├── .gitignore ├── README.md ├── VergaraE15.bib ├── convex.ipynb ├── convex_function.eps ├── convexity.eps ├── inftheory.lyx ├── jensen_idea.eps ├── jensen_ineq_figure.ipynb ├── jensen_proof.eps ├── minorization.eps ├── minorization.ipynb ├── venn1.eps ├── venn2.eps ├── venn3.eps ├── venn_diagrams.ipynb └── venn_inc_exc_princ.eps /.gitignore: -------------------------------------------------------------------------------- 1 | /.ipynb_checkpoints 2 | *.lyx~ 3 | *.pdf 4 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # information-theory-tutorial 2 | 3 | This is the source code of my "Information Theory for Machine Learning" tutorial (the pdf is [here](https://github.com/mtomassoli/papers)). -------------------------------------------------------------------------------- /VergaraE15.bib: -------------------------------------------------------------------------------- 1 | @article{DBLP:journals/corr/VergaraE15, 2 | author = {Jorge R. Vergara and 3 | Pablo A. Est{\'{e}}vez}, 4 | title = {A Review of Feature Selection Methods Based on Mutual Information}, 5 | journal = {CoRR}, 6 | volume = {abs/1509.07577}, 7 | year = {2015}, 8 | url = {http://arxiv.org/abs/1509.07577}, 9 | timestamp = {Thu, 01 Oct 2015 14:28:48 +0200}, 10 | biburl = {http://dblp.uni-trier.de/rec/bib/journals/corr/VergaraE15}, 11 | bibsource = {dblp computer science bibliography, http://dblp.org} 12 | } 13 | 14 | -------------------------------------------------------------------------------- /convex.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 48, 6 | "metadata": { 7 | "collapsed": false 8 | }, 9 | "outputs": [], 10 | "source": [ 11 | "import matplotlib.pyplot as plt\n", 12 | "from matplotlib.path import Path\n", 13 | "import matplotlib.patches as patches" 14 | ] 15 | }, 16 | { 17 | "cell_type": "code", 18 | "execution_count": 206, 19 | "metadata": { 20 | "collapsed": false 21 | }, 22 | "outputs": [], 23 | "source": [ 24 | "# -------------- convex set --------------\n", 25 | "\n", 26 | "plt.subplot(1,2,1)\n", 27 | "\n", 28 | "left,right = -0.1,0.95\n", 29 | "plt.axis([left,right,-0.8,0.8])\n", 30 | "plt.axis('off')\n", 31 | "\n", 32 | "verts = [\n", 33 | " (0., 0.),\n", 34 | " (0.2, 1.),\n", 35 | " (1., 0.8),\n", 36 | " (0.8, 0.),\n", 37 | " (0.4, -0.5),\n", 38 | " (0.3, -0.7),\n", 39 | " (0, 0),\n", 40 | " ]\n", 41 | "\n", 42 | "codes = [Path.MOVETO,\n", 43 | " Path.CURVE4,\n", 44 | " Path.CURVE4,\n", 45 | " Path.CURVE4,\n", 46 | " Path.CURVE4,\n", 47 | " Path.CURVE4,\n", 48 | " Path.CURVE4,\n", 49 | " ]\n", 50 | "\n", 51 | "path = Path(verts, codes)\n", 52 | "\n", 53 | "patch = patches.PathPatch(path, facecolor='none', lw=2, ec='g', fc='lightgreen')\n", 54 | "plt.gca().add_patch(patch)\n", 55 | "\n", 56 | "plt.text((left+right)/2, -0.65, 'Convex Set', fontsize=18, horizontalalignment='center')\n", 57 | "\n", 58 | "# -------------- non-convex set --------------\n", 59 | "\n", 60 | "plt.subplot(1,2,2)\n", 61 | "\n", 62 | "left,right = -0.1,0.82\n", 63 | "plt.axis([left,right,-0.8,0.8])\n", 64 | "plt.axis('off')\n", 65 | "\n", 66 | "verts = [\n", 67 | " (0., 0.),\n", 68 | " (0.7, 1.),\n", 69 | " (1., 0.8),\n", 70 | " (0.4, 0.),\n", 71 | " (0.9, -0.5),\n", 72 | " (0.8, -0.7),\n", 73 | " (0, 0),\n", 74 | " ]\n", 75 | "\n", 76 | "codes = [Path.MOVETO,\n", 77 | " Path.CURVE4,\n", 78 | " Path.CURVE4,\n", 79 | " Path.CURVE4,\n", 80 | " Path.CURVE4,\n", 81 | " Path.CURVE4,\n", 82 | " Path.CURVE4,\n", 83 | " ]\n", 84 | "\n", 85 | "path = Path(verts, codes)\n", 86 | "\n", 87 | "patch = patches.PathPatch(path, facecolor='none', lw=2, ec='r', fc='pink')\n", 88 | "plt.gca().add_patch(patch)\n", 89 | "\n", 90 | "line = [[0.55,0.55], [0.4,-0.3]]\n", 91 | "plt.plot(*line, 'bo-', linewidth=2)\n", 92 | "\n", 93 | "plt.text((left+right)/2, -0.65, 'Non-Convex Set', fontsize=18, horizontalalignment='center')\n", 94 | "\n", 95 | "plt.savefig('convexity.eps', bbox_inches='tight')\n", 96 | "plt.show()" 97 | ] 98 | }, 99 | { 100 | "cell_type": "code", 101 | "execution_count": 227, 102 | "metadata": { 103 | "collapsed": false 104 | }, 105 | "outputs": [], 106 | "source": [ 107 | "x = np.arange(-5, 5, 0.01)\n", 108 | "\n", 109 | "a,b,c = 0.2,2,1\n", 110 | "def f(x):\n", 111 | " return a + b*x + c*x**2\n", 112 | "\n", 113 | "def f_prime(x):\n", 114 | " return b + 2*c*x\n", 115 | "\n", 116 | "def L(p, mean_x):\n", 117 | " return f(mean_x) + f_prime(mean_x)*p\n", 118 | "\n", 119 | "plt.axis([-5,5,-10,35])\n", 120 | "\n", 121 | "y = f(x)\n", 122 | "plt.fill_between(x, y, 35, color='c')\n", 123 | "plt.plot(x, y)\n", 124 | "\n", 125 | "plt.savefig('convex_function.eps', bbox_inches='tight')\n", 126 | "plt.show()" 127 | ] 128 | } 129 | ], 130 | "metadata": { 131 | "kernelspec": { 132 | "display_name": "Python 3", 133 | "language": "python", 134 | "name": "python3" 135 | }, 136 | "language_info": { 137 | "codemirror_mode": { 138 | "name": "ipython", 139 | "version": 3 140 | }, 141 | "file_extension": ".py", 142 | "mimetype": "text/x-python", 143 | "name": "python", 144 | "nbconvert_exporter": "python", 145 | "pygments_lexer": "ipython3", 146 | "version": "3.5.1" 147 | } 148 | }, 149 | "nbformat": 4, 150 | "nbformat_minor": 0 151 | } 152 | -------------------------------------------------------------------------------- /convexity.eps: -------------------------------------------------------------------------------- 1 | %!PS-Adobe-3.0 EPSF-3.0 2 | %%Title: convexity.eps 3 | %%Creator: matplotlib version 1.5.1, http://matplotlib.org/ 4 | %%CreationDate: Thu Jun 9 21:07:43 2016 5 | %%Orientation: portrait 6 | %%BoundingBox: 56 205 555 586 7 | %%EndComments 8 | %%BeginProlog 9 | /mpldict 8 dict def 10 | mpldict begin 11 | /m { moveto } bind def 12 | /l { lineto } bind def 13 | /r { rlineto } bind def 14 | /c { curveto } bind def 15 | /cl { closepath } bind def 16 | /box { 17 | m 18 | 1 index 0 r 19 | 0 exch r 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All Rights Reserved. 31 | %%Creator: Converted from TrueType to type 3 by PPR 32 | 25 dict begin 33 | /_d{bind def}bind def 34 | /_m{moveto}_d 35 | /_l{lineto}_d 36 | /_cl{closepath eofill}_d 37 | /_c{curveto}_d 38 | /_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d 39 | /_e{exec}_d 40 | /FontName /BitstreamVeraSans-Roman def 41 | /PaintType 0 def 42 | /FontMatrix[.001 0 0 .001 0 0]def 43 | /FontBBox[-183 -236 1287 928]def 44 | /FontType 3 def 45 | /Encoding [ /space /hyphen /C /N /S /e /n /o /t /v /x ] def 46 | /FontInfo 10 dict dup begin 47 | /FamilyName (Bitstream Vera Sans) def 48 | /FullName (Bitstream Vera Sans) def 49 | /Notice (Copyright (c) 2003 by Bitstream, Inc. All Rights Reserved. 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"collapsed": false 21 | }, 22 | "outputs": [], 23 | "source": [ 24 | "x = np.arange(-5, 5, 0.01)\n", 25 | "\n", 26 | "a,b,c = 0.2,2,1\n", 27 | "def f(x):\n", 28 | " return a + b*x + c*x**2\n", 29 | "\n", 30 | "def f_prime(x):\n", 31 | " return b + 2*c*x\n", 32 | "\n", 33 | "def L(p, mean_x):\n", 34 | " return f(mean_x) + f_prime(mean_x)*p\n", 35 | "\n", 36 | "plt.axis([-5,5,-10,35])\n", 37 | "\n", 38 | "y = f(x)\n", 39 | "plt.plot(x, y)\n", 40 | "\n", 41 | "mean_x = np.mean(x)\n", 42 | "plt.plot(x, L(x, mean_x), 'r')\n", 43 | "plt.plot(mean_x, f(mean_x), 'bo')\n", 44 | "\n", 45 | "plt.text(mean_x, -2.5, r'$x=\\mathbb{E}[X]$', fontsize=18)\n", 46 | "plt.text(3.5, L(3.5, mean_x) + 3.5, r'$L(x)$', fontsize=18)\n", 47 | "plt.text(3.5, f(3) + 15, r'$f(x)$', fontsize=18)\n", 48 | "\n", 49 | "plt.savefig('jensen_proof.eps', bbox_inches='tight')\n", 50 | "plt.show()" 51 | ] 52 | }, 53 | { 54 | "cell_type": "code", 55 | "execution_count": 105, 56 | "metadata": { 57 | "collapsed": false 58 | }, 59 | "outputs": [], 60 | "source": [ 61 | "x = np.arange(-7, 7, 0.01)\n", 62 | "\n", 63 | "a,b,c = -3,2,1\n", 64 | "def f(x):\n", 65 | " return a + b*x + c*x**2\n", 66 | "\n", 67 | "points_x = np.array([-4,-3,2,3,4])\n", 68 | "\n", 69 | "plt.axis([-7,7,-15,35])\n", 70 | "\n", 71 | "plt.plot(x, f(x))\n", 72 | "\n", 73 | "points = np.array([points_x, f(points_x)]).transpose()\n", 74 | "convex_set = plt.Polygon(points, closed=True, fill=True, fc='c')\n", 75 | "plt.gca().add_patch(convex_set)\n", 76 | "\n", 77 | "convex_x = np.arange(points_x.min(), points_x.max(), 0.01)\n", 78 | "convex_base = plt.plot(convex_x, f(convex_x), 'r', linewidth=3)\n", 79 | "\n", 80 | "plt.plot(points_x, f(points_x), 'go')\n", 81 | "\n", 82 | "plt.text(4.1, f(3) + 15, r'$f$', fontsize=18)\n", 83 | "\n", 84 | "# draw point labels\n", 85 | "plt.text(points_x[0]-2.5, f(points_x[0])-0.5, r'$(x_1,f(x_1))$', fontsize=15)\n", 86 | "plt.text(points_x[1]-2.5, f(points_x[1])-0.5, r'$(x_2,f(x_2))$', fontsize=15)\n", 87 | "plt.text(points_x[2]+0.3, f(points_x[2])-0.5, r'$(x_3,f(x_3))$', fontsize=15)\n", 88 | "plt.text(points_x[3]+0.3, f(points_x[3])-0.5, r'$(x_4,f(x_4))$', fontsize=15)\n", 89 | "plt.text(points_x[4]+0.3, f(points_x[4])-0.5, r'$(x_5,f(x_5))$', fontsize=15)\n", 90 | "\n", 91 | "convex_set_label = r'$\\left\\{ \\mathbb{E}_{X\\sim p}[(X,f(X))]'+\\\n", 92 | " r'\\mid p \\mathrm{\\; is\\; a\\; distribution}\\right\\}$'\n", 93 | "convex_base_label = r'$\\left\\{ (\\mathbb{E}_{X\\sim p}[X], f(\\mathbb{E}_{X\\sim p}[X]))'+\\\n", 94 | " r'\\mid p \\mathrm{\\; is\\; a\\; distribution}\\right\\}$'\n", 95 | "plt.legend([convex_set, convex_base[0]], [convex_set_label, convex_base_label], fontsize=14.5, loc=2)\n", 96 | "\n", 97 | "# Draw example with p=U (uniform distribution).\n", 98 | "mean_point = points.mean(axis=0)\n", 99 | "plt.plot(mean_point[0], mean_point[1], 'ro')\n", 100 | "plt.plot(mean_point[0], f(mean_point[0]), 'ro')\n", 101 | "plt.text(mean_point[0]-2.5, mean_point[1]+2, r'$\\mathbb{E}_{X\\sim U}[(X,f(X))]$', fontsize=15)\n", 102 | "pt_label = r'$(\\mathbb{E}_{X\\sim U}[X],f(\\mathbb{E}_{X\\sim U}[X]))$'\n", 103 | "plt.text(mean_point[0], f(mean_point[0])-3, pt_label, fontsize=15)\n", 104 | "\n", 105 | "note_label = 'Remember that ' + r'$\\mathbb{E}[(X,Y)]=(\\mathbb{E}[X],\\mathbb{E}[Y])$'\n", 106 | "plt.text(0, -11, note_label, fontsize=15, horizontalalignment='center', verticalalignment='center',\n", 107 | " bbox=dict(facecolor='none', edgecolor='c', boxstyle='round'))\n", 108 | "\n", 109 | "plt.savefig('jensen_idea.eps', bbox_inches='tight')\n", 110 | "plt.show()" 111 | ] 112 | } 113 | ], 114 | "metadata": { 115 | "kernelspec": { 116 | "display_name": "Python 3", 117 | "language": "python", 118 | "name": "python3" 119 | }, 120 | "language_info": { 121 | "codemirror_mode": { 122 | "name": "ipython", 123 | "version": 3 124 | }, 125 | "file_extension": ".py", 126 | "mimetype": "text/x-python", 127 | "name": "python", 128 | "nbconvert_exporter": "python", 129 | "pygments_lexer": "ipython3", 130 | "version": "3.5.1" 131 | } 132 | }, 133 | "nbformat": 4, 134 | "nbformat_minor": 0 135 | } 136 | -------------------------------------------------------------------------------- /jensen_proof.eps: -------------------------------------------------------------------------------- 1 | %!PS-Adobe-3.0 EPSF-3.0 2 | %%Title: jensen_proof.eps 3 | %%Creator: matplotlib version 1.5.1, http://matplotlib.org/ 4 | %%CreationDate: Thu Jun 9 21:40:53 2016 5 | %%Orientation: portrait 6 | %%BoundingBox: 60 205 551 586 7 | %%EndComments 8 | %%BeginProlog 9 | /mpldict 11 dict def 10 | mpldict begin 11 | /m { moveto } bind def 12 | /l { lineto } bind def 13 | /r { rlineto } bind def 14 | /c { curveto } bind def 15 | /cl { closepath } bind def 16 | /box { 17 | m 18 | 1 index 0 r 19 | 0 exch r 20 | neg 0 r 21 | cl 22 | } bind def 23 | /clipbox { 24 | box 25 | clip 26 | newpath 27 | } bind def 28 | %!PS-Adobe-3.0 Resource-Font 29 | %%Title: Bitstream Vera Sans 30 | %%Copyright: Copyright (c) 2003 by Bitstream, Inc. All Rights Reserved. 31 | %%Creator: Converted from TrueType to type 3 by PPR 32 | 25 dict begin 33 | /_d{bind def}bind def 34 | /_m{moveto}_d 35 | /_l{lineto}_d 36 | /_cl{closepath eofill}_d 37 | /_c{curveto}_d 38 | /_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d 39 | /_e{exec}_d 40 | /FontName /BitstreamVeraSans-Roman def 41 | /PaintType 0 def 42 | /FontMatrix[.001 0 0 .001 0 0]def 43 | /FontBBox[-183 -236 1287 928]def 44 | /FontType 3 def 45 | /Encoding [ /zero /one /two /three /four /five /minus ] def 46 | /FontInfo 10 dict dup begin 47 | /FamilyName (Bitstream Vera Sans) def 48 | /FullName (Bitstream Vera Sans) def 49 | /Notice (Copyright (c) 2003 by Bitstream, Inc. All Rights Reserved. Bitstream Vera is a trademark of Bitstream, Inc.) def 50 | /Weight (Roman) def 51 | /Version (Release 1.10) def 52 | /ItalicAngle 0.0 def 53 | /isFixedPitch false def 54 | /UnderlinePosition -213 def 55 | /UnderlineThickness 143 def 56 | end readonly def 57 | /CharStrings 7 dict dup begin 58 | /zero{636 0 66 -13 570 742 _sc 59 | 318 664 _m 60 | 267 664 229 639 203 589 _c 61 | 177 539 165 464 165 364 _c 62 | 165 264 177 189 203 139 _c 63 | 229 89 267 64 318 64 _c 64 | 369 64 407 89 433 139 _c 65 | 458 189 471 264 471 364 _c 66 | 471 464 458 539 433 589 _c 67 | 407 639 369 664 318 664 _c 68 | 318 742 _m 69 | 399 742 461 709 505 645 _c 70 | 548 580 570 486 570 364 _c 71 | 570 241 548 147 505 83 _c 72 | 461 19 399 -13 318 -13 _c 73 | 236 -13 173 19 130 83 _c 74 | 87 147 66 241 66 364 _c 75 | 66 486 87 580 130 645 _c 76 | 173 709 236 742 318 742 _c 77 | _cl}_d 78 | /one{636 0 110 0 544 729 _sc 79 | 124 83 _m 80 | 285 83 _l 81 | 285 639 _l 82 | 110 604 _l 83 | 110 694 _l 84 | 284 729 _l 85 | 383 729 _l 86 | 383 83 _l 87 | 544 83 _l 88 | 544 0 _l 89 | 124 0 _l 90 | 124 83 _l 91 | _cl}_d 92 | /two{{636 0 73 0 536 742 _sc 93 | 192 83 _m 94 | 536 83 _l 95 | 536 0 _l 96 | 73 0 _l 97 | 73 83 _l 98 | 110 121 161 173 226 239 _c 99 | 290 304 331 346 348 365 _c 100 | 380 400 402 430 414 455 _c 101 | 426 479 433 504 433 528 _c 102 | 433 566 419 598 392 622 _c 103 | 365 646 330 659 286 659 _c 104 | 255 659 222 653 188 643 _c 105 | 154 632 117 616 78 594 _c 106 | 78 694 _l 107 | 118 710 155 722 189 730 _c 108 | 223 738 255 742 284 742 _c 109 | }_e{359 742 419 723 464 685 _c 110 | 509 647 532 597 532 534 _c 111 | 532 504 526 475 515 449 _c 112 | 504 422 484 390 454 354 _c 113 | 446 344 420 317 376 272 _c 114 | 332 227 271 164 192 83 _c 115 | _cl}_e}_d 116 | /three{{636 0 76 -13 556 742 _sc 117 | 406 393 _m 118 | 453 383 490 362 516 330 _c 119 | 542 298 556 258 556 212 _c 120 | 556 140 531 84 482 45 _c 121 | 432 6 362 -13 271 -13 _c 122 | 240 -13 208 -10 176 -4 _c 123 | 144 1 110 10 76 22 _c 124 | 76 117 _l 125 | 103 101 133 89 166 81 _c 126 | 198 73 232 69 268 69 _c 127 | 330 69 377 81 409 105 _c 128 | 441 129 458 165 458 212 _c 129 | 458 254 443 288 413 312 _c 130 | 383 336 341 349 287 349 _c 131 | }_e{202 349 _l 132 | 202 430 _l 133 | 291 430 _l 134 | 339 430 376 439 402 459 _c 135 | 428 478 441 506 441 543 _c 136 | 441 580 427 609 401 629 _c 137 | 374 649 336 659 287 659 _c 138 | 260 659 231 656 200 650 _c 139 | 169 644 135 635 98 623 _c 140 | 98 711 _l 141 | 135 721 170 729 203 734 _c 142 | 235 739 266 742 296 742 _c 143 | 370 742 429 725 473 691 _c 144 | 517 657 539 611 539 553 _c 145 | 539 513 527 479 504 451 _c 146 | 481 423 448 403 406 393 _c 147 | _cl}_e}_d 148 | /four{636 0 49 0 580 729 _sc 149 | 378 643 _m 150 | 129 254 _l 151 | 378 254 _l 152 | 378 643 _l 153 | 352 729 _m 154 | 476 729 _l 155 | 476 254 _l 156 | 580 254 _l 157 | 580 172 _l 158 | 476 172 _l 159 | 476 0 _l 160 | 378 0 _l 161 | 378 172 _l 162 | 49 172 _l 163 | 49 267 _l 164 | 352 729 _l 165 | _cl}_d 166 | /five{{636 0 77 -13 549 729 _sc 167 | 108 729 _m 168 | 495 729 _l 169 | 495 646 _l 170 | 198 646 _l 171 | 198 467 _l 172 | 212 472 227 476 241 478 _c 173 | 255 480 270 482 284 482 _c 174 | 365 482 429 459 477 415 _c 175 | 525 370 549 310 549 234 _c 176 | 549 155 524 94 475 51 _c 177 | 426 8 357 -13 269 -13 _c 178 | 238 -13 207 -10 175 -6 _c 179 | 143 -1 111 6 77 17 _c 180 | 77 116 _l 181 | 106 100 136 88 168 80 _c 182 | 199 72 232 69 267 69 _c 183 | }_e{323 69 368 83 401 113 _c 184 | 433 143 450 183 450 234 _c 185 | 450 284 433 324 401 354 _c 186 | 368 384 323 399 267 399 _c 187 | 241 399 214 396 188 390 _c 188 | 162 384 135 375 108 363 _c 189 | 108 729 _l 190 | _cl}_e}_d 191 | /minus{838 0 106 272 732 355 _sc 192 | 106 355 _m 193 | 732 355 _l 194 | 732 272 _l 195 | 106 272 _l 196 | 106 355 _l 197 | _cl}_d 198 | end readonly def 199 | 200 | /BuildGlyph 201 | {exch begin 202 | CharStrings exch 203 | 2 copy known not{pop /.notdef}if 204 | true 3 1 roll get exec 205 | end}_d 206 | 207 | /BuildChar { 208 | 1 index /Encoding get exch get 209 | 1 index /BuildGlyph get exec 210 | }_d 211 | 212 | FontName currentdict end definefont pop 213 | %!PS-Adobe-3.0 Resource-Font 214 | %%Title: cmmi10 215 | %%Copyright: Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. 216 | %%Creator: Converted from TrueType to type 3 by PPR 217 | 25 dict begin 218 | /_d{bind def}bind def 219 | /_m{moveto}_d 220 | /_l{lineto}_d 221 | /_cl{closepath eofill}_d 222 | /_c{curveto}_d 223 | /_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d 224 | /_e{exec}_d 225 | /FontName /Cmmi10 def 226 | /PaintType 0 def 227 | /FontMatrix[.001 0 0 .001 0 0]def 228 | /FontBBox[-34 -250 1048 750]def 229 | /FontType 3 def 230 | /Encoding [ /x /L /f /X ] def 231 | /FontInfo 10 dict dup begin 232 | /FamilyName (cmmi10) def 233 | /FullName (cmmi10) def 234 | /Notice (Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. ) def 235 | /Weight (Regular) def 236 | /Version (1.1/12-Nov-94) def 237 | /ItalicAngle 0.0 def 238 | /isFixedPitch false def 239 | /UnderlinePosition -133 def 240 | /UnderlineThickness 20 def 241 | end readonly def 242 | /CharStrings 4 dict dup begin 243 | /x{{571 0 31 -10 526 442 _sc 244 | 78 29 _m 245 | 90 19 106 15 128 15 _c 246 | 148 15 167 25 183 45 _c 247 | 199 65 210 87 216 111 _c 248 | 261 288 _l 249 | 268 320 272 342 272 354 _c 250 | 272 370 267 385 258 397 _c 251 | 248 409 235 416 219 416 _c 252 | 198 416 178 409 160 396 _c 253 | 141 382 125 365 113 345 _c 254 | 100 325 91 304 86 284 _c 255 | 84 280 82 278 78 278 _c 256 | 66 278 _l 257 | 60 278 58 281 58 287 _c 258 | 58 290 _l 259 | }_e{64 314 75 338 91 362 _c 260 | 107 386 126 405 149 420 _c 261 | 171 434 195 442 221 442 _c 262 | 245 442 267 435 287 422 _c 263 | 307 409 321 391 329 369 _c 264 | 340 389 354 407 372 421 _c 265 | 390 435 409 442 431 442 _c 266 | 445 442 460 439 475 434 _c 267 | 490 429 502 421 512 411 _c 268 | 521 401 526 388 526 372 _c 269 | 526 355 520 340 509 328 _c 270 | 498 316 484 310 468 310 _c 271 | 457 310 448 313 441 320 _c 272 | }_e{433 327 430 336 430 346 _c 273 | 430 360 434 372 444 383 _c 274 | 454 393 465 400 479 402 _c 275 | 467 411 450 416 429 416 _c 276 | 407 416 389 406 373 386 _c 277 | 357 366 346 344 340 320 _c 278 | 296 143 _l 279 | 288 116 285 94 285 77 _c 280 | 285 60 289 45 299 33 _c 281 | 309 21 322 15 338 15 _c 282 | 369 15 397 28 421 56 _c 283 | 445 84 462 114 470 147 _c 284 | 471 151 474 153 478 153 _c 285 | 490 153 _l 286 | 492 153 494 152 496 150 _c 287 | }_e{498 148 499 146 499 144 _c 288 | 499 143 498 142 498 141 _c 289 | 488 101 468 66 438 36 _c 290 | 408 5 374 -10 336 -10 _c 291 | 311 -10 289 -3 269 9 _c 292 | 249 21 236 39 228 62 _c 293 | 217 42 202 25 184 11 _c 294 | 166 -3 146 -10 126 -10 _c 295 | 111 -10 96 -7 81 -3 _c 296 | 66 1 54 9 45 19 _c 297 | 35 29 31 43 31 59 _c 298 | 31 75 36 89 47 102 _c 299 | 57 114 71 121 88 121 _c 300 | }_e{98 121 107 117 115 111 _c 301 | 123 104 127 95 127 85 _c 302 | 127 71 122 58 113 48 _c 303 | 103 38 92 31 78 29 _c 304 | _cl}_e}_d 305 | /L{{680 0 37 0 645 683 _sc 306 | 47 0 _m 307 | 40 0 37 4 37 13 _c 308 | 37 15 38 18 39 22 _c 309 | 40 26 41 29 43 31 _c 310 | 45 33 47 35 50 35 _c 311 | 90 35 119 37 135 42 _c 312 | 143 44 150 53 154 69 _c 313 | 291 618 _l 314 | 292 624 293 629 293 632 _c 315 | 293 639 289 643 281 644 _c 316 | 268 646 244 648 209 648 _c 317 | 202 648 199 652 199 661 _c 318 | 201 669 203 675 205 678 _c 319 | 206 681 210 683 216 683 _c 320 | }_e{511 683 _l 321 | 517 683 520 678 520 670 _c 322 | 519 663 518 658 517 654 _c 323 | 515 650 512 648 507 648 _c 324 | 457 648 424 646 408 643 _c 325 | 392 640 382 630 378 614 _c 326 | 241 65 _l 327 | 238 57 237 49 237 43 _c 328 | 237 37 248 35 271 35 _c 329 | 364 35 _l 330 | 416 35 458 45 491 66 _c 331 | 523 87 547 111 563 137 _c 332 | 579 163 592 190 603 218 _c 333 | 613 246 621 261 626 262 _c 334 | 635 262 _l 335 | 641 262 645 257 645 249 _c 336 | }_e{556 7 _l 337 | 555 2 552 0 547 0 _c 338 | 47 0 _l 339 | _cl}_e}_d 340 | /f{{489 0 53 -204 552 705 _sc 341 | 97 -164 _m 342 | 109 -173 124 -178 142 -178 _c 343 | 166 -178 185 -151 200 -99 _c 344 | 206 -73 223 9 251 151 _c 345 | 297 396 _l 346 | 211 396 _l 347 | 204 396 201 400 201 409 _c 348 | 203 423 208 431 214 431 _c 349 | 303 431 _l 350 | 315 496 _l 351 | 319 516 322 533 326 548 _c 352 | 329 562 332 576 336 588 _c 353 | 340 600 345 614 353 630 _c 354 | 364 652 379 670 399 684 _c 355 | 418 698 439 705 462 705 _c 356 | 476 705 490 702 504 697 _c 357 | }_e{518 691 529 683 538 673 _c 358 | 547 662 552 649 552 635 _c 359 | 552 617 546 602 535 590 _c 360 | 523 578 510 572 494 572 _c 361 | 483 572 474 575 466 582 _c 362 | 458 588 455 597 455 608 _c 363 | 455 622 460 635 470 646 _c 364 | 480 657 492 663 507 665 _c 365 | 494 674 479 679 461 679 _c 366 | 451 679 441 674 432 665 _c 367 | 423 655 417 645 415 635 _c 368 | 411 617 401 571 387 497 _c 369 | 375 431 _l 370 | 478 431 _l 371 | 484 431 488 426 488 418 _c 372 | }_e{487 416 486 413 485 409 _c 373 | 484 405 483 401 481 399 _c 374 | 479 397 477 396 475 396 _c 375 | 368 396 _l 376 | 322 152 _l 377 | 316 116 309 80 301 44 _c 378 | 293 8 283 -29 269 -68 _c 379 | 255 -106 238 -139 216 -165 _c 380 | 194 -191 169 -204 140 -204 _c 381 | 117 -204 97 -197 79 -185 _c 382 | 61 -172 53 -155 53 -134 _c 383 | 53 -116 58 -101 69 -89 _c 384 | 80 -77 94 -71 111 -71 _c 385 | 121 -71 130 -74 138 -81 _c 386 | 146 -87 150 -96 150 -107 _c 387 | }_e{150 -121 144 -134 134 -146 _c 388 | 123 -158 111 -164 97 -164 _c 389 | _cl}_e}_d 390 | /X{{828 0 26 0 852 683 _sc 391 | 36 0 _m 392 | 29 0 26 4 26 13 _c 393 | 26 15 26 18 28 22 _c 394 | 29 26 30 29 32 31 _c 395 | 34 33 36 35 40 35 _c 396 | 100 35 152 57 196 103 _c 397 | 196 103 197 104 198 104 _c 398 | 198 104 199 105 199 105 _c 399 | 418 341 _l 400 | 299 628 _l 401 | 292 636 281 642 266 644 _c 402 | 250 646 232 648 212 648 _c 403 | 205 648 202 652 202 661 _c 404 | 204 669 206 675 207 678 _c 405 | }_e{208 681 212 683 219 683 _c 406 | 469 683 _l 407 | 475 683 479 678 479 670 _c 408 | 479 668 478 665 477 661 _c 409 | 475 657 474 653 472 651 _c 410 | 470 649 468 648 465 648 _c 411 | 452 648 439 646 426 642 _c 412 | 413 638 404 631 399 622 _c 413 | 485 415 _l 414 | 649 591 _l 415 | 649 593 651 596 655 602 _c 416 | 659 608 661 613 661 619 _c 417 | 661 629 656 636 648 641 _c 418 | 640 645 630 648 618 648 _c 419 | 611 648 608 652 608 661 _c 420 | }_e{610 669 611 675 613 678 _c 421 | 614 681 618 683 625 683 _c 422 | 842 683 _l 423 | 845 683 847 681 849 679 _c 424 | 851 676 852 673 852 670 _c 425 | 852 668 851 665 850 661 _c 426 | 849 657 848 654 846 652 _c 427 | 844 649 842 648 839 648 _c 428 | 807 648 779 642 753 631 _c 429 | 727 619 704 602 682 580 _c 430 | 682 580 681 579 681 579 _c 431 | 680 579 679 578 679 578 _c 432 | 498 383 _l 433 | 635 55 _l 434 | 645 41 674 35 722 35 _c 435 | }_e{728 35 732 30 732 22 _c 436 | 730 13 728 7 726 4 _c 437 | 724 1 721 0 715 0 _c 438 | 465 0 _l 439 | 458 0 455 4 455 13 _c 440 | 455 15 456 18 457 22 _c 441 | 457 26 459 29 461 31 _c 442 | 463 33 465 35 468 35 _c 443 | 480 35 493 37 507 41 _c 444 | 520 45 529 51 535 61 _c 445 | 431 310 _l 446 | 229 92 _l 447 | 228 89 226 85 222 80 _c 448 | 218 74 217 69 217 64 _c 449 | 217 54 221 46 230 42 _c 450 | }_e{239 37 249 35 260 35 _c 451 | 266 35 270 30 270 22 _c 452 | 268 12 266 6 265 4 _c 453 | 263 1 259 0 253 0 _c 454 | 36 0 _l 455 | _cl}_e}_d 456 | end readonly def 457 | 458 | /BuildGlyph 459 | {exch begin 460 | CharStrings exch 461 | 2 copy known not{pop /.notdef}if 462 | true 3 1 roll get exec 463 | end}_d 464 | 465 | /BuildChar { 466 | 1 index /Encoding get exch get 467 | 1 index /BuildGlyph get exec 468 | }_d 469 | 470 | FontName currentdict end definefont pop 471 | %!PS-Adobe-3.0 Resource-Font 472 | %%Title: STIXNonUnicode-Italic 473 | %%Copyright: Copyright (c) 2001-2010 by the STI Pub Companies, consisting of the American Chemical Society, the American Institute of Physics, the American Mathematical Society, the American Physical Society, Elsevier, Inc., and The Institute of Electrical and Electronic Engineers, Inc. Portions copyright (c) 1998-2003 by MicroPress, Inc. Portions copyright (c) 1990 by Elsevier, Inc. All rights reserved. 474 | %%Creator: Converted from TrueType to type 3 by PPR 475 | 25 dict begin 476 | /_d{bind def}bind def 477 | /_m{moveto}_d 478 | /_l{lineto}_d 479 | /_cl{closepath eofill}_d 480 | /_c{curveto}_d 481 | /_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d 482 | /_e{exec}_d 483 | /FontName /STIXNonUnicode-Italic def 484 | /PaintType 0 def 485 | /FontMatrix[.001 0 0 .001 0 0]def 486 | /FontBBox[-141 -240 1128 795]def 487 | /FontType 3 def 488 | /Encoding [ /uniE156 ] def 489 | /FontInfo 10 dict dup begin 490 | /FamilyName (STIXNonUnicode) def 491 | /FullName (STIXNonUnicode-Italic) def 492 | /Notice (Copyright (c) 2001-2010 by the STI Pub Companies, consisting of the American Chemical Society, the American Institute of Physics, the American Mathematical Society, the American Physical Society, Elsevier, Inc., and The Institute of Electrical and Electronic Engineers, Inc. Portions copyright (c) 1998-2003 by MicroPress, Inc. Portions copyright (c) 1990 by Elsevier, Inc. All rights reserved. STIX Fonts(TM) is a trademark of The Institute of Electrical and Electronics Engineers, Inc.) def 493 | /Weight (Italic) def 494 | /Version (Version 1.0.0) def 495 | /ItalicAngle -17.43909 def 496 | /isFixedPitch false def 497 | /UnderlinePosition -107 def 498 | /UnderlineThickness 53 def 499 | end readonly def 500 | /CharStrings 1 dict dup begin 501 | /uniE156{639 0 17 0 664 653 _sc 502 | 664 653 _m 503 | 655 616 _l 504 | 336 616 _l 505 | 267 354 _l 506 | 549 354 _l 507 | 538 317 _l 508 | 257 317 _l 509 | 182 37 _l 510 | 538 37 _l 511 | 530 0 _l 512 | 17 0 _l 513 | 192 653 _l 514 | 664 653 _l 515 | 299 616 _m 516 | 221 616 _l 517 | 65 37 _l 518 | 145 37 _l 519 | 299 616 _l 520 | _cl}_d 521 | end readonly def 522 | 523 | /BuildGlyph 524 | {exch begin 525 | CharStrings exch 526 | 2 copy known not{pop /.notdef}if 527 | true 3 1 roll get exec 528 | end}_d 529 | 530 | /BuildChar { 531 | 1 index /Encoding get exch get 532 | 1 index /BuildGlyph get exec 533 | }_d 534 | 535 | FontName currentdict end definefont pop 536 | %!PS-Adobe-3.0 Resource-Font 537 | %%Title: cmr10 538 | %%Copyright: Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. 539 | %%Creator: Converted from TrueType to type 3 by PPR 540 | 25 dict begin 541 | /_d{bind def}bind def 542 | /_m{moveto}_d 543 | /_l{lineto}_d 544 | /_cl{closepath eofill}_d 545 | /_c{curveto}_d 546 | /_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d 547 | /_e{exec}_d 548 | /FontName /Cmr10 def 549 | /PaintType 0 def 550 | /FontMatrix[.001 0 0 .001 0 0]def 551 | /FontBBox[-44 -250 1009 750]def 552 | /FontType 3 def 553 | /Encoding [ /equal /bracketleft /parenright /bracketright /parenleft ] def 554 | /FontInfo 10 dict dup begin 555 | /FamilyName (cmr10) def 556 | /FullName (cmr10) def 557 | /Notice (Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. ) def 558 | /Weight (Regular) def 559 | /Version (1.1/12-Nov-94) def 560 | /ItalicAngle 0.0 def 561 | /isFixedPitch false def 562 | /UnderlinePosition -133 def 563 | /UnderlineThickness 20 def 564 | end readonly def 565 | /CharStrings 5 dict dup begin 566 | /equal{{777 0 56 133 721 367 _sc 567 | 75 133 _m 568 | 69 133 65 135 61 139 _c 569 | 57 143 56 148 56 153 _c 570 | 56 158 57 163 61 167 _c 571 | 65 171 69 173 75 173 _c 572 | 703 173 _l 573 | 707 173 711 171 715 167 _c 574 | 719 163 721 158 721 153 _c 575 | 721 148 719 143 715 139 _c 576 | 711 135 707 133 703 133 _c 577 | 75 133 _l 578 | 75 327 _m 579 | 69 327 65 329 61 333 _c 580 | 57 337 56 341 56 347 _c 581 | 56 351 57 356 61 360 _c 582 | }_e{65 364 69 367 75 367 _c 583 | 703 367 _l 584 | 707 367 711 364 715 360 _c 585 | 719 356 721 351 721 347 _c 586 | 721 341 719 337 715 333 _c 587 | 711 329 707 327 703 327 _c 588 | 75 327 _l 589 | _cl}_e}_d 590 | /bracketleft{277 0 118 -249 255 750 _sc 591 | 118 -249 _m 592 | 118 750 _l 593 | 255 750 _l 594 | 255 710 _l 595 | 158 710 _l 596 | 158 -209 _l 597 | 255 -209 _l 598 | 255 -249 _l 599 | 118 -249 _l 600 | _cl}_d 601 | /parenright{{388 0 56 -249 291 750 _sc 602 | 65 -249 _m 603 | 59 -249 56 -246 56 -240 _c 604 | 56 -237 56 -235 58 -234 _c 605 | 172 -122 229 38 229 250 _c 606 | 229 462 172 623 60 733 _c 607 | 57 734 56 737 56 741 _c 608 | 56 743 57 745 59 747 _c 609 | 61 749 63 750 65 750 _c 610 | 74 750 _l 611 | 76 750 77 749 79 748 _c 612 | 127 710 167 664 199 610 _c 613 | 231 556 254 498 269 437 _c 614 | 283 376 291 314 291 250 _c 615 | 291 202 287 156 279 110 _c 616 | }_e{271 64 258 20 241 -24 _c 617 | 223 -68 201 -108 175 -146 _c 618 | 148 -184 116 -217 79 -247 _c 619 | 77 -248 76 -249 74 -249 _c 620 | 65 -249 _l 621 | _cl}_e}_d 622 | /bracketright{277 0 22 -249 159 750 _sc 623 | 22 -249 _m 624 | 22 -209 _l 625 | 119 -209 _l 626 | 119 710 _l 627 | 22 710 _l 628 | 22 750 _l 629 | 159 750 _l 630 | 159 -249 _l 631 | 22 -249 _l 632 | _cl}_d 633 | /parenleft{{388 0 97 -249 332 750 _sc 634 | 310 -247 _m 635 | 272 -217 240 -184 214 -146 _c 636 | 187 -108 165 -67 148 -25 _c 637 | 131 17 118 62 110 109 _c 638 | 101 155 97 202 97 250 _c 639 | 97 298 101 345 110 392 _c 640 | 118 438 131 483 149 527 _c 641 | 166 570 188 611 215 649 _c 642 | 242 687 274 720 310 748 _c 643 | 310 749 311 750 315 750 _c 644 | 324 750 _l 645 | 326 750 327 749 329 747 _c 646 | 331 745 332 743 332 741 _c 647 | 332 738 331 736 330 735 _c 648 | }_e{297 703 270 668 248 632 _c 649 | 226 596 209 557 196 516 _c 650 | 183 474 174 432 168 388 _c 651 | 162 344 159 298 159 250 _c 652 | 159 38 215 -122 329 -232 _c 653 | 331 -234 332 -236 332 -240 _c 654 | 332 -242 331 -244 329 -246 _c 655 | 327 -248 326 -249 324 -249 _c 656 | 315 -249 _l 657 | 311 -249 310 -248 310 -247 _c 658 | _cl}_e}_d 659 | end readonly def 660 | 661 | /BuildGlyph 662 | {exch begin 663 | CharStrings exch 664 | 2 copy known not{pop /.notdef}if 665 | true 3 1 roll get exec 666 | end}_d 667 | 668 | /BuildChar { 669 | 1 index /Encoding get exch get 670 | 1 index /BuildGlyph get exec 671 | }_d 672 | 673 | FontName currentdict end definefont pop 674 | end 675 | %%EndProlog 676 | mpldict begin 677 | 60.928 205.281 translate 678 | 490.144 381.438 0 0 clipbox 679 | 100000 setmiterlimit 680 | gsave 681 | 0 0 m 682 | 490.14375 0 l 683 | 490.14375 381.4375 l 684 | 0 381.4375 l 685 | cl 686 | 1.000 setgray 687 | fill 688 | grestore 689 | gsave 690 | 36.54375 22.825 m 691 | 482.94375 22.825 l 692 | 482.94375 368.425 l 693 | 36.54375 368.425 l 694 | cl 695 | 1.000 setgray 696 | fill 697 | grestore 698 | 1.000 setlinewidth 699 | 1 setlinejoin 700 | 2 setlinecap 701 | [] 0 setdash 702 | 0.000 0.000 1.000 setrgbcolor 703 | gsave 704 | 446.4 345.6 36.54 22.83 clipbox 705 | 36.54375 216.361 m 706 | 43.68615 206.727208 l 707 | 50.38215 198.052648 l 708 | 57.07815 189.723688 l 709 | 63.77415 181.740328 l 710 | 70.47015 174.102568 l 711 | 77.16615 166.810408 l 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bind def 12 | /l { lineto } bind def 13 | /r { rlineto } bind def 14 | /c { curveto } bind def 15 | /cl { closepath } bind def 16 | /box { 17 | m 18 | 1 index 0 r 19 | 0 exch r 20 | neg 0 r 21 | cl 22 | } bind def 23 | /clipbox { 24 | box 25 | clip 26 | newpath 27 | } bind def 28 | %!PS-Adobe-3.0 Resource-Font 29 | %%Title: cmsy10 30 | %%Copyright: Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. 31 | %%Creator: Converted from TrueType to type 3 by PPR 32 | 25 dict begin 33 | /_d{bind def}bind def 34 | /_m{moveto}_d 35 | /_l{lineto}_d 36 | /_cl{closepath eofill}_d 37 | /_c{curveto}_d 38 | /_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d 39 | /_e{exec}_d 40 | /FontName /Cmsy10 def 41 | /PaintType 0 def 42 | /FontMatrix[.001 0 0 .001 0 0]def 43 | /FontBBox[-29 -960 1123 779]def 44 | /FontType 3 def 45 | /Encoding [ /asteriskmath /lessequal /bar ] def 46 | /FontInfo 10 dict dup begin 47 | /FamilyName (cmsy10) def 48 | /FullName (cmsy10) def 49 | /Notice (Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. ) def 50 | /Weight (Regular) def 51 | /Version (1.1/12-Nov-94) def 52 | /ItalicAngle 0.0 def 53 | /isFixedPitch false def 54 | /UnderlinePosition -133 def 55 | /UnderlineThickness 20 def 56 | end readonly def 57 | /CharStrings 3 dict dup begin 58 | /asteriskmath{{500 0 65 34 434 465 _sc 59 | 94 127 _m 60 | 86 127 80 130 74 136 _c 61 | 68 142 65 149 65 157 _c 62 | 65 168 69 176 79 181 _c 63 | 223 250 _l 64 | 79 318 _l 65 | 69 322 65 330 65 342 _c 66 | 65 349 68 356 74 362 _c 67 | 80 368 86 372 94 372 _c 68 | 99 372 104 370 108 367 _c 69 | 236 274 _l 70 | 221 437 _l 71 | 221 445 223 451 229 457 _c 72 | 235 462 242 465 250 465 _c 73 | 258 465 264 462 270 457 _c 74 | 275 452 278 446 278 439 _c 75 | }_e{278 437 _l 76 | 263 274 _l 77 | 391 367 _l 78 | 395 370 399 372 405 372 _c 79 | 413 372 419 368 425 362 _c 80 | 431 356 434 349 434 342 _c 81 | 434 330 429 322 420 318 _c 82 | 276 250 _l 83 | 420 181 _l 84 | 429 176 434 168 434 157 _c 85 | 434 149 431 142 425 136 _c 86 | 419 130 413 127 405 127 _c 87 | 399 127 395 128 391 132 _c 88 | 263 225 _l 89 | 278 63 _l 90 | 278 60 _l 91 | 278 52 275 46 269 41 _c 92 | 263 36 257 34 250 34 _c 93 | }_e{242 34 235 36 229 42 _c 94 | 223 47 221 54 221 62 _c 95 | 236 225 _l 96 | 108 132 _l 97 | 104 128 99 127 94 127 _c 98 | _cl}_e}_d 99 | /lessequal{{777 0 83 -136 694 636 _sc 100 | 102 -136 _m 101 | 96 -136 92 -134 88 -130 _c 102 | 84 -126 83 -121 83 -116 _c 103 | 83 -110 84 -106 88 -102 _c 104 | 92 -98 96 -96 102 -96 _c 105 | 676 -96 _l 106 | 681 -96 685 -98 689 -102 _c 107 | 692 -106 694 -110 694 -116 _c 108 | 694 -121 692 -126 689 -130 _c 109 | 685 -134 681 -136 676 -136 _c 110 | 102 -136 _l 111 | 93 330 _m 112 | 86 332 83 337 83 347 _c 113 | 83 355 87 361 96 365 _c 114 | 667 635 _l 115 | 668 635 670 636 674 636 _c 116 | }_e{679 636 684 634 688 630 _c 117 | 692 626 694 622 694 616 _c 118 | 694 607 690 601 682 598 _c 119 | 150 347 _l 120 | 685 94 _l 121 | 691 90 694 85 694 77 _c 122 | 694 71 692 66 688 62 _c 123 | 684 58 679 57 674 57 _c 124 | 670 57 668 57 667 59 _c 125 | 93 330 _l 126 | _cl}_e}_d 127 | /bar{277 0 119 -249 159 750 _sc 128 | 119 -231 _m 129 | 119 732 _l 130 | 119 737 121 741 125 745 _c 131 | 129 748 133 750 139 750 _c 132 | 143 750 148 748 152 745 _c 133 | 156 741 159 737 159 732 _c 134 | 159 -231 _l 135 | 159 -236 156 -240 152 -244 _c 136 | 148 -247 143 -249 139 -249 _c 137 | 133 -249 129 -247 125 -244 _c 138 | 121 -240 119 -236 119 -231 _c 139 | _cl}_d 140 | end readonly def 141 | 142 | /BuildGlyph 143 | {exch begin 144 | CharStrings exch 145 | 2 copy known not{pop /.notdef}if 146 | true 3 1 roll get exec 147 | end}_d 148 | 149 | /BuildChar { 150 | 1 index /Encoding get exch get 151 | 1 index /BuildGlyph get exec 152 | }_d 153 | 154 | FontName currentdict end definefont pop 155 | %!PS-Adobe-3.0 Resource-Font 156 | %%Title: cmmi10 157 | %%Copyright: Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. 158 | %%Creator: Converted from TrueType to type 3 by PPR 159 | 25 dict begin 160 | /_d{bind def}bind def 161 | /_m{moveto}_d 162 | /_l{lineto}_d 163 | /_cl{closepath eofill}_d 164 | /_c{curveto}_d 165 | /_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d 166 | /_e{exec}_d 167 | /FontName /Cmmi10 def 168 | /PaintType 0 def 169 | /FontMatrix[.001 0 0 .001 0 0]def 170 | /FontBBox[-34 -250 1048 750]def 171 | /FontType 3 def 172 | /Encoding [ /theta /t /Q /f ] def 173 | /FontInfo 10 dict dup begin 174 | /FamilyName (cmmi10) def 175 | /FullName (cmmi10) def 176 | /Notice (Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. ) def 177 | /Weight (Regular) def 178 | /Version (1.1/12-Nov-94) def 179 | /ItalicAngle 0.0 def 180 | /isFixedPitch false def 181 | /UnderlinePosition -133 def 182 | /UnderlineThickness 20 def 183 | end readonly def 184 | /CharStrings 4 dict dup begin 185 | /theta{{469 0 40 -10 457 705 _sc 186 | 161 -10 _m 187 | 131 -10 106 0 88 22 _c 188 | 70 44 57 70 50 102 _c 189 | 43 133 40 164 40 195 _c 190 | 40 196 _l 191 | 40 229 43 263 49 299 _c 192 | 55 335 65 370 77 406 _c 193 | 89 442 102 474 116 502 _c 194 | 126 521 138 543 154 567 _c 195 | 169 591 186 614 205 635 _c 196 | 224 656 245 673 267 686 _c 197 | 289 698 311 705 334 705 _c 198 | 335 705 _l 199 | 359 705 379 698 395 685 _c 200 | }_e{411 671 423 654 432 634 _c 201 | 441 613 447 591 451 567 _c 202 | 455 543 457 520 457 499 _c 203 | 457 448 450 396 436 344 _c 204 | 422 292 404 241 380 192 _c 205 | 370 173 358 151 342 126 _c 206 | 326 101 309 79 291 59 _c 207 | 273 39 252 22 230 9 _c 208 | 207 -3 184 -10 162 -10 _c 209 | 161 -10 _l 210 | 163 15 _m 211 | 185 15 206 26 226 50 _c 212 | 246 74 264 102 280 136 _c 213 | 295 170 308 204 320 240 _c 214 | 332 275 340 305 346 330 _c 215 | }_e{142 330 _l 216 | 131 288 123 251 117 221 _c 217 | 111 191 109 161 109 132 _c 218 | 109 54 127 15 163 15 _c 219 | 150 365 _m 220 | 355 365 _l 221 | 362 394 368 418 372 438 _c 222 | 376 458 379 479 382 501 _c 223 | 385 523 387 543 387 562 _c 224 | 387 640 369 679 334 679 _c 225 | 292 679 255 645 224 577 _c 226 | 193 509 168 438 150 365 _c 227 | _cl}_e}_d 228 | /t{{361 0 22 -10 330 626 _sc 229 | 62 81 _m 230 | 62 91 63 100 65 109 _c 231 | 137 396 _l 232 | 32 396 _l 233 | 25 396 22 400 22 409 _c 234 | 24 423 29 431 35 431 _c 235 | 146 431 _l 236 | 186 594 _l 237 | 188 602 193 610 201 616 _c 238 | 209 622 218 626 228 626 _c 239 | 236 626 243 623 249 618 _c 240 | 255 613 258 606 258 598 _c 241 | 258 596 257 594 257 593 _c 242 | 257 592 257 591 257 590 _c 243 | 217 431 _l 244 | 320 431 _l 245 | 326 431 330 426 330 418 _c 246 | }_e{330 416 329 414 328 410 _c 247 | 327 406 326 402 324 400 _c 248 | 322 397 320 396 317 396 _c 249 | 208 396 _l 250 | 136 107 _l 251 | 131 88 129 72 129 58 _c 252 | 129 29 138 15 158 15 _c 253 | 187 15 213 28 236 56 _c 254 | 258 84 276 114 288 147 _c 255 | 290 151 293 153 296 153 _c 256 | 308 153 _l 257 | 310 153 312 152 314 150 _c 258 | 316 148 317 146 317 144 _c 259 | 317 142 316 141 316 141 _c 260 | 301 101 280 65 252 35 _c 261 | }_e{224 5 192 -10 156 -10 _c 262 | 129 -10 107 -1 89 15 _c 263 | 71 32 62 54 62 81 _c 264 | _cl}_e}_d 265 | /Q{{790 0 50 -193 739 705 _sc 266 | 304 -21 _m 267 | 254 -21 209 -9 171 13 _c 268 | 132 35 102 67 81 108 _c 269 | 60 148 50 194 50 244 _c 270 | 50 316 70 389 111 461 _c 271 | 152 533 206 591 274 637 _c 272 | 341 682 412 705 486 705 _c 273 | 524 705 558 698 590 684 _c 274 | 622 670 648 651 670 627 _c 275 | 692 603 709 574 721 542 _c 276 | 733 510 739 474 739 436 _c 277 | 739 392 731 347 716 302 _c 278 | 700 257 679 215 652 177 _c 279 | }_e{624 139 592 105 556 76 _c 280 | 519 46 480 23 439 6 _c 281 | 443 -24 449 -47 458 -65 _c 282 | 467 -83 484 -92 509 -92 _c 283 | 535 -92 559 -82 582 -63 _c 284 | 605 -44 620 -22 626 2 _c 285 | 627 8 631 11 637 11 _c 286 | 644 11 648 7 648 -1 _c 287 | 643 -22 636 -44 626 -66 _c 288 | 616 -88 605 -108 591 -127 _c 289 | 577 -146 561 -162 543 -174 _c 290 | 525 -186 504 -193 482 -193 _c 291 | 426 -193 398 -157 398 -85 _c 292 | }_e{398 -81 398 -69 400 -51 _c 293 | 402 -32 403 -17 403 -6 _c 294 | 370 -16 337 -21 304 -21 _c 295 | 267 47 _m 296 | 267 20 281 7 311 7 _c 297 | 340 7 371 14 405 29 _c 298 | 405 38 _l 299 | 405 65 400 86 392 101 _c 300 | 383 116 367 124 343 124 _c 301 | 331 124 319 120 307 113 _c 302 | 295 105 285 96 278 84 _c 303 | 270 72 267 59 267 47 _c 304 | 241 45 _m 305 | 241 62 246 79 256 95 _c 306 | 266 111 278 125 294 135 _c 307 | }_e{309 145 326 150 344 150 _c 308 | 373 150 394 140 407 120 _c 309 | 420 100 429 75 434 44 _c 310 | 476 69 514 105 547 153 _c 311 | 579 200 604 252 621 308 _c 312 | 638 364 647 418 647 469 _c 313 | 647 505 640 539 628 571 _c 314 | 616 602 597 627 572 647 _c 315 | 547 666 516 676 479 676 _c 316 | 443 676 408 667 375 649 _c 317 | 342 631 311 608 283 579 _c 318 | 255 551 231 516 209 474 _c 319 | 187 432 171 388 159 342 _c 320 | }_e{147 296 142 253 142 212 _c 321 | 142 169 150 130 167 95 _c 322 | 183 60 209 35 245 20 _c 323 | 242 26 241 35 241 45 _c 324 | _cl}_e}_d 325 | /f{{489 0 53 -204 552 705 _sc 326 | 97 -164 _m 327 | 109 -173 124 -178 142 -178 _c 328 | 166 -178 185 -151 200 -99 _c 329 | 206 -73 223 9 251 151 _c 330 | 297 396 _l 331 | 211 396 _l 332 | 204 396 201 400 201 409 _c 333 | 203 423 208 431 214 431 _c 334 | 303 431 _l 335 | 315 496 _l 336 | 319 516 322 533 326 548 _c 337 | 329 562 332 576 336 588 _c 338 | 340 600 345 614 353 630 _c 339 | 364 652 379 670 399 684 _c 340 | 418 698 439 705 462 705 _c 341 | 476 705 490 702 504 697 _c 342 | }_e{518 691 529 683 538 673 _c 343 | 547 662 552 649 552 635 _c 344 | 552 617 546 602 535 590 _c 345 | 523 578 510 572 494 572 _c 346 | 483 572 474 575 466 582 _c 347 | 458 588 455 597 455 608 _c 348 | 455 622 460 635 470 646 _c 349 | 480 657 492 663 507 665 _c 350 | 494 674 479 679 461 679 _c 351 | 451 679 441 674 432 665 _c 352 | 423 655 417 645 415 635 _c 353 | 411 617 401 571 387 497 _c 354 | 375 431 _l 355 | 478 431 _l 356 | 484 431 488 426 488 418 _c 357 | }_e{487 416 486 413 485 409 _c 358 | 484 405 483 401 481 399 _c 359 | 479 397 477 396 475 396 _c 360 | 368 396 _l 361 | 322 152 _l 362 | 316 116 309 80 301 44 _c 363 | 293 8 283 -29 269 -68 _c 364 | 255 -106 238 -139 216 -165 _c 365 | 194 -191 169 -204 140 -204 _c 366 | 117 -204 97 -197 79 -185 _c 367 | 61 -172 53 -155 53 -134 _c 368 | 53 -116 58 -101 69 -89 _c 369 | 80 -77 94 -71 111 -71 _c 370 | 121 -71 130 -74 138 -81 _c 371 | 146 -87 150 -96 150 -107 _c 372 | }_e{150 -121 144 -134 134 -146 _c 373 | 123 -158 111 -164 97 -164 _c 374 | _cl}_e}_d 375 | end readonly def 376 | 377 | /BuildGlyph 378 | {exch begin 379 | CharStrings exch 380 | 2 copy known not{pop /.notdef}if 381 | true 3 1 roll get exec 382 | end}_d 383 | 384 | /BuildChar { 385 | 1 index /Encoding get exch get 386 | 1 index /BuildGlyph get exec 387 | }_d 388 | 389 | FontName currentdict end definefont pop 390 | %!PS-Adobe-3.0 Resource-Font 391 | %%Title: cmr10 392 | %%Copyright: Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. 393 | %%Creator: Converted from TrueType to type 3 by PPR 394 | 25 dict begin 395 | /_d{bind def}bind def 396 | /_m{moveto}_d 397 | /_l{lineto}_d 398 | /_cl{closepath eofill}_d 399 | /_c{curveto}_d 400 | /_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d 401 | /_e{exec}_d 402 | /FontName /Cmr10 def 403 | /PaintType 0 def 404 | /FontMatrix[.001 0 0 .001 0 0]def 405 | /FontBBox[-44 -250 1009 750]def 406 | /FontType 3 def 407 | /Encoding [ /equal /parenright /parenleft ] def 408 | /FontInfo 10 dict dup begin 409 | /FamilyName (cmr10) def 410 | /FullName (cmr10) def 411 | /Notice (Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. ) def 412 | /Weight (Regular) def 413 | /Version (1.1/12-Nov-94) def 414 | /ItalicAngle 0.0 def 415 | /isFixedPitch false def 416 | /UnderlinePosition -133 def 417 | /UnderlineThickness 20 def 418 | end readonly def 419 | /CharStrings 3 dict dup begin 420 | /equal{{777 0 56 133 721 367 _sc 421 | 75 133 _m 422 | 69 133 65 135 61 139 _c 423 | 57 143 56 148 56 153 _c 424 | 56 158 57 163 61 167 _c 425 | 65 171 69 173 75 173 _c 426 | 703 173 _l 427 | 707 173 711 171 715 167 _c 428 | 719 163 721 158 721 153 _c 429 | 721 148 719 143 715 139 _c 430 | 711 135 707 133 703 133 _c 431 | 75 133 _l 432 | 75 327 _m 433 | 69 327 65 329 61 333 _c 434 | 57 337 56 341 56 347 _c 435 | 56 351 57 356 61 360 _c 436 | }_e{65 364 69 367 75 367 _c 437 | 703 367 _l 438 | 707 367 711 364 715 360 _c 439 | 719 356 721 351 721 347 _c 440 | 721 341 719 337 715 333 _c 441 | 711 329 707 327 703 327 _c 442 | 75 327 _l 443 | _cl}_e}_d 444 | /parenright{{388 0 56 -249 291 750 _sc 445 | 65 -249 _m 446 | 59 -249 56 -246 56 -240 _c 447 | 56 -237 56 -235 58 -234 _c 448 | 172 -122 229 38 229 250 _c 449 | 229 462 172 623 60 733 _c 450 | 57 734 56 737 56 741 _c 451 | 56 743 57 745 59 747 _c 452 | 61 749 63 750 65 750 _c 453 | 74 750 _l 454 | 76 750 77 749 79 748 _c 455 | 127 710 167 664 199 610 _c 456 | 231 556 254 498 269 437 _c 457 | 283 376 291 314 291 250 _c 458 | 291 202 287 156 279 110 _c 459 | }_e{271 64 258 20 241 -24 _c 460 | 223 -68 201 -108 175 -146 _c 461 | 148 -184 116 -217 79 -247 _c 462 | 77 -248 76 -249 74 -249 _c 463 | 65 -249 _l 464 | _cl}_e}_d 465 | /parenleft{{388 0 97 -249 332 750 _sc 466 | 310 -247 _m 467 | 272 -217 240 -184 214 -146 _c 468 | 187 -108 165 -67 148 -25 _c 469 | 131 17 118 62 110 109 _c 470 | 101 155 97 202 97 250 _c 471 | 97 298 101 345 110 392 _c 472 | 118 438 131 483 149 527 _c 473 | 166 570 188 611 215 649 _c 474 | 242 687 274 720 310 748 _c 475 | 310 749 311 750 315 750 _c 476 | 324 750 _l 477 | 326 750 327 749 329 747 _c 478 | 331 745 332 743 332 741 _c 479 | 332 738 331 736 330 735 _c 480 | }_e{297 703 270 668 248 632 _c 481 | 226 596 209 557 196 516 _c 482 | 183 474 174 432 168 388 _c 483 | 162 344 159 298 159 250 _c 484 | 159 38 215 -122 329 -232 _c 485 | 331 -234 332 -236 332 -240 _c 486 | 332 -242 331 -244 329 -246 _c 487 | 327 -248 326 -249 324 -249 _c 488 | 315 -249 _l 489 | 311 -249 310 -248 310 -247 _c 490 | _cl}_e}_d 491 | end readonly def 492 | 493 | /BuildGlyph 494 | {exch begin 495 | CharStrings exch 496 | 2 copy known not{pop /.notdef}if 497 | true 3 1 roll get exec 498 | end}_d 499 | 500 | /BuildChar { 501 | 1 index /Encoding get exch get 502 | 1 index /BuildGlyph get exec 503 | }_d 504 | 505 | FontName currentdict end definefont pop 506 | %!PS-Adobe-3.0 Resource-Font 507 | %%Title: Bitstream Vera Sans 508 | %%Copyright: Copyright (c) 2003 by Bitstream, Inc. All Rights Reserved. 509 | %%Creator: Converted from TrueType to type 3 by PPR 510 | 25 dict begin 511 | /_d{bind def}bind def 512 | /_m{moveto}_d 513 | /_l{lineto}_d 514 | /_cl{closepath eofill}_d 515 | /_c{curveto}_d 516 | /_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d 517 | /_e{exec}_d 518 | /FontName /BitstreamVeraSans-Roman def 519 | /PaintType 0 def 520 | /FontMatrix[.001 0 0 .001 0 0]def 521 | /FontBBox[-183 -236 1287 928]def 522 | /FontType 3 def 523 | /Encoding [ /zero /one /two /three /four /five /minus ] def 524 | /FontInfo 10 dict dup begin 525 | /FamilyName (Bitstream Vera Sans) def 526 | /FullName (Bitstream Vera Sans) def 527 | /Notice (Copyright (c) 2003 by Bitstream, Inc. All Rights Reserved. Bitstream Vera is a trademark of Bitstream, Inc.) def 528 | /Weight (Roman) def 529 | /Version (Release 1.10) def 530 | /ItalicAngle 0.0 def 531 | /isFixedPitch false def 532 | /UnderlinePosition -213 def 533 | /UnderlineThickness 143 def 534 | end readonly def 535 | /CharStrings 7 dict dup begin 536 | /zero{636 0 66 -13 570 742 _sc 537 | 318 664 _m 538 | 267 664 229 639 203 589 _c 539 | 177 539 165 464 165 364 _c 540 | 165 264 177 189 203 139 _c 541 | 229 89 267 64 318 64 _c 542 | 369 64 407 89 433 139 _c 543 | 458 189 471 264 471 364 _c 544 | 471 464 458 539 433 589 _c 545 | 407 639 369 664 318 664 _c 546 | 318 742 _m 547 | 399 742 461 709 505 645 _c 548 | 548 580 570 486 570 364 _c 549 | 570 241 548 147 505 83 _c 550 | 461 19 399 -13 318 -13 _c 551 | 236 -13 173 19 130 83 _c 552 | 87 147 66 241 66 364 _c 553 | 66 486 87 580 130 645 _c 554 | 173 709 236 742 318 742 _c 555 | _cl}_d 556 | /one{636 0 110 0 544 729 _sc 557 | 124 83 _m 558 | 285 83 _l 559 | 285 639 _l 560 | 110 604 _l 561 | 110 694 _l 562 | 284 729 _l 563 | 383 729 _l 564 | 383 83 _l 565 | 544 83 _l 566 | 544 0 _l 567 | 124 0 _l 568 | 124 83 _l 569 | _cl}_d 570 | /two{{636 0 73 0 536 742 _sc 571 | 192 83 _m 572 | 536 83 _l 573 | 536 0 _l 574 | 73 0 _l 575 | 73 83 _l 576 | 110 121 161 173 226 239 _c 577 | 290 304 331 346 348 365 _c 578 | 380 400 402 430 414 455 _c 579 | 426 479 433 504 433 528 _c 580 | 433 566 419 598 392 622 _c 581 | 365 646 330 659 286 659 _c 582 | 255 659 222 653 188 643 _c 583 | 154 632 117 616 78 594 _c 584 | 78 694 _l 585 | 118 710 155 722 189 730 _c 586 | 223 738 255 742 284 742 _c 587 | }_e{359 742 419 723 464 685 _c 588 | 509 647 532 597 532 534 _c 589 | 532 504 526 475 515 449 _c 590 | 504 422 484 390 454 354 _c 591 | 446 344 420 317 376 272 _c 592 | 332 227 271 164 192 83 _c 593 | _cl}_e}_d 594 | /three{{636 0 76 -13 556 742 _sc 595 | 406 393 _m 596 | 453 383 490 362 516 330 _c 597 | 542 298 556 258 556 212 _c 598 | 556 140 531 84 482 45 _c 599 | 432 6 362 -13 271 -13 _c 600 | 240 -13 208 -10 176 -4 _c 601 | 144 1 110 10 76 22 _c 602 | 76 117 _l 603 | 103 101 133 89 166 81 _c 604 | 198 73 232 69 268 69 _c 605 | 330 69 377 81 409 105 _c 606 | 441 129 458 165 458 212 _c 607 | 458 254 443 288 413 312 _c 608 | 383 336 341 349 287 349 _c 609 | }_e{202 349 _l 610 | 202 430 _l 611 | 291 430 _l 612 | 339 430 376 439 402 459 _c 613 | 428 478 441 506 441 543 _c 614 | 441 580 427 609 401 629 _c 615 | 374 649 336 659 287 659 _c 616 | 260 659 231 656 200 650 _c 617 | 169 644 135 635 98 623 _c 618 | 98 711 _l 619 | 135 721 170 729 203 734 _c 620 | 235 739 266 742 296 742 _c 621 | 370 742 429 725 473 691 _c 622 | 517 657 539 611 539 553 _c 623 | 539 513 527 479 504 451 _c 624 | 481 423 448 403 406 393 _c 625 | _cl}_e}_d 626 | /four{636 0 49 0 580 729 _sc 627 | 378 643 _m 628 | 129 254 _l 629 | 378 254 _l 630 | 378 643 _l 631 | 352 729 _m 632 | 476 729 _l 633 | 476 254 _l 634 | 580 254 _l 635 | 580 172 _l 636 | 476 172 _l 637 | 476 0 _l 638 | 378 0 _l 639 | 378 172 _l 640 | 49 172 _l 641 | 49 267 _l 642 | 352 729 _l 643 | _cl}_d 644 | /five{{636 0 77 -13 549 729 _sc 645 | 108 729 _m 646 | 495 729 _l 647 | 495 646 _l 648 | 198 646 _l 649 | 198 467 _l 650 | 212 472 227 476 241 478 _c 651 | 255 480 270 482 284 482 _c 652 | 365 482 429 459 477 415 _c 653 | 525 370 549 310 549 234 _c 654 | 549 155 524 94 475 51 _c 655 | 426 8 357 -13 269 -13 _c 656 | 238 -13 207 -10 175 -6 _c 657 | 143 -1 111 6 77 17 _c 658 | 77 116 _l 659 | 106 100 136 88 168 80 _c 660 | 199 72 232 69 267 69 _c 661 | }_e{323 69 368 83 401 113 _c 662 | 433 143 450 183 450 234 _c 663 | 450 284 433 324 401 354 _c 664 | 368 384 323 399 267 399 _c 665 | 241 399 214 396 188 390 _c 666 | 162 384 135 375 108 363 _c 667 | 108 729 _l 668 | _cl}_e}_d 669 | /minus{838 0 106 272 732 355 _sc 670 | 106 355 _m 671 | 732 355 _l 672 | 732 272 _l 673 | 106 272 _l 674 | 106 355 _l 675 | _cl}_d 676 | end readonly def 677 | 678 | /BuildGlyph 679 | {exch begin 680 | CharStrings exch 681 | 2 copy known not{pop /.notdef}if 682 | true 3 1 roll get exec 683 | end}_d 684 | 685 | /BuildChar { 686 | 1 index /Encoding get exch get 687 | 1 index /BuildGlyph get exec 688 | }_d 689 | 690 | FontName currentdict end definefont pop 691 | end 692 | %%EndProlog 693 | mpldict begin 694 | 40.627 196.008 translate 695 | 530.747 399.984 0 0 clipbox 696 | 100000 setmiterlimit 697 | gsave 698 | 0 0 m 699 | 530.746875 0 l 700 | 530.746875 399.984375 l 701 | 0 399.984375 l 702 | cl 703 | 1.000 setgray 704 | fill 705 | grestore 706 | gsave 707 | 77.146875 47.184375 m 708 | 523.546875 47.184375 l 709 | 523.546875 392.784375 l 710 | 77.146875 392.784375 l 711 | cl 712 | 1.000 setgray 713 | fill 714 | grestore 715 | 1.000 setlinewidth 716 | 1 setlinejoin 717 | 2 setlinecap 718 | [] 0 setdash 719 | 0.000 0.000 1.000 setrgbcolor 720 | gsave 721 | 446.4 345.6 77.15 47.18 clipbox 722 | 77.146875 153.522837 m 723 | 82.016693 155.586858 l 724 | 86.886511 157.387387 l 725 | 91.75633 158.924425 l 726 | 96.626148 160.19797 l 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/Cmr10 findfont 1761 | 18.0 scalefont 1762 | setfont 1763 | 14.220703 0.500000 moveto 1764 | /parenleft glyphshow 1765 | 1766 | /Cmmi10 findfont 1767 | 18.0 scalefont 1768 | setfont 1769 | 21.208008 0.500000 moveto 1770 | /theta glyphshow 1771 | 1772 | /Cmsy10 findfont 1773 | 12.6 scalefont 1774 | setfont 1775 | 33.995358 7.387531 moveto 1776 | /asteriskmath glyphshow 1777 | 1778 | /Cmsy10 findfont 1779 | 18.0 scalefont 1780 | setfont 1781 | 43.655662 0.500000 moveto 1782 | /bar glyphshow 1783 | 1784 | /Cmmi10 findfont 1785 | 18.0 scalefont 1786 | setfont 1787 | 48.639061 0.500000 moveto 1788 | /theta glyphshow 1789 | 1790 | /Cmr10 findfont 1791 | 18.0 scalefont 1792 | setfont 1793 | 57.085350 0.500000 moveto 1794 | /parenright glyphshow 1795 | 1796 | 1797 | grestore 1798 | gsave 1799 | 433.455239 338.665931 translate 1800 | 0.000000 rotate 1801 | /Cmmi10 findfont 1802 | 18.0 scalefont 1803 | setfont 1804 | 0.000000 0.500000 moveto 1805 | /f glyphshow 1806 | 1807 | /Cmr10 findfont 1808 | 18.0 scalefont 1809 | setfont 1810 | 8.797852 0.500000 moveto 1811 | /parenleft glyphshow 1812 | 1813 | /Cmmi10 findfont 1814 | 18.0 scalefont 1815 | setfont 1816 | 15.785156 0.500000 moveto 1817 | /theta glyphshow 1818 | 1819 | /Cmsy10 findfont 1820 | 12.6 scalefont 1821 | setfont 1822 | 28.572506 7.387531 moveto 1823 | /asteriskmath glyphshow 1824 | 1825 | /Cmr10 findfont 1826 | 18.0 scalefont 1827 | setfont 1828 | 38.232811 0.500000 moveto 1829 | /parenright glyphshow 1830 | 1831 | 1832 | grestore 1833 | gsave 1834 | 101.495966 313.030529 translate 1835 | 0.000000 rotate 1836 | /Cmmi10 findfont 1837 | 18.0 scalefont 1838 | setfont 1839 | 0.000000 0.500000 moveto 1840 | /f glyphshow 1841 | 1842 | /Cmr10 findfont 1843 | 18.0 scalefont 1844 | setfont 1845 | 8.797852 0.500000 moveto 1846 | /parenleft glyphshow 1847 | 1848 | /Cmmi10 findfont 1849 | 18.0 scalefont 1850 | setfont 1851 | 15.785156 0.500000 moveto 1852 | /theta glyphshow 1853 | 1854 | /Cmr10 findfont 1855 | 18.0 scalefont 1856 | setfont 1857 | 24.231445 0.500000 moveto 1858 | /parenright glyphshow 1859 | 1860 | 34.379297 0.500000 moveto 1861 | /equal glyphshow 1862 | 1863 | /Cmmi10 findfont 1864 | 18.0 scalefont 1865 | setfont 1866 | 51.523242 0.500000 moveto 1867 | /Q glyphshow 1868 | 1869 | /Cmr10 findfont 1870 | 18.0 scalefont 1871 | setfont 1872 | 65.743945 0.500000 moveto 1873 | /parenleft glyphshow 1874 | 1875 | /Cmmi10 findfont 1876 | 18.0 scalefont 1877 | setfont 1878 | 72.731250 0.500000 moveto 1879 | /theta glyphshow 1880 | 1881 | /Cmsy10 findfont 1882 | 18.0 scalefont 1883 | setfont 1884 | 81.177539 0.500000 moveto 1885 | /bar glyphshow 1886 | 1887 | /Cmmi10 findfont 1888 | 18.0 scalefont 1889 | setfont 1890 | 86.160938 0.500000 moveto 1891 | /theta glyphshow 1892 | 1893 | /Cmr10 findfont 1894 | 18.0 scalefont 1895 | setfont 1896 | 94.607227 0.500000 moveto 1897 | /parenright glyphshow 1898 | 1899 | /Cmsy10 findfont 1900 | 18.0 scalefont 1901 | setfont 1902 | 104.755078 0.500000 moveto 1903 | /lessequal glyphshow 1904 | 1905 | /Cmmi10 findfont 1906 | 18.0 scalefont 1907 | setfont 1908 | 121.899023 0.500000 moveto 1909 | /Q glyphshow 1910 | 1911 | /Cmr10 findfont 1912 | 18.0 scalefont 1913 | setfont 1914 | 136.119727 0.500000 moveto 1915 | /parenleft glyphshow 1916 | 1917 | /Cmmi10 findfont 1918 | 18.0 scalefont 1919 | setfont 1920 | 143.107031 0.500000 moveto 1921 | /theta glyphshow 1922 | 1923 | /Cmsy10 findfont 1924 | 12.6 scalefont 1925 | setfont 1926 | 155.894381 7.387531 moveto 1927 | /asteriskmath glyphshow 1928 | 1929 | /Cmsy10 findfont 1930 | 18.0 scalefont 1931 | setfont 1932 | 165.554686 0.500000 moveto 1933 | /bar glyphshow 1934 | 1935 | /Cmmi10 findfont 1936 | 18.0 scalefont 1937 | setfont 1938 | 170.538084 0.500000 moveto 1939 | /theta glyphshow 1940 | 1941 | /Cmr10 findfont 1942 | 18.0 scalefont 1943 | setfont 1944 | 178.984373 0.500000 moveto 1945 | /parenright glyphshow 1946 | 1947 | /Cmsy10 findfont 1948 | 18.0 scalefont 1949 | setfont 1950 | 189.132225 0.500000 moveto 1951 | /lessequal glyphshow 1952 | 1953 | /Cmmi10 findfont 1954 | 18.0 scalefont 1955 | setfont 1956 | 206.276170 0.500000 moveto 1957 | /f glyphshow 1958 | 1959 | /Cmr10 findfont 1960 | 18.0 scalefont 1961 | setfont 1962 | 215.074022 0.500000 moveto 1963 | /parenleft glyphshow 1964 | 1965 | /Cmmi10 findfont 1966 | 18.0 scalefont 1967 | setfont 1968 | 222.061327 0.500000 moveto 1969 | /theta glyphshow 1970 | 1971 | /Cmsy10 findfont 1972 | 12.6 scalefont 1973 | setfont 1974 | 234.848677 7.387531 moveto 1975 | /asteriskmath glyphshow 1976 | 1977 | /Cmr10 findfont 1978 | 18.0 scalefont 1979 | setfont 1980 | 244.508981 0.500000 moveto 1981 | /parenright glyphshow 1982 | 1983 | 1984 | grestore 1985 | 1986 | end 1987 | showpage 1988 | -------------------------------------------------------------------------------- /minorization.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 1, 6 | "metadata": { 7 | "collapsed": true 8 | }, 9 | "outputs": [], 10 | "source": [ 11 | "import matplotlib.pyplot as plt\n", 12 | "import numpy as np\n", 13 | "from scipy.interpolate import interp1d" 14 | ] 15 | }, 16 | { 17 | "cell_type": "code", 18 | "execution_count": 52, 19 | "metadata": { 20 | "collapsed": false 21 | }, 22 | "outputs": [], 23 | "source": [ 24 | "x1 = np.array([0,1,3,4,5.5])\n", 25 | "y1 = np.array([1,1,2,4,5])\n", 26 | "f1 = interp1d(x1, y1, kind=2)\n", 27 | "x2 = np.array([0,2,3,5.5])\n", 28 | "y2 = np.array([-3,0,2,3])\n", 29 | "f2 = interp1d(x2, y2, kind=2)\n", 30 | "\n", 31 | "x = np.arange(0, 5.5, 0.01)\n", 32 | "fx = np.maximum(f1(x), f2(x))\n", 33 | "Qx = np.minimum(f1(x), f2(x))\n", 34 | "\n", 35 | "plt.axis([0,5.5,-1,5.5])\n", 36 | "\n", 37 | "tangp = (3,2)\n", 38 | "\n", 39 | "idx = np.argmax(Qx)\n", 40 | "maxQ = (x[idx], Qx[idx])\n", 41 | "\n", 42 | "f_star = (x[idx], fx[idx])\n", 43 | "\n", 44 | "plt.xlabel(r'$t$', fontsize=20)\n", 45 | "plt.ylabel(r'$f(t)$' + '\\n' + r'$Q(t|\\theta)$', fontsize=20)\n", 46 | "\n", 47 | "plt.plot(x, fx)\n", 48 | "plt.plot(x, Qx)\n", 49 | "plt.plot(*tangp, 'ro')\n", 50 | "plt.plot(*maxQ, 'ro')\n", 51 | "plt.plot(*f_star, 'ro')\n", 52 | "\n", 53 | "plt.text(0.5, 1.4, r'$f$', fontsize=18)\n", 54 | "plt.text(2.05, -0.2, r'$Q$', fontsize=18)\n", 55 | "plt.text(tangp[0]-1.4, tangp[1]-0.05, r'$Q(\\theta|\\theta)=f(\\theta)$', fontsize=18)\n", 56 | "plt.text(maxQ[0]-0.4, maxQ[1]-0.5, r'$Q(\\theta^*|\\theta)$', fontsize=18)\n", 57 | "plt.text(f_star[0]-0.2, f_star[1]-0.5, r'$f(\\theta^*)$', fontsize=18)\n", 58 | "plt.text(0.3, 4, r'$f(\\theta) = Q(\\theta|\\theta)\\leq Q(\\theta^*|\\theta)\\leq f(\\theta^*)$', fontsize=18)\n", 59 | "\n", 60 | "plt.savefig('minorization.eps', bbox_inches='tight')\n", 61 | "plt.show()" 62 | ] 63 | } 64 | ], 65 | "metadata": { 66 | "kernelspec": { 67 | "display_name": "Python 3", 68 | "language": "python", 69 | "name": "python3" 70 | }, 71 | "language_info": { 72 | "codemirror_mode": { 73 | "name": "ipython", 74 | "version": 3 75 | }, 76 | "file_extension": ".py", 77 | "mimetype": "text/x-python", 78 | "name": "python", 79 | "nbconvert_exporter": "python", 80 | "pygments_lexer": "ipython3", 81 | "version": "3.5.1" 82 | } 83 | }, 84 | "nbformat": 4, 85 | "nbformat_minor": 0 86 | } 87 | -------------------------------------------------------------------------------- /venn1.eps: -------------------------------------------------------------------------------- 1 | %!PS-Adobe-3.0 EPSF-3.0 2 | %%Title: venn1.eps 3 | %%Creator: matplotlib version 1.5.1, http://matplotlib.org/ 4 | %%CreationDate: Sun May 29 01:55:13 2016 5 | %%Orientation: portrait 6 | %%BoundingBox: 75 233 536 558 7 | %%EndComments 8 | %%BeginProlog 9 | /mpldict 11 dict def 10 | mpldict begin 11 | /m { moveto } bind def 12 | /l { lineto } bind def 13 | /r { rlineto } bind def 14 | /c { curveto } bind def 15 | /cl { closepath } bind def 16 | /box { 17 | m 18 | 1 index 0 r 19 | 0 exch r 20 | neg 0 r 21 | cl 22 | } bind def 23 | /clipbox { 24 | box 25 | clip 26 | newpath 27 | } bind def 28 | %!PS-Adobe-3.0 Resource-Font 29 | %%Title: cmmi10 30 | %%Copyright: Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. 31 | %%Creator: Converted from TrueType to type 3 by PPR 32 | 25 dict begin 33 | /_d{bind def}bind def 34 | /_m{moveto}_d 35 | /_l{lineto}_d 36 | /_cl{closepath eofill}_d 37 | /_c{curveto}_d 38 | /_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d 39 | /_e{exec}_d 40 | /FontName /Cmmi10 def 41 | /PaintType 0 def 42 | /FontMatrix[.001 0 0 .001 0 0]def 43 | /FontBBox[-34 -250 1048 750]def 44 | /FontType 3 def 45 | /Encoding [ /B /H /A /I ] def 46 | /FontInfo 10 dict dup begin 47 | /FamilyName (cmmi10) def 48 | /FullName (cmmi10) def 49 | /Notice (Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. ) def 50 | /Weight (Regular) def 51 | /Version (1.1/12-Nov-94) def 52 | /ItalicAngle 0.0 def 53 | /isFixedPitch false def 54 | /UnderlinePosition -133 def 55 | /UnderlineThickness 20 def 56 | end readonly def 57 | /CharStrings 4 dict dup begin 58 | /B{{758 0 40 0 756 683 _sc 59 | 50 0 _m 60 | 43 0 40 4 40 13 _c 61 | 40 15 41 17 42 21 _c 62 | 42 25 43 28 45 31 _c 63 | 47 33 49 35 53 35 _c 64 | 72 35 89 35 103 36 _c 65 | 117 37 128 39 138 42 _c 66 | 146 44 152 53 157 69 _c 67 | 294 618 _l 68 | 295 624 296 629 296 632 _c 69 | 296 639 292 643 284 644 _c 70 | 271 646 247 648 212 648 _c 71 | 205 648 202 652 202 661 _c 72 | 202 663 203 666 204 670 _c 73 | }_e{205 674 206 677 208 679 _c 74 | 210 681 212 683 215 683 _c 75 | 573 683 _l 76 | 595 683 616 680 638 675 _c 77 | 659 669 679 661 697 649 _c 78 | 715 637 729 623 740 606 _c 79 | 750 588 756 568 756 545 _c 80 | 756 519 749 496 736 475 _c 81 | 723 453 706 435 686 419 _c 82 | 666 403 644 389 620 379 _c 83 | 596 369 572 361 547 357 _c 84 | 565 357 583 353 602 346 _c 85 | 620 338 637 328 652 316 _c 86 | 666 304 678 289 687 272 _c 87 | }_e{696 255 701 237 701 217 _c 88 | 701 177 687 140 659 107 _c 89 | 631 73 595 47 553 28 _c 90 | 511 9 470 0 430 0 _c 91 | 50 0 _l 92 | 234 43 _m 93 | 234 37 245 35 268 35 _c 94 | 411 35 _l 95 | 443 35 475 44 505 62 _c 96 | 535 80 559 104 577 134 _c 97 | 595 164 604 195 604 228 _c 98 | 604 248 599 266 591 284 _c 99 | 583 302 571 316 555 326 _c 100 | 539 336 522 342 502 342 _c 101 | 307 342 _l 102 | 238 65 _l 103 | }_e{235 55 234 48 234 43 _c 104 | 314 368 _m 105 | 466 368 _l 106 | 498 368 529 376 559 392 _c 107 | 589 408 613 431 632 459 _c 108 | 651 487 661 516 661 548 _c 109 | 661 576 652 600 634 619 _c 110 | 616 638 592 648 564 648 _c 111 | 427 648 _l 112 | 409 648 396 646 390 643 _c 113 | 384 639 379 630 375 614 _c 114 | 314 368 _l 115 | _cl}_e}_d 116 | /H{{831 0 37 0 883 683 _sc 117 | 47 0 _m 118 | 40 0 37 4 37 13 _c 119 | 37 15 38 18 39 22 _c 120 | 40 26 41 29 43 31 _c 121 | 45 33 47 35 50 35 _c 122 | 90 35 119 37 135 42 _c 123 | 143 44 150 53 154 69 _c 124 | 291 618 _l 125 | 292 624 293 629 293 632 _c 126 | 293 639 289 643 281 644 _c 127 | 268 646 244 648 209 648 _c 128 | 202 648 199 652 199 661 _c 129 | 201 669 203 675 205 678 _c 130 | 206 681 210 683 216 683 _c 131 | }_e{485 683 _l 132 | 491 683 495 678 495 670 _c 133 | 495 668 494 665 493 661 _c 134 | 492 657 491 654 489 652 _c 135 | 487 649 485 648 482 648 _c 136 | 441 648 413 645 397 641 _c 137 | 388 637 382 628 378 614 _c 138 | 318 373 _l 139 | 618 373 _l 140 | 679 618 _l 141 | 680 624 681 629 681 632 _c 142 | 681 639 677 643 669 644 _c 143 | 656 646 632 648 597 648 _c 144 | 590 648 587 652 587 661 _c 145 | 589 669 590 675 592 678 _c 146 | 593 681 597 683 604 683 _c 147 | }_e{873 683 _l 148 | 879 683 883 678 883 670 _c 149 | 882 668 881 665 880 661 _c 150 | 879 657 878 653 876 651 _c 151 | 874 649 872 648 870 648 _c 152 | 829 648 801 645 785 641 _c 153 | 776 638 770 629 766 614 _c 154 | 629 65 _l 155 | 627 58 627 53 627 51 _c 156 | 627 44 631 40 639 39 _c 157 | 651 36 675 35 711 35 _c 158 | 717 35 721 30 721 22 _c 159 | 719 14 717 8 715 5 _c 160 | 713 1 709 0 704 0 _c 161 | 435 0 _l 162 | }_e{428 0 425 4 425 13 _c 163 | 426 18 427 22 428 24 _c 164 | 428 26 429 28 431 31 _c 165 | 433 33 435 35 438 35 _c 166 | 478 35 507 37 523 42 _c 167 | 531 44 538 53 542 69 _c 168 | 609 338 _l 169 | 309 338 _l 170 | 241 65 _l 171 | 239 57 239 52 239 51 _c 172 | 239 44 243 40 251 39 _c 173 | 263 36 287 35 323 35 _c 174 | 329 35 333 30 333 22 _c 175 | 331 13 329 7 327 4 _c 176 | 325 1 322 0 316 0 _c 177 | 47 0 _l 178 | _cl}_e}_d 179 | /A{{750 0 35 0 723 716 _sc 180 | 45 0 _m 181 | 38 0 35 4 35 13 _c 182 | 37 27 42 35 48 35 _c 183 | 74 35 97 40 117 51 _c 184 | 137 61 154 78 169 101 _c 185 | 170 102 171 103 171 103 _c 186 | 528 705 _l 187 | 533 712 539 716 547 716 _c 188 | 560 716 _l 189 | 562 716 564 715 566 714 _c 190 | 568 713 569 712 571 710 _c 191 | 572 708 573 707 573 705 _c 192 | 634 59 _l 193 | 634 56 635 52 638 46 _c 194 | 644 38 669 35 713 35 _c 195 | }_e{719 35 723 30 723 22 _c 196 | 721 13 719 7 717 4 _c 197 | 715 1 712 0 706 0 _c 198 | 456 0 _l 199 | 450 0 447 4 447 13 _c 200 | 450 27 454 35 460 35 _c 201 | 512 35 540 44 544 62 _c 202 | 529 227 _l 203 | 282 227 _l 204 | 202 93 _l 205 | 197 85 195 77 195 68 _c 206 | 195 56 200 47 212 42 _c 207 | 223 37 235 35 249 35 _c 208 | 255 35 259 30 259 22 _c 209 | 256 12 254 6 253 4 _c 210 | 251 1 248 0 242 0 _c 211 | }_e{45 0 _l 212 | 302 262 _m 213 | 525 262 _l 214 | 495 586 _l 215 | 302 262 _l 216 | _cl}_e}_d 217 | /I{{439 0 32 0 500 683 _sc 218 | 42 0 _m 219 | 35 0 32 4 32 13 _c 220 | 34 27 39 35 45 35 _c 221 | 84 35 111 36 125 39 _c 222 | 140 42 150 52 154 69 _c 223 | 291 618 _l 224 | 292 624 293 629 293 631 _c 225 | 293 635 292 638 290 640 _c 226 | 288 642 284 643 280 644 _c 227 | 266 646 241 648 204 648 _c 228 | 197 648 194 652 194 661 _c 229 | 196 669 197 675 199 678 _c 230 | 200 681 204 683 211 683 _c 231 | 490 683 _l 232 | }_e{496 683 500 678 500 670 _c 233 | 500 668 499 665 498 661 _c 234 | 497 657 496 654 494 652 _c 235 | 492 649 490 648 487 648 _c 236 | 447 648 420 646 406 644 _c 237 | 391 640 382 630 378 614 _c 238 | 241 65 _l 239 | 239 57 239 52 239 52 _c 240 | 239 50 239 48 239 47 _c 241 | 239 45 240 44 242 43 _c 242 | 244 42 245 41 247 41 _c 243 | 248 40 250 39 252 39 _c 244 | 264 36 290 35 328 35 _c 245 | 334 35 338 30 338 22 _c 246 | }_e{335 12 333 6 332 4 _c 247 | 331 1 327 0 321 0 _c 248 | 42 0 _l 249 | _cl}_e}_d 250 | end readonly def 251 | 252 | /BuildGlyph 253 | {exch begin 254 | CharStrings exch 255 | 2 copy known not{pop /.notdef}if 256 | true 3 1 roll get exec 257 | end}_d 258 | 259 | /BuildChar { 260 | 1 index /Encoding get exch get 261 | 1 index /BuildGlyph get exec 262 | }_d 263 | 264 | FontName currentdict end definefont pop 265 | %!PS-Adobe-3.0 Resource-Font 266 | %%Title: cmr10 267 | %%Copyright: Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. 268 | %%Creator: Converted from TrueType to type 3 by PPR 269 | 25 dict begin 270 | /_d{bind def}bind def 271 | /_m{moveto}_d 272 | /_l{lineto}_d 273 | /_cl{closepath eofill}_d 274 | /_c{curveto}_d 275 | /_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d 276 | /_e{exec}_d 277 | /FontName /Cmr10 def 278 | /PaintType 0 def 279 | /FontMatrix[.001 0 0 .001 0 0]def 280 | /FontBBox[-44 -250 1009 750]def 281 | /FontType 3 def 282 | /Encoding [ /semicolon /parenright /parenleft ] def 283 | /FontInfo 10 dict dup begin 284 | /FamilyName (cmr10) def 285 | /FullName (cmr10) def 286 | /Notice (Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. ) def 287 | /Weight (Regular) def 288 | /Version (1.1/12-Nov-94) def 289 | /ItalicAngle 0.0 def 290 | /isFixedPitch false def 291 | /UnderlinePosition -133 def 292 | /UnderlineThickness 20 def 293 | end readonly def 294 | /CharStrings 3 dict dup begin 295 | /semicolon{{277 0 84 -193 197 431 _sc 296 | 99 -179 _m 297 | 99 -176 99 -174 101 -173 _c 298 | 147 -122 171 -63 171 4 _c 299 | 171 9 _l 300 | 161 3 150 0 139 0 _c 301 | 123 0 110 5 100 16 _c 302 | 89 26 84 39 84 55 _c 303 | 84 71 89 84 100 94 _c 304 | 110 104 123 110 139 110 _c 305 | 162 110 177 99 185 78 _c 306 | 193 56 197 32 197 4 _c 307 | 197 -18 194 -41 188 -64 _c 308 | 182 -87 174 -109 162 -131 _c 309 | 150 -153 137 -172 121 -190 _c 310 | }_e{119 -192 116 -193 114 -193 _c 311 | 110 -193 107 -191 104 -188 _c 312 | 100 -185 99 -182 99 -179 _c 313 | 84 376 _m 314 | 84 385 86 394 91 403 _c 315 | 96 411 103 418 112 423 _c 316 | 120 428 129 431 139 431 _c 317 | 148 431 157 428 166 423 _c 318 | 174 418 181 411 186 403 _c 319 | 191 394 194 385 194 376 _c 320 | 194 361 188 348 178 337 _c 321 | 167 326 154 321 139 321 _c 322 | 124 321 111 326 100 337 _c 323 | 89 348 84 361 84 376 _c 324 | _cl}_e}_d 325 | /parenright{{388 0 56 -249 291 750 _sc 326 | 65 -249 _m 327 | 59 -249 56 -246 56 -240 _c 328 | 56 -237 56 -235 58 -234 _c 329 | 172 -122 229 38 229 250 _c 330 | 229 462 172 623 60 733 _c 331 | 57 734 56 737 56 741 _c 332 | 56 743 57 745 59 747 _c 333 | 61 749 63 750 65 750 _c 334 | 74 750 _l 335 | 76 750 77 749 79 748 _c 336 | 127 710 167 664 199 610 _c 337 | 231 556 254 498 269 437 _c 338 | 283 376 291 314 291 250 _c 339 | 291 202 287 156 279 110 _c 340 | }_e{271 64 258 20 241 -24 _c 341 | 223 -68 201 -108 175 -146 _c 342 | 148 -184 116 -217 79 -247 _c 343 | 77 -248 76 -249 74 -249 _c 344 | 65 -249 _l 345 | _cl}_e}_d 346 | /parenleft{{388 0 97 -249 332 750 _sc 347 | 310 -247 _m 348 | 272 -217 240 -184 214 -146 _c 349 | 187 -108 165 -67 148 -25 _c 350 | 131 17 118 62 110 109 _c 351 | 101 155 97 202 97 250 _c 352 | 97 298 101 345 110 392 _c 353 | 118 438 131 483 149 527 _c 354 | 166 570 188 611 215 649 _c 355 | 242 687 274 720 310 748 _c 356 | 310 749 311 750 315 750 _c 357 | 324 750 _l 358 | 326 750 327 749 329 747 _c 359 | 331 745 332 743 332 741 _c 360 | 332 738 331 736 330 735 _c 361 | }_e{297 703 270 668 248 632 _c 362 | 226 596 209 557 196 516 _c 363 | 183 474 174 432 168 388 _c 364 | 162 344 159 298 159 250 _c 365 | 159 38 215 -122 329 -232 _c 366 | 331 -234 332 -236 332 -240 _c 367 | 332 -242 331 -244 329 -246 _c 368 | 327 -248 326 -249 324 -249 _c 369 | 315 -249 _l 370 | 311 -249 310 -248 310 -247 _c 371 | _cl}_e}_d 372 | end readonly def 373 | 374 | /BuildGlyph 375 | {exch begin 376 | CharStrings exch 377 | 2 copy known not{pop /.notdef}if 378 | true 3 1 roll get exec 379 | end}_d 380 | 381 | /BuildChar { 382 | 1 index /Encoding get exch get 383 | 1 index /BuildGlyph get exec 384 | }_d 385 | 386 | FontName currentdict end definefont pop 387 | %!PS-Adobe-3.0 Resource-Font 388 | %%Title: Bitstream Vera Sans 389 | %%Copyright: Copyright (c) 2003 by Bitstream, Inc. All Rights Reserved. 390 | %%Creator: Converted from TrueType to type 3 by PPR 391 | 25 dict begin 392 | /_d{bind def}bind def 393 | /_m{moveto}_d 394 | /_l{lineto}_d 395 | /_cl{closepath eofill}_d 396 | /_c{curveto}_d 397 | /_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d 398 | /_e{exec}_d 399 | /FontName /BitstreamVeraSans-Roman def 400 | /PaintType 0 def 401 | /FontMatrix[.001 0 0 .001 0 0]def 402 | /FontBBox[-183 -236 1287 928]def 403 | /FontType 3 def 404 | /Encoding [ /A /B ] def 405 | /FontInfo 10 dict dup begin 406 | /FamilyName (Bitstream Vera Sans) def 407 | /FullName (Bitstream Vera Sans) def 408 | /Notice (Copyright (c) 2003 by Bitstream, Inc. All Rights Reserved. Bitstream Vera is a trademark of Bitstream, Inc.) def 409 | /Weight (Roman) def 410 | /Version (Release 1.10) def 411 | /ItalicAngle 0.0 def 412 | /isFixedPitch false def 413 | /UnderlinePosition -213 def 414 | /UnderlineThickness 143 def 415 | end readonly def 416 | /CharStrings 2 dict dup begin 417 | /A{684 0 8 0 676 729 _sc 418 | 342 632 _m 419 | 208 269 _l 420 | 476 269 _l 421 | 342 632 _l 422 | 286 729 _m 423 | 398 729 _l 424 | 676 0 _l 425 | 573 0 _l 426 | 507 187 _l 427 | 178 187 _l 428 | 112 0 _l 429 | 8 0 _l 430 | 286 729 _l 431 | _cl}_d 432 | /B{{686 0 98 0 615 729 _sc 433 | 197 348 _m 434 | 197 81 _l 435 | 355 81 _l 436 | 408 81 447 92 473 114 _c 437 | 498 136 511 169 511 215 _c 438 | 511 260 498 293 473 315 _c 439 | 447 337 408 348 355 348 _c 440 | 197 348 _l 441 | 197 648 _m 442 | 197 428 _l 443 | 343 428 _l 444 | 391 428 426 437 450 455 _c 445 | 474 473 486 500 486 538 _c 446 | 486 574 474 602 450 620 _c 447 | 426 638 391 648 343 648 _c 448 | 197 648 _l 449 | 98 729 _m 450 | 350 729 _l 451 | }_e{425 729 483 713 524 682 _c 452 | 564 650 585 606 585 549 _c 453 | 585 504 574 468 553 442 _c 454 | 532 416 502 399 462 393 _c 455 | 510 382 548 360 575 327 _c 456 | 601 294 615 253 615 204 _c 457 | 615 138 592 88 548 53 _c 458 | 504 17 441 0 360 0 _c 459 | 98 0 _l 460 | 98 729 _l 461 | _cl}_e}_d 462 | end readonly def 463 | 464 | /BuildGlyph 465 | {exch begin 466 | CharStrings exch 467 | 2 copy known not{pop /.notdef}if 468 | true 3 1 roll get exec 469 | end}_d 470 | 471 | /BuildChar { 472 | 1 index /Encoding get exch get 473 | 1 index /BuildGlyph get exec 474 | }_d 475 | 476 | FontName currentdict end definefont pop 477 | %!PS-Adobe-3.0 Resource-Font 478 | %%Title: cmsy10 479 | %%Copyright: Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. 480 | %%Creator: Converted from TrueType to type 3 by PPR 481 | 25 dict begin 482 | /_d{bind def}bind def 483 | /_m{moveto}_d 484 | /_l{lineto}_d 485 | /_cl{closepath eofill}_d 486 | /_c{curveto}_d 487 | /_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d 488 | /_e{exec}_d 489 | /FontName /Cmsy10 def 490 | /PaintType 0 def 491 | /FontMatrix[.001 0 0 .001 0 0]def 492 | /FontBBox[-29 -960 1123 779]def 493 | /FontType 3 def 494 | /Encoding [ /bar ] def 495 | /FontInfo 10 dict dup begin 496 | /FamilyName (cmsy10) def 497 | /FullName (cmsy10) def 498 | /Notice (Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. ) def 499 | /Weight (Regular) def 500 | /Version (1.1/12-Nov-94) def 501 | /ItalicAngle 0.0 def 502 | /isFixedPitch false def 503 | /UnderlinePosition -133 def 504 | /UnderlineThickness 20 def 505 | end readonly def 506 | /CharStrings 1 dict dup begin 507 | /bar{277 0 119 -249 159 750 _sc 508 | 119 -231 _m 509 | 119 732 _l 510 | 119 737 121 741 125 745 _c 511 | 129 748 133 750 139 750 _c 512 | 143 750 148 748 152 745 _c 513 | 156 741 159 737 159 732 _c 514 | 159 -231 _l 515 | 159 -236 156 -240 152 -244 _c 516 | 148 -247 143 -249 139 -249 _c 517 | 133 -249 129 -247 125 -244 _c 518 | 121 -240 119 -236 119 -231 _c 519 | _cl}_d 520 | end readonly def 521 | 522 | /BuildGlyph 523 | {exch begin 524 | CharStrings exch 525 | 2 copy known not{pop /.notdef}if 526 | true 3 1 roll get exec 527 | end}_d 528 | 529 | /BuildChar { 530 | 1 index /Encoding get exch get 531 | 1 index /BuildGlyph get exec 532 | }_d 533 | 534 | FontName currentdict end definefont pop 535 | end 536 | %%EndProlog 537 | mpldict begin 538 | 75.6 233.284 translate 539 | 460.8 325.431 0 0 clipbox 540 | 100000 setmiterlimit 541 | gsave 542 | 0 0 m 543 | 460.8 0 l 544 | 460.8 325.431405 l 545 | 0 325.431405 l 546 | cl 547 | 1.000 setgray 548 | fill 549 | grestore 550 | 1.000 setlinewidth 551 | 0 setlinejoin 552 | 0 setlinecap 553 | [] 0 setdash 554 | 0.000 0.750 0.750 setrgbcolor 555 | gsave 556 | 446.4 307.8 7.2 10.43 clipbox 557 | 230.4 60.001272 m 558 | 213.196019 71.428627 199.082844 86.936032 189.322001 105.137333 c 559 | 179.561159 123.338634 174.452411 143.674859 174.452411 164.328222 c 560 | 174.452411 184.981585 179.561159 205.317809 189.322001 223.51911 c 561 | 199.082844 241.720411 213.196019 257.227816 230.4 268.655171 c 562 | 211.533415 281.186874 189.616138 288.3692 166.991869 289.434115 c 563 | 144.3676 290.499031 121.872581 285.407174 101.912294 274.703038 c 564 | 81.952008 263.998901 65.264228 248.078132 53.633445 228.643203 c 565 | 42.002663 209.208273 35.858777 186.977539 35.858777 164.328222 c 566 | 35.858777 141.678904 42.002663 119.44817 53.633445 100.013241 c 567 | 65.264228 80.578311 81.952008 64.657542 101.912294 53.953406 c 568 | 121.872581 43.249269 144.3676 38.157412 166.991869 39.222328 c 569 | 189.616138 40.287244 211.533415 47.46957 230.4 60.001272 c 570 | gsave 571 | fill 572 | grestore 573 | stroke 574 | grestore 575 | 0.300 0.900 0.300 setrgbcolor 576 | gsave 577 | 446.4 307.8 7.2 10.43 clipbox 578 | 230.4 268.655171 m 579 | 247.603981 257.227816 261.717156 241.720411 271.477999 223.51911 c 580 | 281.238841 205.317809 286.347589 184.981585 286.347589 164.328222 c 581 | 286.347589 143.674859 281.238841 123.338634 271.477999 105.137333 c 582 | 261.717156 86.936032 247.603981 71.428627 230.4 60.001272 c 583 | 249.266585 47.46957 271.183862 40.287244 293.808131 39.222328 c 584 | 316.4324 38.157412 338.927419 43.249269 358.887706 53.953406 c 585 | 378.847992 64.657542 395.535772 80.578311 407.166555 100.013241 c 586 | 418.797337 119.44817 424.941223 141.678904 424.941223 164.328222 c 587 | 424.941223 186.977539 418.797337 209.208273 407.166555 228.643203 c 588 | 395.535772 248.078132 378.847992 263.998901 358.887706 274.703038 c 589 | 338.927419 285.407174 316.4324 290.499031 293.808131 289.434115 c 590 | 271.183862 288.3692 249.266585 281.186874 230.4 268.655171 c 591 | gsave 592 | fill 593 | grestore 594 | stroke 595 | grestore 596 | 0.500 0.500 1.000 setrgbcolor 597 | gsave 598 | 446.4 307.8 7.2 10.43 clipbox 599 | 230.4 60.001272 m 600 | 247.603981 71.428627 261.717156 86.936032 271.477999 105.137333 c 601 | 281.238841 123.338634 286.347589 143.674859 286.347589 164.328222 c 602 | 286.347589 184.981585 281.238841 205.317809 271.477999 223.51911 c 603 | 261.717156 241.720411 247.603981 257.227816 230.4 268.655171 c 604 | 213.196019 257.227816 199.082844 241.720411 189.322001 223.51911 c 605 | 179.561159 205.317809 174.452411 184.981585 174.452411 164.328222 c 606 | 174.452411 143.674859 179.561159 123.338634 189.322001 105.137333 c 607 | 199.082844 86.936032 213.196019 71.428627 230.4 60.001272 c 608 | gsave 609 | fill 610 | grestore 611 | stroke 612 | grestore 613 | 2.000 setlinewidth 614 | 0.000 setgray 615 | gsave 616 | 446.4 307.8 7.2 10.43 clipbox 617 | 161.103183 39.083816 m 618 | 194.318388 39.083816 226.177655 52.280356 249.664352 75.767053 c 619 | 273.151048 99.253749 286.347589 131.113017 286.347589 164.328222 c 620 | 286.347589 197.543426 273.151048 229.402694 249.664352 252.889391 c 621 | 226.177655 276.376087 194.318388 289.572628 161.103183 289.572628 c 622 | 127.887978 289.572628 96.02871 276.376087 72.542014 252.889391 c 623 | 49.055317 229.402694 35.858777 197.543426 35.858777 164.328222 c 624 | 35.858777 131.113017 49.055317 99.253749 72.542014 75.767053 c 625 | 96.02871 52.280356 127.887978 39.083816 161.103183 39.083816 c 626 | 161.103183 39.083816 l 627 | cl 628 | stroke 629 | grestore 630 | gsave 631 | 446.4 307.8 7.2 10.43 clipbox 632 | 299.696817 39.083816 m 633 | 332.912022 39.083816 364.77129 52.280356 388.257986 75.767053 c 634 | 411.744683 99.253749 424.941223 131.113017 424.941223 164.328222 c 635 | 424.941223 197.543426 411.744683 229.402694 388.257986 252.889391 c 636 | 364.77129 276.376087 332.912022 289.572628 299.696817 289.572628 c 637 | 266.481612 289.572628 234.622345 276.376087 211.135648 252.889391 c 638 | 187.648952 229.402694 174.452411 197.543426 174.452411 164.328222 c 639 | 174.452411 131.113017 187.648952 99.253749 211.135648 75.767053 c 640 | 234.622345 52.280356 266.481612 39.083816 299.696817 39.083816 c 641 | 299.696817 39.083816 l 642 | cl 643 | stroke 644 | grestore 645 | gsave 646 | 71.155594 159.328222 translate 647 | 0.000000 rotate 648 | /Cmmi10 findfont 649 | 20.0 scalefont 650 | setfont 651 | 0.000000 0.000000 moveto 652 | /H glyphshow 653 | 654 | /Cmr10 findfont 655 | 20.0 scalefont 656 | setfont 657 | 16.621094 0.000000 moveto 658 | /parenleft glyphshow 659 | 660 | /Cmmi10 findfont 661 | 20.0 scalefont 662 | setfont 663 | 24.384766 0.000000 moveto 664 | /A glyphshow 665 | 666 | /Cmsy10 findfont 667 | 20.0 scalefont 668 | setfont 669 | 39.384766 0.000000 moveto 670 | /bar glyphshow 671 | 672 | /Cmmi10 findfont 673 | 20.0 scalefont 674 | setfont 675 | 44.921875 0.000000 moveto 676 | /B glyphshow 677 | 678 | /Cmr10 findfont 679 | 20.0 scalefont 680 | setfont 681 | 60.078125 0.000000 moveto 682 | /parenright glyphshow 683 | 684 | 685 | grestore 686 | gsave 687 | 321.644406 159.328222 translate 688 | 0.000000 rotate 689 | /Cmmi10 findfont 690 | 20.0 scalefont 691 | setfont 692 | 0.000000 0.000000 moveto 693 | /H glyphshow 694 | 695 | /Cmr10 findfont 696 | 20.0 scalefont 697 | setfont 698 | 16.621094 0.000000 moveto 699 | /parenleft glyphshow 700 | 701 | /Cmmi10 findfont 702 | 20.0 scalefont 703 | setfont 704 | 24.384766 0.000000 moveto 705 | /B glyphshow 706 | 707 | /Cmsy10 findfont 708 | 20.0 scalefont 709 | setfont 710 | 39.541016 0.000000 moveto 711 | /bar glyphshow 712 | 713 | /Cmmi10 findfont 714 | 20.0 scalefont 715 | setfont 716 | 45.078125 0.000000 moveto 717 | /A glyphshow 718 | 719 | /Cmr10 findfont 720 | 20.0 scalefont 721 | setfont 722 | 60.078125 0.000000 moveto 723 | /parenright glyphshow 724 | 725 | 726 | grestore 727 | gsave 728 | 198.400000 159.328222 translate 729 | 0.000000 rotate 730 | /Cmmi10 findfont 731 | 20.0 scalefont 732 | setfont 733 | 0.000000 0.000000 moveto 734 | /I glyphshow 735 | 736 | /Cmr10 findfont 737 | 20.0 scalefont 738 | setfont 739 | 8.779297 0.000000 moveto 740 | /parenleft glyphshow 741 | 742 | /Cmmi10 findfont 743 | 20.0 scalefont 744 | setfont 745 | 16.542969 0.000000 moveto 746 | /A glyphshow 747 | 748 | /Cmr10 findfont 749 | 20.0 scalefont 750 | setfont 751 | 31.542969 0.000000 moveto 752 | /semicolon glyphshow 753 | 754 | /Cmmi10 findfont 755 | 20.0 scalefont 756 | setfont 757 | 40.591797 0.000000 moveto 758 | /B glyphshow 759 | 760 | /Cmr10 findfont 761 | 20.0 scalefont 762 | setfont 763 | 55.748047 0.000000 moveto 764 | /parenright glyphshow 765 | 766 | 767 | grestore 768 | /BitstreamVeraSans-Roman findfont 769 | 20.000 scalefont 770 | setfont 771 | gsave 772 | 147.415683 11.356250 translate 773 | 0.000000 rotate 774 | 0.000000 0.000000 m /A glyphshow 775 | grestore 776 | gsave 777 | 299.696817 11.356250 translate 778 | 0.000000 rotate 779 | 0.000000 0.000000 m /B glyphshow 780 | grestore 781 | 782 | end 783 | showpage 784 | -------------------------------------------------------------------------------- /venn2.eps: -------------------------------------------------------------------------------- 1 | %!PS-Adobe-3.0 EPSF-3.0 2 | %%Title: venn2.eps 3 | %%Creator: matplotlib version 1.5.1, http://matplotlib.org/ 4 | %%CreationDate: Mon Jun 6 13:22:11 2016 5 | %%Orientation: portrait 6 | %%BoundingBox: 118 214 493 577 7 | %%EndComments 8 | %%BeginProlog 9 | /mpldict 11 dict def 10 | mpldict begin 11 | /m { moveto } bind def 12 | /l { lineto } bind def 13 | /r { rlineto } bind def 14 | /c { curveto } bind def 15 | /cl { closepath } bind def 16 | /box { 17 | m 18 | 1 index 0 r 19 | 0 exch r 20 | neg 0 r 21 | cl 22 | } bind def 23 | /clipbox { 24 | box 25 | clip 26 | newpath 27 | } bind def 28 | %!PS-Adobe-3.0 Resource-Font 29 | %%Title: Bitstream Vera Sans 30 | %%Copyright: Copyright (c) 2003 by Bitstream, Inc. All Rights Reserved. 31 | %%Creator: Converted from TrueType to type 3 by PPR 32 | 25 dict begin 33 | /_d{bind def}bind def 34 | /_m{moveto}_d 35 | /_l{lineto}_d 36 | /_cl{closepath eofill}_d 37 | /_c{curveto}_d 38 | /_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d 39 | /_e{exec}_d 40 | /FontName /BitstreamVeraSans-Roman def 41 | /PaintType 0 def 42 | /FontMatrix[.001 0 0 .001 0 0]def 43 | /FontBBox[-183 -236 1287 928]def 44 | /FontType 3 def 45 | /Encoding [ /X /Y /Z ] def 46 | /FontInfo 10 dict dup begin 47 | /FamilyName (Bitstream Vera Sans) def 48 | /FullName (Bitstream Vera Sans) def 49 | /Notice (Copyright (c) 2003 by Bitstream, Inc. All Rights Reserved. Bitstream Vera is a trademark of Bitstream, Inc.) def 50 | /Weight (Roman) def 51 | /Version (Release 1.10) def 52 | /ItalicAngle 0.0 def 53 | /isFixedPitch false def 54 | /UnderlinePosition -213 def 55 | /UnderlineThickness 143 def 56 | end readonly def 57 | /CharStrings 3 dict dup begin 58 | /X{685 0 30 0 654 729 _sc 59 | 63 729 _m 60 | 169 729 _l 61 | 350 458 _l 62 | 532 729 _l 63 | 638 729 _l 64 | 404 379 _l 65 | 654 0 _l 66 | 548 0 _l 67 | 343 310 _l 68 | 136 0 _l 69 | 30 0 _l 70 | 290 389 _l 71 | 63 729 _l 72 | _cl}_d 73 | /Y{611 0 -1 0 613 729 _sc 74 | -1 729 _m 75 | 104 729 _l 76 | 306 429 _l 77 | 507 729 _l 78 | 613 729 _l 79 | 355 347 _l 80 | 355 0 _l 81 | 256 0 _l 82 | 256 347 _l 83 | -1 729 _l 84 | _cl}_d 85 | /Z{685 0 45 0 640 729 _sc 86 | 56 729 _m 87 | 629 729 _l 88 | 629 654 _l 89 | 168 83 _l 90 | 640 83 _l 91 | 640 0 _l 92 | 45 0 _l 93 | 45 75 _l 94 | 506 646 _l 95 | 56 646 _l 96 | 56 729 _l 97 | _cl}_d 98 | end readonly def 99 | 100 | /BuildGlyph 101 | {exch begin 102 | CharStrings exch 103 | 2 copy known not{pop /.notdef}if 104 | true 3 1 roll get exec 105 | end}_d 106 | 107 | /BuildChar { 108 | 1 index /Encoding get exch get 109 | 1 index /BuildGlyph get exec 110 | }_d 111 | 112 | FontName currentdict end definefont pop 113 | %!PS-Adobe-3.0 Resource-Font 114 | %%Title: cmr10 115 | %%Copyright: Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. 116 | %%Creator: Converted from TrueType to type 3 by PPR 117 | 25 dict begin 118 | /_d{bind def}bind def 119 | /_m{moveto}_d 120 | /_l{lineto}_d 121 | /_cl{closepath eofill}_d 122 | /_c{curveto}_d 123 | /_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d 124 | /_e{exec}_d 125 | /FontName /Cmr10 def 126 | /PaintType 0 def 127 | /FontMatrix[.001 0 0 .001 0 0]def 128 | /FontBBox[-44 -250 1009 750]def 129 | /FontType 3 def 130 | /Encoding [ /semicolon /parenright /parenleft ] def 131 | /FontInfo 10 dict dup begin 132 | /FamilyName (cmr10) def 133 | /FullName (cmr10) def 134 | /Notice (Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. ) def 135 | /Weight (Regular) def 136 | /Version (1.1/12-Nov-94) def 137 | /ItalicAngle 0.0 def 138 | /isFixedPitch false def 139 | /UnderlinePosition -133 def 140 | /UnderlineThickness 20 def 141 | end readonly def 142 | /CharStrings 3 dict dup begin 143 | /semicolon{{277 0 84 -193 197 431 _sc 144 | 99 -179 _m 145 | 99 -176 99 -174 101 -173 _c 146 | 147 -122 171 -63 171 4 _c 147 | 171 9 _l 148 | 161 3 150 0 139 0 _c 149 | 123 0 110 5 100 16 _c 150 | 89 26 84 39 84 55 _c 151 | 84 71 89 84 100 94 _c 152 | 110 104 123 110 139 110 _c 153 | 162 110 177 99 185 78 _c 154 | 193 56 197 32 197 4 _c 155 | 197 -18 194 -41 188 -64 _c 156 | 182 -87 174 -109 162 -131 _c 157 | 150 -153 137 -172 121 -190 _c 158 | }_e{119 -192 116 -193 114 -193 _c 159 | 110 -193 107 -191 104 -188 _c 160 | 100 -185 99 -182 99 -179 _c 161 | 84 376 _m 162 | 84 385 86 394 91 403 _c 163 | 96 411 103 418 112 423 _c 164 | 120 428 129 431 139 431 _c 165 | 148 431 157 428 166 423 _c 166 | 174 418 181 411 186 403 _c 167 | 191 394 194 385 194 376 _c 168 | 194 361 188 348 178 337 _c 169 | 167 326 154 321 139 321 _c 170 | 124 321 111 326 100 337 _c 171 | 89 348 84 361 84 376 _c 172 | _cl}_e}_d 173 | /parenright{{388 0 56 -249 291 750 _sc 174 | 65 -249 _m 175 | 59 -249 56 -246 56 -240 _c 176 | 56 -237 56 -235 58 -234 _c 177 | 172 -122 229 38 229 250 _c 178 | 229 462 172 623 60 733 _c 179 | 57 734 56 737 56 741 _c 180 | 56 743 57 745 59 747 _c 181 | 61 749 63 750 65 750 _c 182 | 74 750 _l 183 | 76 750 77 749 79 748 _c 184 | 127 710 167 664 199 610 _c 185 | 231 556 254 498 269 437 _c 186 | 283 376 291 314 291 250 _c 187 | 291 202 287 156 279 110 _c 188 | }_e{271 64 258 20 241 -24 _c 189 | 223 -68 201 -108 175 -146 _c 190 | 148 -184 116 -217 79 -247 _c 191 | 77 -248 76 -249 74 -249 _c 192 | 65 -249 _l 193 | _cl}_e}_d 194 | /parenleft{{388 0 97 -249 332 750 _sc 195 | 310 -247 _m 196 | 272 -217 240 -184 214 -146 _c 197 | 187 -108 165 -67 148 -25 _c 198 | 131 17 118 62 110 109 _c 199 | 101 155 97 202 97 250 _c 200 | 97 298 101 345 110 392 _c 201 | 118 438 131 483 149 527 _c 202 | 166 570 188 611 215 649 _c 203 | 242 687 274 720 310 748 _c 204 | 310 749 311 750 315 750 _c 205 | 324 750 _l 206 | 326 750 327 749 329 747 _c 207 | 331 745 332 743 332 741 _c 208 | 332 738 331 736 330 735 _c 209 | }_e{297 703 270 668 248 632 _c 210 | 226 596 209 557 196 516 _c 211 | 183 474 174 432 168 388 _c 212 | 162 344 159 298 159 250 _c 213 | 159 38 215 -122 329 -232 _c 214 | 331 -234 332 -236 332 -240 _c 215 | 332 -242 331 -244 329 -246 _c 216 | 327 -248 326 -249 324 -249 _c 217 | 315 -249 _l 218 | 311 -249 310 -248 310 -247 _c 219 | _cl}_e}_d 220 | end readonly def 221 | 222 | /BuildGlyph 223 | {exch begin 224 | CharStrings exch 225 | 2 copy known not{pop /.notdef}if 226 | true 3 1 roll get exec 227 | end}_d 228 | 229 | /BuildChar { 230 | 1 index /Encoding get exch get 231 | 1 index /BuildGlyph get exec 232 | }_d 233 | 234 | FontName currentdict end definefont pop 235 | %!PS-Adobe-3.0 Resource-Font 236 | %%Title: cmmi10 237 | %%Copyright: Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. 238 | %%Creator: Converted from TrueType to type 3 by PPR 239 | 25 dict begin 240 | /_d{bind def}bind def 241 | /_m{moveto}_d 242 | /_l{lineto}_d 243 | /_cl{closepath eofill}_d 244 | /_c{curveto}_d 245 | /_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d 246 | /_e{exec}_d 247 | /FontName /Cmmi10 def 248 | /PaintType 0 def 249 | /FontMatrix[.001 0 0 .001 0 0]def 250 | /FontBBox[-34 -250 1048 750]def 251 | /FontType 3 def 252 | /Encoding [ /comma /Z /H /Y /I /X ] def 253 | /FontInfo 10 dict dup begin 254 | /FamilyName (cmmi10) def 255 | /FullName (cmmi10) def 256 | /Notice (Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. ) def 257 | /Weight (Regular) def 258 | /Version (1.1/12-Nov-94) def 259 | /ItalicAngle 0.0 def 260 | /isFixedPitch false def 261 | /UnderlinePosition -133 def 262 | /UnderlineThickness 20 def 263 | end readonly def 264 | /CharStrings 6 dict dup begin 265 | /comma{277 0 84 -193 205 110 _sc 266 | 99 -179 _m 267 | 99 -176 100 -173 103 -171 _c 268 | 127 -147 145 -120 159 -90 _c 269 | 172 -60 179 -28 179 4 _c 270 | 179 16 _l 271 | 168 5 155 0 139 0 _c 272 | 123 0 110 5 100 16 _c 273 | 89 26 84 39 84 55 _c 274 | 84 71 89 84 100 94 _c 275 | 110 104 123 110 139 110 _c 276 | 163 110 180 99 190 77 _c 277 | 200 55 205 30 205 4 _c 278 | 205 -32 197 -67 183 -101 _c 279 | 168 -134 147 -164 120 -191 _c 280 | 117 -192 115 -193 114 -193 _c 281 | 110 -193 107 -191 104 -188 _c 282 | 100 -185 99 -182 99 -179 _c 283 | _cl}_d 284 | /Z{{682 0 58 0 722 683 _sc 285 | 58 8 _m 286 | 58 17 60 25 65 31 _c 287 | 615 648 _l 288 | 468 648 _l 289 | 419 648 378 642 346 630 _c 290 | 314 618 287 599 266 573 _c 291 | 245 546 228 509 214 463 _c 292 | 212 457 209 454 204 454 _c 293 | 195 454 _l 294 | 188 454 185 458 185 467 _c 295 | 248 674 _l 296 | 249 680 252 683 258 683 _c 297 | 714 683 _l 298 | 719 683 722 680 722 675 _c 299 | 722 665 720 658 716 654 _c 300 | 168 38 _l 301 | 320 38 _l 302 | }_e{378 38 424 45 458 60 _c 303 | 492 74 518 97 538 128 _c 304 | 558 159 577 204 596 262 _c 305 | 596 264 598 266 600 268 _c 306 | 602 270 604 271 606 271 _c 307 | 615 271 _l 308 | 621 271 625 266 625 258 _c 309 | 546 9 _l 310 | 543 3 540 0 536 0 _c 311 | 67 0 _l 312 | 61 0 58 2 58 8 _c 313 | _cl}_e}_d 314 | /H{{831 0 37 0 883 683 _sc 315 | 47 0 _m 316 | 40 0 37 4 37 13 _c 317 | 37 15 38 18 39 22 _c 318 | 40 26 41 29 43 31 _c 319 | 45 33 47 35 50 35 _c 320 | 90 35 119 37 135 42 _c 321 | 143 44 150 53 154 69 _c 322 | 291 618 _l 323 | 292 624 293 629 293 632 _c 324 | 293 639 289 643 281 644 _c 325 | 268 646 244 648 209 648 _c 326 | 202 648 199 652 199 661 _c 327 | 201 669 203 675 205 678 _c 328 | 206 681 210 683 216 683 _c 329 | }_e{485 683 _l 330 | 491 683 495 678 495 670 _c 331 | 495 668 494 665 493 661 _c 332 | 492 657 491 654 489 652 _c 333 | 487 649 485 648 482 648 _c 334 | 441 648 413 645 397 641 _c 335 | 388 637 382 628 378 614 _c 336 | 318 373 _l 337 | 618 373 _l 338 | 679 618 _l 339 | 680 624 681 629 681 632 _c 340 | 681 639 677 643 669 644 _c 341 | 656 646 632 648 597 648 _c 342 | 590 648 587 652 587 661 _c 343 | 589 669 590 675 592 678 _c 344 | 593 681 597 683 604 683 _c 345 | }_e{873 683 _l 346 | 879 683 883 678 883 670 _c 347 | 882 668 881 665 880 661 _c 348 | 879 657 878 653 876 651 _c 349 | 874 649 872 648 870 648 _c 350 | 829 648 801 645 785 641 _c 351 | 776 638 770 629 766 614 _c 352 | 629 65 _l 353 | 627 58 627 53 627 51 _c 354 | 627 44 631 40 639 39 _c 355 | 651 36 675 35 711 35 _c 356 | 717 35 721 30 721 22 _c 357 | 719 14 717 8 715 5 _c 358 | 713 1 709 0 704 0 _c 359 | 435 0 _l 360 | }_e{428 0 425 4 425 13 _c 361 | 426 18 427 22 428 24 _c 362 | 428 26 429 28 431 31 _c 363 | 433 33 435 35 438 35 _c 364 | 478 35 507 37 523 42 _c 365 | 531 44 538 53 542 69 _c 366 | 609 338 _l 367 | 309 338 _l 368 | 241 65 _l 369 | 239 57 239 52 239 51 _c 370 | 239 44 243 40 251 39 _c 371 | 263 36 287 35 323 35 _c 372 | 329 35 333 30 333 22 _c 373 | 331 13 329 7 327 4 _c 374 | 325 1 322 0 316 0 _c 375 | 47 0 _l 376 | _cl}_e}_d 377 | /Y{{580 0 33 0 763 683 _sc 378 | 89 13 _m 379 | 89 15 89 17 90 21 _c 380 | 91 25 92 28 94 31 _c 381 | 96 33 98 35 102 35 _c 382 | 142 35 171 37 187 42 _c 383 | 190 42 193 44 196 48 _c 384 | 198 52 200 56 202 60 _c 385 | 204 64 205 68 207 72 _c 386 | 257 273 _l 387 | 128 628 _l 388 | 122 636 111 642 96 644 _c 389 | 80 646 63 648 43 648 _c 390 | 36 648 33 652 33 661 _c 391 | 35 669 36 674 38 678 _c 392 | }_e{40 681 44 683 50 683 _c 393 | 302 683 _l 394 | 308 683 311 678 311 670 _c 395 | 308 655 304 648 298 648 _c 396 | 250 648 227 640 227 626 _c 397 | 340 318 _l 398 | 576 591 _l 399 | 577 594 579 598 583 603 _c 400 | 586 607 588 611 590 615 _c 401 | 592 618 593 622 593 626 _c 402 | 593 640 579 648 552 648 _c 403 | 545 648 542 652 542 661 _c 404 | 543 666 544 670 545 673 _c 405 | 545 676 547 678 549 680 _c 406 | 551 682 555 683 559 683 _c 407 | 753 683 _l 408 | }_e{755 683 758 681 760 678 _c 409 | 762 675 763 672 763 670 _c 410 | 761 665 760 661 760 659 _c 411 | 759 657 758 654 756 652 _c 412 | 754 649 752 648 749 648 _c 413 | 722 648 697 642 673 630 _c 414 | 649 618 629 602 611 582 _c 415 | 610 581 609 580 608 580 _c 416 | 607 580 606 579 606 578 _c 417 | 342 273 _l 418 | 290 66 _l 419 | 290 64 289 61 289 58 _c 420 | 288 55 288 53 288 51 _c 421 | 288 48 288 46 289 44 _c 422 | 290 42 291 41 293 41 _c 423 | }_e{294 40 296 39 300 39 _c 424 | 312 36 336 35 372 35 _c 425 | 378 35 382 30 382 22 _c 426 | 379 12 377 6 376 4 _c 427 | 375 1 371 0 365 0 _c 428 | 99 0 _l 429 | 92 0 89 4 89 13 _c 430 | _cl}_e}_d 431 | /I{{439 0 32 0 500 683 _sc 432 | 42 0 _m 433 | 35 0 32 4 32 13 _c 434 | 34 27 39 35 45 35 _c 435 | 84 35 111 36 125 39 _c 436 | 140 42 150 52 154 69 _c 437 | 291 618 _l 438 | 292 624 293 629 293 631 _c 439 | 293 635 292 638 290 640 _c 440 | 288 642 284 643 280 644 _c 441 | 266 646 241 648 204 648 _c 442 | 197 648 194 652 194 661 _c 443 | 196 669 197 675 199 678 _c 444 | 200 681 204 683 211 683 _c 445 | 490 683 _l 446 | }_e{496 683 500 678 500 670 _c 447 | 500 668 499 665 498 661 _c 448 | 497 657 496 654 494 652 _c 449 | 492 649 490 648 487 648 _c 450 | 447 648 420 646 406 644 _c 451 | 391 640 382 630 378 614 _c 452 | 241 65 _l 453 | 239 57 239 52 239 52 _c 454 | 239 50 239 48 239 47 _c 455 | 239 45 240 44 242 43 _c 456 | 244 42 245 41 247 41 _c 457 | 248 40 250 39 252 39 _c 458 | 264 36 290 35 328 35 _c 459 | 334 35 338 30 338 22 _c 460 | }_e{335 12 333 6 332 4 _c 461 | 331 1 327 0 321 0 _c 462 | 42 0 _l 463 | _cl}_e}_d 464 | /X{{828 0 26 0 852 683 _sc 465 | 36 0 _m 466 | 29 0 26 4 26 13 _c 467 | 26 15 26 18 28 22 _c 468 | 29 26 30 29 32 31 _c 469 | 34 33 36 35 40 35 _c 470 | 100 35 152 57 196 103 _c 471 | 196 103 197 104 198 104 _c 472 | 198 104 199 105 199 105 _c 473 | 418 341 _l 474 | 299 628 _l 475 | 292 636 281 642 266 644 _c 476 | 250 646 232 648 212 648 _c 477 | 205 648 202 652 202 661 _c 478 | 204 669 206 675 207 678 _c 479 | }_e{208 681 212 683 219 683 _c 480 | 469 683 _l 481 | 475 683 479 678 479 670 _c 482 | 479 668 478 665 477 661 _c 483 | 475 657 474 653 472 651 _c 484 | 470 649 468 648 465 648 _c 485 | 452 648 439 646 426 642 _c 486 | 413 638 404 631 399 622 _c 487 | 485 415 _l 488 | 649 591 _l 489 | 649 593 651 596 655 602 _c 490 | 659 608 661 613 661 619 _c 491 | 661 629 656 636 648 641 _c 492 | 640 645 630 648 618 648 _c 493 | 611 648 608 652 608 661 _c 494 | }_e{610 669 611 675 613 678 _c 495 | 614 681 618 683 625 683 _c 496 | 842 683 _l 497 | 845 683 847 681 849 679 _c 498 | 851 676 852 673 852 670 _c 499 | 852 668 851 665 850 661 _c 500 | 849 657 848 654 846 652 _c 501 | 844 649 842 648 839 648 _c 502 | 807 648 779 642 753 631 _c 503 | 727 619 704 602 682 580 _c 504 | 682 580 681 579 681 579 _c 505 | 680 579 679 578 679 578 _c 506 | 498 383 _l 507 | 635 55 _l 508 | 645 41 674 35 722 35 _c 509 | }_e{728 35 732 30 732 22 _c 510 | 730 13 728 7 726 4 _c 511 | 724 1 721 0 715 0 _c 512 | 465 0 _l 513 | 458 0 455 4 455 13 _c 514 | 455 15 456 18 457 22 _c 515 | 457 26 459 29 461 31 _c 516 | 463 33 465 35 468 35 _c 517 | 480 35 493 37 507 41 _c 518 | 520 45 529 51 535 61 _c 519 | 431 310 _l 520 | 229 92 _l 521 | 228 89 226 85 222 80 _c 522 | 218 74 217 69 217 64 _c 523 | 217 54 221 46 230 42 _c 524 | }_e{239 37 249 35 260 35 _c 525 | 266 35 270 30 270 22 _c 526 | 268 12 266 6 265 4 _c 527 | 263 1 259 0 253 0 _c 528 | 36 0 _l 529 | _cl}_e}_d 530 | end readonly def 531 | 532 | /BuildGlyph 533 | {exch begin 534 | CharStrings exch 535 | 2 copy known not{pop /.notdef}if 536 | true 3 1 roll get exec 537 | end}_d 538 | 539 | /BuildChar { 540 | 1 index /Encoding get exch get 541 | 1 index /BuildGlyph get exec 542 | }_d 543 | 544 | FontName currentdict end definefont pop 545 | %!PS-Adobe-3.0 Resource-Font 546 | %%Title: cmsy10 547 | %%Copyright: Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. 548 | %%Creator: Converted from TrueType to type 3 by PPR 549 | 25 dict begin 550 | /_d{bind def}bind def 551 | /_m{moveto}_d 552 | /_l{lineto}_d 553 | /_cl{closepath eofill}_d 554 | /_c{curveto}_d 555 | /_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d 556 | /_e{exec}_d 557 | /FontName /Cmsy10 def 558 | /PaintType 0 def 559 | /FontMatrix[.001 0 0 .001 0 0]def 560 | /FontBBox[-29 -960 1123 779]def 561 | /FontType 3 def 562 | /Encoding [ /bar ] def 563 | /FontInfo 10 dict dup begin 564 | /FamilyName (cmsy10) def 565 | /FullName (cmsy10) def 566 | /Notice (Copyright (C) 1994, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-B. ) def 567 | /Weight (Regular) def 568 | /Version (1.1/12-Nov-94) def 569 | /ItalicAngle 0.0 def 570 | /isFixedPitch false def 571 | /UnderlinePosition -133 def 572 | /UnderlineThickness 20 def 573 | end readonly def 574 | /CharStrings 1 dict dup begin 575 | /bar{277 0 119 -249 159 750 _sc 576 | 119 -231 _m 577 | 119 732 _l 578 | 119 737 121 741 125 745 _c 579 | 129 748 133 750 139 750 _c 580 | 143 750 148 748 152 745 _c 581 | 156 741 159 737 159 732 _c 582 | 159 -231 _l 583 | 159 -236 156 -240 152 -244 _c 584 | 148 -247 143 -249 139 -249 _c 585 | 133 -249 129 -247 125 -244 _c 586 | 121 -240 119 -236 119 -231 _c 587 | _cl}_d 588 | end readonly def 589 | 590 | /BuildGlyph 591 | {exch begin 592 | CharStrings exch 593 | 2 copy known not{pop /.notdef}if 594 | true 3 1 roll get exec 595 | end}_d 596 | 597 | /BuildChar { 598 | 1 index /Encoding get exch get 599 | 1 index /BuildGlyph get exec 600 | }_d 601 | 602 | FontName currentdict end definefont pop 603 | end 604 | %%EndProlog 605 | mpldict begin 606 | 118.238 214.443 translate 607 | 375.524 363.115 0 0 clipbox 608 | 100000 setmiterlimit 609 | gsave 610 | 0 0 m 611 | 375.523796 0 l 612 | 375.523796 363.114888 l 613 | 0 363.114888 l 614 | cl 615 | 1.000 setgray 616 | fill 617 | grestore 618 | 1.000 setlinewidth 619 | 0 setlinejoin 620 | 0 setlinecap 621 | [] 0 setdash 622 | 0.000 0.750 0.750 setrgbcolor 623 | gsave 624 | 361.1 345.6 7.2 10.31 clipbox 625 | 187.761898 310.725233 m 626 | 176.818941 318.912399 164.263801 324.687733 150.926368 327.669487 c 627 | 137.588935 330.651242 123.769696 330.772239 110.382097 328.024482 c 628 | 96.994498 325.276725 84.340156 319.722119 73.255519 311.727821 c 629 | 62.170882 303.733523 52.905681 293.479642 46.072344 281.643955 c 630 | 39.239007 269.808268 34.991486 256.657428 33.610539 243.060702 c 631 | 32.229593 229.463976 33.746334 215.727691 38.060506 202.759812 c 632 | 42.374677 189.791932 49.389084 177.884618 58.640076 167.82494 c 633 | 67.891068 157.765261 79.170223 149.779858 91.731995 144.396563 c 634 | 93.742683 161.252076 100.156184 177.284826 110.325248 190.876785 c 635 | 120.494312 204.468745 134.064942 215.146762 149.667589 221.833212 c 636 | 147.656901 238.688726 150.119021 255.780245 156.805471 271.382892 c 637 | 163.491921 286.98554 174.169939 300.556169 187.761898 310.725233 c 638 | gsave 639 | fill 640 | grestore 641 | stroke 642 | grestore 643 | 0.900 0.900 0.500 setrgbcolor 644 | gsave 645 | 361.1 345.6 7.2 10.31 clipbox 646 | 187.761898 310.725233 m 647 | 201.353857 300.556169 212.031875 286.98554 218.718325 271.382892 c 648 | 225.404775 255.780245 227.866895 238.688726 225.856207 221.833212 c 649 | 241.458854 215.146762 255.029484 204.468745 265.198547 190.876785 c 650 | 275.367611 177.284826 281.781112 161.252076 283.7918 144.396563 c 651 | 296.353572 149.779858 307.632728 157.765261 316.88372 167.82494 c 652 | 326.134711 177.884618 333.149118 189.791932 337.46329 202.759812 c 653 | 341.777462 215.727691 343.294203 229.463976 341.913256 243.060702 c 654 | 340.53231 256.657428 336.284788 269.808268 329.451451 281.643955 c 655 | 322.618114 293.479642 313.352914 303.733523 302.268277 311.727821 c 656 | 291.18364 319.722119 278.529298 325.276725 265.141699 328.024482 c 657 | 251.754099 330.772239 237.93486 330.651242 224.597427 327.669487 c 658 | 211.259994 324.687733 198.704854 318.912399 187.761898 310.725233 c 659 | gsave 660 | fill 661 | grestore 662 | stroke 663 | grestore 664 | 0.200 0.800 0.200 setrgbcolor 665 | gsave 666 | 361.1 345.6 7.2 10.31 clipbox 667 | 187.761898 310.725233 m 668 | 174.169939 300.556169 163.491921 286.98554 156.805471 271.382892 c 669 | 150.119021 255.780245 147.656901 238.688726 149.667589 221.833212 c 670 | 161.704984 226.991788 174.665723 229.651934 187.761898 229.651934 c 671 | 200.858072 229.651934 213.818812 226.991788 225.856207 221.833212 c 672 | 227.866895 238.688726 225.404775 255.780245 218.718325 271.382892 c 673 | 212.031875 286.98554 201.353857 300.556169 187.761898 310.725233 c 674 | gsave 675 | fill 676 | grestore 677 | stroke 678 | grestore 679 | 0.300 0.600 0.900 setrgbcolor 680 | gsave 681 | 361.1 345.6 7.2 10.31 clipbox 682 | 91.731995 144.396563 m 683 | 90.11318 130.826101 91.389164 117.065365 95.475605 104.023931 c 684 | 99.562047 90.982498 106.366879 78.954187 115.440306 68.734065 c 685 | 124.513734 58.513943 135.651335 50.332264 148.116918 44.729836 c 686 | 160.582502 39.127407 174.095224 36.230449 187.761898 36.230449 c 687 | 201.428572 36.230449 214.941294 39.127407 227.406877 44.729836 c 688 | 239.872461 50.332264 251.010062 58.513943 260.083489 68.734065 c 689 | 269.156916 78.954187 275.961749 90.982498 280.04819 104.023931 c 690 | 284.134632 117.065365 285.410616 130.826101 283.7918 144.396563 c 691 | 268.189153 137.710113 251.097634 135.247993 234.24212 137.258681 c 692 | 217.386607 139.269369 201.353857 145.68287 187.761898 155.851934 c 693 | 174.169939 145.68287 158.137189 139.269369 141.281675 137.258681 c 694 | 124.426161 135.247993 107.334642 137.710113 91.731995 144.396563 c 695 | gsave 696 | fill 697 | grestore 698 | stroke 699 | grestore 700 | 0.700 0.400 0.700 setrgbcolor 701 | gsave 702 | 361.1 345.6 7.2 10.31 clipbox 703 | 91.731995 144.396563 m 704 | 107.334642 137.710113 124.426161 135.247993 141.281675 137.258681 c 705 | 158.137189 139.269369 174.169939 145.68287 187.761898 155.851934 c 706 | 177.275742 163.697336 168.491619 173.591592 161.943531 184.933212 c 707 | 155.395444 196.274832 151.218828 208.829235 149.667589 221.833212 c 708 | 134.064942 215.146762 120.494312 204.468745 110.325248 190.876785 c 709 | 100.156184 177.284826 93.742683 161.252076 91.731995 144.396563 c 710 | gsave 711 | fill 712 | grestore 713 | stroke 714 | grestore 715 | 0.400 0.400 1.000 setrgbcolor 716 | gsave 717 | 361.1 345.6 7.2 10.31 clipbox 718 | 225.856207 221.833212 m 719 | 224.304967 208.829235 220.128351 196.274832 213.580264 184.933212 c 720 | 207.032177 173.591592 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{ 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 1, 6 | "metadata": { 7 | "collapsed": false 8 | }, 9 | "outputs": [], 10 | "source": [ 11 | "from matplotlib import pyplot as plt\n", 12 | "from matplotlib_venn import venn2, venn2_circles, venn3, venn3_circles" 13 | ] 14 | }, 15 | { 16 | "cell_type": "code", 17 | "execution_count": 121, 18 | "metadata": { 19 | "collapsed": false 20 | }, 21 | "outputs": [], 22 | "source": [ 23 | "# Subset sizes\n", 24 | "s = (\n", 25 | " 1, # Ab\n", 26 | " 1, # aB\n", 27 | " 0.5, # AB\n", 28 | ")\n", 29 | "\n", 30 | "v = venn2(subsets=s, set_labels=('A', 'B'))\n", 31 | "\n", 32 | "v.get_label_by_id('10').set_text('$H(A|B)$')\n", 33 | "v.get_label_by_id('11').set_text('$I(A;B)$')\n", 34 | "v.get_label_by_id('01').set_text('$H(B|A)$')\n", 35 | "\n", 36 | "v.get_patch_by_id('10').set_color('c')\n", 37 | "v.get_patch_by_id('11').set_color((0.5,0.5,1))\n", 38 | "v.get_patch_by_id('01').set_color((0.3,0.9,0.3))\n", 39 | "\n", 40 | "v.get_patch_by_id('10').set_alpha(0.4)\n", 41 | "v.get_patch_by_id('01').set_alpha(1.0)\n", 42 | "v.get_patch_by_id('11').set_alpha(0.7)\n", 43 | "\n", 44 | "venn2_circles(subsets=s, linestyle='solid')\n", 45 | "\n", 46 | "for labels in v.set_labels:\n", 47 | " labels.set_fontsize(20)\n", 48 | "\n", 49 | "for labels in v.subset_labels:\n", 50 | " labels.set_fontsize(20)\n", 51 | "\n", 52 | "plt.savefig('venn1.eps', bbox_inches='tight')\n", 53 | "plt.show()" 54 | ] 55 | }, 56 | { 57 | "cell_type": "code", 58 | "execution_count": 2, 59 | "metadata": { 60 | "collapsed": false 61 | }, 62 | "outputs": [], 63 | "source": [ 64 | "5# Subset sizes\n", 65 | "s = (\n", 66 | " 4, # Abc\n", 67 | " 4, # aBc\n", 68 | " 1, # ABc\n", 69 | " 4, # abC\n", 70 | " 1, # AbC\n", 71 | " 1, # aBC\n", 72 | " 1, # ABC\n", 73 | ")\n", 74 | "\n", 75 | "v = venn3(subsets=s, set_labels=('X', 'Y', 'Z'))\n", 76 | "\n", 77 | "# Subset labels\n", 78 | "v.get_label_by_id('100').set_text('$H(X|Y,Z)$')\n", 79 | "v.get_label_by_id('010').set_text('$H(Y|X,Z)$')\n", 80 | "v.get_label_by_id('110').set_text('$I(X;Y|Z)$')\n", 81 | "v.get_label_by_id('001').set_text('$H(Z|X,Y)$')\n", 82 | "v.get_label_by_id('101').set_text('$I(X;Z|Y)$')\n", 83 | "v.get_label_by_id('011').set_text('$I(Y;Z|X)$')\n", 84 | "v.get_label_by_id('111').set_text('$I(X;Y;Z)$')\n", 85 | "\n", 86 | "# Subset colors\n", 87 | "v.get_patch_by_id('100').set_color('c')\n", 88 | "v.get_patch_by_id('010').set_color((0.9,0.9,0.5))\n", 89 | "v.get_patch_by_id('110').set_color((0.2,0.8,0.2))\n", 90 | "v.get_patch_by_id('001').set_color((0.3,0.6,0.9))\n", 91 | "v.get_patch_by_id('011').set_color((0.4,0.4,1))\n", 92 | "v.get_patch_by_id('101').set_color((0.7,0.4,0.7))\n", 93 | "v.get_patch_by_id('111').set_color((0.8,0.8,0.8))\n", 94 | "\n", 95 | "# Subset alphas\n", 96 | "#v.get_patch_by_id('101').set_alpha(0.4)\n", 97 | "#v.get_patch_by_id('011').set_alpha(1.0)\n", 98 | "#v.get_patch_by_id('111').set_alpha(0.7)\n", 99 | "#v.get_patch_by_id('001').set_alpha(0.5)\n", 100 | "\n", 101 | "# Border styles\n", 102 | "venn3_circles(subsets=s, linestyle='solid')\n", 103 | "\n", 104 | "for labels in v.set_labels:\n", 105 | " labels.set_fontsize(20)\n", 106 | "\n", 107 | "for labels in v.subset_labels:\n", 108 | " labels.set_fontsize(14)\n", 109 | "\n", 110 | "plt.savefig('venn2.eps', bbox_inches='tight')\n", 111 | "plt.show()" 112 | ] 113 | }, 114 | { 115 | "cell_type": "code", 116 | "execution_count": 194, 117 | "metadata": { 118 | "collapsed": false 119 | }, 120 | "outputs": [], 121 | "source": [ 122 | "# Subset sizes\n", 123 | "s = (\n", 124 | " 2, # Abc\n", 125 | " 2, # aBc\n", 126 | " 1, # ABc\n", 127 | " 2, # abC\n", 128 | " 1, # AbC\n", 129 | " 1, # aBC\n", 130 | " 0.5, # ABC\n", 131 | ")\n", 132 | "\n", 133 | "def draw3(*counts):\n", 134 | " v = venn3(subsets=s, set_labels=('X', 'Y', 'Z'))\n", 135 | "\n", 136 | " # Subset labels\n", 137 | " labels = ('100', '110', '010', '101', '111', '011', '001')\n", 138 | " for label, c in zip(labels, counts):\n", 139 | " v.get_label_by_id(label).set_text('$%d$' % c)\n", 140 | "\n", 141 | " # Subset colors\n", 142 | " v.get_patch_by_id('100').set_color('c')\n", 143 | " v.get_patch_by_id('010').set_color((0.9,0.9,0.5))\n", 144 | " v.get_patch_by_id('110').set_color((0.2,0.8,0.2))\n", 145 | " v.get_patch_by_id('001').set_color((0.3,0.6,0.9))\n", 146 | " v.get_patch_by_id('011').set_color((0.4,0.4,1))\n", 147 | " v.get_patch_by_id('101').set_color((0.7,0.4,0.7))\n", 148 | " v.get_patch_by_id('111').set_color((0.8,0.8,0.8))\n", 149 | "\n", 150 | " # Subset alphas\n", 151 | " v.get_patch_by_id('101').set_alpha(0.4)\n", 152 | " v.get_patch_by_id('011').set_alpha(1.0)\n", 153 | " v.get_patch_by_id('111').set_alpha(0.7)\n", 154 | "\n", 155 | " # Border styles\n", 156 | " venn3_circles(subsets=s, linestyle='solid')\n", 157 | "\n", 158 | " for labels in v.set_labels:\n", 159 | " labels.set_fontsize(16)\n", 160 | "\n", 161 | " for labels in v.subset_labels:\n", 162 | " labels.set_fontsize(10)\n", 163 | " \n", 164 | " return v\n", 165 | " \n", 166 | "sub = plt.subplot(2,3,1)\n", 167 | "draw3(1,2,1,1,2,1,0)\n", 168 | "\n", 169 | "sub.set_title('''\n", 170 | " $H(X)+H(Y)$\n", 171 | "''')\n", 172 | "\n", 173 | "sub = plt.subplot(2,3,2)\n", 174 | "draw3(1,2,1,2,3,2,1)\n", 175 | "\n", 176 | "sub.set_title('''\n", 177 | " $H(X)+H(Y)+H(Z)$\n", 178 | "''')\n", 179 | "\n", 180 | "sub = plt.subplot(2,3,3)\n", 181 | "draw3(0,1,0,1,2,1,1)\n", 182 | "\n", 183 | "sub.set_title('''\n", 184 | " $H(X)+H(Y)+H(Z)$\n", 185 | " $-H(X,Y)$\n", 186 | "''')\n", 187 | "\n", 188 | "sub = plt.subplot(2,3,4)\n", 189 | "draw3(-1,0,0,0,1,0,0)\n", 190 | "\n", 191 | "sub.set_title('''\n", 192 | " $H(X)+H(Y)+H(Z)$\n", 193 | " $-H(X,Y)-H(X,Z)$\n", 194 | "''')\n", 195 | "\n", 196 | "sub = plt.subplot(2,3,5)\n", 197 | "draw3(-1,-1,-1,-1,0,-1,-1)\n", 198 | "\n", 199 | "sub.set_title('''\n", 200 | " $H(X)+H(Y)+H(Z)$\n", 201 | " $-H(X,Y)-H(X,Z)-H(Y,Z)$\n", 202 | "''')\n", 203 | "\n", 204 | "sub = plt.subplot(2,3,6)\n", 205 | "draw3(0,0,0,0,1,0,0)\n", 206 | "\n", 207 | "sub.set_title('''\n", 208 | " $H(X)+H(Y)+H(Z)$\n", 209 | " $-H(X,Y)-H(X,Z)-H(Y,Z)$\n", 210 | " $+H(X,Y,Z)$\n", 211 | "''')\n", 212 | "\n", 213 | "plt.tight_layout()#(pad=0, w_pad=1, h_pad=1)\n", 214 | "\n", 215 | "plt.savefig('venn3.eps', bbox_inches='tight')\n", 216 | "plt.show()" 217 | ] 218 | }, 219 | { 220 | "cell_type": "code", 221 | "execution_count": 2, 222 | "metadata": { 223 | "collapsed": true 224 | }, 225 | "outputs": [], 226 | "source": [ 227 | "# Subset sizes\n", 228 | "s = (\n", 229 | " 2, # Abc\n", 230 | " 2, # aBc\n", 231 | " 1, # ABc\n", 232 | " 2, # abC\n", 233 | " 1, # AbC\n", 234 | " 1, # aBC\n", 235 | " 0.5, # ABC\n", 236 | ")\n", 237 | "\n", 238 | "def draw3(*counts):\n", 239 | " v = venn3(subsets=s, set_labels=('X', 'Y', 'Z'))\n", 240 | "\n", 241 | " # Subset labels\n", 242 | " labels = ('100', '110', '010', '101', '111', '011', '001')\n", 243 | " for label, c in zip(labels, counts):\n", 244 | " v.get_label_by_id(label).set_text('$%d$' % c)\n", 245 | "\n", 246 | " # Subset colors\n", 247 | " v.get_patch_by_id('100').set_color('c')\n", 248 | " v.get_patch_by_id('010').set_color((0.9,0.9,0.5))\n", 249 | " v.get_patch_by_id('110').set_color((0.2,0.8,0.2))\n", 250 | " v.get_patch_by_id('001').set_color((0.3,0.6,0.9))\n", 251 | " v.get_patch_by_id('011').set_color((0.4,0.4,1))\n", 252 | " v.get_patch_by_id('101').set_color((0.7,0.4,0.7))\n", 253 | " v.get_patch_by_id('111').set_color((0.8,0.8,0.8))\n", 254 | "\n", 255 | " # Subset alphas\n", 256 | " v.get_patch_by_id('101').set_alpha(0.4)\n", 257 | " v.get_patch_by_id('011').set_alpha(1.0)\n", 258 | " v.get_patch_by_id('111').set_alpha(0.7)\n", 259 | "\n", 260 | " # Border styles\n", 261 | " venn3_circles(subsets=s, linestyle='solid')\n", 262 | "\n", 263 | " for labels in v.set_labels:\n", 264 | " labels.set_fontsize(16)\n", 265 | "\n", 266 | " for labels in v.subset_labels:\n", 267 | " labels.set_fontsize(10)\n", 268 | " \n", 269 | " return v\n", 270 | " \n", 271 | "sub = plt.subplot(2,3,1)\n", 272 | "draw3(1,2,1,1,2,1,0)\n", 273 | "\n", 274 | "sub.set_title('''\n", 275 | " $|X|+|Y|$\n", 276 | "''')\n", 277 | "\n", 278 | "sub = plt.subplot(2,3,2)\n", 279 | "draw3(1,2,1,2,3,2,1)\n", 280 | "\n", 281 | "sub.set_title('''\n", 282 | " $|X|+|Y|+|Z|$\n", 283 | "''')\n", 284 | "\n", 285 | "sub = plt.subplot(2,3,3)\n", 286 | "draw3(1,1,1,2,2,2,1)\n", 287 | "\n", 288 | "sub.set_title('''\n", 289 | " $|X|+|Y|+|Z|$\n", 290 | " $-|X\\cap Y|$\n", 291 | "''')\n", 292 | "\n", 293 | "sub = plt.subplot(2,3,4)\n", 294 | "draw3(1,1,1,1,1,2,1)\n", 295 | "\n", 296 | "sub.set_title('''\n", 297 | " $|X|+|Y|+|Z|$\n", 298 | " $-|X\\cap Y|-|X\\cap Z|$\n", 299 | "''')\n", 300 | "\n", 301 | "sub = plt.subplot(2,3,5)\n", 302 | "draw3(1,1,1,1,0,1,1)\n", 303 | "\n", 304 | "sub.set_title('''\n", 305 | " $|X|+|Y|+|Z|$\n", 306 | " $-|X\\cap Y|-|X\\cap Z|-|Y\\cap Z|$\n", 307 | "''')\n", 308 | "\n", 309 | "sub = plt.subplot(2,3,6)\n", 310 | "draw3(1,1,1,1,1,1,1)\n", 311 | "\n", 312 | "sub.set_title('''\n", 313 | " $|X|+|Y|+|Z|$\n", 314 | " $-|X\\cap Y|-|X\\cap Z|-|Y\\cap Z|$\n", 315 | " $+|X\\cap Y\\cap Z|$\n", 316 | "''')\n", 317 | "\n", 318 | "plt.tight_layout()#(pad=0, w_pad=1, h_pad=1)\n", 319 | "\n", 320 | "plt.savefig('venn_inc_exc_princ.eps', bbox_inches='tight')\n", 321 | "plt.show()" 322 | ] 323 | } 324 | ], 325 | "metadata": { 326 | "kernelspec": { 327 | "display_name": "Python 3", 328 | "language": "python", 329 | "name": "python3" 330 | }, 331 | "language_info": { 332 | "codemirror_mode": { 333 | "name": "ipython", 334 | "version": 3 335 | }, 336 | "file_extension": ".py", 337 | "mimetype": "text/x-python", 338 | "name": "python", 339 | "nbconvert_exporter": "python", 340 | "pygments_lexer": "ipython3", 341 | "version": "3.5.1" 342 | } 343 | }, 344 | "nbformat": 4, 345 | "nbformat_minor": 0 346 | } 347 | 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