{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "cb90833d", "metadata": {}, "outputs": [], "source": [ "badfraction=1/3\n", "def dumbforwardinggoodbadweakprob(badvalfraction):\n", " badprob=badvalfraction\n", " goodprob=(1-badprob)^2\n", " weakprob=1-badprob-goodprob\n", " return(goodprob,badprob,weakprob)" ] }, { "cell_type": "code", "execution_count": 45, "id": "ff900e74", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.381966011250105, (0.381966011250105, 0.381966011250105, 0.236067977499790))" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "RR(3-sqrt(5))/2,dumbforwardinggoodbadweakprob(RR(3-sqrt(5))/2)" ] }, { "cell_type": "code", "execution_count": 26, "id": "42a80695", "metadata": {}, "outputs": [], "source": [ "goodprob,badprob,wealprob=dumbforwardinggoodbadweakprob(badfraction)" ] }, { "cell_type": "code", "execution_count": 73, "id": "814dcfef", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "list(range(19,0,-1))" ] }, { "cell_type": "code", "execution_count": 57, "id": "8970268c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[, , ]" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import random\n", "from enum import Enum\n", "class slottype(Enum):\n", " GOOD=0\n", " BAD=1\n", " WEAK=2\n", "def randslot():\n", " ran=random.random()\n", " if ran < goodprob:\n", " return slottype.GOOD\n", " if ran > 1- badprob:\n", " return slottype.BAD\n", " return slottype.WEAK\n", "def generateepoch(epochlen):\n", " return [randslot() for slotnum in range(epochlen)]\n", "epochlen = 600\n", "slots=generateepoch(epochlen)\n", "generateepoch(3)" ] }, { "cell_type": "code", "execution_count": 67, "id": "9c47373f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(10,\n", " [0.239699999999990,\n", " 0.245999999999989,\n", " 0.109900000000002,\n", " 0.0500000000000004,\n", " 0.0216999999999999,\n", " 0.00870000000000000,\n", " 0.00490000000000000,\n", " 0.00200000000000000,\n", " 0.000400000000000000,\n", " 0.000400000000000000,\n", " 0.000300000000000000,\n", " 0,\n", " 0,\n", " 0,\n", " 0,\n", " 0,\n", " 0,\n", " 0,\n", " 0,\n", " 0])" ] }, "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def maxadv(slots):\n", " advs=[]\n", " curradv=0\n", " for slot in slots:\n", " match slot:\n", " case slottype.GOOD:\n", " curradv -= 1\n", " case slottype.BAD:\n", " curradv += 1\n", " advs +=[curradv]\n", " return max(advs)\n", "maxadvsim=0\n", "dist=[0 for i in range(20)]\n", "iters=10000\n", "for i in range(iters):\n", " adv=maxadv(generateepoch(epochlen))\n", " if adv > maxadvsim:\n", " maxadvsim = adv\n", " if adv < 20 and adv >= 0:\n", " dist[adv] += RR(1/iters)\n", "maxadvsim,dist " ] }, { "cell_type": "code", "execution_count": 89, "id": "a736462a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1, [1, 1, 1, 1, 4, 5, 7, 9, 12, 15, 17, 21, 27, 31, 33])" ] }, "execution_count": 89, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def randoptions(slots):\n", " negadvoptions=1\n", " options=[1 for i in range(15)]\n", " for slot in slots:\n", " match slot:\n", " case slottype.GOOD:\n", " for i in range(14,0,-1):\n", " options[i]=options[i-1]\n", " options[0]=negadvoptions\n", " negadvoptions=1\n", " case slottype.BAD:\n", " for i in range(14,0,-1):\n", " options[i]+=options[i-1]\n", " options[0]+=negadvoptions\n", " negadvoptions*=2\n", " return negadvoptions,options\n", "randoptions(generateepoch(epochlen))\n", " \n", " " ] }, { "cell_type": "code", "execution_count": 97, "id": "12b0b761", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(8945,\n", " 44.6270000000000,\n", " [8,\n", " 1,\n", " 4,\n", " 1,\n", " 1,\n", " 2,\n", " 2,\n", " 2,\n", " 2,\n", " 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2,\n", " 2,\n", " 2,\n", " 1,\n", " 4,\n", " 1,\n", " 8,\n", " 8,\n", " 1,\n", " 1,\n", " 2,\n", " 1,\n", " 9,\n", " 2,\n", " 1,\n", " 1,\n", " 1,\n", " 2,\n", " 2,\n", " 1,\n", " 3,\n", " 2,\n", " 1,\n", " 1,\n", " 2,\n", " 1,\n", " 4,\n", " 3,\n", " 1,\n", " 1,\n", " 1,\n", " 1,\n", " 2,\n", " 4,\n", " 1,\n", " 1,\n", " 4,\n", " 3,\n", " 1,\n", " 1,\n", " 2,\n", " 1,\n", " 2,\n", " 12,\n", " 1,\n", " 1,\n", " 1,\n", " 5,\n", " 3,\n", " 5,\n", " 2,\n", " 2,\n", " 2,\n", " 2,\n", " 1,\n", " 1,\n", " 1,\n", " 2,\n", " 2,\n", " 2,\n", " 2,\n", " 1,\n", " 3,\n", " 5,\n", " 1,\n", " 9,\n", " 29,\n", " 2,\n", " 1])" ] }, "execution_count": 97, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def epochssim(numepochs,epochlength):\n", " epoch=generateepoch(epochlen)\n", " epochoptions=[]\n", " for i in range(numepochs):\n", " lastepoch=epoch\n", " epoch=generateepoch(epochlen)\n", " negadvoptions,options=randoptions(lastepoch)\n", " adv=maxadv(epoch)\n", " if adv < 0:\n", " epochoptions +=[negadvoptions]\n", " elif adv > 14:\n", " print(\"high adv\",adv)\n", " else:\n", " epochoptions +=[options[adv]]\n", " return epochoptions\n", "a=epochssim(10000,600)\n", "max(a),RR(sum(a)/1000),a " ] }, { "cell_type": "code", "execution_count": null, "id": "6a33fd29", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 10.1", "language": "sage", "name": "sagemath-10.1" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.1" } }, "nbformat": 4, "nbformat_minor": 5 }