Morten Hjorth-Jensen
376 lines
25 KiB
HTML
376 lines
25 KiB
HTML
<!--
|
|
HTML file automatically generated from DocOnce source
|
|
(https://github.com/doconce/doconce/)
|
|
doconce format html week45.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week45-bs --no_mako
|
|
-->
|
|
<html>
|
|
<head>
|
|
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
|
|
<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
|
|
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
|
|
<meta name="description" content="Week 45, Recurrent Neural Networks">
|
|
<title>Week 45, Recurrent Neural Networks</title>
|
|
<!-- Bootstrap style: bootstrap -->
|
|
<!-- doconce format html week45.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week45-bs --no_mako -->
|
|
<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
|
|
<!-- not necessary
|
|
<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
|
|
-->
|
|
<style type="text/css">
|
|
/* Add scrollbar to dropdown menus in bootstrap navigation bar */
|
|
.dropdown-menu {
|
|
height: auto;
|
|
max-height: 400px;
|
|
overflow-x: hidden;
|
|
}
|
|
/* Adds an invisible element before each target to offset for the navigation
|
|
bar */
|
|
.anchor::before {
|
|
content:"";
|
|
display:block;
|
|
height:50px; /* fixed header height for style bootstrap */
|
|
margin:-50px 0 0; /* negative fixed header height */
|
|
}
|
|
</style>
|
|
</head>
|
|
|
|
<!-- tocinfo
|
|
{'highest level': 2,
|
|
'sections': [('Plan for week 45', 2, None, 'plan-for-week-45'),
|
|
('Material for the lab sessions, additional ways to present '
|
|
'classification results and other practicalities',
|
|
2,
|
|
None,
|
|
'material-for-the-lab-sessions-additional-ways-to-present-classification-results-and-other-practicalities'),
|
|
('Searching for Optimal Regularization Parameters $\\lambda$',
|
|
2,
|
|
None,
|
|
'searching-for-optimal-regularization-parameters-lambda'),
|
|
('Grid Search', 2, None, 'grid-search'),
|
|
('Randomized Grid Search', 2, None, 'randomized-grid-search'),
|
|
('Wisconsin Cancer Data', 2, None, 'wisconsin-cancer-data'),
|
|
('Using the correlation matrix',
|
|
2,
|
|
None,
|
|
'using-the-correlation-matrix'),
|
|
('Discussing the correlation data',
|
|
2,
|
|
None,
|
|
'discussing-the-correlation-data'),
|
|
('Other ways of presenting a classification problem',
|
|
2,
|
|
None,
|
|
'other-ways-of-presenting-a-classification-problem'),
|
|
('Combinations of classification results',
|
|
2,
|
|
None,
|
|
'combinations-of-classification-results'),
|
|
('Positive and negative prediction values',
|
|
2,
|
|
None,
|
|
'positive-and-negative-prediction-values'),
|
|
('Other quantities', 2, None, 'other-quantities'),
|
|
('$F_1$ score', 2, None, 'f-1-score'),
|
|
('ROC curve', 2, None, 'roc-curve'),
|
|
('Cumulative gain curve', 2, None, 'cumulative-gain-curve'),
|
|
('Other measures in classification studies: Cancer Data again',
|
|
2,
|
|
None,
|
|
'other-measures-in-classification-studies-cancer-data-again'),
|
|
('Material for Lecture Thursday November 9',
|
|
2,
|
|
None,
|
|
'material-for-lecture-thursday-november-9'),
|
|
('Recurrent neural networks (RNNs): Overarching view',
|
|
2,
|
|
None,
|
|
'recurrent-neural-networks-rnns-overarching-view'),
|
|
('A simple example', 2, None, 'a-simple-example'),
|
|
('RNNs', 3, None, 'rnns'),
|
|
('Basic layout', 2, None, 'basic-layout'),
|
|
('We need to specify the initial activity state of all the '
|
|
'hidden and output units',
|
|
3,
|
|
None,
|
|
'we-need-to-specify-the-initial-activity-state-of-all-the-hidden-and-output-units'),
|
|
('We can specify inputs in several ways',
|
|
3,
|
|
None,
|
|
'we-can-specify-inputs-in-several-ways'),
|
|
('We can specify targets in several ways',
|
|
3,
|
|
None,
|
|
'we-can-specify-targets-in-several-ways'),
|
|
('Backpropagation through time',
|
|
3,
|
|
None,
|
|
'backpropagation-through-time'),
|
|
('The backward pass is linear',
|
|
3,
|
|
None,
|
|
'the-backward-pass-is-linear'),
|
|
('The problem of exploding or vanishing gradients',
|
|
2,
|
|
None,
|
|
'the-problem-of-exploding-or-vanishing-gradients'),
|
|
('Four effective ways to learn an RNN',
|
|
2,
|
|
None,
|
|
'four-effective-ways-to-learn-an-rnn'),
|
|
('Long Short Term Memory (LSTM)',
|
|
3,
|
|
None,
|
|
'long-short-term-memory-lstm'),
|
|
('Implementing a memory cell in a neural network',
|
|
3,
|
|
None,
|
|
'implementing-a-memory-cell-in-a-neural-network'),
|
|
('An extrapolation example', 2, None, 'an-extrapolation-example'),
|
|
('Formatting the Data', 2, None, 'formatting-the-data'),
|
|
('Predicting New Points With A Trained Recurrent Neural Network',
|
|
2,
|
|
None,
|
|
'predicting-new-points-with-a-trained-recurrent-neural-network'),
|
|
('Other Things to Try', 2, None, 'other-things-to-try'),
|
|
('Other Types of Recurrent Neural Networks',
|
|
2,
|
|
None,
|
|
'other-types-of-recurrent-neural-networks')]}
|
|
end of tocinfo -->
|
|
|
|
<body>
|
|
|
|
|
|
|
|
<script type="text/x-mathjax-config">
|
|
MathJax.Hub.Config({
|
|
TeX: {
|
|
equationNumbers: { autoNumber: "none" },
|
|
extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
|
|
}
|
|
});
|
|
</script>
|
|
<script type="text/javascript" async
|
|
src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
|
|
</script>
|
|
|
|
|
|
<!-- Bootstrap navigation bar -->
|
|
<div class="navbar navbar-default navbar-fixed-top">
|
|
<div class="navbar-header">
|
|
<button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
|
|
<span class="icon-bar"></span>
|
|
<span class="icon-bar"></span>
|
|
<span class="icon-bar"></span>
|
|
</button>
|
|
<a class="navbar-brand" href="week45-bs.html">Week 45, Recurrent Neural Networks</a>
|
|
</div>
|
|
<div class="navbar-collapse collapse navbar-responsive-collapse">
|
|
<ul class="nav navbar-nav navbar-right">
|
|
<li class="dropdown">
|
|
<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
|
|
<ul class="dropdown-menu">
|
|
<!-- navigation toc: --> <li><a href="._week45-bs001.html#plan-for-week-45" style="font-size: 80%;"><b>Plan for week 45</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs002.html#material-for-the-lab-sessions-additional-ways-to-present-classification-results-and-other-practicalities" style="font-size: 80%;"><b>Material for the lab sessions, additional ways to present classification results and other practicalities</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs003.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;"><b>Searching for Optimal Regularization Parameters \( \lambda \)</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs004.html#grid-search" style="font-size: 80%;"><b>Grid Search</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs005.html#randomized-grid-search" style="font-size: 80%;"><b>Randomized Grid Search</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs006.html#wisconsin-cancer-data" style="font-size: 80%;"><b>Wisconsin Cancer Data</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs007.html#using-the-correlation-matrix" style="font-size: 80%;"><b>Using the correlation matrix</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs008.html#discussing-the-correlation-data" style="font-size: 80%;"><b>Discussing the correlation data</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs009.html#other-ways-of-presenting-a-classification-problem" style="font-size: 80%;"><b>Other ways of presenting a classification problem</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs010.html#combinations-of-classification-results" style="font-size: 80%;"><b>Combinations of classification results</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs011.html#positive-and-negative-prediction-values" style="font-size: 80%;"><b>Positive and negative prediction values</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs012.html#other-quantities" style="font-size: 80%;"><b>Other quantities</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs013.html#f-1-score" style="font-size: 80%;"><b>\( F_1 \) score</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs014.html#roc-curve" style="font-size: 80%;"><b>ROC curve</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs015.html#cumulative-gain-curve" style="font-size: 80%;"><b>Cumulative gain curve</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs016.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;"><b>Other measures in classification studies: Cancer Data again</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs017.html#material-for-lecture-thursday-november-9" style="font-size: 80%;"><b>Material for Lecture Thursday November 9</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs018.html#recurrent-neural-networks-rnns-overarching-view" style="font-size: 80%;"><b>Recurrent neural networks (RNNs): Overarching view</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs019.html#a-simple-example" style="font-size: 80%;"><b>A simple example</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs019.html#rnns" style="font-size: 80%;"> RNNs</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs020.html#basic-layout" style="font-size: 80%;"><b>Basic layout</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs020.html#we-need-to-specify-the-initial-activity-state-of-all-the-hidden-and-output-units" style="font-size: 80%;"> We need to specify the initial activity state of all the hidden and output units</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs020.html#we-can-specify-inputs-in-several-ways" style="font-size: 80%;"> We can specify inputs in several ways</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs020.html#we-can-specify-targets-in-several-ways" style="font-size: 80%;"> We can specify targets in several ways</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs020.html#backpropagation-through-time" style="font-size: 80%;"> Backpropagation through time</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs020.html#the-backward-pass-is-linear" style="font-size: 80%;"> The backward pass is linear</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs021.html#the-problem-of-exploding-or-vanishing-gradients" style="font-size: 80%;"><b>The problem of exploding or vanishing gradients</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs022.html#four-effective-ways-to-learn-an-rnn" style="font-size: 80%;"><b>Four effective ways to learn an RNN</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs022.html#long-short-term-memory-lstm" style="font-size: 80%;"> Long Short Term Memory (LSTM)</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs022.html#implementing-a-memory-cell-in-a-neural-network" style="font-size: 80%;"> Implementing a memory cell in a neural network</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs023.html#an-extrapolation-example" style="font-size: 80%;"><b>An extrapolation example</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs024.html#formatting-the-data" style="font-size: 80%;"><b>Formatting the Data</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs025.html#predicting-new-points-with-a-trained-recurrent-neural-network" style="font-size: 80%;"><b>Predicting New Points With A Trained Recurrent Neural Network</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="#other-things-to-try" style="font-size: 80%;"><b>Other Things to Try</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week45-bs027.html#other-types-of-recurrent-neural-networks" style="font-size: 80%;"><b>Other Types of Recurrent Neural Networks</b></a></li>
|
|
|
|
</ul>
|
|
</li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
</div> <!-- end of navigation bar -->
|
|
<div class="container">
|
|
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
|
<a name="part0026"></a>
|
|
<!-- !split -->
|
|
<h2 id="other-things-to-try" class="anchor">Other Things to Try </h2>
|
|
|
|
<p>Changing the size of the recurrent neural network and its parameters
|
|
can drastically change the results you get from the model. The below
|
|
code takes the simple recurrent neural network from above and adds a
|
|
second hidden layer, changes the number of neurons in the hidden
|
|
layer, and explicitly declares the activation function of the hidden
|
|
layers to be a sigmoid function. The loss function and optimizer can
|
|
also be changed but are kept the same as the above network. These
|
|
parameters can be tuned to provide the optimal result from the
|
|
network. For some ideas on how to improve the performance of a
|
|
<a href="https://danijar.com/tips-for-training-recurrent-neural-networks" target="_self">recurrent neural network</a>.
|
|
</p>
|
|
|
|
|
|
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
|
<div class="cell border-box-sizing code_cell rendered">
|
|
<div class="input">
|
|
<div class="inner_cell">
|
|
<div class="input_area">
|
|
<div class="highlight" style="background: #f8f8f8">
|
|
<pre style="line-height: 125%;"><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">rnn_2layers</span>(length_of_sequences, batch_size <span style="color: #666666">=</span> <span style="color: #008000; font-weight: bold">None</span>, stateful <span style="color: #666666">=</span> <span style="color: #008000; font-weight: bold">False</span>):
|
|
<span style="color: #BA2121; font-style: italic">"""</span>
|
|
<span style="color: #BA2121; font-style: italic"> Inputs:</span>
|
|
<span style="color: #BA2121; font-style: italic"> length_of_sequences (an int): the number of y values in "x data". This is determined</span>
|
|
<span style="color: #BA2121; font-style: italic"> when the data is formatted</span>
|
|
<span style="color: #BA2121; font-style: italic"> batch_size (an int): Default value is None. See Keras documentation of SimpleRNN.</span>
|
|
<span style="color: #BA2121; font-style: italic"> stateful (a boolean): Default value is False. See Keras documentation of SimpleRNN.</span>
|
|
<span style="color: #BA2121; font-style: italic"> Returns:</span>
|
|
<span style="color: #BA2121; font-style: italic"> model (a Keras model): The recurrent neural network that is built and compiled by this</span>
|
|
<span style="color: #BA2121; font-style: italic"> method</span>
|
|
<span style="color: #BA2121; font-style: italic"> Builds and compiles a recurrent neural network with two hidden layers and returns the model.</span>
|
|
<span style="color: #BA2121; font-style: italic"> """</span>
|
|
<span style="color: #408080; font-style: italic"># Number of neurons in the input and output layers</span>
|
|
in_out_neurons <span style="color: #666666">=</span> <span style="color: #666666">1</span>
|
|
<span style="color: #408080; font-style: italic"># Number of neurons in the hidden layer, increased from the first network</span>
|
|
hidden_neurons <span style="color: #666666">=</span> <span style="color: #666666">500</span>
|
|
<span style="color: #408080; font-style: italic"># Define the input layer</span>
|
|
inp <span style="color: #666666">=</span> Input(batch_shape<span style="color: #666666">=</span>(batch_size,
|
|
length_of_sequences,
|
|
in_out_neurons))
|
|
<span style="color: #408080; font-style: italic"># Create two hidden layers instead of one hidden layer. Explicitly set the activation</span>
|
|
<span style="color: #408080; font-style: italic"># function to be the sigmoid function (the default value is hyperbolic tangent)</span>
|
|
rnn1 <span style="color: #666666">=</span> SimpleRNN(hidden_neurons,
|
|
return_sequences<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">True</span>, <span style="color: #408080; font-style: italic"># This needs to be True if another hidden layer is to follow</span>
|
|
stateful <span style="color: #666666">=</span> stateful, activation <span style="color: #666666">=</span> <span style="color: #BA2121">'sigmoid'</span>,
|
|
name<span style="color: #666666">=</span><span style="color: #BA2121">"RNN1"</span>)(inp)
|
|
rnn2 <span style="color: #666666">=</span> SimpleRNN(hidden_neurons,
|
|
return_sequences<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">False</span>, activation <span style="color: #666666">=</span> <span style="color: #BA2121">'sigmoid'</span>,
|
|
stateful <span style="color: #666666">=</span> stateful,
|
|
name<span style="color: #666666">=</span><span style="color: #BA2121">"RNN2"</span>)(rnn1)
|
|
<span style="color: #408080; font-style: italic"># Define the output layer as a dense neural network layer (standard neural network layer)</span>
|
|
<span style="color: #408080; font-style: italic">#and add it to the network immediately after the hidden layer.</span>
|
|
dens <span style="color: #666666">=</span> Dense(in_out_neurons,name<span style="color: #666666">=</span><span style="color: #BA2121">"dense"</span>)(rnn2)
|
|
<span style="color: #408080; font-style: italic"># Create the machine learning model starting with the input layer and ending with the </span>
|
|
<span style="color: #408080; font-style: italic"># output layer</span>
|
|
model <span style="color: #666666">=</span> Model(inputs<span style="color: #666666">=</span>[inp],outputs<span style="color: #666666">=</span>[dens])
|
|
<span style="color: #408080; font-style: italic"># Compile the machine learning model using the mean squared error function as the loss </span>
|
|
<span style="color: #408080; font-style: italic"># function and an Adams optimizer.</span>
|
|
model<span style="color: #666666">.</span>compile(loss<span style="color: #666666">=</span><span style="color: #BA2121">"mean_squared_error"</span>, optimizer<span style="color: #666666">=</span><span style="color: #BA2121">"adam"</span>)
|
|
<span style="color: #008000; font-weight: bold">return</span> model
|
|
|
|
<span style="color: #408080; font-style: italic"># Check to make sure the data set is complete</span>
|
|
<span style="color: #008000; font-weight: bold">assert</span> <span style="color: #008000">len</span>(X_tot) <span style="color: #666666">==</span> <span style="color: #008000">len</span>(y_tot)
|
|
|
|
<span style="color: #408080; font-style: italic"># This is the number of points that will be used in as the training data</span>
|
|
dim<span style="color: #666666">=12</span>
|
|
|
|
<span style="color: #408080; font-style: italic"># Separate the training data from the whole data set</span>
|
|
X_train <span style="color: #666666">=</span> X_tot[:dim]
|
|
y_train <span style="color: #666666">=</span> y_tot[:dim]
|
|
|
|
|
|
<span style="color: #408080; font-style: italic"># Generate the training data for the RNN, using a sequence of 2</span>
|
|
rnn_input, rnn_training <span style="color: #666666">=</span> format_data(y_train, <span style="color: #666666">2</span>)
|
|
|
|
|
|
<span style="color: #408080; font-style: italic"># Create a recurrent neural network in Keras and produce a summary of the </span>
|
|
<span style="color: #408080; font-style: italic"># machine learning model</span>
|
|
model <span style="color: #666666">=</span> rnn_2layers(length_of_sequences <span style="color: #666666">=</span> <span style="color: #666666">2</span>)
|
|
model<span style="color: #666666">.</span>summary()
|
|
|
|
<span style="color: #408080; font-style: italic"># Start the timer. Want to time training+testing</span>
|
|
start <span style="color: #666666">=</span> timer()
|
|
<span style="color: #408080; font-style: italic"># Fit the model using the training data genenerated above using 150 training iterations and a 5%</span>
|
|
<span style="color: #408080; font-style: italic"># validation split. Setting verbose to True prints information about each training iteration.</span>
|
|
hist <span style="color: #666666">=</span> model<span style="color: #666666">.</span>fit(rnn_input, rnn_training, batch_size<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">None</span>, epochs<span style="color: #666666">=150</span>,
|
|
verbose<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">True</span>,validation_split<span style="color: #666666">=0.05</span>)
|
|
|
|
|
|
<span style="color: #408080; font-style: italic"># This section plots the training loss and the validation loss as a function of training iteration.</span>
|
|
<span style="color: #408080; font-style: italic"># This is not required for analyzing the couple cluster data but can help determine if the network is</span>
|
|
<span style="color: #408080; font-style: italic"># being overtrained.</span>
|
|
<span style="color: #008000; font-weight: bold">for</span> label <span style="color: #AA22FF; font-weight: bold">in</span> [<span style="color: #BA2121">"loss"</span>,<span style="color: #BA2121">"val_loss"</span>]:
|
|
plt<span style="color: #666666">.</span>plot(hist<span style="color: #666666">.</span>history[label],label<span style="color: #666666">=</span>label)
|
|
|
|
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">"loss"</span>)
|
|
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">"epoch"</span>)
|
|
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"The final validation loss: </span><span style="color: #BB6688; font-weight: bold">{}</span><span style="color: #BA2121">"</span><span style="color: #666666">.</span>format(hist<span style="color: #666666">.</span>history[<span style="color: #BA2121">"val_loss"</span>][<span style="color: #666666">-1</span>]))
|
|
plt<span style="color: #666666">.</span>legend()
|
|
plt<span style="color: #666666">.</span>show()
|
|
|
|
<span style="color: #408080; font-style: italic"># Use the trained neural network to predict more points of the data set</span>
|
|
test_rnn(X_tot, y_tot, X_tot[<span style="color: #666666">0</span>], X_tot[dim<span style="color: #666666">-1</span>])
|
|
<span style="color: #408080; font-style: italic"># Stop the timer and calculate the total time needed.</span>
|
|
end <span style="color: #666666">=</span> timer()
|
|
<span style="color: #008000">print</span>(<span style="color: #BA2121">'Time: '</span>, end<span style="color: #666666">-</span>start)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div class="output_wrapper">
|
|
<div class="output">
|
|
<div class="output_area">
|
|
<div class="output_subarea output_stream output_stdout output_text">
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<p>
|
|
<!-- navigation buttons at the bottom of the page -->
|
|
<ul class="pagination">
|
|
<li><a href="._week45-bs025.html">«</a></li>
|
|
<li><a href="._week45-bs000.html">1</a></li>
|
|
<li><a href="">...</a></li>
|
|
<li><a href="._week45-bs018.html">19</a></li>
|
|
<li><a href="._week45-bs019.html">20</a></li>
|
|
<li><a href="._week45-bs020.html">21</a></li>
|
|
<li><a href="._week45-bs021.html">22</a></li>
|
|
<li><a href="._week45-bs022.html">23</a></li>
|
|
<li><a href="._week45-bs023.html">24</a></li>
|
|
<li><a href="._week45-bs024.html">25</a></li>
|
|
<li><a href="._week45-bs025.html">26</a></li>
|
|
<li class="active"><a href="._week45-bs026.html">27</a></li>
|
|
<li><a href="._week45-bs027.html">28</a></li>
|
|
<li><a href="._week45-bs027.html">»</a></li>
|
|
</ul>
|
|
<!-- ------------------- end of main content --------------- -->
|
|
</div> <!-- end container -->
|
|
<!-- include javascript, jQuery *first* -->
|
|
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
|
|
<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
|
|
<!-- Bootstrap footer
|
|
<footer>
|
|
<a href="https://..."><img width="250" align=right src="https://..."></a>
|
|
</footer>
|
|
-->
|
|
<center style="font-size:80%">
|
|
<!-- copyright only on the titlepage -->
|
|
</center>
|
|
</body>
|
|
</html>
|
|
|