Biological-Sequences-and-Godel-numbers.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: magrittr\n"
     ]
    }
   ],
   "source": [
    "library(seqinr)\n",
    "library(MASS)\n",
    "library(ggplot2)\n",
    "library(ggpubr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First of all, in order to produce the list of prime numbers required, we will use a function for the [Sieve of Eratosthenes](https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "sieve <- function(n) {\n",
    "  n <- as.integer(n)\n",
    "  if(n > 1e6) stop(\"n too large\")\n",
    "  primes <- rep(TRUE, n)\n",
    "  primes[1] <- FALSE\n",
    "  last.prime <- 2L\n",
    "  for(i in last.prime:floor(sqrt(n)))\n",
    "  {\n",
    "    primes[seq.int(2L*last.prime, n, last.prime)] <- FALSE\n",
    "    last.prime <- last.prime + min(which(primes[(last.prime+1):n]))\n",
    "  }\n",
    "  which(primes)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next function reads a FASTA formated text file, either for DNA or AA sequences:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "seqList <- function(x, type) {\n",
    "  if (type == \"DNA\") {\n",
    "    as.list(read.fasta(x,\n",
    "                       as.string = FALSE,\n",
    "                       seqtype=\"DNA\",\n",
    "                       seqonly = FALSE,\n",
    "                       strip.desc = TRUE))\n",
    "  }\n",
    "  else {\n",
    "    if (type == \"AA\") {\n",
    "      as.list(read.fasta(x,\n",
    "                         as.string = FALSE,\n",
    "                         seqtype=\"AA\",\n",
    "                         seqonly = FALSE,\n",
    "                         strip.desc = TRUE))\n",
    "    }\n",
    "    else {\n",
    "      NULL\n",
    "    }\n",
    "  }\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function produces `count` nucleotide sequences of length `length`, with the probability of appearance for each nucleotide adhering to the parameter `prob` (default is equal distribution), and stores them in fasta format in the file `fileNameRandSeqs`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "createRandomSequencesBasedOnDistr <- function(count, length, prob=c(0.25,0.25,0.25,0.25), fileNameRandSeqs) {\n",
    "  \n",
    "  sink(fileNameRandSeqs)\n",
    "  for (i in 1:count) {\n",
    "    cat(\">Seq\", i, \"\\n\", sep = \"\")\n",
    "    seqX <- sample(c(\"A\",\"C\",\"G\",\"T\"), length, rep=TRUE, prob)\n",
    "    cat(paste(seqX,collapse=\"\"), \"\\n\", sep = \"\")\n",
    "  }\n",
    "  sink()\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function creates a random permutation of values (1 to 4, or 1 to 23 based on the `type` value), for as many times as the number of seeds provided in the `seedList`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "createRandomSequenceValues <- function(seedList, type) {\n",
    "  \n",
    "  if ( type == \"DNA\" ) {\n",
    "    results <- matrix(, nrow = length(seedList), ncol = 4)\n",
    "  }\n",
    "  else if ( type == \"AA\" ) {\n",
    "    results <- matrix(, nrow = length(seedList), ncol = 23)\n",
    "  }\n",
    "  \n",
    "  for (i in 1:length(seedList)) {\n",
    "    if ( type == \"DNA\" ) {\n",
    "      results[i,] <- sample(seq(from = 1, to = 4, by = 1), size = 4, replace = FALSE)\n",
    "    }\n",
    "    else if ( type == \"AA\" ) {\n",
    "      results[i,] <- sample(seq(from = 1, to = 23, by = 1), size = 23, replace = FALSE)\n",
    "    }\n",
    "  }\n",
    "  return(results)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next function assigns random values to each of the letters (either the four bases in DNA or the 22+1 aminoacids). In each case, the exact random sequence is printed out, in order to retrieve the exact allocation if necessary:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "assignSets <- function(randSequenceValues, type) {\n",
    "  \n",
    "  stringValues <- \"\"\n",
    "  \n",
    "  if (type == \"DNA\") {\n",
    "    #DNA Set\n",
    "    cat(\"Sequence Values: (\")\n",
    "    \n",
    "    for (i in 1:4) {\n",
    "      stringValues <- paste(stringValues, randSequenceValues[i], \", \")\n",
    "    }\n",
    "    cat(stringValues)\n",
    "    cat(\")\\n\")\n",
    "    assign(\"a\", randSequenceValues[1], envir = .GlobalEnv)\n",
    "    assign(\"t\", randSequenceValues[2], envir = .GlobalEnv)\n",
    "    assign(\"g\", randSequenceValues[3], envir = .GlobalEnv)\n",
    "    assign(\"c\", randSequenceValues[4], envir = .GlobalEnv)\n",
    "  }\n",
    "  else if ( type == \"AA\") {\n",
    "    # AA Set 1\n",
    "    cat(\"Sequence Values: (\")\n",
    "    for (i in 1:23) {\n",
    "      stringValues <- paste(stringValues, randSequenceValues[i], \", \")\n",
    "    }\n",
    "    cat(stringValues)\n",
    "    cat(\")\\n\")\n",
    "    assign(\"A\", randSequenceValues[1], envir = .GlobalEnv) # alanine, ala\n",
    "    assign(\"R\", randSequenceValues[2], envir = .GlobalEnv) # arginine, arg\n",
    "    assign(\"N\", randSequenceValues[3], envir = .GlobalEnv) # asparagine, asn\n",
    "    assign(\"D\", randSequenceValues[4], envir = .GlobalEnv) # aspartic acid, asp\n",
    "    assign(\"B\", randSequenceValues[5], envir = .GlobalEnv) # sparagine or aspartic acid, asx\n",
    "    assign(\"C\", randSequenceValues[6], envir = .GlobalEnv) # cysteine, cys\n",
    "    assign(\"E\", randSequenceValues[7], envir = .GlobalEnv) # glutamic acid, glu\n",
    "    assign(\"Q\", randSequenceValues[8], envir = .GlobalEnv) # glutamine, gln\n",
    "    assign(\"Z\", randSequenceValues[9], envir = .GlobalEnv) # glutamine or glutamic acid, glx\n",
    "    assign(\"G\", randSequenceValues[10], envir = .GlobalEnv) # glycine, gly\n",
    "    assign(\"H\", randSequenceValues[11], envir = .GlobalEnv) # histidine, his\n",
    "    assign(\"I\", randSequenceValues[12], envir = .GlobalEnv) # isoleucine, ile\n",
    "    assign(\"L\", randSequenceValues[13], envir = .GlobalEnv) # leucine, leu\n",
    "    assign(\"K\", randSequenceValues[14], envir = .GlobalEnv) # lysine, lys\n",
    "    assign(\"M\", randSequenceValues[15], envir = .GlobalEnv) # methionine, met\n",
    "    assign(\"F\", randSequenceValues[16], envir = .GlobalEnv) # phenylalanine, phe\n",
    "    assign(\"P\", randSequenceValues[17], envir = .GlobalEnv) # proline, pro\n",
    "    assign(\"S\", randSequenceValues[18], envir = .GlobalEnv) # serine, ser\n",
    "    assign(\"T\", randSequenceValues[19], envir = .GlobalEnv) # threonine, thr\n",
    "    assign(\"W\", randSequenceValues[20], envir = .GlobalEnv) # tryptophan, trp\n",
    "    assign(\"Y\", randSequenceValues[21], envir = .GlobalEnv) # tyrosine, tyr\n",
    "    assign(\"V\", randSequenceValues[22], envir = .GlobalEnv) # valine, val\n",
    "    assign(\"X\", randSequenceValues[23], envir = .GlobalEnv) # undetermined\n",
    "  }\n",
    "  \n",
    "  stringValues\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next function is purely for support, and prints out the statistical summaries of the input variables:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "godelStatistics <- function(x) {\n",
    "    \n",
    "  if (logOutput) {\n",
    "    cat(paste(\"  Min  : \", summary(x)[1], \"\\n\"))\n",
    "    cat(paste(\"1st Qu.: \", summary(x)[2], \"\\n\"))\n",
    "    cat(paste(\"Median : \", summary(x)[3], \"\\n\"))\n",
    "    cat(paste(\" Mean  : \", summary(x)[4], \"\\n\"))\n",
    "    cat(paste(\"3rd Qu.: \", summary(x)[5], \"\\n\"))\n",
    "    cat(paste(\"  Max  : \", summary(x)[6], \"\\n\"))\n",
    "    cat(paste(\"St. Dev: \", sd(x), \"\\n\"))\n",
    "  }\n",
    "  \n",
    "  results <- list(minG = summary(x)[1], firstQG = summary(x)[2],\n",
    "       medianG = summary(x)[3], meanG = summary(x)[4], \n",
    "       thirdQG = summary(x)[5], maxG = summary(x)[6],\n",
    "       stdG = sd(x))\n",
    "  \n",
    "  return(results)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Starting the application, the next step is to create the list of primes as well as set the input parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "primes <- sieve(20000) # length of primes should be >= max sequence length\n",
    "logOutput <- FALSE     # debug output\n",
    "numberOfPoints <- 4;   # number of different assignments of letters for Godel numbers\n",
    "replicate <- FALSE     # if we need to set specific seed numbers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a list of seeds and print out the seeds.\n",
    "\n",
    "Based on `replicate` value, a given experiment can be reproduced. You can replicate the figures produced in the [bioRxiv paper]() by setting the value of `replicate` above to `TRUE` and loading the `seeds.csv` file (this will take ~15' runtime)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "974 , 325 , 8 , 476 , "
     ]
    }
   ],
   "source": [
    "if (replicate == FALSE) {\n",
    "  seedValuesList <- sample(seq(from = 1, to = 1000, by = 1), size = numberOfPoints, replace = FALSE)\n",
    "  for (i in 1:numberOfPoints) {\n",
    "    cat(paste(seedValuesList[i], \", \"))\n",
    "  }\n",
    "} else {\n",
    "  seedValuesList <- as.numeric(unlist(read.csv(file=\"seeds.csv\", header = FALSE)))\n",
    "  numberOfPoints <- length(seedValuesList)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Decribe the experiment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "type <- \"DNA\"\n",
    "# The following values should execute within 5 minutes with a good enough resolution\n",
    "seqLengthLimit <- 361\n",
    "numberOfArtificialSeqs <- 821     # \"A\",\"C\",\"G\",\"T\"\n",
    "# amend the following line for your particular distribution on nucloetide presence.\n",
    "createRandomSequencesBasedOnDistr(numberOfArtificialSeqs, seqLengthLimit, c(0.25,0.25,0.25,0.25), \"data/artificialSeqs.fasta\")\n",
    "ompGene.list <- seqList(\"data/artificialSeqs.fasta\", type)\n",
    "# ompGene.list <- seqList(\"data/realSeqs.fasta\", type)\n",
    "ompGene.list.raw <- ompGene.list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the matrix of rand value assignments for the particular type (AA, DNA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 4 x 4 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>3</td><td>2</td><td>4</td><td>1</td></tr>\n",
       "\t<tr><td>3</td><td>2</td><td>1</td><td>4</td></tr>\n",
       "\t<tr><td>3</td><td>1</td><td>2</td><td>4</td></tr>\n",
       "\t<tr><td>4</td><td>2</td><td>1</td><td>3</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 4 x 4 of type dbl\n",
       "\\begin{tabular}{llll}\n",
       "\t 3 & 2 & 4 & 1\\\\\n",
       "\t 3 & 2 & 1 & 4\\\\\n",
       "\t 3 & 1 & 2 & 4\\\\\n",
       "\t 4 & 2 & 1 & 3\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 4 x 4 of type dbl\n",
       "\n",
       "| 3 | 2 | 4 | 1 |\n",
       "| 3 | 2 | 1 | 4 |\n",
       "| 3 | 1 | 2 | 4 |\n",
       "| 4 | 2 | 1 | 3 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3] [,4]\n",
       "[1,] 3    2    4    1   \n",
       "[2,] 3    2    1    4   \n",
       "[3,] 3    1    2    4   \n",
       "[4,] 4    2    1    3   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "randValues <- createRandomSequenceValues(seedValuesList, type)\n",
    "\n",
    "randValues"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, we will also set the first association to the following:\n",
    "\n",
    "`A: 1`, `T: 0`, `G: 0` and `C: 0`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 4 x 4 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>3</td><td>2</td><td>4</td><td>1</td></tr>\n",
       "\t<tr><td>3</td><td>2</td><td>1</td><td>4</td></tr>\n",
       "\t<tr><td>3</td><td>1</td><td>2</td><td>4</td></tr>\n",
       "\t<tr><td>4</td><td>2</td><td>1</td><td>3</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 4 x 4 of type dbl\n",
       "\\begin{tabular}{llll}\n",
       "\t 3 & 2 & 4 & 1\\\\\n",
       "\t 3 & 2 & 1 & 4\\\\\n",
       "\t 3 & 1 & 2 & 4\\\\\n",
       "\t 4 & 2 & 1 & 3\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 4 x 4 of type dbl\n",
       "\n",
       "| 3 | 2 | 4 | 1 |\n",
       "| 3 | 2 | 1 | 4 |\n",
       "| 3 | 1 | 2 | 4 |\n",
       "| 4 | 2 | 1 | 3 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3] [,4]\n",
       "[1,] 3    2    4    1   \n",
       "[2,] 3    2    1    4   \n",
       "[3,] 3    1    2    4   \n",
       "[4,] 4    2    1    3   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Do not run this cell if you want to check for all nucleotides and not just for A\n",
    "# randValues[1,] <- c(3, 2, 1, 4)\n",
    "randValues"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get a set of sequences of equal length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "ompGene.list <- ompGene.list.raw[which(getLength(ompGene.list.raw) >= 1)]\n",
    "sizeExp <- length(ompGene.list)\n",
    "selectedSequences <- c(1:sizeExp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the data frame that will contain godel numbers per iteration and the names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "godelValuePoints <- data.frame(matrix(0, ncol = numberOfPoints, nrow = sizeExp))\n",
    "namesList <- list()\n",
    "for (i in 1:numberOfPoints) {\n",
    "  namesList[i] <- paste('godel_log_pos', i, sep = '')\n",
    "}\n",
    "godelValuePoints <- setNames(godelValuePoints, namesList)\n",
    "godelValuePoints$seqNames <- unlist(attributes(ompGene.list)$name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are now ready to calculate the Godel number per sequence, both using the exponential formula as well as the logarithmic formula.\n",
    "\n",
    "For reference purposes, the formulas are as shown below:\n",
    "\n",
    "$$g_{seq} = \\prod_{k=1}^n p_k^{a_k}$$\n",
    "\n",
    "$$G_{seq} = \\sum_{k=1}^n ({a_k} logp_k)$$\n",
    "\n",
    "where $a_k$ is the value corresponding to the base in sequence position $k$, and $p_k$ is the $k$th prime number.\n",
    "\n",
    "We will run the process of constructed the Godel numbers for `numberOfPoints` iterations. The code performing this calculation is the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sequence Values: ( 3 ,  2 ,  4 ,  1 , )\n",
      "Sequence Values: ( 3 ,  2 ,  1 ,  4 , )\n",
      "Sequence Values: ( 3 ,  1 ,  2 ,  4 , )\n",
      "Sequence Values: ( 4 ,  2 ,  1 ,  3 , )\n"
     ]
    }
   ],
   "source": [
    "stringAssignValues <- vector(mode=\"character\", length=numberOfPoints)\n",
    "\n",
    "for (indexPos in 1:numberOfPoints) {\n",
    "  stringAssignValues[indexPos] <- assignSets(randValues[indexPos,], type)\n",
    "  \n",
    "  godel.value.exp <- list()\n",
    "  godel.value.log <- list()\n",
    "  \n",
    "  for (indexSeq in selectedSequences) {\n",
    "    \n",
    "    godel.value.exp[[indexSeq]] <- 1\n",
    "    godel.value.log[[indexSeq]] <- 0\n",
    "    \n",
    "    if (logOutput) {\n",
    "      cat(\"Sequence length  \")\n",
    "      cat(indexSeq)\n",
    "      cat(\"  :\")\n",
    "      cat(length(ompGene.list[indexSeq][[1]]))\n",
    "      cat(\"\\n\")\n",
    "    }\n",
    "\n",
    "    for (i in 1:length(ompGene.list[indexSeq][[1]])) {\n",
    "      \n",
    "      prime <- as.numeric(primes[i])\n",
    "      alpha <- as.numeric(get(as.character(ompGene.list[[indexSeq]])[i]))\n",
    "      \n",
    "      godel.value.exp[[indexSeq]] <- godel.value.exp[[indexSeq]] * prime ** alpha\n",
    "      godel.value.log[[indexSeq]] <- godel.value.log[[indexSeq]] + alpha*log(prime)\n",
    "    }\n",
    "    \n",
    "  }\n",
    "  \n",
    "  godelValuePoints[, paste('godel_log_pos', indexPos, sep = '')] <- unlist(godel.value.log)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is important to note that, given the average length of the sequences involved, the sum of exponentials reaches the limit of the calculable numbers, and therefore an Infinity indication is returned. The logarithmic produces much more manageable values.\n",
    "\n",
    "Finally, we can produce for each \"coordinate\" the summary of the base statistcs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 4 x 7</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>minG</th><th scope=col>firstQG</th><th scope=col>medianG</th><th scope=col>meanG</th><th scope=col>thirdQG</th><th scope=col>maxG</th><th scope=col>stdG</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>5577.526</td><td>5876.150</td><td>5969.809</td><td>5964.351</td><td>6068.379</td><td>6397.746</td><td>146.3888</td></tr>\n",
       "\t<tr><td>5557.299</td><td>5872.284</td><td>5978.491</td><td>5974.229</td><td>6067.484</td><td>6501.258</td><td>143.9502</td></tr>\n",
       "\t<tr><td>5490.507</td><td>5878.510</td><td>5979.453</td><td>5976.740</td><td>6073.236</td><td>6531.718</td><td>145.7073</td></tr>\n",
       "\t<tr><td>5576.471</td><td>5872.480</td><td>5969.244</td><td>5973.236</td><td>6072.649</td><td>6398.579</td><td>141.3233</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 4 x 7\n",
       "\\begin{tabular}{r|lllllll}\n",
       " minG & firstQG & medianG & meanG & thirdQG & maxG & stdG\\\\\n",
       " <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 5577.526 & 5876.150 & 5969.809 & 5964.351 & 6068.379 & 6397.746 & 146.3888\\\\\n",
       "\t 5557.299 & 5872.284 & 5978.491 & 5974.229 & 6067.484 & 6501.258 & 143.9502\\\\\n",
       "\t 5490.507 & 5878.510 & 5979.453 & 5976.740 & 6073.236 & 6531.718 & 145.7073\\\\\n",
       "\t 5576.471 & 5872.480 & 5969.244 & 5973.236 & 6072.649 & 6398.579 & 141.3233\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 4 x 7\n",
       "\n",
       "| minG &lt;dbl&gt; | firstQG &lt;dbl&gt; | medianG &lt;dbl&gt; | meanG &lt;dbl&gt; | thirdQG &lt;dbl&gt; | maxG &lt;dbl&gt; | stdG &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|\n",
       "| 5577.526 | 5876.150 | 5969.809 | 5964.351 | 6068.379 | 6397.746 | 146.3888 |\n",
       "| 5557.299 | 5872.284 | 5978.491 | 5974.229 | 6067.484 | 6501.258 | 143.9502 |\n",
       "| 5490.507 | 5878.510 | 5979.453 | 5976.740 | 6073.236 | 6531.718 | 145.7073 |\n",
       "| 5576.471 | 5872.480 | 5969.244 | 5973.236 | 6072.649 | 6398.579 | 141.3233 |\n",
       "\n"
      ],
      "text/plain": [
       "  minG     firstQG  medianG  meanG    thirdQG  maxG     stdG    \n",
       "1 5577.526 5876.150 5969.809 5964.351 6068.379 6397.746 146.3888\n",
       "2 5557.299 5872.284 5978.491 5974.229 6067.484 6501.258 143.9502\n",
       "3 5490.507 5878.510 5979.453 5976.740 6073.236 6531.718 145.7073\n",
       "4 5576.471 5872.480 5969.244 5973.236 6072.649 6398.579 141.3233"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "statsPos <- data.frame(matrix(0, ncol = 7, nrow = numberOfPoints))\n",
    "statsPos <- setNames(statsPos, c(\"minG\", \"firstQG\", \"medianG\", \"meanG\", \"thirdQG\", \"maxG\", \"stdG\"))\n",
    "for (indexPos in 1:numberOfPoints) {\n",
    "  statsPos[indexPos, ] <- godelStatistics(godelValuePoints[, paste('godel_log_pos', indexPos, sep = '')])\n",
    "}\n",
    "\n",
    "statsPos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compare the theoretical mean and std with the ones infered above. For reference, the corresponding base values are the following:\n",
    "\n",
    "\n",
    "$$P_1 = \\sum_{k=1}^n log(p_k)$$\n",
    "\n",
    "$$P_2 = \\sum_{k=1}^n (log(p_k))^2$$\n",
    "\n",
    "where $p_k$ is the $k$th prime number.\n",
    "\n",
    "We can distinguish the following two cases:\n",
    "\n",
    "1. Each base has equal probability of appearance, equal to 0.25\n",
    "\n",
    "$$mean_{theory-all-0.25} = P1 * 2.5$$\n",
    "\n",
    "$$std_{theory-all-0.25} = \\sqrt{P2 * 1.25}$$\n",
    "\n",
    "2. A has a probability of 0.3 (and we ignore the probabilities of the other bases)\n",
    "\n",
    "$$mean_{theory-A-0.3} = P1 * 0.3$$\n",
    "\n",
    "$$std_{theory-A-0.3} = \\sqrt{P2 * 0.3 * (1-0.3)}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "P1 <- sum(log(primes[1:seqLengthLimit]))\n",
    "P2 <- sum((log(primes[1:seqLengthLimit]))^2)\n",
    "\n",
    "theoreticalMeanEqual <- P1*2.5\n",
    "theoreticalStdEqual <- sqrt(P2*1.25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The theoretical values are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "5966.88428247596"
      ],
      "text/latex": [
       "5966.88428247596"
      ],
      "text/markdown": [
       "5966.88428247596"
      ],
      "text/plain": [
       "[1] 5966.884"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "142.752138094607"
      ],
      "text/latex": [
       "142.752138094607"
      ],
      "text/markdown": [
       "142.752138094607"
      ],
      "text/plain": [
       "[1] 142.7521"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "theoreticalMeanEqual\n",
    "theoreticalStdEqual"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can investigate how close our estimation is to the expected value, by attempting to review the relationship of the produced numbers to a normal distribution, using a fitting curve:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "para <- matrix(nrow=numberOfPoints, ncol = 2)\n",
    "for (indexPos in 1:numberOfPoints) {\n",
    "  fit <- fitdistr(godelValuePoints[, indexPos], \"normal\")\n",
    "  para[indexPos, 1] <- fit$estimate[\"mean\"]\n",
    "  para[indexPos, 2] <- fit$estimate[\"sd\"]\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is quite useful information, so we will add this to the `statsPos` data frame, including the number-to-letter assignment used in each case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "statsPos$stringAssignValues <- as.factor(stringAssignValues)\n",
    "statsPos$fit_estimate <- ((para[,1]-theoreticalMeanEqual)/para[,1])*100\n",
    "statsPos$fit_sd <- ((para[,2]-theoreticalStdEqual)/para[,2])*100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have the parameteres that fit the closest normal distribution to the numbers produced by each of the iterations, we can quantify this relationship as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0879245875058572"
      ],
      "text/latex": [
       "0.0879245875058572"
      ],
      "text/markdown": [
       "0.0879245875058572"
      ],
      "text/plain": [
       "[1] 0.08792459"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Mean of the difference in the Mean value (as a percentage)\n",
    "mean(statsPos$fit_estimate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.02312515200517"
      ],
      "text/latex": [
       "1.02312515200517"
      ],
      "text/markdown": [
       "1.02312515200517"
      ],
      "text/plain": [
       "[1] 1.023125"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Mean of the difference in the Standard Deviation value (as a percentage)\n",
    "mean(statsPos$fit_sd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can visualize these results for one of the iterations. We overlay the histogram of all Godel numbers, the corresponding density distribution (light red area), as well as the curve of the best fitted normal distribution (dotted dark red line): \n",
    "\n",
    "_The example is for iteration #1. Change the value of `indexPos` to produce the figure for a different iteration_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qFsBQQAANC3iG9ynDp16ooVK9THK1as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APXWROYdqfcdp0zZphq4Qqg8mdgg9FR4e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\n2ejL1AAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "indexPos = 1\n",
    "\n",
    "binwidthPlot = 5\n",
    "\n",
    "ggplot(godelValuePoints, aes(x=godelValuePoints[, indexPos]), environment = environment()) + \n",
    "  geom_histogram(aes(y=..density..), colour=\"black\", fill=\"white\", binwidth=binwidthPlot)+\n",
    "  geom_density(alpha=.2, fill=\"#FF6666\") +\n",
    "  stat_function(fun = dnorm, args = list(mean = para[indexPos, 1], sd = para[indexPos, 2]), color = \"darkred\", size = 2, linetype = \"dotdash\") +\n",
    "  labs(title= \"Histogram and Density plot of Godel numbers\",x=\"Godel numbers\", y = \"Density\")+\n",
    "  scale_color_brewer(palette=\"Accent\") + \n",
    "  theme_minimal()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will also visualize the difference between theoretical (expected) and observed mean and standard deviation values, for each of the assignments used throughout this experiment, in the following figure. The assignments are sorted in increasing order in relation to the difference in mean - the same order is used in the difference in standard deviation (i.e. the order of assignments is kept consistent for subplots A and B)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AEAAKQIEjsAAIAUQWIHAACQIkjsAAAA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55ZcDBgwQOyJvw6hYqTKbzcuXL09PT79x4xSbt7kAACAASURBVAYhJDw8XKPRDBw4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\n2DCTyUQISUxMPHbsWFJSEh0NBgDQcLEmdhzH4ZYH4B3p6ekvv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4MGIC0tDUUFWKCouB3msQMAa7m5uYSQlJSUsrIylUpFLKYMzc3N7dSp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\nQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 <- ggplot(statsPos, aes(x = reorder(stringAssignValues, fit_estimate), y = fit_estimate, group=1)) +\n",
    "  geom_point() +\n",
    "  geom_line() +\n",
    "  labs(title= \"Difference between theoretical and observed value of Mean (%)\",x=\"Assignments\", y = \"Difference in mean (%)\")+\n",
    "  theme_minimal() +\n",
    "  theme(axis.text.x = element_text(angle = 90, hjust = 1))\n",
    "\n",
    "p2 <- ggplot(statsPos, aes(x = reorder(stringAssignValues, fit_estimate), y = fit_sd, group=1)) +\n",
    "  geom_point() +\n",
    "  geom_line() +\n",
    "  labs(title= \"Difference between theoretical and observed value of standard deviation (%)\",x=\"Assignments\", y = \"Difference in  st. dev. (%)\")+\n",
    "  theme_minimal() +\n",
    "  theme(axis.text.x = element_text(angle = 90, hjust = 1))\n",
    "\n",
    "ggarrange(p1 + rremove(\"x.text\"), p2,\n",
    "          labels = c(\"A\", \"B\"),\n",
    "          ncol = 1, nrow = 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_**the end**_"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}