diff --git a/16_11_18 delay.ipynb b/16_11_18 delay.ipynb
new file mode 100644
index 0000000..9c1fa7f
--- /dev/null
+++ b/16_11_18 delay.ipynb	
@@ -0,0 +1,83 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Populating the interactive namespace from numpy and matplotlib\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x74c3c88>]"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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CwArML8xrX+8+BbcFFdkVsZ2DNeJ2uVnfBVCwzn16Tt03u5U6kpJ3ndd2DvIA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hPzJs/zQ9IL+Krj1lZg/34gPl6TX+8zSu2FPLFd1KCugfhzGi0CpTo+epTe961v6S+TN8LCqEXI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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x3f6f9b0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "%pylab inline\n",
+    "\n",
+    "import math\n",
+    "def calc_bmin(n, l, m):\n",
+    "    n, l, m = float(n), float(l), float(m)\n",
+    "    one = math.floor((l * n) / m)\n",
+    "    two = m / l\n",
+    "    return int(math.floor(one * two))\n",
+    "\n",
+    "cascades = []\n",
+    "directs = []\n",
+    "for n in xrange(100):\n",
+    "    cascade = (n - calc_bmin(n, 1, 2)) + (n - calc_bmin(n, 1, 5)) + (n - calc_bmin(n, 1, 5))\n",
+    "    direct = (n - calc_bmin(n, 1, 50))\n",
+    "    cascades.append(cascade)\n",
+    "    directs.append(direct)\n",
+    "\n",
+    "plt.figure(figsize(16, 9))\n",
+    "plt.plot(range(100), cascades)\n",
+    "plt.plot(range(100), directs)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python [Root]",
+   "language": "python",
+   "name": "Python [Root]"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.12"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/16_11_22 perplexity test.ipynb b/16_11_22 perplexity test.ipynb
new file mode 100644
index 0000000..1411d48
--- /dev/null
+++ b/16_11_22 perplexity test.ipynb	
@@ -0,0 +1,219 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Populating the interactive namespace from numpy and matplotlib\n"
+     ]
+    }
+   ],
+   "source": [
+    "%pylab inline"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Perplexity experiment\n",
+    "\n",
+    "Trying to get my head around perplexity as a measure. This notebook does the following:\n",
+    "\n",
+    "* Generate data from a ground truth unigram distribution (p(0)=0.9, p(1)=0.09, p(2)=0.01)\n",
+    "* Estimate the ground truth n-gram distributions from the data\n",
+    "* Interpret the n-gram distribution as a posterior distribution conditioned on n-1 (for 3-gram, P(x[n] | x[n-1], x[n-2]))\n",
+    "* Measure the perplexity of the sequence as described by each posterior"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 78,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0\n",
+      " 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0\n",
+      " 1 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 0 0 0 1 0 0 0 0]\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Create sparse data\n",
+    "true_unigram = [0.9, 0.09, 0.01]\n",
+    "seq_len = 10000\n",
+    "sequence = np.random.choice(len(true_unigram), seq_len, p=true_unigram)\n",
+    "print sequence[:100]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 79,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1-gram distribution\n",
+      "(0,): 0.8972\n",
+      "(1,): 0.0922\n",
+      "(2,): 0.0106\n",
+      "2-gram distribution\n",
+      "(0, 0): 0.804680468047\n",
+      "(1, 0): 0.0831083108311\n",
+      "(0, 1): 0.0828082808281\n",
+      "(0, 2): 0.00970097009701\n",
+      "(2, 0): 0.00940094009401\n",
+      "(1, 1): 0.00820082008201\n",
+      "(2, 1): 0.001200120012\n",
+      "(1, 2): 0.000900090009001\n",
+      "3-gram distribution\n",
+      "(0, 0, 0): 0.72274454891\n",
+      "(0, 1, 0): 0.0746149229846\n",
+      "(0, 0, 1): 0.0739147829566\n",
+      "(1, 0, 0): 0.0736147229446\n",
+      "(0, 2, 0): 0.00850170034007\n",
+      "(2, 0, 0): 0.00830166033207\n",
+      "(1, 0, 1): 0.00820164032807\n",
+      "(0, 0, 2): 0.00800160032006\n",
+      "(0, 1, 1): 0.00740148029606\n",
+      "(1, 1, 0): 0.00730146029206\n",
+      "(1, 0, 2): 0.00130026005201\n",
+      "(2, 1, 0): 0.00120024004801\n",
+      "(0, 2, 1): 0.00120024004801\n",
+      "(1, 2, 0): 0.000900180036007\n",
+      "(0, 1, 2): 0.000800160032006\n",
+      "(1, 1, 1): 0.000800160032006\n",
+      "(2, 0, 1): 0.000700140028006\n",
+      "(2, 0, 2): 0.000400080016003\n",
+      "(1, 1, 2): 0.000100020004001\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Calculate n-gram distrbutions from sample of ground truth unigram distribution\n",
+    "max_ngram = 6\n",
+    "n_to_distribution = {}\n",
+    "for n in xrange(1, max_ngram + 1):\n",
+    "    ngrams = []\n",
+    "    for i in xrange(seq_len):\n",
+    "        ngram = sequence[i:i + n]\n",
+    "        if len(ngram) != n:\n",
+    "            break\n",
+    "        ngrams.append(ngram)\n",
+    "    ngram_to_count = {}\n",
+    "    for ngram in ngrams:\n",
+    "        ngram = tuple(ngram)\n",
+    "        if ngram not in ngram_to_count:\n",
+    "            ngram_to_count[ngram] = 0\n",
+    "        ngram_to_count[ngram] += 1\n",
+    "    ngram_distribution = {i:float(c) / len(ngrams) for i, c in ngram_to_count.items()}\n",
+    "    n_to_distribution[n] = ngram_distribution\n",
+    "\n",
+    "for n in xrange(1, min(4, max_ngram + 1)):\n",
+    "    print '{}-gram distribution'.format(n)\n",
+    "    for ngram, proportion in sorted(n_to_distribution[n].items(), key=lambda x: -x[1]):\n",
+    "        print '{}: {}'.format(ngram, n_to_distribution[n][ngram])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 80,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "# Calculate perplexity of n-gram distribution against the sample\n",
+    "n_to_perplexity = {}\n",
+    "for n in xrange(1, max_ngram + 1):\n",
+    "    distribution = n_to_distribution[n]\n",
+    "    ncontext = n - 1\n",
+    "    log_prob_cum = 0.0\n",
+    "    for i in xrange(seq_len):\n",
+    "        ngram = tuple(sequence[i:i + n])\n",
+    "        if len(ngram) != n:\n",
+    "            break\n",
+    "        posterior = distribution[ngram]\n",
+    "        log_prob_cum += np.log(posterior)\n",
+    "    negative_log_prob = -log_prob_cum / (len(sequence) - (n - 1))\n",
+    "    perplexity = np.exp(negative_log_prob)\n",
+    "    n_to_perplexity[n] = perplexity"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 81,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.text.Text at 0x90f76a0>"
+      ]
+     },
+     "execution_count": 81,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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MczJzB2AwsCYwPiIujYidyyxOkqTFNXMmDB0KG2wAvXsX9xE89NDisVS2uq8ijIjewHq1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\nAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x898b7b8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Plot perplexity values\n",
+    "plt.figure(figsize=(10, 5))\n",
+    "ns = range(1, max_ngram + 1)\n",
+    "plt.plot(ns, [n_to_perplexity[n] for n in ns])\n",
+    "plt.xlabel('N-gram size')\n",
+    "plt.ylabel('Perplexity')"
+   ]
+  }
+ ],
+ "metadata": {
+  "anaconda-cloud": {},
+  "kernelspec": {
+   "display_name": "Python [Root]",
+   "language": "python",
+   "name": "Python [Root]"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.12"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}