5TniIoTwFP\nHvSLVLm8UCFnCgBwavU8uA4ehZSdm+ERWDB7aWF4N5+NqycDoVHXgInJMXz9tRhffFFlTiqM7Gzg\ns8+AsDDdFqB5cWCVBq02BytbTYbNfXs02NEdNTydjS1SmZPfFJehTkK2JhXZ6tQ8U5xOEWm0j5SQ\nzi37kVdcbk5WnikubxZEFUR5HnFiaFHDJAsP1GK9a7ZcBJB5SogCNLliaKkr/Z8pLk8JCfK82KC8\nmVDeLEgsVkAqVkKulcLpxEVUO3QZNofvQR6vwa1aIvwj74xpQVFInTkD4HAoFAq8//77mDFjBjw8\nPHD79m00aNAAWVlZuHLlSoEZwSPzUU5Ojv583bp1cenSJbRq1aqwmYIawA0AdWFoPloNoG++R70f\nQEtUkMDlsosLLwV2N5ByTYhDkcuHrl1HQYjnhYu36eu7mMAdymQ7OW7c+lKUsmKzbp0u4+q0aRU3\n42pWVhZNTEz0eavMzc25uMX/2Mf8VYpFYgqCQJFIxObNm3PixIkkyaVLl9LOzo5+fn709vamSCSi\nVqtldHS0QX4tsVhMb29v+vj48Oeff9b3qVQq9eUkEgmXL19Okpw+fTotLCyM8RjKlJAQ0MzMjHK5\nnD4+Ppw1axbvxt9kNXs7ymRSKpWmdHSuRi9vV+65MIc7zkxmWPTnXHf0Q/65dxC9GtiyTkNrTlrY\nhDVqmlIqFyiRCrSxF/PdL6y5eFs1LtlmxeXblFz3t4xbJtiyVddWhEnBPGUA6OXlRYVCUeA8SY4d\nO7bQOvfv36eLi0uh1/L9PcgbS7MLufaIdAAVJnjFyF+d4hH2cQiv24LZGUVL0kWSEukZfvz9PJJk\nXFwymzZdTOA6JZI9HDlyFbXaCjrylSIxMWRAABkSQt67Z2xpnp8FCxYQAOPj45mRkUEADDZtztoe\ntWlnZ0e1Ws0pU6bQ2dmZ8fHxJMlly5Zx1KhRJMlWrVqxbt26JMnLly/rB5OTJ0/Szs6OqampTEtL\no5eXF8+fP0+SbNmyJevVq0eSbN68OZs3b66XRywWc+/evWV2/8Zg/Hiwdu3a9Pb2plarZYcOHTh8\n+HBOnapLOz5lyhT6+/vzu+++K1A3NDSUr7/+OqdNm8bLly9z9+7dvHr1KmNjY2lvb09HR0empqaS\nJHeei2PtDVHEzJmUOzhRAhA4TVPTGty0aRNJsk2bNgwICOC9fF/etm3bUiwWc2chmSIdHByoUCgY\nFhbGxo0b08/Pr0AZGA78XgBOQKcYCh1nAQws7cG8pCiRL4CxUGVn84yzwPVvNy1yHQ/f+fTwnW9w\nLiUlg0FBoQQuUiQ6xAED/qxSDo+hVusS6lWvrkuwV5F4//33KZVKmZSUxLltPqcIItb2qE2ZTMbB\ngweTJI8dO0ZTU1N9naVLl/LDDz8kSUokEi5evFh/Lf/vpmHDhvqEeN27d+fu3btJkpMmTaKjoyOT\nk5M5btw4uru76+t4eXmxUaNGpXfD5YBJk8C+ffvS19eXJPndd9+xWrVqeqUbGxtbIJngIzp06MCA\ngABeunSpwLWGDRuyXr16nL0hitU37qUQEcnG6/YzoO0rtJSI6SMXUSYz5+TJ/+15MWXKFHbv3p3z\n5s3Tn9uyZQt9fX0LTZR48+ZNAqBarX7i/cFwJvATdDOBGYWMscsAFO4mWcKEALgI4AqAJ237NSfv\n+ikAjZ5QpuifcjlldU937vcSF7n8mMnzKJGeKfRaZqaKnTotoyCcoiBEs1u35VSpKmFa0WKwc6cu\nFfeECRUn4+qWLVt0adbz3u4EQWCDBg0IgCYmJlQoFLS0tKREIiFJbt++nWKxmE5OTvT29iYA3r59\nW98eAJqamtLU1JR2dnYkyRs3btDV1ZVpabpZ66RJk6hUKunh4UETExMOGzZMX3/kyJEGCqgysnw5\n6OHhwbp16zIjI4MtWrSgTCbTX9+zZw/FYt3v9u7du2zXrh0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HKdkVScW2SH6246zB97+0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\n1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vlFGPqd+eyuU1f3+ZN2RI0fHpNWskwsA5Qfbv3y8+Pj7y4osvVmgNQW3gnklM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\n8mFp6uz169dTJpNx48aN9Y7Cbu4o5HLu+/hj9re1ZQcTE/7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8FEqSy5aRX3+tZ6sblpLC\nQh718OBJBwcW5OToptKQEGWbX7jAB506cayrK50lEi4bMaLqPO4N1ObBffvy9SeeoANAa6mUgiDQ\nzMyMrVu35sGDB0mSo0aNYmxsLEnyxRdfpK+vL/38/Dh69Gimp6er61q6dCm/bmLXQ2XUR1suWViw\nd5cu6vxL/fv3p6OjIy0tLats86KiIr7wwgv08fFhYGAgIzW6jPTR5hC7fZoe95KSmAYw/fx55QoT\nEzIwkOzdm5fs7Bgzc2bFnXbvJufMUX4vL0QREWQTGuCTFxczunNnnm7Vinl37uim0pISUuXquWsX\nOWoUOW4cH7Vvzz22tnQEuCg4uOyMVQ3Q5rdOneLcHj1oBbCnTMbkUtE5fvw427Vrx9DQUBYUFJAU\nHQDKU1dtuXH0KO8IAjeuX29UDgDlgSj+TZD0dKabmvLToUOVyyof/pQU5tvY8HT5fv+8PLJXL1L1\nBOzhQZb2NZIkL15Ubm8CKORyRvn58ZyNDXN1OUduejqpmjN5xw6yZUvy2jXlTWH8eKa/+656rtoF\nQUFMj4vTa5tfOXyYr3TpQjtB4Jzu3Xn12LEyDgAkef/+fY4dO5aBgYFM1jK9dXNwAFBRV22JevZZ\nxnToUMHpoq7oq80h9vk3TVo5OGBtZCSKHz0CSv3K0b49EBKCTpmZKNDI3YOrV4HUVMDfX1nm5k2g\nR4/Hfc4koOGr3lihQoHoPn3geOUK2l64ABsXFx0foPS31Lo1EBAAeHgAUikwZgycCwqwISkJZ44d\nQ96jRxjXqxdyT59GSZcuOm3zhF278LyHB4JCQuAkkyHpwgWsPH0aHXr0wBFBgEAqbereHXZDhuBn\nhQLTp09H3759sW3btscV7dgBeHsry54+rV7tB2CDntJHNBWsIyIgHT0aZqSyzQHg77+B4cOBbt2U\n7Xr9esUdxTavNTq/IzZ6SrsgBrZsyV2zZys9f0jyzh2yY0desrJSTkgSFqbsoihP+S6Iw4ebRLdP\n5KBBTDY3571aTuKiFZrdPiUlpL+/sr1JcupUUpUaorTNb585w3lPPEF7QeCsLl1Y5OJSrzaP3bCB\no11c6FLVGMPGjaQq3XTpGJAmZ86cYadOnTh9+nQ+fPhQ+eaRlEQOGkSeOlW2cHAwKXb7VEpuWtrj\nuXo12zw4mFS52ublkY8eVdy5gdsc4pN/E0QqBXx8EDZmDP73/fdAz57KJ9EhQ4DwcKQFB+PR9u1A\nQsLjtwJNyj9xxsUBjTzCN+qpp9D2+HG0+usv2HfsqPsDlLY5kpKU37/4Ahg6VOm5IwjArFnKcqVt\n7hoQgH+ePInkpCS4ODriVno6ZgcG4uLvvyvLadHmVCgQsWIFQuztMfHVVzFswACk3LmDBfv3w7Z1\n67KF//MfoDTCtzICAgJw6tQpFBcXo2fPnjhfXAx06lR54ZEjlU+pIhVIWLkSyfb2yvZXtXliIiCX\nK68HQOl9Z2lZcecuXcQ2ryU6vRs2GTZvZsknn9BdIuHZn34qs+nKnj28JZVSMXy4dnU18ie9qAkT\nmGpiwtsaEZN6YfNmpZdOdVQxwJd9/To/Gz6cToLACe7uzO3atco2lxcXc3d4OIOsrdnZzIxbZs5k\nUV5e1cfUfCshyzgAcPfuCsW///57ymQyrl27lorKnkKbmANAVdRFW4507MiosWOrdABg9+7ke+8p\n42+qooHaHOKAbxOlsJAcMIBLhg7lzM6dy2xSyOW8ZmrKi9u21VxPfDzZiAf4jrz0Em9IpbwRE6P/\ng5W2OesxwPcwI4P/HjSIPwJ82smJx9etU28rzs/nD7Nn09vcnIGWltw5b552gWmag9FkGQcAeniQ\nV69W2OXSpUv08/PjeUdHPtAIPCLZpBwAqqO22lJmzuwaHAC4cWPVFVUm/npoc4ji37TJSEhgK0Eo\n62JIMrJHD0YOHmwgqxqGo7Nn87ZEwmul7o2NifysLH43ebJyPtxWrbike3e2l0g4sGVLHliypHZz\n46ank6XppiswdSq5c2flNuTnM8nNjaPc3HjixInHGxITSTHCtwLnN2zgZdVcvZpt/uefyrdnFVu3\nkm+8UXVFlYm/HtocBujztwfwB4BkAAcBtKqiXCqAcwDOAIirx/GaNU7e3vhH+/bY9PbbZda3euEF\nOJ04YSCr9M+f770Hr3XrkLdrFzyGDTO0ObXGolUrvPDll3jrySchzc7GpjNn4GRqigXvvIPh4eEQ\nJLX4CcpkgGqax+xsoLBQ+f3uXeDYMaWHCQCEhwOl0aYAYGFhgU6dOmHO229j1KhRWLFiBRQKBZCW\nVjYiWQQAcHfzZtwMCFAuaLZ5z57Kdr97V7l8+HCVba6mvHdPE2nz5QDml35fAGBZFeWuQXmjqAmd\n3g2bIic2baKHiUmZLoKivDzeEwT994MbgLhFi5gpCNp1axkh965c4ceDB9NREDixTRue2b6dJYWF\n3B4aSl8LC3a3tOTP771XqyR0DAkhL10ijx8nfX2V3ki+vuSmTY/LjBpFlkab8pdfyNatSQsL0tmZ\necHB7N27N0eOHMnchQubXMR3ZdRWWy5ZWDD+m28er1C1OUn+8Qfp56ds82nTSNX/rpo254gRj+ta\nulTnbQ4DdPtcAuBc+t2ldLkyrgFw0KI+nTZIU6WXtTV/W7iwzLqj7doxesoUA1mkH059/jkzBYHn\nN2wwtCm1RtP9c3rHjkw6cKBCGXlxMX99/332tLZmN3Nz/jB7Novz82uuvB6D0SqKioq4YMECHjcz\n49Fffqn5mI2c2mjLjaNHeVcQyo7B6KDN1RiRq2d9yNL4LpRb1iQFyi6fvwDMqqY+nTZIU+Xfr77K\nYfb2ZdYdCw1lnKOjgSzSPWfXrOEdQeDZNWsMbUqtSImO5mvdutFOEBjq78/rGjNwVYVCLufBpUs5\nsGVLepqYcP1LL7EwN7fqHXQwGE2SjI/njSefpIuLCz/66COWlJTUrz4jpjbaEjVpEmM6dCi7Uodt\nrg+nC+hJ/P8AcL6SzzOoKPb3q6hD5YDuCOAsgAFVlOOiRYvUH81kSCKPKcjJoZMg8OLevep12dev\nMwfgw0bsxqkiYdMmZgoCT33+uaFN0ZqE3bv5Qvv2tBcEvt+3LzMSEupUz5E1a/ikgwPbSKVcM2EC\nH2kGi+mJ27dvc+jQoRw4cCBv3ryp9+MZAtRC/ONkMh5/5x09WlN/IiMjy2glDNTto4qrd0XV3T6a\nLALwbhXbDN2mjYYP+vXjm76+ZdadsrNjbFiYgSzSDZe2b2emIPDEhx8a2hStiNuyhWNcXekkCPxs\n+HBmX7+u03pdys25qy9KSkq4ZMkSOjs78/fff9frsQyBttqiiurV1f+xoYABxH85lAO9ABCGygd8\nrQC0KP1uDeAYgOFV1GfoNmw03IiLo50glAn9jxo3jkc0fcAbGZd//ZXpEgmPz5tnaFOqRSGXM3Ll\nSg6zt2cbqZSrx4/XXUbRcpzbuZPPtW1LR0Hgx4MH835Kil6OoyImJoZt2rTh3LlzWVjHCXGMEW21\nJTYsjKfs7PRsje6BAcTfHsAhVHT1dAOwt/R7Byi7es4CSAAQXk19hm7DRsUEd3eumTBBvfx3dDQz\nyw9UNRKuHTzI2xIJj772mqFNqRKFXM7fFi5kbxsbdjI15aZp06rvm9chSQcOcFrHjrQXBIb36cPM\nquZx0AF3797lM888w549e/JqJUFjjRFttUUd1dvIgBjk1byIXr2anc3MyrgJJpub85xGJGlj4EZM\nDG9IpTzy0kuGNqVSivPzue3NN+lrYcEAS0v1JO+G4FpMDGd7e6vTO9/Uk3uvQqHgqlWrKJPJuH37\ndr0coyHRRlvkxcXMkEiYevhwA1ikWyCKf/NCIZfT18KCB5cuVa+L7NOHkX36GNCq2nH75Emmmpgw\navx4Q5tSgYKcHP7rxRfpaWLCfi1acN/HH9cuGlePqCZ2sRMEvtq1K1Oio/VynL/++oteXl6cNWsW\n86rLOWTkaKMt5zds4BUzswawRvdAFP/mx79efJH/cHZWL59fv57JqrB0Iyfz/HleNTNj5MiRhjal\nDA8zMvjl6NF0l0g4QibjESN2N81MTOT7ffvSQRD4sqcnL+3bp/Nj5OTkcMqUKfT29uaFCxd0Xn9D\noI22RPbvz8hGmucIovg3P/Lu3KGDIKif/FSvrteN3E32XnIykywsGKmZJ8XA3E9J4adDh6qzcZ76\n4QdDm6Q1Wamp/HToUHUkcfyOHTqtX6FQcOPGjZTJZNywYUO9Z7RqaLTRlgpRvY0IiOLfPHm3Rw/O\ne+IJ9bKxD1plX7/OC1ZWjOzVyyi6UdLPn+eCoCDaCwKnenmViZ9obOSmpfGLUaPoKpHwGRcXntBM\n+aADLly4QB8fH06ePJk5qmkrGwE1acvN48crRvU2IiCKf/PkamQkHQRB7W4YGx5utO5quWlpjG/R\nglG+vgYX/msxMXzdx4d2gsA3fX2ZevSoQe3RJflZWfxm0iS2lUo5zN6e0atX66zuR48e8ZVXXqGn\npydPNpJ8UjVpS9SkSYxp376BrNE9EMW/+TLKyYnrS71lHmZkMAdgdmqqga0qy6N793i6VStGd+5c\nu0RmOiZxzx6+1KED7QWBYb17M/38eYPZom8Kc3O5cepUepmasr+tbe1TSFfDTz/9RJlMxpUrVxp9\nN1BN2hLn6Mhjc+Y0kDW6B6L4N1/+99ln9LewUP+wTzg58dhbbxnYqscU5OQwTibjUQ8Pg71a/7V1\nK8e5udFJELgkJIRZRnZz1Ccqd1Vvc3P2sLLirrAwndyAr169yp49e3LUqFG8e/euDizVD9Vpi/ph\nqZFF9WoCUfybL/LiYnYyNVV7pkRPmcKj7doZ1qhSivLyGOviwuPu7tplrdQhCrm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CqoJKbUCiHpNTWAtOu5ryigg6QzTD7eRxeQjYAwRdczlnqRWrNX+J8FOVYgTiD4AT2AgE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\nZhxlHPEmNqH+9NWb7jxMWvIg3nx2DP2ifZgy2a1e0j0hhOh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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "main = Main(radius=1/3.)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "subslide_end", "slideshow": { "slide_type": "subslide" } }, "source": [ "これらのグラフからも確かめられることだが、[例1](../simple1/simple1.ipynb)で考えたとおり、意見の近さに関する閾値$r$を定めて、その範囲に既になされた発言が存在するときにリンクを張るようにすると、時刻$k$にある点が選ばれたときに張られるリンクの数は、二項分布$B(k, p)$にしたがっていたので、その期待値は試行回数$k$に比例する($E(X) = kp(x,r)$)(実際には複数回これを実施して平均を取ってやる必要がある←あとでやる?:GUIとか全部切って繰り返す)。\n", "\n", "このときの傾きは、$p(x,r)$が\n", "\n", "$$p(x,r)= \\left\\{ \\begin{array}{ll}x+r & 0\\le x< \\min(r,1-r) \\\\\n", "p(r) = \\min(2r, 1) & \\min(r, 1-r)\\le x \\le \\max(1-r, r) \\\\\n", "1 - x+r & \\max(1-r, r) < x \\le 1\n", "\\end{array}\\right.$$\n", "\n", "のように$x$によって決まる関数として与えられていることから$p(x,r)$の$x$に関する期待値として求められて、" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "subslide_end", "slideshow": { "slide_type": "subslide" } }, "source": [ "$0" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "r = np.linspace(0., 1., 100)\n", "plt.plot(r, -r**2+2*r)\n", "plt.xlabel(r'$r$')\n", "plt.ylabel(r'$E(p(x,r))$')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_number": 13, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "fragment" } }, "source": [ "上図の場合、$r$に対応する値として`self.radius=1/.3`としているので、傾きの平均値は$-1/3(1/3-2) = 5/9$である(緑の線)。また、累積のリンク数についても、同じように曲線でフィットすることができている。" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 13, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "## 結論と展望" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 15 }, "slideshow": { "slide_type": "fragment" } }, "source": [ "上までに考えてきたように、実際にはこの例はほとんど例1と同じであることが分かる(沈黙を[0,1]の間の一様乱数の期待値0.5とした場合)。実際にこの場合についてシミュレーションを作成したので、これを元に新たに改良していくことは可能だろう。また、上では議論しなかったが、誰が発言したかという時系列については、ネットワークとしての解析の余地は残されている。次の例では、距離と発言者の間の関係の統計的性質について調べる。また、その結果を踏まえて、人による意見の差異の効果をうまく取り込む方法を探る。" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 15 }, "slideshow": { "slide_type": "skip" } }, "source": [ "# その他メモ" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 15 }, "slideshow": { "slide_type": "skip" } }, "source": [ "今回考えた意見同士にリンクを張る方法は、閾値モデルの変形と考えることができる。\n", "\n", "閾値モデル:\n", "\n", "- 各ノードに確率的に重みをつけ、重みの和が一定値以上の場合に枝をおく\n", "\n", "\n", "重み$w_{i}$が指数分布\n", "\n", "$$f(x) = \\left\\{\\begin{array}{ll}\n", "\\lambda e^{-\\lambda x} & (x \\ge 0) \\\\\n", "0 & (x< 0) \\end{array} \\right.,\\ \\ \\lambda > 0$$\n", "\n", "に従う時、次数分布$p(k)$は\n", "\n", "$$p(k)\\propto k^{-2}$$\n", "\n", "になる。\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 15 }, "slideshow": { "slide_type": "skip" } }, "source": [ "一方で、今回考えたように重みを一様分布とした場合に次数分布を求めてみると" ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 15 }, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{0: 58, 1: 75, 2: 76, 3: 41, 4: 58, 5: 70, 6: 58, 7: 67, 8: 62, 9: 33, 10: 71, 11: 73, 12: 35, 13: 65, 14: 61, 15: 32, 16: 77, 17: 33, 18: 65, 19: 76, 20: 58, 21: 36, 22: 72, 23: 75, 24: 38, 25: 58, 26: 42, 27: 69, 28: 71, 29: 37, 30: 36, 31: 66, 32: 58, 33: 73, 34: 71, 35: 63, 36: 75, 37: 37, 38: 77, 39: 34, 40: 39, 41: 34, 42: 58, 43: 31, 44: 70, 45: 65, 46: 71, 47: 58, 48: 59, 49: 65, 50: 71, 51: 65, 52: 58, 53: 38, 54: 75, 55: 73, 56: 66, 57: 58, 58: 59, 59: 77, 60: 60, 61: 74, 62: 75, 63: 42, 64: 67, 65: 41, 66: 67, 67: 58, 68: 61, 69: 26, 70: 61, 71: 71, 72: 62, 73: 58, 74: 75, 75: 70, 76: 59, 77: 39, 78: 31, 79: 76, 80: 75, 81: 58, 82: 61, 83: 67, 84: 62, 85: 61, 86: 58, 87: 58, 88: 58, 89: 61, 90: 69, 91: 35, 92: 26, 93: 34, 94: 37, 95: 69, 96: 40, 97: 58, 98: 67, 99: 70, 100: 71, 101: 58}\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import networkx as nx\n", "import matplotlib.pyplot as plt\n", "from collections import Counter\n", "\n", "# グラフの作成\n", "G = nx.Graph()\n", "G.add_edges_from(main.app.links)\n", "\n", "# print len(G.neighbors(0))\n", "\n", "#nx.draw_circular(G)\n", "#plt.show()\n", "\n", "# ランキングプロット ---\n", "#degree_sequence = sorted(nx.degree(G).values(), reverse=True)\n", "print nx.degree(G)\n", "#dmax = max(degree_sequence)\n", "\n", "#plt.loglog(degree_sequence, 'b-', marker='o')\n", "#plt.title(\"Degree reank plot\")\n", "#plt.ylabel(\"degree\")\n", "#plt.xlabel(\"rank\")\n", "#plt.show()\n", "# ---\n", "\n", "# 次数分布\n", "c = Counter(nx.degree(G).values())\n", "s = sum(c.values())\n", "x = []\n", "y = []\n", "for _x, _y in c.items():\n", " x.append(_x)\n", " y.append(_y)\n", "\n", "plt.scatter(x, np.array(y)/float(s))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 15 }, "slideshow": { "slide_type": "skip" } }, "source": [ "???" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 15 }, "slideshow": { "slide_type": "skip" } }, "source": [ "### 参考:対人距離について" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 15 }, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import HTML\n", "HTML('')" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 15 }, "slideshow": { "slide_type": "skip" } }, "source": [ "### 参考:スティンガー効果" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 15 }, "slideshow": { "slide_type": "skip" } }, "source": [ "1. 以前に口論した相手は会議でも口論相手の正面に座りたがる\n", "2. ある発言の次になされる発言は、多くの場合は反対意見である\n", "3. 会議のリーダーの力が弱いときは正面同士で私語が起こり、リーダーの力が強いときは隣同士で私語が起こる" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 15 }, "slideshow": { "slide_type": "skip" } }, "source": [ "### 備考:マハラノビス距離について" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 15, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import HTML\n", "HTML('')" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.6" } }, "nbformat": 4, "nbformat_minor": 0 }