From 88b667df81b50675ccf86cfe26ca5eb521e9e2c4 Mon Sep 17 00:00:00 2001 From: mhjensen Date: Thu, 10 Oct 2019 13:13:09 +0200 Subject: [PATCH] adding material to dim red --- doc/pub/DimRed/html/._DimRed-bs000.html | 49 +- doc/pub/DimRed/html/._DimRed-bs001.html | 42 +- doc/pub/DimRed/html/._DimRed-bs002.html | 81 +- doc/pub/DimRed/html/._DimRed-bs003.html | 83 +- doc/pub/DimRed/html/._DimRed-bs004.html | 79 +- doc/pub/DimRed/html/._DimRed-bs005.html | 72 +- doc/pub/DimRed/html/._DimRed-bs006.html | 60 +- doc/pub/DimRed/html/._DimRed-bs007.html | 66 +- doc/pub/DimRed/html/._DimRed-bs008.html | 72 +- doc/pub/DimRed/html/._DimRed-bs009.html | 61 +- doc/pub/DimRed/html/DimRed-bs.html | 49 +- doc/pub/DimRed/html/DimRed-reveal.html | 49 +- doc/pub/DimRed/html/DimRed-solarized.html | 68 +- doc/pub/DimRed/html/DimRed.html | 68 +- doc/pub/DimRed/html/reveal.js/.gitignore | 7 +- doc/pub/DimRed/html/reveal.js/.travis.yml | 6 +- doc/pub/DimRed/html/reveal.js/LICENSE | 2 +- doc/pub/DimRed/html/reveal.js/README.md | 592 +++---- doc/pub/DimRed/html/reveal.js/bower.json | 6 +- .../DimRed/html/reveal.js/css/print/paper.css | 7 +- .../DimRed/html/reveal.js/css/print/pdf.css | 97 +- doc/pub/DimRed/html/reveal.js/css/reveal.scss | 588 ++----- .../DimRed/html/reveal.js/css/theme/README.md | 6 +- .../reveal.js/css/theme/source/black.scss | 4 +- .../reveal.js/css/theme/source/white.scss | 4 +- doc/pub/DimRed/html/reveal.js/index.html | 390 ++++- doc/pub/DimRed/html/reveal.js/js/reveal.js | 1419 ++++------------- .../DimRed/html/reveal.js/lib/css/zenburn.css | 119 +- .../DimRed/html/reveal.js/lib/js/head.min.js | 17 +- doc/pub/DimRed/html/reveal.js/package.json | 42 +- .../reveal.js/plugin/highlight/highlight.js | 55 +- .../reveal.js/plugin/markdown/example.html | 7 - .../html/reveal.js/plugin/markdown/example.md | 5 - .../reveal.js/plugin/markdown/markdown.js | 57 +- .../html/reveal.js/plugin/markdown/marked.js | 2 +- .../DimRed/html/reveal.js/plugin/math/math.js | 7 +- .../html/reveal.js/plugin/multiplex/client.js | 2 +- .../html/reveal.js/plugin/multiplex/index.js | 38 +- .../html/reveal.js/plugin/multiplex/master.js | 61 +- .../reveal.js/plugin/notes-server/client.js | 7 +- .../reveal.js/plugin/notes-server/index.js | 31 +- .../reveal.js/plugin/notes-server/notes.html | 241 +-- .../html/reveal.js/plugin/notes/notes.html | 417 +---- .../html/reveal.js/plugin/notes/notes.js | 45 +- .../reveal.js/plugin/print-pdf/print-pdf.js | 75 +- .../html/reveal.js/plugin/search/search.js | 72 +- .../html/reveal.js/plugin/zoom-js/zoom.js | 40 +- .../html/reveal.js/test/examples/math.html | 2 +- .../test/examples/slide-backgrounds.html | 2 +- .../html/reveal.js/test/test-markdown.html | 2 +- doc/pub/DimRed/html/reveal.js/test/test.html | 3 +- doc/pub/DimRed/html/reveal.js/test/test.js | 10 +- doc/pub/DimRed/ipynb/DimRed.ipynb | 23 +- doc/pub/DimRed/ipynb/ipynb-DimRed-src.tar.gz | Bin 207 -> 191 bytes doc/pub/DimRed/pdf/DimRed-minted.pdf | Bin 248019 -> 199386 bytes 55 files changed, 1955 insertions(+), 3454 deletions(-) diff --git a/doc/pub/DimRed/html/._DimRed-bs000.html b/doc/pub/DimRed/html/._DimRed-bs000.html index 011b06a83..bbc53cf32 100644 --- a/doc/pub/DimRed/html/._DimRed-bs000.html +++ b/doc/pub/DimRed/html/._DimRed-bs000.html @@ -6,9 +6,10 @@ Automatically generated HTML file from DocOnce source - + + -Data Analysis and Machine Learning: Dimensionality Reduction +Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction @@ -44,14 +45,15 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec0'), - ('Principal Component Analysis', 2, None, '___sec1'), - ('PCA and scikit-learn', 2, None, '___sec2'), - ('More on the PCA', 2, None, '___sec3'), - ('Incremental PCA', 2, None, '___sec4'), - ('Randomized PCA', 2, None, '___sec5'), - ('Kernel PCA', 2, None, '___sec6'), - ('LLE', 2, None, '___sec7'), - ('Other techniques', 2, None, '___sec8')]} + ('Preprocessing our data', 2, None, '___sec1'), + ('Principal Component Analysis', 2, None, '___sec2'), + ('PCA and scikit-learn', 2, None, '___sec3'), + ('More on the PCA', 2, None, '___sec4'), + ('Incremental PCA', 2, None, '___sec5'), + ('Randomized PCA', 2, None, '___sec6'), + ('Kernel PCA', 2, None, '___sec7'), + ('LLE', 2, None, '___sec8'), + ('Other techniques', 2, None, '___sec9')]} end of tocinfo --> @@ -81,7 +83,7 @@ MathJax.Hub.Config({ - Data Analysis and Machine Learning: Dimensionality Reduction + Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
@@ -90,14 +92,15 @@ MathJax.Hub.Config({ Contents @@ -116,7 +119,7 @@ MathJax.Hub.Config({
-

Data Analysis and Machine Learning: Dimensionality Reduction

+

Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction

@@ -132,7 +135,7 @@ MathJax.Hub.Config({

[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Oct 26, 2018

+

Oct 10, 2019


@@ -155,6 +158,8 @@ MathJax.Hub.Config({

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    • @@ -172,7 +177,7 @@ MathJax.Hub.Config({
    - © 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license + © 1999-2019, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
    diff --git a/doc/pub/DimRed/html/._DimRed-bs001.html b/doc/pub/DimRed/html/._DimRed-bs001.html index ad53ab15e..c7963e4f4 100644 --- a/doc/pub/DimRed/html/._DimRed-bs001.html +++ b/doc/pub/DimRed/html/._DimRed-bs001.html @@ -6,9 +6,10 @@ Automatically generated HTML file from DocOnce source - + + -Data Analysis and Machine Learning: Dimensionality Reduction +Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction @@ -44,14 +45,15 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec0'), - ('Principal Component Analysis', 2, None, '___sec1'), - ('PCA and scikit-learn', 2, None, '___sec2'), - ('More on the PCA', 2, None, '___sec3'), - ('Incremental PCA', 2, None, '___sec4'), - ('Randomized PCA', 2, None, '___sec5'), - ('Kernel PCA', 2, None, '___sec6'), - ('LLE', 2, None, '___sec7'), - ('Other techniques', 2, None, '___sec8')]} + ('Preprocessing our data', 2, None, '___sec1'), + ('Principal Component Analysis', 2, None, '___sec2'), + ('PCA and scikit-learn', 2, None, '___sec3'), + ('More on the PCA', 2, None, '___sec4'), + ('Incremental PCA', 2, None, '___sec5'), + ('Randomized PCA', 2, None, '___sec6'), + ('Kernel PCA', 2, None, '___sec7'), + ('LLE', 2, None, '___sec8'), + ('Other techniques', 2, None, '___sec9')]} end of tocinfo --> @@ -81,7 +83,7 @@ MathJax.Hub.Config({ - Data Analysis and Machine Learning: Dimensionality Reduction + Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
    @@ -90,14 +92,15 @@ MathJax.Hub.Config({ Contents @@ -149,6 +152,7 @@ reduction techniques: the principal component analysis PCA, Kernel PCA, and Loca
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs002.html b/doc/pub/DimRed/html/._DimRed-bs002.html index dab0b773d..a720c0ad3 100644 --- a/doc/pub/DimRed/html/._DimRed-bs002.html +++ b/doc/pub/DimRed/html/._DimRed-bs002.html @@ -6,9 +6,10 @@ Automatically generated HTML file from DocOnce source - + + -Data Analysis and Machine Learning: Dimensionality Reduction +Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction @@ -44,14 +45,15 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec0'), - ('Principal Component Analysis', 2, None, '___sec1'), - ('PCA and scikit-learn', 2, None, '___sec2'), - ('More on the PCA', 2, None, '___sec3'), - ('Incremental PCA', 2, None, '___sec4'), - ('Randomized PCA', 2, None, '___sec5'), - ('Kernel PCA', 2, None, '___sec6'), - ('LLE', 2, None, '___sec7'), - ('Other techniques', 2, None, '___sec8')]} + ('Preprocessing our data', 2, None, '___sec1'), + ('Principal Component Analysis', 2, None, '___sec2'), + ('PCA and scikit-learn', 2, None, '___sec3'), + ('More on the PCA', 2, None, '___sec4'), + ('Incremental PCA', 2, None, '___sec5'), + ('Randomized PCA', 2, None, '___sec6'), + ('Kernel PCA', 2, None, '___sec7'), + ('LLE', 2, None, '___sec8'), + ('Other techniques', 2, None, '___sec9')]} end of tocinfo --> @@ -81,7 +83,7 @@ MathJax.Hub.Config({ - Data Analysis and Machine Learning: Dimensionality Reduction + Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
    @@ -90,14 +92,15 @@ MathJax.Hub.Config({ Contents @@ -113,39 +116,28 @@ MathJax.Hub.Config({ -

    Principal Component Analysis

    +

    Preprocessing our data

    -Principal Component Analysis (PCA) is by far the most popular dimensionality reduction algorithm. -First it identifies the hyperplane that lies closest to the data, and then it projects the data onto it.

    -The following Python code uses NumPy’s svd() function to obtain all the principal components of the -training set, then extracts the first two principal components -

    - - -

    X_centered = X - X.mean(axis=0)
-U, s, V = np.linalg.svd(X_centered)
-c1 = V.T[:, 0]
-c2 = V.T[:, 1]
-
    -

    -PCA assumes that the dataset is centered around the origin. Scikit-Learn’s PCA classes take care of centering -the data for you. However, if you implement PCA yourself (as in the preceding example), or if you use other libraries, don’t -forget to center the data first. +Before we proceed however, we will discuss how to preprocess our +data. Till now and in connection with project 1 not met so many cases +where we are too sensitive to the scaling of our data. Normally the +data may need a rescaling and/or may be sensitive to extreme +values. Scaling the data renders our inputs much more suitable for the +algorithms we want to emply.

    -Once you have identified all the principal components, you can reduce the dimensionality of the dataset -down to \( d \) dimensions by projecting it onto the hyperplane defined by the first \( d \) principal components. -Selecting this hyperplane ensures that the projection will preserve as much variance as possible. -

    +Scikit-Learn has several functions which allow us to rescale the data, normally resulting in much better results in terms of various accuracy scores. The StandardScaler function in Scikit-Learn ensures that for each feature/predictor we study the mean value is zero and the variance is zero (every column in the design/feature matrix). +This scaling has the drawback that it does not ensure that we have a particular maximum or minumum in our data set. Another function included in Scikit-Learn is the MinMaxScaler which ensures that all features are exactly between \( 0 \) and \( 1 \). The Normalizer function scale each column of the design matrix so that + +

    +

    +
    + - -
    W2 = V.T[:, :2]
-X2D = X_centered.dot(W2)
-

    @@ -161,6 +153,7 @@ X2D = X_centered8

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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs003.html b/doc/pub/DimRed/html/._DimRed-bs003.html index 361939a72..c0ba3abc6 100644 --- a/doc/pub/DimRed/html/._DimRed-bs003.html +++ b/doc/pub/DimRed/html/._DimRed-bs003.html @@ -6,9 +6,10 @@ Automatically generated HTML file from DocOnce source - + + -Data Analysis and Machine Learning: Dimensionality Reduction +Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction @@ -44,14 +45,15 @@ Automatically generated HTML file from DocOnce source 2, None, '___sec0'), - ('Principal Component Analysis', 2, None, '___sec1'), - ('PCA and scikit-learn', 2, None, '___sec2'), - ('More on the PCA', 2, None, '___sec3'), - ('Incremental PCA', 2, None, '___sec4'), - ('Randomized PCA', 2, None, '___sec5'), - ('Kernel PCA', 2, None, '___sec6'), - ('LLE', 2, None, '___sec7'), - ('Other techniques', 2, None, '___sec8')]} + ('Preprocessing our data', 2, None, '___sec1'), + ('Principal Component Analysis', 2, None, '___sec2'), + ('PCA and scikit-learn', 2, None, '___sec3'), + ('More on the PCA', 2, None, '___sec4'), + ('Incremental PCA', 2, None, '___sec5'), + ('Randomized PCA', 2, None, '___sec6'), + ('Kernel PCA', 2, None, '___sec7'), + ('LLE', 2, None, '___sec8'), + ('Other techniques', 2, None, '___sec9')]} end of tocinfo --> @@ -81,7 +83,7 @@ MathJax.Hub.Config({ - Data Analysis and Machine Learning: Dimensionality Reduction + Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
    @@ -90,14 +92,15 @@ MathJax.Hub.Config({ Contents @@ -111,36 +114,41 @@ MathJax.Hub.Config({

     

     

     

    - + -

    PCA and scikit-learn

    +

    Principal Component Analysis

    +
    +
    +

    +Principal Component Analysis (PCA) is by far the most popular dimensionality reduction algorithm. +First it identifies the hyperplane that lies closest to the data, and then it projects the data onto it.

    -Scikit-Learn’s PCA class implements PCA using SVD decomposition just like we did before. The -following code applies PCA to reduce the dimensionality of the dataset down to two dimensions (note -that it automatically takes care of centering the data): +The following Python code uses NumPy’s svd() function to obtain all the principal components of the +training set, then extracts the first two principal components

    -

    from sklearn.decomposition import PCA
-pca = PCA(n_components = 2)
-X2D = pca.fit_transform(X)
+
    X_centered = X - X.mean(axis=0)
+U, s, V = np.linalg.svd(X_centered)
+c1 = V.T[:, 0]
+c2 = V.T[:, 1]
 
    
 
    
-After fitting the PCA transformer to the dataset, you can access the principal components using the
-components variable (note that it contains the PCs as horizontal vectors, so, for example, the first
-principal component is equal to 
+PCA assumes that the dataset is centered around the origin. Scikit-Learn’s PCA classes take care of centering
+the data for you. However, if you implement PCA yourself (as in the preceding example), or if you use other libraries, don’t
+forget to center the data first.
+
+
    
+Once you have identified all the principal components, you can reduce the dimensionality of the dataset
+down to \( d \) dimensions by projecting it onto the hyperplane defined by the first \( d \) principal components.
+Selecting this hyperplane ensures that the projection will preserve as much variance as possible. 
 
    
 
 
-
    pca.components_.T[:, 0]).
+
    W2 = V.T[:, :2]
+X2D = X_centered.dot(W2)
 
    
-
    
-Another very useful piece of information is the explained variance ratio of each principal component,
-available via the \( explained\_variance\_ratio \) variable. It indicates the proportion of the dataset’s
-variance that lies along the axis of each principal component. 
-More material to come here.
-
 
    
 
    
 
@@ -156,6 +164,7 @@ More material to come here.
   
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diff --git a/doc/pub/DimRed/html/._DimRed-bs004.html b/doc/pub/DimRed/html/._DimRed-bs004.html
index 406b44c9d..e94811a79 100644
--- a/doc/pub/DimRed/html/._DimRed-bs004.html
+++ b/doc/pub/DimRed/html/._DimRed-bs004.html
@@ -6,9 +6,10 @@ Automatically generated HTML file from DocOnce source
 
 
 
-
+
+
 
-Data Analysis and Machine Learning: Dimensionality Reduction
+Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
 
 
 
@@ -44,14 +45,15 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec0'),
-              ('Principal Component Analysis', 2, None, '___sec1'),
-              ('PCA and scikit-learn', 2, None, '___sec2'),
-              ('More on the PCA', 2, None, '___sec3'),
-              ('Incremental PCA', 2, None, '___sec4'),
-              ('Randomized PCA', 2, None, '___sec5'),
-              ('Kernel PCA', 2, None, '___sec6'),
-              ('LLE', 2, None, '___sec7'),
-              ('Other techniques', 2, None, '___sec8')]}
+              ('Preprocessing our data', 2, None, '___sec1'),
+              ('Principal Component Analysis', 2, None, '___sec2'),
+              ('PCA and scikit-learn', 2, None, '___sec3'),
+              ('More on the PCA', 2, None, '___sec4'),
+              ('Incremental PCA', 2, None, '___sec5'),
+              ('Randomized PCA', 2, None, '___sec6'),
+              ('Kernel PCA', 2, None, '___sec7'),
+              ('LLE', 2, None, '___sec8'),
+              ('Other techniques', 2, None, '___sec9')]}
 end of tocinfo -->
 
 
@@ -81,7 +83,7 @@ MathJax.Hub.Config({
       
       
     
-    Data Analysis and Machine Learning: Dimensionality Reduction
+    Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
   
    
 
   
    
@@ -90,14 +92,15 @@ MathJax.Hub.Config({
         Contents 
         
       
@@ -111,33 +114,36 @@ MathJax.Hub.Config({
 
     
     
     
     
 
 
-
+
 
-
    More on the PCA 
    
-Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to
-choose the number of dimensions that add up to a sufficiently large portion of the variance (e.g., 95%).
-Unless, of course, you are reducing dimensionality for data visualization — in that case you will
-generally want to reduce the dimensionality down to 2 or 3.
-The following code computes PCA without reducing dimensionality, then computes the minimum number
-of dimensions required to preserve 95% of the training set’s variance:
+
    PCA and scikit-learn 
    
+
+
    
+Scikit-Learn’s PCA class implements PCA using SVD decomposition just like we did before. The
+following code applies PCA to reduce the dimensionality of the dataset down to two dimensions (note
+that it automatically takes care of centering the data):
 
    
 
 
-
    pca = PCA()
-pca.fit(X)
-cumsum = np.cumsum(pca.explained_variance_ratio_)
-d = np.argmax(cumsum >= 0.95) + 1
+
    from sklearn.decomposition import PCA
+pca = PCA(n_components = 2)
+X2D = pca.fit_transform(X)
 
    
 
    
-You could then set \( n\_components=d \) and run PCA again. However, there is a much better option: instead
-of specifying the number of principal components you want to preserve, you can set \( n\_components \) to be
-a float between 0.0 and 1.0, indicating the ratio of variance you wish to preserve:
+After fitting the PCA transformer to the dataset, you can access the principal components using the
+components variable (note that it contains the PCs as horizontal vectors, so, for example, the first
+principal component is equal to 
 
    
 
 
-
    pca = PCA(n_components=0.95)
-X_reduced = pca.fit_transform(X)
+
    pca.components_.T[:, 0]).
 
    
+
    
+Another very useful piece of information is the explained variance ratio of each principal component,
+available via the \( explained\_variance\_ratio \) variable. It indicates the proportion of the dataset’s
+variance that lies along the axis of each principal component. 
+More material to come here.
+
 
    
 
    
 
@@ -153,6 +159,7 @@ X_reduced = pca
   
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diff --git a/doc/pub/DimRed/html/._DimRed-bs005.html b/doc/pub/DimRed/html/._DimRed-bs005.html
index 8b899a8b6..5d9967a80 100644
--- a/doc/pub/DimRed/html/._DimRed-bs005.html
+++ b/doc/pub/DimRed/html/._DimRed-bs005.html
@@ -6,9 +6,10 @@ Automatically generated HTML file from DocOnce source
 
 
 
-
+
+
 
-Data Analysis and Machine Learning: Dimensionality Reduction
+Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
 
 
 
@@ -44,14 +45,15 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec0'),
-              ('Principal Component Analysis', 2, None, '___sec1'),
-              ('PCA and scikit-learn', 2, None, '___sec2'),
-              ('More on the PCA', 2, None, '___sec3'),
-              ('Incremental PCA', 2, None, '___sec4'),
-              ('Randomized PCA', 2, None, '___sec5'),
-              ('Kernel PCA', 2, None, '___sec6'),
-              ('LLE', 2, None, '___sec7'),
-              ('Other techniques', 2, None, '___sec8')]}
+              ('Preprocessing our data', 2, None, '___sec1'),
+              ('Principal Component Analysis', 2, None, '___sec2'),
+              ('PCA and scikit-learn', 2, None, '___sec3'),
+              ('More on the PCA', 2, None, '___sec4'),
+              ('Incremental PCA', 2, None, '___sec5'),
+              ('Randomized PCA', 2, None, '___sec6'),
+              ('Kernel PCA', 2, None, '___sec7'),
+              ('LLE', 2, None, '___sec8'),
+              ('Other techniques', 2, None, '___sec9')]}
 end of tocinfo -->
 
 
@@ -81,7 +83,7 @@ MathJax.Hub.Config({
       
       
     
-    Data Analysis and Machine Learning: Dimensionality Reduction
+    Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
   
    
 
   
    
@@ -90,14 +92,15 @@ MathJax.Hub.Config({
         Contents 
         
       
@@ -113,13 +116,31 @@ MathJax.Hub.Config({
 
 
 
-
    Incremental PCA 
    
-One problem with the preceding implementation of PCA is that it requires the whole training set to fit in
-memory in order for the SVD algorithm to run. Fortunately, Incremental PCA (IPCA) algorithms have
-been developed: you can split the training set into mini-batches and feed an IPCA algorithm one minibatch
-at a time. This is useful for large training sets, and also to apply PCA online (i.e., on the fly, as new
-instances arrive).
+
    More on the PCA 
    
+Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to
+choose the number of dimensions that add up to a sufficiently large portion of the variance (e.g., 95%).
+Unless, of course, you are reducing dimensionality for data visualization — in that case you will
+generally want to reduce the dimensionality down to 2 or 3.
+The following code computes PCA without reducing dimensionality, then computes the minimum number
+of dimensions required to preserve 95% of the training set’s variance:
+
    
 
+
+
    pca = PCA()
+pca.fit(X)
+cumsum = np.cumsum(pca.explained_variance_ratio_)
+d = np.argmax(cumsum >= 0.95) + 1
+
    
+
    
+You could then set \( n\_components=d \) and run PCA again. However, there is a much better option: instead
+of specifying the number of principal components you want to preserve, you can set \( n\_components \) to be
+a float between 0.0 and 1.0, indicating the ratio of variance you wish to preserve:
+
    
+
+
+
    pca = PCA(n_components=0.95)
+X_reduced = pca.fit_transform(X)
+
    
 
    
 
    
 
@@ -135,6 +156,7 @@ instances arrive).
   
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diff --git a/doc/pub/DimRed/html/._DimRed-bs006.html b/doc/pub/DimRed/html/._DimRed-bs006.html
index ef72a6801..8376feceb 100644
--- a/doc/pub/DimRed/html/._DimRed-bs006.html
+++ b/doc/pub/DimRed/html/._DimRed-bs006.html
@@ -6,9 +6,10 @@ Automatically generated HTML file from DocOnce source
 
 
 
-
+
+
 
-Data Analysis and Machine Learning: Dimensionality Reduction
+Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
 
 
 
@@ -44,14 +45,15 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec0'),
-              ('Principal Component Analysis', 2, None, '___sec1'),
-              ('PCA and scikit-learn', 2, None, '___sec2'),
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-              ('Randomized PCA', 2, None, '___sec5'),
-              ('Kernel PCA', 2, None, '___sec6'),
-              ('LLE', 2, None, '___sec7'),
-              ('Other techniques', 2, None, '___sec8')]}
+              ('Preprocessing our data', 2, None, '___sec1'),
+              ('Principal Component Analysis', 2, None, '___sec2'),
+              ('PCA and scikit-learn', 2, None, '___sec3'),
+              ('More on the PCA', 2, None, '___sec4'),
+              ('Incremental PCA', 2, None, '___sec5'),
+              ('Randomized PCA', 2, None, '___sec6'),
+              ('Kernel PCA', 2, None, '___sec7'),
+              ('LLE', 2, None, '___sec8'),
+              ('Other techniques', 2, None, '___sec9')]}
 end of tocinfo -->
 
 
@@ -81,7 +83,7 @@ MathJax.Hub.Config({
       
       
     
-    Data Analysis and Machine Learning: Dimensionality Reduction
+    Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
   
    
 
   
    
@@ -90,14 +92,15 @@ MathJax.Hub.Config({
         Contents 
         
       
@@ -113,18 +116,12 @@ MathJax.Hub.Config({
 
 
 
-
    Randomized PCA 
    
-
-
    
-Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic
-algorithm that quickly finds an approximation of the first d principal components. Its computational
-complexity is \( O(m \times d^2)+O(d^3) \), instead of \( O(m \times n^2) + O(n^3) \), so it is dramatically faster than the
-previous algorithms when \( d \) is much smaller than \( n \).
-
-
    
-
    
-
    
-
+
    Incremental PCA 
    
+One problem with the preceding implementation of PCA is that it requires the whole training set to fit in
+memory in order for the SVD algorithm to run. Fortunately, Incremental PCA (IPCA) algorithms have
+been developed: you can split the training set into mini-batches and feed an IPCA algorithm one minibatch
+at a time. This is useful for large training sets, and also to apply PCA online (i.e., on the fly, as new
+instances arrive).
 
 
    
 
    
@@ -141,6 +138,7 @@ previous algorithms when \( d \) is much smaller than \( n \).
   
  • 8
    • 
   
  • 9
    • 
   
  • 10
    • 
+  
  • 11
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/DimRed/html/._DimRed-bs007.html b/doc/pub/DimRed/html/._DimRed-bs007.html
index 4e6403ff4..a064b2321 100644
--- a/doc/pub/DimRed/html/._DimRed-bs007.html
+++ b/doc/pub/DimRed/html/._DimRed-bs007.html
@@ -6,9 +6,10 @@ Automatically generated HTML file from DocOnce source
 
 
 
-
+
+
 
-Data Analysis and Machine Learning: Dimensionality Reduction
+Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
 
 
 
@@ -44,14 +45,15 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec0'),
-              ('Principal Component Analysis', 2, None, '___sec1'),
-              ('PCA and scikit-learn', 2, None, '___sec2'),
-              ('More on the PCA', 2, None, '___sec3'),
-              ('Incremental PCA', 2, None, '___sec4'),
-              ('Randomized PCA', 2, None, '___sec5'),
-              ('Kernel PCA', 2, None, '___sec6'),
-              ('LLE', 2, None, '___sec7'),
-              ('Other techniques', 2, None, '___sec8')]}
+              ('Preprocessing our data', 2, None, '___sec1'),
+              ('Principal Component Analysis', 2, None, '___sec2'),
+              ('PCA and scikit-learn', 2, None, '___sec3'),
+              ('More on the PCA', 2, None, '___sec4'),
+              ('Incremental PCA', 2, None, '___sec5'),
+              ('Randomized PCA', 2, None, '___sec6'),
+              ('Kernel PCA', 2, None, '___sec7'),
+              ('LLE', 2, None, '___sec8'),
+              ('Other techniques', 2, None, '___sec9')]}
 end of tocinfo -->
 
 
@@ -81,7 +83,7 @@ MathJax.Hub.Config({
       
       
     
-    Data Analysis and Machine Learning: Dimensionality Reduction
+    Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
   
    
 
   
    
@@ -90,14 +92,15 @@ MathJax.Hub.Config({
         Contents 
         
       
@@ -113,28 +116,14 @@ MathJax.Hub.Config({
 
 
 
-
    Kernel PCA 
    
-
    
-
    
-
     
+
    Randomized PCA 
    
 
 
    
-The kernel trick is a mathematical technique that implicitly maps instances into a
-very high-dimensional space (called the feature space), enabling nonlinear classification and regression
-with Support Vector Machines. Recall that a linear decision boundary in the high-dimensional feature
-space corresponds to a complex nonlinear decision boundary in the original space.
-It turns out that the same trick can be applied to PCA, making it possible to perform complex nonlinear
-projections for dimensionality reduction. This is called Kernel PCA (kPCA). It is often good at
-preserving clusters of instances after projection, or sometimes even unrolling datasets that lie close to a
-twisted manifold.
-For example, the following code uses Scikit-Learn’s KernelPCA class to perform kPCA with an
-
    
+Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic
+algorithm that quickly finds an approximation of the first d principal components. Its computational
+complexity is \( O(m \times d^2)+O(d^3) \), instead of \( O(m \times n^2) + O(n^3) \), so it is dramatically faster than the
+previous algorithms when \( d \) is much smaller than \( n \).
 
-
-
    from sklearn.decomposition import KernelPCA
-rbf_pca = KernelPCA(n_components = 2, kernel="rbf", gamma=0.04)
-X_reduced = rbf_pca.fit_transform(X)
-
    
 
    
 
    
 
    
@@ -155,6 +144,7 @@ X_reduced = rbf_pca8
   
  • 9
    • 
   
  • 10
    • 
+  
  • 11
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/DimRed/html/._DimRed-bs008.html b/doc/pub/DimRed/html/._DimRed-bs008.html
index 48a5d39ca..cb888f35f 100644
--- a/doc/pub/DimRed/html/._DimRed-bs008.html
+++ b/doc/pub/DimRed/html/._DimRed-bs008.html
@@ -6,9 +6,10 @@ Automatically generated HTML file from DocOnce source
 
 
 
-
+
+
 
-Data Analysis and Machine Learning: Dimensionality Reduction
+Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
 
 
 
@@ -44,14 +45,15 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec0'),
-              ('Principal Component Analysis', 2, None, '___sec1'),
-              ('PCA and scikit-learn', 2, None, '___sec2'),
-              ('More on the PCA', 2, None, '___sec3'),
-              ('Incremental PCA', 2, None, '___sec4'),
-              ('Randomized PCA', 2, None, '___sec5'),
-              ('Kernel PCA', 2, None, '___sec6'),
-              ('LLE', 2, None, '___sec7'),
-              ('Other techniques', 2, None, '___sec8')]}
+              ('Preprocessing our data', 2, None, '___sec1'),
+              ('Principal Component Analysis', 2, None, '___sec2'),
+              ('PCA and scikit-learn', 2, None, '___sec3'),
+              ('More on the PCA', 2, None, '___sec4'),
+              ('Incremental PCA', 2, None, '___sec5'),
+              ('Randomized PCA', 2, None, '___sec6'),
+              ('Kernel PCA', 2, None, '___sec7'),
+              ('LLE', 2, None, '___sec8'),
+              ('Other techniques', 2, None, '___sec9')]}
 end of tocinfo -->
 
 
@@ -81,7 +83,7 @@ MathJax.Hub.Config({
       
       
     
-    Data Analysis and Machine Learning: Dimensionality Reduction
+    Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
   
    
 
   
    
@@ -90,14 +92,15 @@ MathJax.Hub.Config({
         Contents 
         
       
@@ -113,14 +116,32 @@ MathJax.Hub.Config({
 
 
 
-
    LLE 
    
+
    Kernel PCA 
    
+
    
+
    
+
     
 
 
    
-Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction
-(NLDR) technique. It is a Manifold Learning technique that does not rely on projections like the previous
-algorithms. In a nutshell, LLE works by first measuring how each training instance linearly relates to its
-closest neighbors (c.n.), and then looking for a low-dimensional representation of the training set where
-these local relationships are best preserved (more details shortly).
+The kernel trick is a mathematical technique that implicitly maps instances into a
+very high-dimensional space (called the feature space), enabling nonlinear classification and regression
+with Support Vector Machines. Recall that a linear decision boundary in the high-dimensional feature
+space corresponds to a complex nonlinear decision boundary in the original space.
+It turns out that the same trick can be applied to PCA, making it possible to perform complex nonlinear
+projections for dimensionality reduction. This is called Kernel PCA (kPCA). It is often good at
+preserving clusters of instances after projection, or sometimes even unrolling datasets that lie close to a
+twisted manifold.
+For example, the following code uses Scikit-Learn’s KernelPCA class to perform kPCA with an
+
    
+
+
+
    from sklearn.decomposition import KernelPCA
+rbf_pca = KernelPCA(n_components = 2, kernel="rbf", gamma=0.04)
+X_reduced = rbf_pca.fit_transform(X)
+
    
+
    
+
    
+
    
+
 
 
    
 
    
@@ -137,6 +158,7 @@ these local relationships are best preserved (more details shortly).
   
  • 8
    • 
   
  • 9
    • 
   
  • 10
    • 
+  
  • 11
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/DimRed/html/._DimRed-bs009.html b/doc/pub/DimRed/html/._DimRed-bs009.html
index 463d4e804..e95aeda9c 100644
--- a/doc/pub/DimRed/html/._DimRed-bs009.html
+++ b/doc/pub/DimRed/html/._DimRed-bs009.html
@@ -6,9 +6,10 @@ Automatically generated HTML file from DocOnce source
 
 
 
-
+
+
 
-Data Analysis and Machine Learning: Dimensionality Reduction
+Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
 
 
 
@@ -44,14 +45,15 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec0'),
-              ('Principal Component Analysis', 2, None, '___sec1'),
-              ('PCA and scikit-learn', 2, None, '___sec2'),
-              ('More on the PCA', 2, None, '___sec3'),
-              ('Incremental PCA', 2, None, '___sec4'),
-              ('Randomized PCA', 2, None, '___sec5'),
-              ('Kernel PCA', 2, None, '___sec6'),
-              ('LLE', 2, None, '___sec7'),
-              ('Other techniques', 2, None, '___sec8')]}
+              ('Preprocessing our data', 2, None, '___sec1'),
+              ('Principal Component Analysis', 2, None, '___sec2'),
+              ('PCA and scikit-learn', 2, None, '___sec3'),
+              ('More on the PCA', 2, None, '___sec4'),
+              ('Incremental PCA', 2, None, '___sec5'),
+              ('Randomized PCA', 2, None, '___sec6'),
+              ('Kernel PCA', 2, None, '___sec7'),
+              ('LLE', 2, None, '___sec8'),
+              ('Other techniques', 2, None, '___sec9')]}
 end of tocinfo -->
 
 
@@ -81,7 +83,7 @@ MathJax.Hub.Config({
       
       
     
-    Data Analysis and Machine Learning: Dimensionality Reduction
+    Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
   
    
 
   
    
@@ -90,14 +92,15 @@ MathJax.Hub.Config({
         Contents 
         
       
@@ -113,22 +116,16 @@ MathJax.Hub.Config({
 
 
 
-
    Other techniques 
    
+
    LLE 
    
 
 
    
-There are many other dimensionality reduction techniques, several of which are available in Scikit-Learn.
+Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction
+(NLDR) technique. It is a Manifold Learning technique that does not rely on projections like the previous
+algorithms. In a nutshell, LLE works by first measuring how each training instance linearly relates to its
+closest neighbors (c.n.), and then looking for a low-dimensional representation of the training set where
+these local relationships are best preserved (more details shortly).
 
 
    
-Here are some of the most popular:
-
-
      
-
    •  Multidimensional Scaling (MDS) reduces dimensionality while trying to preserve the distances between the instances.
      • 
-
    •  Isomap creates a graph by connecting each instance to its nearest neighbors, then reduces dimensionality while trying to preserve the geodesic distances between the instances.
      • 
-
    •  t-Distributed Stochastic Neighbor Embedding (t-SNE) reduces dimensionality while trying to keep similar instances close and dissimilar instances apart. It is mostly used for visualization, in particular to visualize clusters of instances in high-dimensional space (e.g., to visualize the MNIST images in 2D).
      • 
-
    •  Linear Discriminant Analysis (LDA) is actually a classification algorithm, but during training it learns the most discriminative axes between the classes, and these axes can then be used to define a hyperplane onto which to project the data. The benefit is that the projection will keep classes as far apart as possible, so LDA is a good technique to reduce dimensionality before running another classification algorithm such as a Support Vector Machine (SVM) classifier discussed in the SVM lectures.
      • 
-
    
-
-
 
    
 
 
      
@@ -143,6 +140,8 @@ Here are some of the most popular:
   
    • 8
      • 
   
    • 9
      • 
   
    • 10
      • 
+  
    • 11
      • 
+  
    • »
      • 
 
    
 
 
diff --git a/doc/pub/DimRed/html/DimRed-bs.html b/doc/pub/DimRed/html/DimRed-bs.html
index 011b06a83..bbc53cf32 100644
--- a/doc/pub/DimRed/html/DimRed-bs.html
+++ b/doc/pub/DimRed/html/DimRed-bs.html
@@ -6,9 +6,10 @@ Automatically generated HTML file from DocOnce source
 
 
 
-
+
+
 
-Data Analysis and Machine Learning: Dimensionality Reduction
+Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
 
 
 
@@ -44,14 +45,15 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec0'),
-              ('Principal Component Analysis', 2, None, '___sec1'),
-              ('PCA and scikit-learn', 2, None, '___sec2'),
-              ('More on the PCA', 2, None, '___sec3'),
-              ('Incremental PCA', 2, None, '___sec4'),
-              ('Randomized PCA', 2, None, '___sec5'),
-              ('Kernel PCA', 2, None, '___sec6'),
-              ('LLE', 2, None, '___sec7'),
-              ('Other techniques', 2, None, '___sec8')]}
+              ('Preprocessing our data', 2, None, '___sec1'),
+              ('Principal Component Analysis', 2, None, '___sec2'),
+              ('PCA and scikit-learn', 2, None, '___sec3'),
+              ('More on the PCA', 2, None, '___sec4'),
+              ('Incremental PCA', 2, None, '___sec5'),
+              ('Randomized PCA', 2, None, '___sec6'),
+              ('Kernel PCA', 2, None, '___sec7'),
+              ('LLE', 2, None, '___sec8'),
+              ('Other techniques', 2, None, '___sec9')]}
 end of tocinfo -->
 
 
@@ -81,7 +83,7 @@ MathJax.Hub.Config({
       
       
     
-    Data Analysis and Machine Learning: Dimensionality Reduction
+    Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
   
    
 
   
    
@@ -90,14 +92,15 @@ MathJax.Hub.Config({
         Contents 
         
       
@@ -116,7 +119,7 @@ MathJax.Hub.Config({
 
 
 
    
-
    Data Analysis and Machine Learning: Dimensionality Reduction
      
+
    Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
      
 
 
    
 
@@ -132,7 +135,7 @@ MathJax.Hub.Config({
 
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
    
 
    
 
    
-
    Oct 26, 2018
     
+
    Oct 10, 2019
     
 
    
 
    
 
@@ -155,6 +158,8 @@ MathJax.Hub.Config({
   
  • 8
    • 
   
  • 9
    • 
   
  • 10
    • 
+  
  • ...
    • 
+  
  • 11
    • 
   
  • »
    • 
 
 
@@ -172,7 +177,7 @@ MathJax.Hub.Config({
 
 
 
    
- © 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
+ © 1999-2019, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
 
    
 
 
diff --git a/doc/pub/DimRed/html/DimRed-reveal.html b/doc/pub/DimRed/html/DimRed-reveal.html
index 9060a6dd3..fadbd8544 100644
--- a/doc/pub/DimRed/html/DimRed-reveal.html
+++ b/doc/pub/DimRed/html/DimRed-reveal.html
@@ -1,11 +1,11 @@
-\
 
 
 
 
-
+
+
 
-Data Analysis and Machine Learning: Dimensionality Reduction
+Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
 
 
 
@@ -132,7 +132,7 @@ MathJax.Hub.Config({
 
 
 
-
    Data Analysis and Machine Learning: Dimensionality Reduction
      
+
    Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
      
 
 
    
 
@@ -148,12 +148,12 @@ MathJax.Hub.Config({
 
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
    
 
    
 
     
    
-
    Oct 26, 2018
     
+
    Oct 10, 2019
     
 
    
 
    
 
 
    
- © 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
+ © 1999-2019, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
 
    
 
 
@@ -179,7 +179,28 @@ reduction techniques: the principal component analysis PCA, Kernel PCA, and Loca
 
 
 
    
-
    Principal Component Analysis 
    
+
    Preprocessing our data  
    
+
    
+
+
    
+Before we proceed however, we will discuss how to preprocess our
+data. Till now and in connection with project 1 not met so many cases
+where we are too sensitive to the scaling of our data. Normally the
+data may need a rescaling and/or may be sensitive to extreme
+values. Scaling the data renders our inputs much more suitable for the
+algorithms we want to emply.
+
+
    
+Scikit-Learn has several functions which allow us to rescale the data, normally resulting in much better results in terms of various accuracy scores.  The StandardScaler function in Scikit-Learn ensures that for each feature/predictor we study the mean value is zero and the variance is zero (every column in the design/feature matrix).
+This scaling has the drawback that it does not ensure that we have a particular maximum or minumum in our data set. Another function included in Scikit-Learn is the MinMaxScaler which ensures that all features are exactly between \( 0 \) and \( 1 \). The Normalizer function scale each column of the design matrix so that
+
+
+
    
+
    
+
+
+
    
+
    Principal Component Analysis 
    
 
    
 
 
    
@@ -216,7 +237,7 @@ X2D = X_centered.dot(W2)
 
 
 
    
-
    PCA and scikit-learn 
    
+
    PCA and scikit-learn 
    
 
 
    
 Scikit-Learn’s PCA class implements PCA using SVD decomposition just like we did before. The
@@ -247,7 +268,7 @@ More material to come here.
 
 
 
    
-
    More on the PCA 
    
+
    More on the PCA 
    
 Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to
 choose the number of dimensions that add up to a sufficiently large portion of the variance (e.g., 95%).
 Unless, of course, you are reducing dimensionality for data visualization — in that case you will
@@ -276,7 +297,7 @@ X_reduced = pca.fit_transform(X)
 
 
 
    
-
    Incremental PCA 
    
+
    Incremental PCA 
    
 One problem with the preceding implementation of PCA is that it requires the whole training set to fit in
 memory in order for the SVD algorithm to run. Fortunately, Incremental PCA (IPCA) algorithms have
 been developed: you can split the training set into mini-batches and feed an IPCA algorithm one minibatch
@@ -286,7 +307,7 @@ instances arrive).
 
 
 
    
-
    Randomized PCA 
    
+
    Randomized PCA 
    
 
 
    
 Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic
@@ -300,7 +321,7 @@ previous algorithms when \( d \) is much smaller than \( n \).
 
 
 
    
-
    Kernel PCA 
    
+
    Kernel PCA 
    
 
    
 
 
    
@@ -326,7 +347,7 @@ X_reduced = rbf_pca.fit_transform(X)
 
 
 
    
-
    LLE 
    
+
    LLE 
    
 
 
    
 Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction
@@ -338,7 +359,7 @@ these local relationships are best preserved (more details shortly).
 
 
 
    
-
    Other techniques 
    
+
    Other techniques 
    
 
 
    
 There are many other dimensionality reduction techniques, several of which are available in Scikit-Learn.
diff --git a/doc/pub/DimRed/html/DimRed-solarized.html b/doc/pub/DimRed/html/DimRed-solarized.html
index 913391872..79620e5a8 100644
--- a/doc/pub/DimRed/html/DimRed-solarized.html
+++ b/doc/pub/DimRed/html/DimRed-solarized.html
@@ -6,9 +6,10 @@ Automatically generated HTML file from DocOnce source
 
 
 
-
+
+
 
-Data Analysis and Machine Learning: Dimensionality Reduction
+Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
 
 
 
@@ -64,14 +65,15 @@ div { text-align: justify; text-justify: inter-word; }
                2,
                None,
                '___sec0'),
-              ('Principal Component Analysis', 2, None, '___sec1'),
-              ('PCA and scikit-learn', 2, None, '___sec2'),
-              ('More on the PCA', 2, None, '___sec3'),
-              ('Incremental PCA', 2, None, '___sec4'),
-              ('Randomized PCA', 2, None, '___sec5'),
-              ('Kernel PCA', 2, None, '___sec6'),
-              ('LLE', 2, None, '___sec7'),
-              ('Other techniques', 2, None, '___sec8')]}
+              ('Preprocessing our data', 2, None, '___sec1'),
+              ('Principal Component Analysis', 2, None, '___sec2'),
+              ('PCA and scikit-learn', 2, None, '___sec3'),
+              ('More on the PCA', 2, None, '___sec4'),
+              ('Incremental PCA', 2, None, '___sec5'),
+              ('Randomized PCA', 2, None, '___sec6'),
+              ('Kernel PCA', 2, None, '___sec7'),
+              ('LLE', 2, None, '___sec8'),
+              ('Other techniques', 2, None, '___sec9')]}
 end of tocinfo -->
 
 
@@ -97,7 +99,7 @@ MathJax.Hub.Config({
 
 
 
-
    Data Analysis and Machine Learning: Dimensionality Reduction
      
+
    Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
      
 
 
    
 
@@ -113,7 +115,7 @@ MathJax.Hub.Config({
 
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
    
 
    
 
    
-
    Oct 26, 2018
     
+
    Oct 10, 2019
     
 
    
 
    
 









    
@@ -141,7 +143,31 @@ reduction techniques: the principal component analysis PCA, Kernel PCA, and Loca
 
    
 









    
 
-
    Principal Component Analysis 
    
+
    Preprocessing our data  
    
+
    
+
+
    
+
+
    
+Before we proceed however, we will discuss how to preprocess our
+data. Till now and in connection with project 1 not met so many cases
+where we are too sensitive to the scaling of our data. Normally the
+data may need a rescaling and/or may be sensitive to extreme
+values. Scaling the data renders our inputs much more suitable for the
+algorithms we want to emply.
+
+
    
+Scikit-Learn has several functions which allow us to rescale the data, normally resulting in much better results in terms of various accuracy scores.  The StandardScaler function in Scikit-Learn ensures that for each feature/predictor we study the mean value is zero and the variance is zero (every column in the design/feature matrix).
+This scaling has the drawback that it does not ensure that we have a particular maximum or minumum in our data set. Another function included in Scikit-Learn is the MinMaxScaler which ensures that all features are exactly between \( 0 \) and \( 1 \). The Normalizer function scale each column of the design matrix so that
+
+
+
    
+
+
+
    
+









    
+
+
    Principal Component Analysis 
    
 
    
 
 
    
@@ -177,7 +203,7 @@ X2D = X_centered.dot(W2)
 
    
 
 
-
    PCA and scikit-learn 
    
+
    PCA and scikit-learn 
    
 
 
    
 Scikit-Learn’s PCA class implements PCA using SVD decomposition just like we did before. The
@@ -208,7 +234,7 @@ More material to come here.
 
    
 









    
 
-
    More on the PCA 
    
+
    More on the PCA 
    
 Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to
 choose the number of dimensions that add up to a sufficiently large portion of the variance (e.g., 95%).
 Unless, of course, you are reducing dimensionality for data visualization — in that case you will
@@ -236,7 +262,7 @@ X_reduced = pca.fit_transform(X)
 
    
 









    
 
-
    Incremental PCA 
    
+
    Incremental PCA 
    
 One problem with the preceding implementation of PCA is that it requires the whole training set to fit in
 memory in order for the SVD algorithm to run. Fortunately, Incremental PCA (IPCA) algorithms have
 been developed: you can split the training set into mini-batches and feed an IPCA algorithm one minibatch
@@ -246,7 +272,7 @@ instances arrive).
 
    
 









    
 
-
    Randomized PCA 
    
+
    Randomized PCA 
    
 
 
    
 Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic
@@ -261,7 +287,7 @@ previous algorithms when \( d \) is much smaller than \( n \).
 
    
 









    
 
-
    Kernel PCA 
    
+
    Kernel PCA 
    
 
    
 
 
    
@@ -290,7 +316,7 @@ X_reduced = rbf_pca.fit_transform(X)
 
    
 









    
 
-
    LLE 
    
+
    LLE 
    
 
 
    
 Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction
@@ -302,7 +328,7 @@ these local relationships are best preserved (more details shortly).
 
    
 









    
 
-
    Other techniques 
    
+
    Other techniques 
    
 
 
    
 There are many other dimensionality reduction techniques, several of which are available in Scikit-Learn.
@@ -322,7 +348,7 @@ Here are some of the most popular:
 
 
 
    
- © 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
+ © 1999-2019, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
 
    
 
 
diff --git a/doc/pub/DimRed/html/DimRed.html b/doc/pub/DimRed/html/DimRed.html
index ad55a105d..426a673ac 100644
--- a/doc/pub/DimRed/html/DimRed.html
+++ b/doc/pub/DimRed/html/DimRed.html
@@ -6,9 +6,10 @@ Automatically generated HTML file from DocOnce source
 
 
 
-
+
+
 
-Data Analysis and Machine Learning: Dimensionality Reduction
+Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
 
 
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Chebyshev1FilterModel Chebyshev2FilterModel ChebyshevDistance ChebyshevT ChebyshevU Check CheckAbort CheckAll Checkbox CheckboxBar CheckboxBox CheckboxBoxOptions ChemicalData ChessboardDistance ChiDistribution ChineseRemainder ChiSquareDistribution ChoiceButtons ChoiceDialog CholeskyDecomposition Chop Circle CircleBox CircleDot CircleMinus CirclePlus CircleTimes CirculantGraph CityData Clear ClearAll ClearAttributes ClearSystemCache ClebschGordan ClickPane Clip ClipboardNotebook ClipFill ClippingStyle ClipPlanes ClipRange Clock ClockGauge ClockwiseContourIntegral Close Closed CloseKernels ClosenessCentrality Closing ClosingAutoSave ClosingEvent ClusteringComponents CMYKColor Coarse Coefficient CoefficientArrays CoefficientDomain CoefficientList CoefficientRules CoifletWavelet Collect Colon ColonForm ColorCombine ColorConvert ColorData ColorDataFunction ColorFunction ColorFunctionScaling Colorize ColorNegate ColorOutput ColorProfileData ColorQuantize ColorReplace ColorRules ColorSelectorSettings ColorSeparate ColorSetter ColorSetterBox ColorSetterBoxOptions ColorSlider ColorSpace Column ColumnAlignments ColumnBackgrounds ColumnForm ColumnLines ColumnsEqual ColumnSpacings ColumnWidths CommonDefaultFormatTypes Commonest CommonestFilter CommonUnits CommunityBoundaryStyle CommunityGraphPlot CommunityLabels CommunityRegionStyle CompatibleUnitQ CompilationOptions CompilationTarget Compile Compiled CompiledFunction Complement CompleteGraph CompleteGraphQ CompleteKaryTree CompletionsListPacket Complex Complexes ComplexExpand ComplexInfinity ComplexityFunction ComponentMeasurements ComponentwiseContextMenu Compose ComposeList ComposeSeries Composition CompoundExpression CompoundPoissonDistribution CompoundPoissonProcess CompoundRenewalProcess Compress CompressedData Condition ConditionalExpression Conditioned Cone ConeBox ConfidenceLevel ConfidenceRange ConfidenceTransform ConfigurationPath Congruent Conjugate ConjugateTranspose Conjunction Connect ConnectedComponents ConnectedGraphQ ConnesWindow ConoverTest ConsoleMessage ConsoleMessagePacket ConsolePrint Constant ConstantArray Constants ConstrainedMax ConstrainedMin ContentPadding ContentsBoundingBox ContentSelectable ContentSize Context ContextMenu Contexts ContextToFilename ContextToFileName Continuation Continue ContinuedFraction ContinuedFractionK ContinuousAction ContinuousMarkovProcess ContinuousTimeModelQ ContinuousWaveletData ContinuousWaveletTransform ContourDetect ContourGraphics ContourIntegral ContourLabels ContourLines ContourPlot ContourPlot3D Contours ContourShading ContourSmoothing ContourStyle ContraharmonicMean Control ControlActive ControlAlignment ControllabilityGramian ControllabilityMatrix ControllableDecomposition ControllableModelQ ControllerDuration ControllerInformation ControllerInformationData ControllerLinking ControllerManipulate ControllerMethod ControllerPath ControllerState ControlPlacement ControlsRendering ControlType Convergents ConversionOptions ConversionRules ConvertToBitmapPacket ConvertToPostScript ConvertToPostScriptPacket Convolve ConwayGroupCo1 ConwayGroupCo2 ConwayGroupCo3 CoordinateChartData CoordinatesToolOptions CoordinateTransform CoordinateTransformData CoprimeQ Coproduct CopulaDistribution Copyable CopyDirectory CopyFile CopyTag CopyToClipboard CornerFilter CornerNeighbors Correlation CorrelationDistance CorrelationFunction CorrelationTest Cos Cosh CoshIntegral CosineDistance CosineWindow CosIntegral Cot Coth Count CounterAssignments CounterBox CounterBoxOptions CounterClockwiseContourIntegral CounterEvaluator CounterFunction CounterIncrements CounterStyle CounterStyleMenuListing CountRoots CountryData Covariance CovarianceEstimatorFunction CovarianceFunction CoxianDistribution CoxIngersollRossProcess CoxModel CoxModelFit CramerVonMisesTest CreateArchive CreateDialog CreateDirectory CreateDocument CreateIntermediateDirectories CreatePalette CreatePalettePacket CreateScheduledTask CreateTemporary CreateWindow CriticalityFailureImportance CriticalitySuccessImportance CriticalSection Cross CrossingDetect CrossMatrix Csc Csch CubeRoot Cubics Cuboid CuboidBox Cumulant CumulantGeneratingFunction Cup CupCap Curl CurlyDoubleQuote CurlyQuote CurrentImage CurrentlySpeakingPacket CurrentValue CurvatureFlowFilter CurveClosed Cyan CycleGraph CycleIndexPolynomial Cycles CyclicGroup Cyclotomic Cylinder CylinderBox CylindricalDecomposition D DagumDistribution DamerauLevenshteinDistance DampingFactor Darker Dashed Dashing DataCompression DataDistribution DataRange DataReversed Date DateDelimiters DateDifference DateFunction DateList DateListLogPlot DateListPlot DatePattern DatePlus DateRange DateString DateTicksFormat DaubechiesWavelet DavisDistribution DawsonF DayCount DayCountConvention DayMatchQ DayName DayPlus DayRange DayRound DeBruijnGraph Debug DebugTag Decimal DeclareKnownSymbols DeclarePackage Decompose Decrement DedekindEta Default DefaultAxesStyle DefaultBaseStyle DefaultBoxStyle DefaultButton DefaultColor DefaultControlPlacement DefaultDuplicateCellStyle DefaultDuration DefaultElement DefaultFaceGridsStyle DefaultFieldHintStyle DefaultFont DefaultFontProperties DefaultFormatType DefaultFormatTypeForStyle DefaultFrameStyle DefaultFrameTicksStyle DefaultGridLinesStyle DefaultInlineFormatType DefaultInputFormatType DefaultLabelStyle DefaultMenuStyle DefaultNaturalLanguage DefaultNewCellStyle DefaultNewInlineCellStyle DefaultNotebook DefaultOptions DefaultOutputFormatType DefaultStyle DefaultStyleDefinitions DefaultTextFormatType DefaultTextInlineFormatType DefaultTicksStyle DefaultTooltipStyle DefaultValues Defer DefineExternal DefineInputStreamMethod DefineOutputStreamMethod Definition Degree DegreeCentrality DegreeGraphDistribution DegreeLexicographic DegreeReverseLexicographic Deinitialization Del Deletable Delete DeleteBorderComponents DeleteCases DeleteContents DeleteDirectory DeleteDuplicates DeleteFile DeleteSmallComponents DeleteWithContents DeletionWarning Delimiter DelimiterFlashTime DelimiterMatching Delimiters Denominator DensityGraphics DensityHistogram DensityPlot DependentVariables Deploy Deployed Depth DepthFirstScan Derivative DerivativeFilter DescriptorStateSpace DesignMatrix Det DGaussianWavelet DiacriticalPositioning Diagonal DiagonalMatrix Dialog DialogIndent DialogInput DialogLevel DialogNotebook DialogProlog DialogReturn DialogSymbols Diamond DiamondMatrix DiceDissimilarity DictionaryLookup DifferenceDelta DifferenceOrder DifferenceRoot DifferenceRootReduce Differences DifferentialD DifferentialRoot DifferentialRootReduce DifferentiatorFilter DigitBlock DigitBlockMinimum DigitCharacter DigitCount DigitQ DihedralGroup Dilation Dimensions DiracComb DiracDelta DirectedEdge DirectedEdges DirectedGraph DirectedGraphQ DirectedInfinity Direction Directive Directory DirectoryName DirectoryQ DirectoryStack DirichletCharacter DirichletConvolve DirichletDistribution DirichletL DirichletTransform DirichletWindow DisableConsolePrintPacket DiscreteChirpZTransform DiscreteConvolve DiscreteDelta DiscreteHadamardTransform DiscreteIndicator DiscreteLQEstimatorGains DiscreteLQRegulatorGains DiscreteLyapunovSolve DiscreteMarkovProcess DiscretePlot DiscretePlot3D DiscreteRatio DiscreteRiccatiSolve DiscreteShift DiscreteTimeModelQ DiscreteUniformDistribution DiscreteVariables DiscreteWaveletData DiscreteWaveletPacketTransform DiscreteWaveletTransform Discriminant Disjunction Disk DiskBox DiskMatrix Dispatch DispersionEstimatorFunction Display DisplayAllSteps DisplayEndPacket DisplayFlushImagePacket DisplayForm DisplayFunction DisplayPacket DisplayRules DisplaySetSizePacket DisplayString DisplayTemporary DisplayWith DisplayWithRef DisplayWithVariable DistanceFunction DistanceTransform Distribute Distributed DistributedContexts DistributeDefinitions DistributionChart DistributionDomain DistributionFitTest DistributionParameterAssumptions DistributionParameterQ Dithering Div Divergence Divide DivideBy Dividers Divisible Divisors DivisorSigma DivisorSum DMSList DMSString Do DockedCells DocumentNotebook DominantColors DOSTextFormat Dot DotDashed DotEqual Dotted DoubleBracketingBar DoubleContourIntegral DoubleDownArrow DoubleLeftArrow DoubleLeftRightArrow DoubleLeftTee DoubleLongLeftArrow DoubleLongLeftRightArrow DoubleLongRightArrow DoubleRightArrow DoubleRightTee DoubleUpArrow DoubleUpDownArrow DoubleVerticalBar DoublyInfinite Down DownArrow DownArrowBar DownArrowUpArrow DownLeftRightVector DownLeftTeeVector DownLeftVector DownLeftVectorBar DownRightTeeVector DownRightVector DownRightVectorBar Downsample DownTee DownTeeArrow DownValues DragAndDrop DrawEdges DrawFrontFaces DrawHighlighted Drop DSolve Dt DualLinearProgramming DualSystemsModel DumpGet DumpSave DuplicateFreeQ Dynamic DynamicBox DynamicBoxOptions DynamicEvaluationTimeout DynamicLocation DynamicModule DynamicModuleBox DynamicModuleBoxOptions DynamicModuleParent DynamicModuleValues DynamicName DynamicNamespace DynamicReference DynamicSetting DynamicUpdating DynamicWrapper DynamicWrapperBox DynamicWrapperBoxOptions E EccentricityCentrality EdgeAdd EdgeBetweennessCentrality EdgeCapacity EdgeCapForm EdgeColor EdgeConnectivity EdgeCost EdgeCount EdgeCoverQ EdgeDashing EdgeDelete EdgeDetect EdgeForm EdgeIndex EdgeJoinForm EdgeLabeling EdgeLabels EdgeLabelStyle EdgeList EdgeOpacity EdgeQ EdgeRenderingFunction EdgeRules EdgeShapeFunction EdgeStyle EdgeThickness EdgeWeight Editable EditButtonSettings EditCellTagsSettings EditDistance EffectiveInterest Eigensystem Eigenvalues EigenvectorCentrality Eigenvectors Element ElementData Eliminate EliminationOrder EllipticE EllipticExp EllipticExpPrime EllipticF EllipticFilterModel EllipticK EllipticLog EllipticNomeQ EllipticPi EllipticReducedHalfPeriods EllipticTheta EllipticThetaPrime EmitSound EmphasizeSyntaxErrors EmpiricalDistribution Empty EmptyGraphQ EnableConsolePrintPacket Enabled Encode End EndAdd EndDialogPacket EndFrontEndInteractionPacket EndOfFile EndOfLine EndOfString EndPackage EngineeringForm Enter EnterExpressionPacket EnterTextPacket Entropy EntropyFilter Environment Epilog Equal EqualColumns EqualRows EqualTilde EquatedTo Equilibrium EquirippleFilterKernel Equivalent Erf Erfc Erfi ErlangB ErlangC ErlangDistribution Erosion ErrorBox ErrorBoxOptions ErrorNorm ErrorPacket ErrorsDialogSettings EstimatedDistribution EstimatedProcess EstimatorGains EstimatorRegulator EuclideanDistance EulerE EulerGamma EulerianGraphQ EulerPhi Evaluatable Evaluate Evaluated EvaluatePacket EvaluationCell EvaluationCompletionAction EvaluationElements EvaluationMode EvaluationMonitor EvaluationNotebook EvaluationObject EvaluationOrder Evaluator EvaluatorNames EvenQ EventData EventEvaluator EventHandler EventHandlerTag EventLabels ExactBlackmanWindow ExactNumberQ ExactRootIsolation ExampleData Except ExcludedForms ExcludePods Exclusions ExclusionsStyle Exists Exit ExitDialog Exp Expand ExpandAll ExpandDenominator ExpandFileName ExpandNumerator Expectation ExpectationE ExpectedValue ExpGammaDistribution ExpIntegralE ExpIntegralEi Exponent ExponentFunction ExponentialDistribution ExponentialFamily ExponentialGeneratingFunction ExponentialMovingAverage ExponentialPowerDistribution ExponentPosition ExponentStep Export ExportAutoReplacements ExportPacket ExportString Expression ExpressionCell ExpressionPacket ExpToTrig ExtendedGCD Extension ExtentElementFunction ExtentMarkers ExtentSize ExternalCall ExternalDataCharacterEncoding Extract ExtractArchive ExtremeValueDistribution FaceForm FaceGrids FaceGridsStyle Factor FactorComplete Factorial Factorial2 FactorialMoment FactorialMomentGeneratingFunction FactorialPower FactorInteger FactorList FactorSquareFree FactorSquareFreeList FactorTerms FactorTermsList Fail FailureDistribution False FARIMAProcess FEDisableConsolePrintPacket FeedbackSector FeedbackSectorStyle FeedbackType FEEnableConsolePrintPacket Fibonacci FieldHint FieldHintStyle FieldMasked FieldSize File FileBaseName FileByteCount FileDate FileExistsQ FileExtension FileFormat FileHash FileInformation FileName FileNameDepth FileNameDialogSettings FileNameDrop FileNameJoin FileNames FileNameSetter FileNameSplit FileNameTake FilePrint FileType FilledCurve FilledCurveBox Filling FillingStyle FillingTransform FilterRules FinancialBond FinancialData FinancialDerivative FinancialIndicator Find FindArgMax FindArgMin FindClique FindClusters FindCurvePath FindDistributionParameters FindDivisions FindEdgeCover FindEdgeCut FindEulerianCycle FindFaces FindFile FindFit FindGeneratingFunction FindGeoLocation FindGeometricTransform FindGraphCommunities FindGraphIsomorphism FindGraphPartition FindHamiltonianCycle FindIndependentEdgeSet FindIndependentVertexSet FindInstance FindIntegerNullVector FindKClan FindKClique FindKClub FindKPlex FindLibrary FindLinearRecurrence FindList FindMaximum FindMaximumFlow FindMaxValue FindMinimum FindMinimumCostFlow FindMinimumCut FindMinValue FindPermutation FindPostmanTour FindProcessParameters FindRoot FindSequenceFunction FindSettings FindShortestPath FindShortestTour FindThreshold FindVertexCover FindVertexCut Fine FinishDynamic FiniteAbelianGroupCount FiniteGroupCount FiniteGroupData First FirstPassageTimeDistribution FischerGroupFi22 FischerGroupFi23 FischerGroupFi24Prime FisherHypergeometricDistribution FisherRatioTest FisherZDistribution Fit FitAll FittedModel FixedPoint FixedPointList FlashSelection Flat Flatten FlattenAt FlatTopWindow FlipView Floor FlushPrintOutputPacket Fold FoldList Font FontColor FontFamily FontForm FontName FontOpacity FontPostScriptName FontProperties FontReencoding FontSize FontSlant FontSubstitutions FontTracking FontVariations FontWeight For ForAll Format FormatRules FormatType FormatTypeAutoConvert FormatValues FormBox FormBoxOptions FortranForm Forward ForwardBackward Fourier FourierCoefficient FourierCosCoefficient FourierCosSeries FourierCosTransform FourierDCT FourierDCTFilter FourierDCTMatrix FourierDST FourierDSTMatrix FourierMatrix FourierParameters FourierSequenceTransform FourierSeries FourierSinCoefficient FourierSinSeries FourierSinTransform FourierTransform FourierTrigSeries FractionalBrownianMotionProcess FractionalPart FractionBox FractionBoxOptions FractionLine Frame FrameBox FrameBoxOptions Framed FrameInset FrameLabel Frameless FrameMargins FrameStyle FrameTicks FrameTicksStyle FRatioDistribution FrechetDistribution FreeQ FrequencySamplingFilterKernel FresnelC FresnelS Friday FrobeniusNumber FrobeniusSolve FromCharacterCode FromCoefficientRules FromContinuedFraction FromDate FromDigits FromDMS Front FrontEndDynamicExpression FrontEndEventActions FrontEndExecute FrontEndObject FrontEndResource FrontEndResourceString FrontEndStackSize FrontEndToken FrontEndTokenExecute FrontEndValueCache FrontEndVersion FrontFaceColor FrontFaceOpacity Full FullAxes FullDefinition FullForm FullGraphics FullOptions FullSimplify Function FunctionExpand FunctionInterpolation FunctionSpace FussellVeselyImportance GaborFilter GaborMatrix GaborWavelet GainMargins GainPhaseMargins Gamma GammaDistribution GammaRegularized GapPenalty Gather GatherBy GaugeFaceElementFunction GaugeFaceStyle GaugeFrameElementFunction GaugeFrameSize GaugeFrameStyle GaugeLabels GaugeMarkers GaugeStyle GaussianFilter GaussianIntegers GaussianMatrix GaussianWindow GCD GegenbauerC General GeneralizedLinearModelFit GenerateConditions GeneratedCell GeneratedParameters GeneratingFunction Generic GenericCylindricalDecomposition GenomeData GenomeLookup GeodesicClosing GeodesicDilation GeodesicErosion GeodesicOpening GeoDestination GeodesyData GeoDirection GeoDistance GeoGridPosition GeometricBrownianMotionProcess GeometricDistribution GeometricMean GeometricMeanFilter GeometricTransformation GeometricTransformation3DBox GeometricTransformation3DBoxOptions GeometricTransformationBox GeometricTransformationBoxOptions GeoPosition GeoPositionENU GeoPositionXYZ GeoProjectionData GestureHandler GestureHandlerTag Get GetBoundingBoxSizePacket GetContext GetEnvironment GetFileName GetFrontEndOptionsDataPacket GetLinebreakInformationPacket GetMenusPacket GetPageBreakInformationPacket Glaisher GlobalClusteringCoefficient GlobalPreferences GlobalSession Glow GoldenRatio GompertzMakehamDistribution GoodmanKruskalGamma GoodmanKruskalGammaTest Goto Grad Gradient GradientFilter GradientOrientationFilter Graph GraphAssortativity GraphCenter GraphComplement GraphData GraphDensity GraphDiameter GraphDifference GraphDisjointUnion GraphDistance GraphDistanceMatrix GraphElementData GraphEmbedding GraphHighlight GraphHighlightStyle GraphHub Graphics Graphics3D Graphics3DBox Graphics3DBoxOptions GraphicsArray GraphicsBaseline GraphicsBox GraphicsBoxOptions GraphicsColor GraphicsColumn GraphicsComplex GraphicsComplex3DBox GraphicsComplex3DBoxOptions GraphicsComplexBox GraphicsComplexBoxOptions GraphicsContents GraphicsData GraphicsGrid GraphicsGridBox GraphicsGroup GraphicsGroup3DBox GraphicsGroup3DBoxOptions GraphicsGroupBox GraphicsGroupBoxOptions GraphicsGrouping GraphicsHighlightColor GraphicsRow GraphicsSpacing GraphicsStyle GraphIntersection GraphLayout GraphLinkEfficiency GraphPeriphery GraphPlot GraphPlot3D GraphPower GraphPropertyDistribution GraphQ GraphRadius GraphReciprocity GraphRoot GraphStyle GraphUnion Gray GrayLevel GreatCircleDistance Greater GreaterEqual GreaterEqualLess GreaterFullEqual GreaterGreater GreaterLess GreaterSlantEqual GreaterTilde Green Grid GridBaseline GridBox GridBoxAlignment GridBoxBackground GridBoxDividers GridBoxFrame GridBoxItemSize GridBoxItemStyle GridBoxOptions GridBoxSpacings GridCreationSettings GridDefaultElement GridElementStyleOptions GridFrame GridFrameMargins GridGraph GridLines GridLinesStyle GroebnerBasis GroupActionBase GroupCentralizer GroupElementFromWord GroupElementPosition GroupElementQ GroupElements GroupElementToWord GroupGenerators GroupMultiplicationTable GroupOrbits GroupOrder GroupPageBreakWithin GroupSetwiseStabilizer GroupStabilizer GroupStabilizerChain Gudermannian GumbelDistribution HaarWavelet HadamardMatrix HalfNormalDistribution HamiltonianGraphQ HammingDistance HammingWindow HankelH1 HankelH2 HankelMatrix HannPoissonWindow HannWindow HaradaNortonGroupHN HararyGraph HarmonicMean HarmonicMeanFilter HarmonicNumber Hash HashTable Haversine HazardFunction Head HeadCompose Heads HeavisideLambda HeavisidePi HeavisideTheta HeldGroupHe HeldPart HelpBrowserLookup HelpBrowserNotebook HelpBrowserSettings HermiteDecomposition HermiteH HermitianMatrixQ HessenbergDecomposition Hessian HexadecimalCharacter Hexahedron HexahedronBox HexahedronBoxOptions HiddenSurface HighlightGraph HighlightImage HighpassFilter HigmanSimsGroupHS HilbertFilter HilbertMatrix Histogram Histogram3D HistogramDistribution HistogramList HistogramTransform HistogramTransformInterpolation HitMissTransform HITSCentrality HodgeDual HoeffdingD HoeffdingDTest Hold HoldAll HoldAllComplete HoldComplete HoldFirst HoldForm HoldPattern HoldRest HolidayCalendar HomeDirectory HomePage Horizontal HorizontalForm HorizontalGauge HorizontalScrollPosition HornerForm HotellingTSquareDistribution HoytDistribution HTMLSave Hue HumpDownHump HumpEqual HurwitzLerchPhi HurwitzZeta HyperbolicDistribution HypercubeGraph HyperexponentialDistribution Hyperfactorial Hypergeometric0F1 Hypergeometric0F1Regularized Hypergeometric1F1 Hypergeometric1F1Regularized Hypergeometric2F1 Hypergeometric2F1Regularized HypergeometricDistribution HypergeometricPFQ HypergeometricPFQRegularized HypergeometricU Hyperlink HyperlinkCreationSettings Hyphenation HyphenationOptions HypoexponentialDistribution HypothesisTestData I Identity IdentityMatrix If IgnoreCase Im Image Image3D Image3DSlices ImageAccumulate ImageAdd ImageAdjust ImageAlign ImageApply ImageAspectRatio ImageAssemble ImageCache ImageCacheValid ImageCapture ImageChannels ImageClip ImageColorSpace ImageCompose ImageConvolve ImageCooccurrence ImageCorners ImageCorrelate ImageCorrespondingPoints ImageCrop ImageData ImageDataPacket ImageDeconvolve ImageDemosaic ImageDifference ImageDimensions ImageDistance ImageEffect ImageFeatureTrack ImageFileApply ImageFileFilter ImageFileScan ImageFilter ImageForestingComponents ImageForwardTransformation ImageHistogram ImageKeypoints ImageLevels ImageLines ImageMargins ImageMarkers ImageMeasurements ImageMultiply ImageOffset ImagePad ImagePadding ImagePartition ImagePeriodogram ImagePerspectiveTransformation ImageQ ImageRangeCache ImageReflect ImageRegion ImageResize ImageResolution ImageRotate ImageRotated ImageScaled ImageScan ImageSize ImageSizeAction ImageSizeCache ImageSizeMultipliers ImageSizeRaw ImageSubtract ImageTake ImageTransformation ImageTrim ImageType ImageValue ImageValuePositions Implies Import ImportAutoReplacements ImportString ImprovementImportance In IncidenceGraph IncidenceList IncidenceMatrix IncludeConstantBasis IncludeFileExtension IncludePods IncludeSingularTerm Increment Indent IndentingNewlineSpacings IndentMaxFraction IndependenceTest IndependentEdgeSetQ IndependentUnit IndependentVertexSetQ Indeterminate IndexCreationOptions Indexed IndexGraph IndexTag Inequality InexactNumberQ InexactNumbers Infinity Infix Information Inherited InheritScope Initialization InitializationCell InitializationCellEvaluation InitializationCellWarning InlineCounterAssignments InlineCounterIncrements InlineRules Inner Inpaint Input InputAliases InputAssumptions InputAutoReplacements InputField InputFieldBox InputFieldBoxOptions InputForm InputGrouping InputNamePacket InputNotebook InputPacket InputSettings InputStream InputString InputStringPacket InputToBoxFormPacket Insert InsertionPointObject InsertResults Inset Inset3DBox Inset3DBoxOptions InsetBox InsetBoxOptions Install InstallService InString Integer IntegerDigits IntegerExponent IntegerLength IntegerPart IntegerPartitions IntegerQ Integers IntegerString Integral Integrate Interactive InteractiveTradingChart Interlaced Interleaving InternallyBalancedDecomposition InterpolatingFunction InterpolatingPolynomial Interpolation InterpolationOrder InterpolationPoints InterpolationPrecision Interpretation InterpretationBox InterpretationBoxOptions InterpretationFunction InterpretTemplate InterquartileRange Interrupt InterruptSettings Intersection Interval IntervalIntersection IntervalMemberQ IntervalUnion Inverse InverseBetaRegularized InverseCDF InverseChiSquareDistribution InverseContinuousWaveletTransform InverseDistanceTransform InverseEllipticNomeQ InverseErf InverseErfc InverseFourier InverseFourierCosTransform InverseFourierSequenceTransform InverseFourierSinTransform InverseFourierTransform InverseFunction InverseFunctions InverseGammaDistribution InverseGammaRegularized InverseGaussianDistribution InverseGudermannian InverseHaversine InverseJacobiCD InverseJacobiCN InverseJacobiCS InverseJacobiDC InverseJacobiDN InverseJacobiDS InverseJacobiNC InverseJacobiND InverseJacobiNS InverseJacobiSC InverseJacobiSD InverseJacobiSN InverseLaplaceTransform InversePermutation InverseRadon InverseSeries InverseSurvivalFunction InverseWaveletTransform InverseWeierstrassP InverseZTransform Invisible InvisibleApplication InvisibleTimes IrreduciblePolynomialQ IsolatingInterval IsomorphicGraphQ IsotopeData Italic Item ItemBox ItemBoxOptions ItemSize ItemStyle ItoProcess JaccardDissimilarity JacobiAmplitude Jacobian JacobiCD JacobiCN JacobiCS JacobiDC JacobiDN JacobiDS JacobiNC JacobiND JacobiNS JacobiP JacobiSC JacobiSD JacobiSN JacobiSymbol JacobiZeta JankoGroupJ1 JankoGroupJ2 JankoGroupJ3 JankoGroupJ4 JarqueBeraALMTest JohnsonDistribution Join Joined JoinedCurve JoinedCurveBox JoinForm JordanDecomposition JordanModelDecomposition K KagiChart KaiserBesselWindow KaiserWindow KalmanEstimator KalmanFilter KarhunenLoeveDecomposition KaryTree KatzCentrality KCoreComponents KDistribution KelvinBei KelvinBer KelvinKei KelvinKer KendallTau KendallTauTest KernelExecute KernelMixtureDistribution KernelObject Kernels Ket Khinchin KirchhoffGraph KirchhoffMatrix KleinInvariantJ KnightTourGraph KnotData KnownUnitQ KolmogorovSmirnovTest KroneckerDelta KroneckerModelDecomposition KroneckerProduct KroneckerSymbol KuiperTest KumaraswamyDistribution Kurtosis KuwaharaFilter Label Labeled LabeledSlider LabelingFunction LabelStyle LaguerreL LambdaComponents LambertW LanczosWindow LandauDistribution Language LanguageCategory LaplaceDistribution LaplaceTransform Laplacian LaplacianFilter LaplacianGaussianFilter Large Larger Last Latitude LatitudeLongitude LatticeData LatticeReduce Launch LaunchKernels LayeredGraphPlot LayerSizeFunction LayoutInformation LCM LeafCount LeapYearQ LeastSquares LeastSquaresFilterKernel Left LeftArrow LeftArrowBar LeftArrowRightArrow LeftDownTeeVector LeftDownVector LeftDownVectorBar LeftRightArrow LeftRightVector LeftTee LeftTeeArrow LeftTeeVector LeftTriangle LeftTriangleBar LeftTriangleEqual LeftUpDownVector LeftUpTeeVector LeftUpVector LeftUpVectorBar LeftVector LeftVectorBar LegendAppearance Legended LegendFunction LegendLabel LegendLayout LegendMargins LegendMarkers LegendMarkerSize LegendreP LegendreQ LegendreType Length LengthWhile LerchPhi Less LessEqual LessEqualGreater LessFullEqual LessGreater LessLess LessSlantEqual LessTilde LetterCharacter LetterQ Level LeveneTest LeviCivitaTensor LevyDistribution Lexicographic LibraryFunction LibraryFunctionError LibraryFunctionInformation LibraryFunctionLoad LibraryFunctionUnload LibraryLoad LibraryUnload LicenseID LiftingFilterData LiftingWaveletTransform LightBlue LightBrown LightCyan Lighter LightGray LightGreen Lighting LightingAngle LightMagenta LightOrange LightPink LightPurple LightRed LightSources LightYellow Likelihood Limit LimitsPositioning LimitsPositioningTokens LindleyDistribution Line Line3DBox LinearFilter LinearFractionalTransform LinearModelFit LinearOffsetFunction LinearProgramming LinearRecurrence LinearSolve LinearSolveFunction LineBox LineBreak LinebreakAdjustments LineBreakChart LineBreakWithin LineColor LineForm LineGraph LineIndent LineIndentMaxFraction LineIntegralConvolutionPlot LineIntegralConvolutionScale LineLegend LineOpacity LineSpacing LineWrapParts LinkActivate LinkClose LinkConnect LinkConnectedQ LinkCreate LinkError LinkFlush LinkFunction LinkHost LinkInterrupt LinkLaunch LinkMode LinkObject LinkOpen LinkOptions LinkPatterns LinkProtocol LinkRead LinkReadHeld LinkReadyQ Links LinkWrite LinkWriteHeld LiouvilleLambda List Listable ListAnimate ListContourPlot ListContourPlot3D ListConvolve ListCorrelate ListCurvePathPlot ListDeconvolve ListDensityPlot Listen ListFourierSequenceTransform ListInterpolation ListLineIntegralConvolutionPlot ListLinePlot ListLogLinearPlot ListLogLogPlot ListLogPlot ListPicker ListPickerBox ListPickerBoxBackground ListPickerBoxOptions ListPlay ListPlot ListPlot3D ListPointPlot3D ListPolarPlot ListQ ListStreamDensityPlot ListStreamPlot ListSurfacePlot3D ListVectorDensityPlot ListVectorPlot ListVectorPlot3D ListZTransform Literal LiteralSearch LocalClusteringCoefficient LocalizeVariables LocationEquivalenceTest LocationTest Locator LocatorAutoCreate LocatorBox LocatorBoxOptions LocatorCentering LocatorPane LocatorPaneBox LocatorPaneBoxOptions LocatorRegion Locked Log Log10 Log2 LogBarnesG LogGamma LogGammaDistribution LogicalExpand LogIntegral LogisticDistribution LogitModelFit LogLikelihood LogLinearPlot LogLogisticDistribution LogLogPlot LogMultinormalDistribution LogNormalDistribution LogPlot LogRankTest LogSeriesDistribution LongEqual Longest LongestAscendingSequence LongestCommonSequence LongestCommonSequencePositions LongestCommonSubsequence LongestCommonSubsequencePositions LongestMatch LongForm Longitude LongLeftArrow LongLeftRightArrow LongRightArrow Loopback LoopFreeGraphQ LowerCaseQ LowerLeftArrow LowerRightArrow LowerTriangularize LowpassFilter LQEstimatorGains LQGRegulator LQOutputRegulatorGains LQRegulatorGains LUBackSubstitution LucasL LuccioSamiComponents LUDecomposition LyapunovSolve LyonsGroupLy MachineID MachineName MachineNumberQ MachinePrecision MacintoshSystemPageSetup Magenta Magnification Magnify MainSolve MaintainDynamicCaches Majority MakeBoxes MakeExpression MakeRules MangoldtLambda ManhattanDistance Manipulate Manipulator MannWhitneyTest MantissaExponent Manual Map MapAll MapAt MapIndexed MAProcess MapThread MarcumQ MardiaCombinedTest MardiaKurtosisTest MardiaSkewnessTest MarginalDistribution MarkovProcessProperties Masking MatchingDissimilarity MatchLocalNameQ MatchLocalNames MatchQ Material MathematicaNotation MathieuC MathieuCharacteristicA MathieuCharacteristicB MathieuCharacteristicExponent MathieuCPrime MathieuGroupM11 MathieuGroupM12 MathieuGroupM22 MathieuGroupM23 MathieuGroupM24 MathieuS MathieuSPrime MathMLForm MathMLText Matrices MatrixExp MatrixForm MatrixFunction MatrixLog MatrixPlot MatrixPower MatrixQ MatrixRank Max MaxBend MaxDetect MaxExtraBandwidths MaxExtraConditions MaxFeatures MaxFilter Maximize MaxIterations MaxMemoryUsed MaxMixtureKernels MaxPlotPoints MaxPoints MaxRecursion MaxStableDistribution MaxStepFraction MaxSteps MaxStepSize MaxValue MaxwellDistribution McLaughlinGroupMcL Mean MeanClusteringCoefficient MeanDegreeConnectivity MeanDeviation MeanFilter MeanGraphDistance MeanNeighborDegree MeanShift MeanShiftFilter Median MedianDeviation MedianFilter Medium MeijerG MeixnerDistribution MemberQ MemoryConstrained MemoryInUse Menu MenuAppearance MenuCommandKey MenuEvaluator MenuItem MenuPacket MenuSortingValue MenuStyle MenuView MergeDifferences Mesh MeshFunctions MeshRange MeshShading MeshStyle Message MessageDialog MessageList MessageName MessageOptions MessagePacket Messages MessagesNotebook MetaCharacters MetaInformation Method MethodOptions MexicanHatWavelet MeyerWavelet Min MinDetect MinFilter MinimalPolynomial MinimalStateSpaceModel Minimize Minors MinRecursion MinSize MinStableDistribution Minus MinusPlus MinValue Missing MissingDataMethod MittagLefflerE MixedRadix MixedRadixQuantity MixtureDistribution Mod Modal Mode Modular ModularLambda Module Modulus MoebiusMu Moment Momentary MomentConvert MomentEvaluate MomentGeneratingFunction Monday Monitor MonomialList MonomialOrder MonsterGroupM MorletWavelet MorphologicalBinarize MorphologicalBranchPoints MorphologicalComponents MorphologicalEulerNumber MorphologicalGraph MorphologicalPerimeter MorphologicalTransform Most MouseAnnotation MouseAppearance MouseAppearanceTag MouseButtons Mouseover MousePointerNote MousePosition MovingAverage MovingMedian MoyalDistribution MultiedgeStyle MultilaunchWarning MultiLetterItalics MultiLetterStyle MultilineFunction Multinomial MultinomialDistribution MultinormalDistribution MultiplicativeOrder Multiplicity Multiselection MultivariateHypergeometricDistribution MultivariatePoissonDistribution MultivariateTDistribution N NakagamiDistribution NameQ Names NamespaceBox Nand NArgMax NArgMin NBernoulliB NCache NDSolve NDSolveValue Nearest NearestFunction NeedCurrentFrontEndPackagePacket NeedCurrentFrontEndSymbolsPacket NeedlemanWunschSimilarity Needs Negative NegativeBinomialDistribution NegativeMultinomialDistribution NeighborhoodGraph Nest NestedGreaterGreater NestedLessLess NestedScriptRules NestList NestWhile NestWhileList NevilleThetaC NevilleThetaD NevilleThetaN NevilleThetaS NewPrimitiveStyle NExpectation Next NextPrime NHoldAll NHoldFirst NHoldRest NicholsGridLines NicholsPlot NIntegrate NMaximize NMaxValue NMinimize NMinValue NominalVariables NonAssociative NoncentralBetaDistribution NoncentralChiSquareDistribution NoncentralFRatioDistribution NoncentralStudentTDistribution NonCommutativeMultiply NonConstants None NonlinearModelFit NonlocalMeansFilter NonNegative NonPositive Nor NorlundB Norm Normal NormalDistribution NormalGrouping Normalize NormalizedSquaredEuclideanDistance NormalsFunction NormFunction Not NotCongruent NotCupCap NotDoubleVerticalBar Notebook NotebookApply NotebookAutoSave NotebookClose NotebookConvertSettings NotebookCreate NotebookCreateReturnObject NotebookDefault NotebookDelete NotebookDirectory NotebookDynamicExpression NotebookEvaluate NotebookEventActions NotebookFileName NotebookFind NotebookFindReturnObject NotebookGet NotebookGetLayoutInformationPacket NotebookGetMisspellingsPacket NotebookInformation NotebookInterfaceObject NotebookLocate NotebookObject NotebookOpen NotebookOpenReturnObject NotebookPath NotebookPrint NotebookPut NotebookPutReturnObject NotebookRead NotebookResetGeneratedCells Notebooks NotebookSave NotebookSaveAs NotebookSelection NotebookSetupLayoutInformationPacket NotebooksMenu NotebookWrite NotElement NotEqualTilde NotExists NotGreater NotGreaterEqual NotGreaterFullEqual NotGreaterGreater NotGreaterLess NotGreaterSlantEqual NotGreaterTilde NotHumpDownHump NotHumpEqual NotLeftTriangle NotLeftTriangleBar NotLeftTriangleEqual NotLess NotLessEqual NotLessFullEqual NotLessGreater NotLessLess NotLessSlantEqual NotLessTilde NotNestedGreaterGreater NotNestedLessLess NotPrecedes NotPrecedesEqual NotPrecedesSlantEqual NotPrecedesTilde NotReverseElement NotRightTriangle NotRightTriangleBar NotRightTriangleEqual NotSquareSubset NotSquareSubsetEqual NotSquareSuperset NotSquareSupersetEqual NotSubset NotSubsetEqual NotSucceeds NotSucceedsEqual NotSucceedsSlantEqual NotSucceedsTilde NotSuperset NotSupersetEqual NotTilde NotTildeEqual NotTildeFullEqual NotTildeTilde NotVerticalBar NProbability NProduct NProductFactors NRoots NSolve NSum NSumTerms Null NullRecords NullSpace NullWords Number NumberFieldClassNumber NumberFieldDiscriminant NumberFieldFundamentalUnits NumberFieldIntegralBasis NumberFieldNormRepresentatives NumberFieldRegulator NumberFieldRootsOfUnity NumberFieldSignature NumberForm NumberFormat NumberMarks NumberMultiplier NumberPadding NumberPoint NumberQ NumberSeparator NumberSigns NumberString Numerator NumericFunction NumericQ NuttallWindow NValues NyquistGridLines NyquistPlot O ObservabilityGramian ObservabilityMatrix ObservableDecomposition ObservableModelQ OddQ Off Offset OLEData On ONanGroupON OneIdentity Opacity Open OpenAppend Opener OpenerBox OpenerBoxOptions OpenerView OpenFunctionInspectorPacket Opening OpenRead OpenSpecialOptions OpenTemporary OpenWrite Operate OperatingSystem OptimumFlowData Optional OptionInspectorSettings OptionQ Options OptionsPacket OptionsPattern OptionValue OptionValueBox OptionValueBoxOptions Or Orange Order OrderDistribution OrderedQ Ordering Orderless OrnsteinUhlenbeckProcess Orthogonalize Out Outer OutputAutoOverwrite OutputControllabilityMatrix OutputControllableModelQ OutputForm OutputFormData OutputGrouping OutputMathEditExpression OutputNamePacket OutputResponse OutputSizeLimit OutputStream Over OverBar OverDot Overflow OverHat Overlaps Overlay OverlayBox OverlayBoxOptions Overscript OverscriptBox OverscriptBoxOptions OverTilde OverVector OwenT OwnValues PackingMethod PaddedForm Padding PadeApproximant PadLeft PadRight PageBreakAbove PageBreakBelow PageBreakWithin PageFooterLines PageFooters PageHeaderLines PageHeaders PageHeight PageRankCentrality PageWidth PairedBarChart PairedHistogram PairedSmoothHistogram PairedTTest PairedZTest PaletteNotebook PalettePath Pane PaneBox PaneBoxOptions Panel PanelBox PanelBoxOptions Paneled PaneSelector PaneSelectorBox PaneSelectorBoxOptions PaperWidth ParabolicCylinderD ParagraphIndent ParagraphSpacing ParallelArray ParallelCombine ParallelDo ParallelEvaluate Parallelization Parallelize ParallelMap ParallelNeeds ParallelProduct ParallelSubmit ParallelSum ParallelTable ParallelTry Parameter ParameterEstimator ParameterMixtureDistribution ParameterVariables ParametricFunction ParametricNDSolve ParametricNDSolveValue ParametricPlot ParametricPlot3D ParentConnect ParentDirectory ParentForm Parenthesize ParentList ParetoDistribution Part PartialCorrelationFunction PartialD ParticleData Partition PartitionsP PartitionsQ ParzenWindow PascalDistribution PassEventsDown PassEventsUp Paste PasteBoxFormInlineCells PasteButton Path PathGraph PathGraphQ Pattern PatternSequence PatternTest PauliMatrix PaulWavelet Pause PausedTime PDF PearsonChiSquareTest PearsonCorrelationTest PearsonDistribution PerformanceGoal PeriodicInterpolation Periodogram PeriodogramArray PermutationCycles PermutationCyclesQ PermutationGroup PermutationLength PermutationList PermutationListQ PermutationMax PermutationMin PermutationOrder PermutationPower PermutationProduct PermutationReplace Permutations PermutationSupport Permute PeronaMalikFilter Perpendicular PERTDistribution PetersenGraph PhaseMargins Pi Pick PIDData PIDDerivativeFilter PIDFeedforward PIDTune Piecewise PiecewiseExpand PieChart PieChart3D PillaiTrace PillaiTraceTest Pink Pivoting PixelConstrained PixelValue PixelValuePositions Placed Placeholder PlaceholderReplace Plain PlanarGraphQ Play PlayRange Plot Plot3D Plot3Matrix PlotDivision PlotJoined PlotLabel PlotLayout PlotLegends PlotMarkers PlotPoints PlotRange PlotRangeClipping PlotRangePadding PlotRegion PlotStyle Plus PlusMinus Pochhammer PodStates PodWidth Point Point3DBox PointBox PointFigureChart PointForm PointLegend PointSize PoissonConsulDistribution PoissonDistribution PoissonProcess PoissonWindow PolarAxes PolarAxesOrigin PolarGridLines PolarPlot PolarTicks PoleZeroMarkers PolyaAeppliDistribution PolyGamma Polygon Polygon3DBox Polygon3DBoxOptions PolygonBox PolygonBoxOptions PolygonHoleScale PolygonIntersections PolygonScale PolyhedronData PolyLog PolynomialExtendedGCD PolynomialForm PolynomialGCD PolynomialLCM PolynomialMod PolynomialQ PolynomialQuotient PolynomialQuotientRemainder PolynomialReduce PolynomialRemainder Polynomials PopupMenu PopupMenuBox PopupMenuBoxOptions PopupView PopupWindow Position Positive PositiveDefiniteMatrixQ PossibleZeroQ Postfix PostScript Power PowerDistribution PowerExpand PowerMod PowerModList PowerSpectralDensity PowersRepresentations PowerSymmetricPolynomial Precedence PrecedenceForm Precedes PrecedesEqual PrecedesSlantEqual PrecedesTilde Precision PrecisionGoal PreDecrement PredictionRoot PreemptProtect PreferencesPath Prefix PreIncrement Prepend PrependTo PreserveImageOptions Previous PriceGraphDistribution PrimaryPlaceholder Prime PrimeNu PrimeOmega PrimePi PrimePowerQ PrimeQ Primes PrimeZetaP PrimitiveRoot PrincipalComponents PrincipalValue Print PrintAction PrintForm PrintingCopies PrintingOptions PrintingPageRange PrintingStartingPageNumber PrintingStyleEnvironment PrintPrecision PrintTemporary Prism PrismBox PrismBoxOptions PrivateCellOptions PrivateEvaluationOptions PrivateFontOptions PrivateFrontEndOptions PrivateNotebookOptions PrivatePaths Probability ProbabilityDistribution ProbabilityPlot ProbabilityPr ProbabilityScalePlot ProbitModelFit ProcessEstimator ProcessParameterAssumptions ProcessParameterQ ProcessStateDomain ProcessTimeDomain Product ProductDistribution ProductLog ProgressIndicator ProgressIndicatorBox ProgressIndicatorBoxOptions Projection Prolog PromptForm Properties Property PropertyList PropertyValue Proportion Proportional Protect Protected ProteinData Pruning PseudoInverse Purple Put PutAppend Pyramid PyramidBox PyramidBoxOptions QBinomial QFactorial QGamma QHypergeometricPFQ QPochhammer QPolyGamma QRDecomposition QuadraticIrrationalQ Quantile QuantilePlot Quantity QuantityForm QuantityMagnitude QuantityQ QuantityUnit Quartics QuartileDeviation Quartiles QuartileSkewness QueueingNetworkProcess QueueingProcess QueueProperties Quiet Quit Quotient QuotientRemainder RadialityCentrality RadicalBox RadicalBoxOptions RadioButton RadioButtonBar RadioButtonBox RadioButtonBoxOptions Radon RamanujanTau RamanujanTauL RamanujanTauTheta RamanujanTauZ Random RandomChoice RandomComplex RandomFunction RandomGraph RandomImage RandomInteger RandomPermutation RandomPrime RandomReal RandomSample RandomSeed RandomVariate RandomWalkProcess Range RangeFilter RangeSpecification RankedMax RankedMin Raster Raster3D Raster3DBox Raster3DBoxOptions RasterArray RasterBox RasterBoxOptions Rasterize RasterSize Rational RationalFunctions Rationalize Rationals Ratios Raw RawArray RawBoxes RawData RawMedium RayleighDistribution Re Read ReadList ReadProtected Real RealBlockDiagonalForm RealDigits RealExponent Reals Reap Record RecordLists RecordSeparators Rectangle RectangleBox RectangleBoxOptions RectangleChart RectangleChart3D RecurrenceFilter RecurrenceTable RecurringDigitsForm Red Reduce RefBox ReferenceLineStyle ReferenceMarkers ReferenceMarkerStyle Refine ReflectionMatrix ReflectionTransform Refresh RefreshRate RegionBinarize RegionFunction RegionPlot RegionPlot3D RegularExpression Regularization Reinstall Release ReleaseHold ReliabilityDistribution ReliefImage ReliefPlot Remove RemoveAlphaChannel RemoveAsynchronousTask Removed RemoveInputStreamMethod RemoveOutputStreamMethod RemoveProperty RemoveScheduledTask RenameDirectory RenameFile RenderAll RenderingOptions RenewalProcess RenkoChart Repeated RepeatedNull RepeatedString Replace ReplaceAll ReplaceHeldPart ReplaceImageValue ReplaceList ReplacePart ReplacePixelValue ReplaceRepeated Resampling Rescale RescalingTransform ResetDirectory ResetMenusPacket ResetScheduledTask Residue Resolve Rest Resultant ResumePacket Return ReturnExpressionPacket ReturnInputFormPacket ReturnPacket ReturnTextPacket Reverse ReverseBiorthogonalSplineWavelet ReverseElement ReverseEquilibrium ReverseGraph ReverseUpEquilibrium RevolutionAxis RevolutionPlot3D RGBColor RiccatiSolve RiceDistribution RidgeFilter RiemannR RiemannSiegelTheta RiemannSiegelZ Riffle Right RightArrow RightArrowBar RightArrowLeftArrow RightCosetRepresentative RightDownTeeVector RightDownVector RightDownVectorBar RightTee RightTeeArrow RightTeeVector RightTriangle RightTriangleBar RightTriangleEqual RightUpDownVector RightUpTeeVector RightUpVector RightUpVectorBar RightVector RightVectorBar RiskAchievementImportance RiskReductionImportance RogersTanimotoDissimilarity Root RootApproximant RootIntervals RootLocusPlot RootMeanSquare RootOfUnityQ RootReduce Roots RootSum Rotate RotateLabel RotateLeft RotateRight RotationAction RotationBox RotationBoxOptions RotationMatrix RotationTransform Round RoundImplies RoundingRadius Row RowAlignments RowBackgrounds RowBox RowHeights RowLines RowMinHeight RowReduce RowsEqual RowSpacings RSolve RudvalisGroupRu Rule RuleCondition RuleDelayed RuleForm RulerUnits Run RunScheduledTask RunThrough RuntimeAttributes RuntimeOptions RussellRaoDissimilarity SameQ SameTest SampleDepth SampledSoundFunction SampledSoundList SampleRate SamplingPeriod SARIMAProcess SARMAProcess SatisfiabilityCount SatisfiabilityInstances SatisfiableQ Saturday Save Saveable SaveAutoDelete SaveDefinitions SawtoothWave Scale Scaled ScaleDivisions ScaledMousePosition ScaleOrigin ScalePadding ScaleRanges ScaleRangeStyle ScalingFunctions ScalingMatrix ScalingTransform Scan ScheduledTaskActiveQ ScheduledTaskData ScheduledTaskObject ScheduledTasks SchurDecomposition ScientificForm ScreenRectangle ScreenStyleEnvironment ScriptBaselineShifts ScriptLevel ScriptMinSize ScriptRules ScriptSizeMultipliers Scrollbars ScrollingOptions ScrollPosition Sec Sech SechDistribution SectionGrouping SectorChart SectorChart3D SectorOrigin SectorSpacing SeedRandom Select Selectable SelectComponents SelectedCells SelectedNotebook Selection SelectionAnimate SelectionCell SelectionCellCreateCell SelectionCellDefaultStyle SelectionCellParentStyle SelectionCreateCell SelectionDebuggerTag SelectionDuplicateCell SelectionEvaluate SelectionEvaluateCreateCell SelectionMove SelectionPlaceholder SelectionSetStyle SelectWithContents SelfLoops SelfLoopStyle SemialgebraicComponentInstances SendMail Sequence SequenceAlignment SequenceForm SequenceHold SequenceLimit Series SeriesCoefficient SeriesData SessionTime Set SetAccuracy SetAlphaChannel SetAttributes Setbacks SetBoxFormNamesPacket SetDelayed SetDirectory SetEnvironment SetEvaluationNotebook SetFileDate SetFileLoadingContext SetNotebookStatusLine SetOptions SetOptionsPacket SetPrecision SetProperty SetSelectedNotebook SetSharedFunction SetSharedVariable SetSpeechParametersPacket SetStreamPosition SetSystemOptions Setter SetterBar SetterBox SetterBoxOptions Setting SetValue Shading Shallow ShannonWavelet ShapiroWilkTest Share Sharpen ShearingMatrix ShearingTransform ShenCastanMatrix Short ShortDownArrow Shortest ShortestMatch ShortestPathFunction ShortLeftArrow ShortRightArrow ShortUpArrow Show ShowAutoStyles ShowCellBracket ShowCellLabel ShowCellTags ShowClosedCellArea ShowContents ShowControls ShowCursorTracker ShowGroupOpenCloseIcon ShowGroupOpener ShowInvisibleCharacters ShowPageBreaks ShowPredictiveInterface ShowSelection ShowShortBoxForm ShowSpecialCharacters ShowStringCharacters ShowSyntaxStyles ShrinkingDelay ShrinkWrapBoundingBox SiegelTheta SiegelTukeyTest Sign Signature SignedRankTest SignificanceLevel SignPadding SignTest SimilarityRules SimpleGraph SimpleGraphQ Simplify Sin Sinc SinghMaddalaDistribution SingleEvaluation SingleLetterItalics SingleLetterStyle SingularValueDecomposition SingularValueList SingularValuePlot SingularValues Sinh SinhIntegral SinIntegral SixJSymbol Skeleton SkeletonTransform SkellamDistribution Skewness SkewNormalDistribution Skip SliceDistribution Slider Slider2D Slider2DBox Slider2DBoxOptions SliderBox SliderBoxOptions SlideView Slot SlotSequence Small SmallCircle Smaller SmithDelayCompensator SmithWatermanSimilarity SmoothDensityHistogram SmoothHistogram SmoothHistogram3D SmoothKernelDistribution SocialMediaData Socket SokalSneathDissimilarity Solve SolveAlways SolveDelayed Sort SortBy Sound SoundAndGraphics SoundNote SoundVolume Sow Space SpaceForm Spacer Spacings Span SpanAdjustments SpanCharacterRounding SpanFromAbove SpanFromBoth SpanFromLeft SpanLineThickness SpanMaxSize SpanMinSize SpanningCharacters SpanSymmetric SparseArray SpatialGraphDistribution Speak SpeakTextPacket SpearmanRankTest SpearmanRho Spectrogram SpectrogramArray Specularity SpellingCorrection SpellingDictionaries SpellingDictionariesPath SpellingOptions SpellingSuggestionsPacket Sphere SphereBox SphericalBesselJ SphericalBesselY SphericalHankelH1 SphericalHankelH2 SphericalHarmonicY SphericalPlot3D SphericalRegion SpheroidalEigenvalue SpheroidalJoiningFactor SpheroidalPS SpheroidalPSPrime SpheroidalQS SpheroidalQSPrime SpheroidalRadialFactor SpheroidalS1 SpheroidalS1Prime SpheroidalS2 SpheroidalS2Prime Splice SplicedDistribution SplineClosed SplineDegree SplineKnots SplineWeights Split SplitBy SpokenString Sqrt SqrtBox SqrtBoxOptions Square SquaredEuclideanDistance SquareFreeQ SquareIntersection SquaresR SquareSubset SquareSubsetEqual SquareSuperset SquareSupersetEqual SquareUnion SquareWave StabilityMargins StabilityMarginsStyle StableDistribution Stack StackBegin StackComplete StackInhibit StandardDeviation StandardDeviationFilter StandardForm Standardize StandbyDistribution Star StarGraph StartAsynchronousTask StartingStepSize StartOfLine StartOfString StartScheduledTask StartupSound StateDimensions StateFeedbackGains StateOutputEstimator StateResponse StateSpaceModel StateSpaceRealization StateSpaceTransform StationaryDistribution StationaryWaveletPacketTransform StationaryWaveletTransform StatusArea StatusCentrality StepMonitor StieltjesGamma StirlingS1 StirlingS2 StopAsynchronousTask StopScheduledTask StrataVariables StratonovichProcess StreamColorFunction StreamColorFunctionScaling StreamDensityPlot StreamPlot StreamPoints StreamPosition Streams StreamScale StreamStyle String StringBreak StringByteCount StringCases StringCount StringDrop StringExpression StringForm StringFormat StringFreeQ StringInsert StringJoin StringLength StringMatchQ StringPosition StringQ StringReplace StringReplaceList StringReplacePart StringReverse StringRotateLeft StringRotateRight StringSkeleton StringSplit StringTake StringToStream StringTrim StripBoxes StripOnInput StripWrapperBoxes StrokeForm StructuralImportance StructuredArray StructuredSelection StruveH StruveL Stub StudentTDistribution Style StyleBox StyleBoxAutoDelete StyleBoxOptions StyleData StyleDefinitions StyleForm StyleKeyMapping StyleMenuListing StyleNameDialogSettings StyleNames StylePrint StyleSheetPath Subfactorial Subgraph SubMinus SubPlus SubresultantPolynomialRemainders SubresultantPolynomials Subresultants Subscript SubscriptBox SubscriptBoxOptions Subscripted Subset SubsetEqual Subsets SubStar Subsuperscript SubsuperscriptBox SubsuperscriptBoxOptions Subtract SubtractFrom SubValues Succeeds SucceedsEqual SucceedsSlantEqual SucceedsTilde SuchThat Sum SumConvergence Sunday SuperDagger SuperMinus SuperPlus Superscript SuperscriptBox SuperscriptBoxOptions Superset SupersetEqual SuperStar Surd SurdForm SurfaceColor SurfaceGraphics SurvivalDistribution SurvivalFunction SurvivalModel SurvivalModelFit SuspendPacket SuzukiDistribution SuzukiGroupSuz SwatchLegend Switch Symbol SymbolName SymletWavelet Symmetric SymmetricGroup SymmetricMatrixQ SymmetricPolynomial SymmetricReduction Symmetrize SymmetrizedArray SymmetrizedArrayRules SymmetrizedDependentComponents SymmetrizedIndependentComponents SymmetrizedReplacePart SynchronousInitialization SynchronousUpdating Syntax SyntaxForm SyntaxInformation SyntaxLength SyntaxPacket SyntaxQ SystemDialogInput SystemException SystemHelpPath SystemInformation SystemInformationData SystemOpen SystemOptions SystemsModelDelay SystemsModelDelayApproximate SystemsModelDelete SystemsModelDimensions SystemsModelExtract SystemsModelFeedbackConnect SystemsModelLabels SystemsModelOrder SystemsModelParallelConnect SystemsModelSeriesConnect SystemsModelStateFeedbackConnect SystemStub Tab TabFilling Table TableAlignments TableDepth TableDirections TableForm TableHeadings TableSpacing TableView TableViewBox TabSpacings TabView TabViewBox TabViewBoxOptions TagBox TagBoxNote TagBoxOptions TaggingRules TagSet TagSetDelayed TagStyle TagUnset Take TakeWhile Tally Tan Tanh TargetFunctions TargetUnits TautologyQ TelegraphProcess TemplateBox TemplateBoxOptions TemplateSlotSequence TemporalData Temporary TemporaryVariable TensorContract TensorDimensions TensorExpand TensorProduct TensorQ TensorRank TensorReduce TensorSymmetry TensorTranspose TensorWedge Tetrahedron TetrahedronBox TetrahedronBoxOptions TeXForm TeXSave Text Text3DBox Text3DBoxOptions TextAlignment TextBand TextBoundingBox TextBox TextCell TextClipboardType TextData TextForm TextJustification TextLine TextPacket TextParagraph TextRecognize TextRendering TextStyle Texture TextureCoordinateFunction TextureCoordinateScaling Therefore ThermometerGauge Thick Thickness Thin Thinning ThisLink ThompsonGroupTh Thread ThreeJSymbol Threshold Through Throw Thumbnail Thursday Ticks TicksStyle Tilde TildeEqual TildeFullEqual TildeTilde TimeConstrained TimeConstraint Times TimesBy TimeSeriesForecast TimeSeriesInvertibility TimeUsed TimeValue TimeZone Timing Tiny TitleGrouping TitsGroupT ToBoxes ToCharacterCode ToColor ToContinuousTimeModel ToDate ToDiscreteTimeModel ToeplitzMatrix ToExpression ToFileName Together Toggle ToggleFalse Toggler TogglerBar TogglerBox TogglerBoxOptions ToHeldExpression ToInvertibleTimeSeries TokenWords Tolerance ToLowerCase ToNumberField TooBig Tooltip TooltipBox TooltipBoxOptions TooltipDelay TooltipStyle Top TopHatTransform TopologicalSort ToRadicals ToRules ToString Total TotalHeight TotalVariationFilter TotalWidth TouchscreenAutoZoom TouchscreenControlPlacement ToUpperCase Tr Trace TraceAbove TraceAction TraceBackward TraceDepth TraceDialog TraceForward TraceInternal TraceLevel TraceOff TraceOn TraceOriginal TracePrint TraceScan TrackedSymbols TradingChart TraditionalForm TraditionalFunctionNotation TraditionalNotation TraditionalOrder TransferFunctionCancel TransferFunctionExpand TransferFunctionFactor TransferFunctionModel TransferFunctionPoles TransferFunctionTransform TransferFunctionZeros TransformationFunction TransformationFunctions TransformationMatrix TransformedDistribution TransformedField Translate TranslationTransform TransparentColor Transpose TreeForm TreeGraph TreeGraphQ TreePlot TrendStyle TriangleWave TriangularDistribution Trig TrigExpand TrigFactor TrigFactorList Trigger TrigReduce TrigToExp TrimmedMean True TrueQ TruncatedDistribution TsallisQExponentialDistribution TsallisQGaussianDistribution TTest Tube TubeBezierCurveBox TubeBezierCurveBoxOptions TubeBox TubeBSplineCurveBox TubeBSplineCurveBoxOptions Tuesday TukeyLambdaDistribution TukeyWindow Tuples TuranGraph TuringMachine Transparent UnateQ Uncompress Undefined UnderBar Underflow Underlined Underoverscript UnderoverscriptBox UnderoverscriptBoxOptions Underscript UnderscriptBox UnderscriptBoxOptions UndirectedEdge UndirectedGraph UndirectedGraphQ UndocumentedTestFEParserPacket UndocumentedTestGetSelectionPacket Unequal Unevaluated UniformDistribution UniformGraphDistribution UniformSumDistribution Uninstall Union UnionPlus Unique UnitBox UnitConvert UnitDimensions Unitize UnitRootTest UnitSimplify UnitStep UnitTriangle UnitVector Unprotect UnsameQ UnsavedVariables Unset UnsetShared UntrackedVariables Up UpArrow UpArrowBar UpArrowDownArrow Update UpdateDynamicObjects UpdateDynamicObjectsSynchronous UpdateInterval UpDownArrow UpEquilibrium UpperCaseQ UpperLeftArrow UpperRightArrow UpperTriangularize Upsample UpSet UpSetDelayed UpTee UpTeeArrow UpValues URL URLFetch URLFetchAsynchronous URLSave URLSaveAsynchronous UseGraphicsRange Using UsingFrontEnd V2Get ValidationLength Value ValueBox ValueBoxOptions ValueForm ValueQ ValuesData Variables Variance VarianceEquivalenceTest VarianceEstimatorFunction VarianceGammaDistribution VarianceTest VectorAngle VectorColorFunction VectorColorFunctionScaling VectorDensityPlot VectorGlyphData VectorPlot VectorPlot3D VectorPoints VectorQ Vectors VectorScale VectorStyle Vee Verbatim Verbose VerboseConvertToPostScriptPacket VerifyConvergence VerifySolutions VerifyTestAssumptions Version VersionNumber VertexAdd VertexCapacity VertexColors VertexComponent VertexConnectivity VertexCoordinateRules VertexCoordinates VertexCorrelationSimilarity VertexCosineSimilarity VertexCount VertexCoverQ VertexDataCoordinates VertexDegree VertexDelete VertexDiceSimilarity VertexEccentricity VertexInComponent VertexInDegree VertexIndex VertexJaccardSimilarity VertexLabeling VertexLabels VertexLabelStyle VertexList VertexNormals VertexOutComponent VertexOutDegree VertexQ VertexRenderingFunction VertexReplace VertexShape VertexShapeFunction VertexSize VertexStyle VertexTextureCoordinates VertexWeight Vertical VerticalBar VerticalForm VerticalGauge VerticalSeparator VerticalSlider VerticalTilde ViewAngle ViewCenter ViewMatrix ViewPoint ViewPointSelectorSettings ViewPort ViewRange ViewVector ViewVertical VirtualGroupData Visible VisibleCell VoigtDistribution VonMisesDistribution WaitAll WaitAsynchronousTask WaitNext WaitUntil WakebyDistribution WalleniusHypergeometricDistribution WaringYuleDistribution WatershedComponents WatsonUSquareTest WattsStrogatzGraphDistribution WaveletBestBasis WaveletFilterCoefficients WaveletImagePlot WaveletListPlot WaveletMapIndexed WaveletMatrixPlot WaveletPhi WaveletPsi WaveletScale WaveletScalogram WaveletThreshold WeaklyConnectedComponents WeaklyConnectedGraphQ WeakStationarity WeatherData WeberE Wedge Wednesday WeibullDistribution WeierstrassHalfPeriods WeierstrassInvariants WeierstrassP WeierstrassPPrime WeierstrassSigma WeierstrassZeta WeightedAdjacencyGraph WeightedAdjacencyMatrix WeightedData WeightedGraphQ Weights WelchWindow WheelGraph WhenEvent Which While White Whitespace WhitespaceCharacter WhittakerM WhittakerW WienerFilter WienerProcess WignerD WignerSemicircleDistribution WilksW WilksWTest WindowClickSelect WindowElements WindowFloating WindowFrame WindowFrameElements WindowMargins WindowMovable WindowOpacity WindowSelected WindowSize WindowStatusArea WindowTitle WindowToolbars WindowWidth With WolframAlpha WolframAlphaDate WolframAlphaQuantity WolframAlphaResult Word WordBoundary WordCharacter WordData WordSearch WordSeparators WorkingPrecision Write WriteString Wronskian XMLElement XMLObject Xnor Xor Yellow YuleDissimilarity ZernikeR ZeroSymmetric ZeroTest ZeroWidthTimes Zeta ZetaZero ZipfDistribution ZTest ZTransform $Aborted $ActivationGroupID $ActivationKey $ActivationUserRegistered $AddOnsDirectory $AssertFunction $Assumptions $AsynchronousTask $BaseDirectory $BatchInput $BatchOutput $BoxForms $ByteOrdering $Canceled $CharacterEncoding $CharacterEncodings $CommandLine $CompilationTarget $ConditionHold $ConfiguredKernels $Context $ContextPath $ControlActiveSetting $CreationDate $CurrentLink $DateStringFormat $DefaultFont $DefaultFrontEnd $DefaultImagingDevice $DefaultPath $Display $DisplayFunction $DistributedContexts $DynamicEvaluation $Echo $Epilog $ExportFormats $Failed $FinancialDataSource $FormatType $FrontEnd $FrontEndSession $GeoLocation $HistoryLength $HomeDirectory 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DefaultButton DefaultColor DefaultControlPlacement DefaultDuplicateCellStyle DefaultDuration DefaultElement DefaultFaceGridsStyle DefaultFieldHintStyle DefaultFont DefaultFontProperties DefaultFormatType DefaultFormatTypeForStyle DefaultFrameStyle DefaultFrameTicksStyle DefaultGridLinesStyle DefaultInlineFormatType DefaultInputFormatType DefaultLabelStyle DefaultMenuStyle DefaultNaturalLanguage DefaultNewCellStyle DefaultNewInlineCellStyle DefaultNotebook DefaultOptions DefaultOutputFormatType DefaultStyle DefaultStyleDefinitions DefaultTextFormatType DefaultTextInlineFormatType DefaultTicksStyle DefaultTooltipStyle DefaultValues Defer DefineExternal DefineInputStreamMethod DefineOutputStreamMethod Definition Degree DegreeCentrality DegreeGraphDistribution DegreeLexicographic DegreeReverseLexicographic Deinitialization Del Deletable Delete DeleteBorderComponents DeleteCases DeleteContents DeleteDirectory DeleteDuplicates DeleteFile DeleteSmallComponents DeleteWithContents DeletionWarning Delimiter DelimiterFlashTime DelimiterMatching Delimiters Denominator DensityGraphics DensityHistogram DensityPlot DependentVariables Deploy Deployed Depth DepthFirstScan Derivative DerivativeFilter DescriptorStateSpace DesignMatrix Det DGaussianWavelet DiacriticalPositioning Diagonal DiagonalMatrix Dialog DialogIndent DialogInput DialogLevel DialogNotebook DialogProlog DialogReturn DialogSymbols Diamond DiamondMatrix DiceDissimilarity DictionaryLookup DifferenceDelta DifferenceOrder DifferenceRoot DifferenceRootReduce Differences DifferentialD DifferentialRoot DifferentialRootReduce DifferentiatorFilter DigitBlock DigitBlockMinimum DigitCharacter DigitCount DigitQ DihedralGroup Dilation Dimensions DiracComb DiracDelta DirectedEdge DirectedEdges DirectedGraph DirectedGraphQ DirectedInfinity Direction Directive Directory DirectoryName DirectoryQ DirectoryStack DirichletCharacter DirichletConvolve DirichletDistribution DirichletL DirichletTransform DirichletWindow DisableConsolePrintPacket DiscreteChirpZTransform DiscreteConvolve DiscreteDelta DiscreteHadamardTransform DiscreteIndicator DiscreteLQEstimatorGains DiscreteLQRegulatorGains DiscreteLyapunovSolve DiscreteMarkovProcess DiscretePlot DiscretePlot3D DiscreteRatio DiscreteRiccatiSolve DiscreteShift DiscreteTimeModelQ DiscreteUniformDistribution DiscreteVariables DiscreteWaveletData DiscreteWaveletPacketTransform DiscreteWaveletTransform Discriminant Disjunction Disk DiskBox DiskMatrix Dispatch DispersionEstimatorFunction Display DisplayAllSteps DisplayEndPacket DisplayFlushImagePacket DisplayForm DisplayFunction DisplayPacket DisplayRules DisplaySetSizePacket DisplayString DisplayTemporary DisplayWith DisplayWithRef DisplayWithVariable DistanceFunction DistanceTransform Distribute Distributed DistributedContexts DistributeDefinitions DistributionChart DistributionDomain DistributionFitTest DistributionParameterAssumptions DistributionParameterQ Dithering Div Divergence Divide DivideBy Dividers Divisible Divisors DivisorSigma DivisorSum DMSList DMSString Do DockedCells DocumentNotebook DominantColors DOSTextFormat Dot DotDashed DotEqual Dotted DoubleBracketingBar DoubleContourIntegral DoubleDownArrow DoubleLeftArrow DoubleLeftRightArrow DoubleLeftTee DoubleLongLeftArrow DoubleLongLeftRightArrow DoubleLongRightArrow DoubleRightArrow DoubleRightTee DoubleUpArrow DoubleUpDownArrow DoubleVerticalBar DoublyInfinite Down DownArrow DownArrowBar DownArrowUpArrow DownLeftRightVector DownLeftTeeVector DownLeftVector DownLeftVectorBar DownRightTeeVector DownRightVector DownRightVectorBar Downsample DownTee DownTeeArrow DownValues DragAndDrop DrawEdges DrawFrontFaces DrawHighlighted Drop DSolve Dt DualLinearProgramming DualSystemsModel DumpGet DumpSave DuplicateFreeQ Dynamic DynamicBox DynamicBoxOptions DynamicEvaluationTimeout DynamicLocation DynamicModule DynamicModuleBox DynamicModuleBoxOptions DynamicModuleParent DynamicModuleValues DynamicName DynamicNamespace DynamicReference DynamicSetting DynamicUpdating DynamicWrapper DynamicWrapperBox DynamicWrapperBoxOptions E EccentricityCentrality EdgeAdd EdgeBetweennessCentrality EdgeCapacity EdgeCapForm EdgeColor EdgeConnectivity EdgeCost EdgeCount EdgeCoverQ EdgeDashing EdgeDelete EdgeDetect EdgeForm EdgeIndex EdgeJoinForm EdgeLabeling EdgeLabels EdgeLabelStyle EdgeList EdgeOpacity EdgeQ EdgeRenderingFunction EdgeRules EdgeShapeFunction EdgeStyle EdgeThickness EdgeWeight Editable EditButtonSettings EditCellTagsSettings EditDistance EffectiveInterest Eigensystem Eigenvalues EigenvectorCentrality Eigenvectors Element ElementData Eliminate EliminationOrder EllipticE EllipticExp EllipticExpPrime EllipticF EllipticFilterModel EllipticK EllipticLog EllipticNomeQ EllipticPi EllipticReducedHalfPeriods EllipticTheta EllipticThetaPrime EmitSound EmphasizeSyntaxErrors EmpiricalDistribution Empty EmptyGraphQ EnableConsolePrintPacket Enabled Encode End EndAdd EndDialogPacket EndFrontEndInteractionPacket EndOfFile EndOfLine EndOfString EndPackage EngineeringForm Enter EnterExpressionPacket EnterTextPacket Entropy EntropyFilter Environment Epilog Equal EqualColumns EqualRows EqualTilde EquatedTo Equilibrium EquirippleFilterKernel Equivalent Erf Erfc Erfi ErlangB ErlangC ErlangDistribution Erosion ErrorBox ErrorBoxOptions ErrorNorm ErrorPacket ErrorsDialogSettings EstimatedDistribution EstimatedProcess EstimatorGains EstimatorRegulator EuclideanDistance EulerE EulerGamma EulerianGraphQ EulerPhi Evaluatable Evaluate Evaluated EvaluatePacket EvaluationCell EvaluationCompletionAction EvaluationElements EvaluationMode EvaluationMonitor EvaluationNotebook EvaluationObject EvaluationOrder Evaluator EvaluatorNames EvenQ EventData EventEvaluator EventHandler EventHandlerTag EventLabels ExactBlackmanWindow ExactNumberQ ExactRootIsolation ExampleData Except ExcludedForms ExcludePods Exclusions ExclusionsStyle Exists Exit ExitDialog Exp Expand ExpandAll ExpandDenominator ExpandFileName ExpandNumerator Expectation ExpectationE ExpectedValue ExpGammaDistribution ExpIntegralE ExpIntegralEi Exponent ExponentFunction ExponentialDistribution ExponentialFamily ExponentialGeneratingFunction ExponentialMovingAverage ExponentialPowerDistribution ExponentPosition ExponentStep Export ExportAutoReplacements ExportPacket ExportString Expression ExpressionCell ExpressionPacket ExpToTrig ExtendedGCD Extension ExtentElementFunction ExtentMarkers ExtentSize ExternalCall ExternalDataCharacterEncoding Extract ExtractArchive ExtremeValueDistribution FaceForm FaceGrids FaceGridsStyle Factor FactorComplete Factorial Factorial2 FactorialMoment FactorialMomentGeneratingFunction FactorialPower FactorInteger FactorList FactorSquareFree FactorSquareFreeList FactorTerms FactorTermsList Fail FailureDistribution False FARIMAProcess FEDisableConsolePrintPacket FeedbackSector FeedbackSectorStyle FeedbackType FEEnableConsolePrintPacket Fibonacci FieldHint FieldHintStyle FieldMasked FieldSize File FileBaseName FileByteCount FileDate FileExistsQ FileExtension FileFormat FileHash FileInformation FileName FileNameDepth FileNameDialogSettings FileNameDrop FileNameJoin FileNames FileNameSetter FileNameSplit FileNameTake FilePrint FileType FilledCurve FilledCurveBox Filling FillingStyle FillingTransform FilterRules FinancialBond FinancialData FinancialDerivative FinancialIndicator Find FindArgMax FindArgMin FindClique FindClusters FindCurvePath FindDistributionParameters FindDivisions FindEdgeCover FindEdgeCut FindEulerianCycle FindFaces FindFile FindFit FindGeneratingFunction FindGeoLocation FindGeometricTransform FindGraphCommunities FindGraphIsomorphism FindGraphPartition FindHamiltonianCycle FindIndependentEdgeSet FindIndependentVertexSet FindInstance FindIntegerNullVector FindKClan FindKClique FindKClub FindKPlex FindLibrary FindLinearRecurrence FindList FindMaximum FindMaximumFlow FindMaxValue FindMinimum FindMinimumCostFlow FindMinimumCut FindMinValue FindPermutation FindPostmanTour FindProcessParameters FindRoot FindSequenceFunction FindSettings FindShortestPath FindShortestTour FindThreshold FindVertexCover FindVertexCut Fine FinishDynamic FiniteAbelianGroupCount FiniteGroupCount FiniteGroupData First FirstPassageTimeDistribution FischerGroupFi22 FischerGroupFi23 FischerGroupFi24Prime FisherHypergeometricDistribution FisherRatioTest FisherZDistribution Fit FitAll FittedModel FixedPoint FixedPointList FlashSelection Flat Flatten FlattenAt FlatTopWindow FlipView Floor FlushPrintOutputPacket Fold FoldList Font FontColor FontFamily FontForm FontName FontOpacity FontPostScriptName FontProperties FontReencoding FontSize FontSlant FontSubstitutions FontTracking FontVariations FontWeight For ForAll Format FormatRules FormatType FormatTypeAutoConvert FormatValues FormBox FormBoxOptions FortranForm Forward ForwardBackward Fourier FourierCoefficient FourierCosCoefficient FourierCosSeries FourierCosTransform FourierDCT FourierDCTFilter FourierDCTMatrix FourierDST FourierDSTMatrix FourierMatrix FourierParameters FourierSequenceTransform FourierSeries FourierSinCoefficient FourierSinSeries FourierSinTransform FourierTransform FourierTrigSeries FractionalBrownianMotionProcess FractionalPart FractionBox FractionBoxOptions FractionLine Frame FrameBox FrameBoxOptions Framed FrameInset FrameLabel Frameless FrameMargins FrameStyle FrameTicks FrameTicksStyle FRatioDistribution FrechetDistribution FreeQ FrequencySamplingFilterKernel FresnelC FresnelS Friday FrobeniusNumber FrobeniusSolve FromCharacterCode FromCoefficientRules FromContinuedFraction FromDate FromDigits FromDMS Front FrontEndDynamicExpression FrontEndEventActions FrontEndExecute FrontEndObject FrontEndResource FrontEndResourceString FrontEndStackSize FrontEndToken FrontEndTokenExecute FrontEndValueCache FrontEndVersion FrontFaceColor FrontFaceOpacity Full FullAxes FullDefinition FullForm FullGraphics FullOptions FullSimplify Function FunctionExpand FunctionInterpolation FunctionSpace FussellVeselyImportance GaborFilter GaborMatrix GaborWavelet GainMargins GainPhaseMargins Gamma GammaDistribution GammaRegularized GapPenalty Gather GatherBy GaugeFaceElementFunction GaugeFaceStyle GaugeFrameElementFunction GaugeFrameSize GaugeFrameStyle GaugeLabels GaugeMarkers GaugeStyle GaussianFilter GaussianIntegers GaussianMatrix GaussianWindow GCD GegenbauerC General GeneralizedLinearModelFit GenerateConditions GeneratedCell GeneratedParameters GeneratingFunction Generic GenericCylindricalDecomposition GenomeData GenomeLookup GeodesicClosing GeodesicDilation GeodesicErosion GeodesicOpening GeoDestination GeodesyData GeoDirection GeoDistance GeoGridPosition GeometricBrownianMotionProcess GeometricDistribution GeometricMean GeometricMeanFilter GeometricTransformation GeometricTransformation3DBox GeometricTransformation3DBoxOptions GeometricTransformationBox GeometricTransformationBoxOptions GeoPosition GeoPositionENU GeoPositionXYZ GeoProjectionData GestureHandler GestureHandlerTag Get GetBoundingBoxSizePacket GetContext GetEnvironment GetFileName GetFrontEndOptionsDataPacket GetLinebreakInformationPacket GetMenusPacket GetPageBreakInformationPacket Glaisher GlobalClusteringCoefficient GlobalPreferences GlobalSession Glow GoldenRatio GompertzMakehamDistribution GoodmanKruskalGamma GoodmanKruskalGammaTest Goto Grad Gradient GradientFilter GradientOrientationFilter Graph GraphAssortativity GraphCenter GraphComplement GraphData GraphDensity GraphDiameter GraphDifference GraphDisjointUnion GraphDistance GraphDistanceMatrix GraphElementData GraphEmbedding GraphHighlight GraphHighlightStyle GraphHub Graphics Graphics3D Graphics3DBox Graphics3DBoxOptions GraphicsArray GraphicsBaseline GraphicsBox GraphicsBoxOptions GraphicsColor GraphicsColumn GraphicsComplex GraphicsComplex3DBox GraphicsComplex3DBoxOptions GraphicsComplexBox GraphicsComplexBoxOptions GraphicsContents GraphicsData GraphicsGrid GraphicsGridBox GraphicsGroup GraphicsGroup3DBox GraphicsGroup3DBoxOptions GraphicsGroupBox GraphicsGroupBoxOptions GraphicsGrouping GraphicsHighlightColor GraphicsRow GraphicsSpacing GraphicsStyle GraphIntersection GraphLayout GraphLinkEfficiency GraphPeriphery GraphPlot GraphPlot3D GraphPower GraphPropertyDistribution GraphQ GraphRadius GraphReciprocity GraphRoot GraphStyle GraphUnion Gray GrayLevel GreatCircleDistance Greater GreaterEqual GreaterEqualLess GreaterFullEqual GreaterGreater GreaterLess GreaterSlantEqual GreaterTilde Green Grid GridBaseline GridBox GridBoxAlignment GridBoxBackground GridBoxDividers GridBoxFrame GridBoxItemSize GridBoxItemStyle GridBoxOptions GridBoxSpacings GridCreationSettings GridDefaultElement GridElementStyleOptions GridFrame GridFrameMargins GridGraph GridLines GridLinesStyle GroebnerBasis GroupActionBase GroupCentralizer GroupElementFromWord GroupElementPosition GroupElementQ GroupElements GroupElementToWord GroupGenerators GroupMultiplicationTable GroupOrbits GroupOrder GroupPageBreakWithin GroupSetwiseStabilizer GroupStabilizer GroupStabilizerChain Gudermannian GumbelDistribution HaarWavelet HadamardMatrix HalfNormalDistribution HamiltonianGraphQ HammingDistance HammingWindow HankelH1 HankelH2 HankelMatrix HannPoissonWindow HannWindow HaradaNortonGroupHN HararyGraph HarmonicMean HarmonicMeanFilter HarmonicNumber Hash HashTable Haversine HazardFunction Head HeadCompose Heads HeavisideLambda HeavisidePi HeavisideTheta HeldGroupHe HeldPart HelpBrowserLookup HelpBrowserNotebook HelpBrowserSettings HermiteDecomposition HermiteH HermitianMatrixQ HessenbergDecomposition Hessian HexadecimalCharacter Hexahedron HexahedronBox HexahedronBoxOptions HiddenSurface HighlightGraph HighlightImage HighpassFilter HigmanSimsGroupHS HilbertFilter HilbertMatrix Histogram Histogram3D HistogramDistribution HistogramList HistogramTransform HistogramTransformInterpolation HitMissTransform HITSCentrality HodgeDual HoeffdingD HoeffdingDTest Hold HoldAll HoldAllComplete HoldComplete HoldFirst HoldForm HoldPattern HoldRest HolidayCalendar HomeDirectory HomePage Horizontal HorizontalForm HorizontalGauge HorizontalScrollPosition HornerForm HotellingTSquareDistribution HoytDistribution HTMLSave Hue HumpDownHump HumpEqual HurwitzLerchPhi HurwitzZeta HyperbolicDistribution HypercubeGraph HyperexponentialDistribution Hyperfactorial Hypergeometric0F1 Hypergeometric0F1Regularized Hypergeometric1F1 Hypergeometric1F1Regularized Hypergeometric2F1 Hypergeometric2F1Regularized HypergeometricDistribution HypergeometricPFQ HypergeometricPFQRegularized HypergeometricU Hyperlink HyperlinkCreationSettings Hyphenation HyphenationOptions HypoexponentialDistribution HypothesisTestData I Identity IdentityMatrix If IgnoreCase Im Image Image3D Image3DSlices ImageAccumulate ImageAdd ImageAdjust ImageAlign ImageApply ImageAspectRatio ImageAssemble ImageCache ImageCacheValid ImageCapture ImageChannels ImageClip ImageColorSpace ImageCompose ImageConvolve ImageCooccurrence ImageCorners ImageCorrelate ImageCorrespondingPoints ImageCrop ImageData ImageDataPacket ImageDeconvolve ImageDemosaic ImageDifference ImageDimensions ImageDistance ImageEffect ImageFeatureTrack ImageFileApply ImageFileFilter ImageFileScan ImageFilter ImageForestingComponents ImageForwardTransformation ImageHistogram ImageKeypoints ImageLevels ImageLines ImageMargins ImageMarkers ImageMeasurements ImageMultiply ImageOffset ImagePad ImagePadding ImagePartition ImagePeriodogram ImagePerspectiveTransformation ImageQ ImageRangeCache ImageReflect ImageRegion ImageResize ImageResolution ImageRotate ImageRotated ImageScaled ImageScan ImageSize ImageSizeAction ImageSizeCache ImageSizeMultipliers ImageSizeRaw ImageSubtract ImageTake ImageTransformation ImageTrim ImageType ImageValue ImageValuePositions Implies Import ImportAutoReplacements ImportString ImprovementImportance In IncidenceGraph IncidenceList IncidenceMatrix IncludeConstantBasis IncludeFileExtension IncludePods IncludeSingularTerm Increment Indent IndentingNewlineSpacings IndentMaxFraction IndependenceTest IndependentEdgeSetQ IndependentUnit IndependentVertexSetQ Indeterminate IndexCreationOptions Indexed IndexGraph IndexTag Inequality InexactNumberQ InexactNumbers Infinity Infix Information Inherited InheritScope Initialization InitializationCell InitializationCellEvaluation InitializationCellWarning InlineCounterAssignments InlineCounterIncrements InlineRules Inner Inpaint Input InputAliases InputAssumptions InputAutoReplacements InputField InputFieldBox InputFieldBoxOptions InputForm InputGrouping InputNamePacket InputNotebook InputPacket InputSettings InputStream InputString InputStringPacket InputToBoxFormPacket Insert InsertionPointObject InsertResults Inset Inset3DBox Inset3DBoxOptions InsetBox InsetBoxOptions Install InstallService InString Integer IntegerDigits IntegerExponent IntegerLength IntegerPart IntegerPartitions IntegerQ Integers IntegerString Integral Integrate Interactive InteractiveTradingChart Interlaced Interleaving InternallyBalancedDecomposition InterpolatingFunction InterpolatingPolynomial Interpolation InterpolationOrder InterpolationPoints InterpolationPrecision Interpretation InterpretationBox InterpretationBoxOptions InterpretationFunction InterpretTemplate InterquartileRange Interrupt InterruptSettings Intersection Interval IntervalIntersection IntervalMemberQ IntervalUnion Inverse InverseBetaRegularized InverseCDF InverseChiSquareDistribution InverseContinuousWaveletTransform InverseDistanceTransform InverseEllipticNomeQ InverseErf InverseErfc InverseFourier InverseFourierCosTransform InverseFourierSequenceTransform InverseFourierSinTransform InverseFourierTransform InverseFunction InverseFunctions InverseGammaDistribution InverseGammaRegularized InverseGaussianDistribution InverseGudermannian InverseHaversine InverseJacobiCD InverseJacobiCN InverseJacobiCS InverseJacobiDC InverseJacobiDN InverseJacobiDS InverseJacobiNC InverseJacobiND InverseJacobiNS InverseJacobiSC InverseJacobiSD InverseJacobiSN InverseLaplaceTransform InversePermutation InverseRadon InverseSeries InverseSurvivalFunction InverseWaveletTransform InverseWeierstrassP InverseZTransform Invisible InvisibleApplication InvisibleTimes IrreduciblePolynomialQ IsolatingInterval IsomorphicGraphQ IsotopeData Italic Item ItemBox ItemBoxOptions ItemSize ItemStyle ItoProcess JaccardDissimilarity JacobiAmplitude Jacobian JacobiCD JacobiCN JacobiCS JacobiDC JacobiDN JacobiDS JacobiNC JacobiND JacobiNS JacobiP JacobiSC JacobiSD JacobiSN JacobiSymbol JacobiZeta JankoGroupJ1 JankoGroupJ2 JankoGroupJ3 JankoGroupJ4 JarqueBeraALMTest JohnsonDistribution Join Joined JoinedCurve JoinedCurveBox JoinForm JordanDecomposition JordanModelDecomposition K KagiChart KaiserBesselWindow KaiserWindow KalmanEstimator KalmanFilter KarhunenLoeveDecomposition KaryTree KatzCentrality KCoreComponents KDistribution KelvinBei KelvinBer KelvinKei KelvinKer KendallTau KendallTauTest KernelExecute KernelMixtureDistribution KernelObject Kernels Ket Khinchin KirchhoffGraph KirchhoffMatrix KleinInvariantJ KnightTourGraph KnotData KnownUnitQ KolmogorovSmirnovTest KroneckerDelta KroneckerModelDecomposition KroneckerProduct KroneckerSymbol KuiperTest KumaraswamyDistribution Kurtosis KuwaharaFilter Label Labeled LabeledSlider LabelingFunction LabelStyle LaguerreL LambdaComponents LambertW LanczosWindow LandauDistribution Language LanguageCategory LaplaceDistribution LaplaceTransform Laplacian LaplacianFilter LaplacianGaussianFilter Large Larger Last Latitude LatitudeLongitude LatticeData LatticeReduce Launch LaunchKernels LayeredGraphPlot LayerSizeFunction LayoutInformation LCM LeafCount LeapYearQ LeastSquares LeastSquaresFilterKernel Left LeftArrow LeftArrowBar LeftArrowRightArrow LeftDownTeeVector LeftDownVector LeftDownVectorBar LeftRightArrow LeftRightVector LeftTee LeftTeeArrow LeftTeeVector LeftTriangle LeftTriangleBar LeftTriangleEqual LeftUpDownVector LeftUpTeeVector LeftUpVector LeftUpVectorBar LeftVector LeftVectorBar LegendAppearance Legended LegendFunction LegendLabel LegendLayout LegendMargins LegendMarkers LegendMarkerSize LegendreP LegendreQ LegendreType Length LengthWhile LerchPhi Less LessEqual LessEqualGreater LessFullEqual LessGreater LessLess LessSlantEqual LessTilde LetterCharacter LetterQ Level LeveneTest LeviCivitaTensor LevyDistribution Lexicographic LibraryFunction LibraryFunctionError LibraryFunctionInformation LibraryFunctionLoad LibraryFunctionUnload LibraryLoad LibraryUnload LicenseID LiftingFilterData LiftingWaveletTransform LightBlue LightBrown LightCyan Lighter LightGray LightGreen Lighting LightingAngle LightMagenta LightOrange LightPink LightPurple LightRed LightSources LightYellow Likelihood Limit LimitsPositioning LimitsPositioningTokens LindleyDistribution Line Line3DBox LinearFilter LinearFractionalTransform LinearModelFit LinearOffsetFunction LinearProgramming LinearRecurrence LinearSolve LinearSolveFunction LineBox LineBreak LinebreakAdjustments LineBreakChart LineBreakWithin LineColor LineForm LineGraph LineIndent LineIndentMaxFraction LineIntegralConvolutionPlot LineIntegralConvolutionScale LineLegend LineOpacity LineSpacing LineWrapParts LinkActivate LinkClose LinkConnect LinkConnectedQ LinkCreate LinkError LinkFlush LinkFunction LinkHost LinkInterrupt LinkLaunch LinkMode LinkObject LinkOpen LinkOptions LinkPatterns LinkProtocol LinkRead LinkReadHeld LinkReadyQ Links LinkWrite LinkWriteHeld LiouvilleLambda List Listable ListAnimate ListContourPlot ListContourPlot3D ListConvolve ListCorrelate ListCurvePathPlot ListDeconvolve ListDensityPlot Listen ListFourierSequenceTransform ListInterpolation ListLineIntegralConvolutionPlot ListLinePlot ListLogLinearPlot ListLogLogPlot ListLogPlot ListPicker ListPickerBox ListPickerBoxBackground ListPickerBoxOptions ListPlay ListPlot ListPlot3D ListPointPlot3D ListPolarPlot ListQ ListStreamDensityPlot ListStreamPlot ListSurfacePlot3D ListVectorDensityPlot ListVectorPlot ListVectorPlot3D ListZTransform Literal LiteralSearch LocalClusteringCoefficient LocalizeVariables LocationEquivalenceTest LocationTest Locator LocatorAutoCreate LocatorBox LocatorBoxOptions LocatorCentering LocatorPane LocatorPaneBox LocatorPaneBoxOptions LocatorRegion Locked Log Log10 Log2 LogBarnesG LogGamma LogGammaDistribution LogicalExpand LogIntegral LogisticDistribution LogitModelFit LogLikelihood LogLinearPlot LogLogisticDistribution LogLogPlot LogMultinormalDistribution LogNormalDistribution LogPlot LogRankTest LogSeriesDistribution LongEqual Longest LongestAscendingSequence LongestCommonSequence LongestCommonSequencePositions LongestCommonSubsequence LongestCommonSubsequencePositions LongestMatch LongForm Longitude LongLeftArrow LongLeftRightArrow LongRightArrow Loopback LoopFreeGraphQ LowerCaseQ LowerLeftArrow LowerRightArrow LowerTriangularize LowpassFilter LQEstimatorGains LQGRegulator LQOutputRegulatorGains LQRegulatorGains LUBackSubstitution LucasL LuccioSamiComponents LUDecomposition LyapunovSolve LyonsGroupLy MachineID MachineName MachineNumberQ MachinePrecision MacintoshSystemPageSetup Magenta Magnification Magnify MainSolve MaintainDynamicCaches Majority MakeBoxes MakeExpression MakeRules MangoldtLambda ManhattanDistance Manipulate Manipulator MannWhitneyTest MantissaExponent Manual Map MapAll MapAt MapIndexed MAProcess MapThread MarcumQ MardiaCombinedTest MardiaKurtosisTest MardiaSkewnessTest MarginalDistribution MarkovProcessProperties Masking MatchingDissimilarity MatchLocalNameQ MatchLocalNames MatchQ Material MathematicaNotation MathieuC MathieuCharacteristicA MathieuCharacteristicB MathieuCharacteristicExponent MathieuCPrime MathieuGroupM11 MathieuGroupM12 MathieuGroupM22 MathieuGroupM23 MathieuGroupM24 MathieuS MathieuSPrime MathMLForm MathMLText Matrices MatrixExp MatrixForm MatrixFunction MatrixLog MatrixPlot MatrixPower MatrixQ MatrixRank Max MaxBend MaxDetect MaxExtraBandwidths MaxExtraConditions MaxFeatures MaxFilter Maximize MaxIterations MaxMemoryUsed MaxMixtureKernels MaxPlotPoints MaxPoints MaxRecursion MaxStableDistribution MaxStepFraction MaxSteps MaxStepSize MaxValue MaxwellDistribution McLaughlinGroupMcL Mean MeanClusteringCoefficient MeanDegreeConnectivity MeanDeviation MeanFilter MeanGraphDistance MeanNeighborDegree MeanShift MeanShiftFilter Median MedianDeviation MedianFilter Medium MeijerG MeixnerDistribution MemberQ MemoryConstrained MemoryInUse Menu MenuAppearance MenuCommandKey MenuEvaluator MenuItem MenuPacket MenuSortingValue MenuStyle MenuView MergeDifferences Mesh MeshFunctions MeshRange MeshShading MeshStyle Message MessageDialog MessageList MessageName MessageOptions MessagePacket Messages MessagesNotebook MetaCharacters MetaInformation Method MethodOptions MexicanHatWavelet MeyerWavelet Min MinDetect MinFilter MinimalPolynomial MinimalStateSpaceModel Minimize Minors MinRecursion MinSize MinStableDistribution Minus MinusPlus MinValue Missing MissingDataMethod MittagLefflerE MixedRadix MixedRadixQuantity MixtureDistribution Mod Modal Mode Modular ModularLambda Module Modulus MoebiusMu Moment Momentary MomentConvert MomentEvaluate MomentGeneratingFunction Monday Monitor MonomialList MonomialOrder MonsterGroupM MorletWavelet MorphologicalBinarize MorphologicalBranchPoints MorphologicalComponents MorphologicalEulerNumber MorphologicalGraph MorphologicalPerimeter MorphologicalTransform Most MouseAnnotation MouseAppearance MouseAppearanceTag MouseButtons Mouseover MousePointerNote MousePosition MovingAverage MovingMedian MoyalDistribution MultiedgeStyle MultilaunchWarning MultiLetterItalics MultiLetterStyle MultilineFunction Multinomial MultinomialDistribution MultinormalDistribution MultiplicativeOrder Multiplicity Multiselection MultivariateHypergeometricDistribution MultivariatePoissonDistribution MultivariateTDistribution N NakagamiDistribution NameQ Names NamespaceBox Nand NArgMax NArgMin NBernoulliB NCache NDSolve NDSolveValue Nearest NearestFunction NeedCurrentFrontEndPackagePacket NeedCurrentFrontEndSymbolsPacket NeedlemanWunschSimilarity Needs Negative NegativeBinomialDistribution NegativeMultinomialDistribution NeighborhoodGraph Nest NestedGreaterGreater NestedLessLess NestedScriptRules NestList NestWhile NestWhileList NevilleThetaC NevilleThetaD NevilleThetaN NevilleThetaS NewPrimitiveStyle NExpectation Next NextPrime NHoldAll NHoldFirst NHoldRest NicholsGridLines NicholsPlot NIntegrate NMaximize NMaxValue NMinimize NMinValue NominalVariables NonAssociative NoncentralBetaDistribution NoncentralChiSquareDistribution NoncentralFRatioDistribution NoncentralStudentTDistribution NonCommutativeMultiply NonConstants None NonlinearModelFit NonlocalMeansFilter NonNegative NonPositive Nor NorlundB Norm Normal NormalDistribution NormalGrouping Normalize NormalizedSquaredEuclideanDistance NormalsFunction NormFunction Not NotCongruent NotCupCap NotDoubleVerticalBar Notebook NotebookApply NotebookAutoSave NotebookClose NotebookConvertSettings NotebookCreate NotebookCreateReturnObject NotebookDefault NotebookDelete NotebookDirectory NotebookDynamicExpression NotebookEvaluate NotebookEventActions NotebookFileName NotebookFind NotebookFindReturnObject NotebookGet NotebookGetLayoutInformationPacket NotebookGetMisspellingsPacket NotebookInformation NotebookInterfaceObject NotebookLocate NotebookObject NotebookOpen NotebookOpenReturnObject NotebookPath NotebookPrint NotebookPut NotebookPutReturnObject NotebookRead NotebookResetGeneratedCells Notebooks NotebookSave NotebookSaveAs NotebookSelection NotebookSetupLayoutInformationPacket NotebooksMenu NotebookWrite NotElement NotEqualTilde NotExists NotGreater NotGreaterEqual NotGreaterFullEqual NotGreaterGreater NotGreaterLess NotGreaterSlantEqual NotGreaterTilde NotHumpDownHump NotHumpEqual NotLeftTriangle NotLeftTriangleBar NotLeftTriangleEqual NotLess NotLessEqual NotLessFullEqual NotLessGreater NotLessLess NotLessSlantEqual NotLessTilde NotNestedGreaterGreater NotNestedLessLess NotPrecedes NotPrecedesEqual NotPrecedesSlantEqual NotPrecedesTilde NotReverseElement NotRightTriangle NotRightTriangleBar NotRightTriangleEqual NotSquareSubset NotSquareSubsetEqual NotSquareSuperset NotSquareSupersetEqual NotSubset NotSubsetEqual NotSucceeds NotSucceedsEqual NotSucceedsSlantEqual NotSucceedsTilde NotSuperset NotSupersetEqual NotTilde NotTildeEqual NotTildeFullEqual NotTildeTilde NotVerticalBar NProbability NProduct NProductFactors NRoots NSolve NSum NSumTerms Null NullRecords NullSpace NullWords Number NumberFieldClassNumber NumberFieldDiscriminant NumberFieldFundamentalUnits NumberFieldIntegralBasis NumberFieldNormRepresentatives NumberFieldRegulator NumberFieldRootsOfUnity NumberFieldSignature NumberForm NumberFormat NumberMarks NumberMultiplier NumberPadding NumberPoint NumberQ NumberSeparator NumberSigns NumberString Numerator NumericFunction NumericQ NuttallWindow NValues NyquistGridLines NyquistPlot O ObservabilityGramian ObservabilityMatrix ObservableDecomposition ObservableModelQ OddQ Off Offset OLEData On ONanGroupON OneIdentity Opacity Open OpenAppend Opener OpenerBox OpenerBoxOptions OpenerView OpenFunctionInspectorPacket Opening OpenRead OpenSpecialOptions OpenTemporary OpenWrite Operate OperatingSystem OptimumFlowData Optional OptionInspectorSettings OptionQ Options OptionsPacket OptionsPattern OptionValue OptionValueBox OptionValueBoxOptions Or Orange Order OrderDistribution OrderedQ Ordering Orderless OrnsteinUhlenbeckProcess Orthogonalize Out Outer OutputAutoOverwrite OutputControllabilityMatrix OutputControllableModelQ OutputForm OutputFormData OutputGrouping OutputMathEditExpression OutputNamePacket OutputResponse OutputSizeLimit OutputStream Over OverBar OverDot Overflow OverHat Overlaps Overlay OverlayBox OverlayBoxOptions Overscript OverscriptBox OverscriptBoxOptions OverTilde OverVector OwenT OwnValues PackingMethod PaddedForm Padding PadeApproximant PadLeft PadRight PageBreakAbove PageBreakBelow PageBreakWithin PageFooterLines PageFooters PageHeaderLines PageHeaders PageHeight PageRankCentrality PageWidth PairedBarChart PairedHistogram PairedSmoothHistogram PairedTTest PairedZTest PaletteNotebook PalettePath Pane PaneBox PaneBoxOptions Panel PanelBox PanelBoxOptions Paneled PaneSelector PaneSelectorBox PaneSelectorBoxOptions PaperWidth ParabolicCylinderD ParagraphIndent ParagraphSpacing ParallelArray ParallelCombine ParallelDo ParallelEvaluate Parallelization Parallelize ParallelMap ParallelNeeds ParallelProduct ParallelSubmit ParallelSum ParallelTable ParallelTry Parameter ParameterEstimator ParameterMixtureDistribution ParameterVariables ParametricFunction ParametricNDSolve ParametricNDSolveValue ParametricPlot ParametricPlot3D ParentConnect ParentDirectory ParentForm Parenthesize ParentList ParetoDistribution Part PartialCorrelationFunction PartialD ParticleData Partition PartitionsP PartitionsQ ParzenWindow PascalDistribution PassEventsDown PassEventsUp Paste PasteBoxFormInlineCells PasteButton Path PathGraph PathGraphQ Pattern PatternSequence PatternTest PauliMatrix PaulWavelet Pause PausedTime PDF PearsonChiSquareTest PearsonCorrelationTest PearsonDistribution PerformanceGoal PeriodicInterpolation Periodogram PeriodogramArray PermutationCycles PermutationCyclesQ PermutationGroup PermutationLength PermutationList PermutationListQ PermutationMax PermutationMin PermutationOrder PermutationPower PermutationProduct PermutationReplace Permutations PermutationSupport Permute PeronaMalikFilter Perpendicular PERTDistribution PetersenGraph PhaseMargins Pi Pick PIDData PIDDerivativeFilter PIDFeedforward PIDTune Piecewise PiecewiseExpand PieChart PieChart3D PillaiTrace PillaiTraceTest Pink Pivoting PixelConstrained PixelValue PixelValuePositions Placed Placeholder PlaceholderReplace Plain PlanarGraphQ Play PlayRange Plot Plot3D Plot3Matrix PlotDivision PlotJoined PlotLabel PlotLayout PlotLegends PlotMarkers PlotPoints PlotRange PlotRangeClipping PlotRangePadding PlotRegion PlotStyle Plus PlusMinus Pochhammer PodStates PodWidth Point Point3DBox PointBox PointFigureChart PointForm PointLegend PointSize PoissonConsulDistribution PoissonDistribution PoissonProcess PoissonWindow PolarAxes PolarAxesOrigin PolarGridLines PolarPlot PolarTicks PoleZeroMarkers PolyaAeppliDistribution PolyGamma Polygon Polygon3DBox Polygon3DBoxOptions PolygonBox PolygonBoxOptions PolygonHoleScale PolygonIntersections PolygonScale PolyhedronData PolyLog PolynomialExtendedGCD PolynomialForm PolynomialGCD PolynomialLCM PolynomialMod PolynomialQ PolynomialQuotient PolynomialQuotientRemainder PolynomialReduce PolynomialRemainder Polynomials PopupMenu PopupMenuBox PopupMenuBoxOptions PopupView PopupWindow Position Positive PositiveDefiniteMatrixQ PossibleZeroQ Postfix PostScript Power PowerDistribution PowerExpand PowerMod PowerModList PowerSpectralDensity PowersRepresentations PowerSymmetricPolynomial Precedence PrecedenceForm Precedes PrecedesEqual PrecedesSlantEqual PrecedesTilde Precision PrecisionGoal PreDecrement PredictionRoot PreemptProtect PreferencesPath Prefix PreIncrement Prepend PrependTo PreserveImageOptions Previous PriceGraphDistribution PrimaryPlaceholder Prime PrimeNu PrimeOmega PrimePi PrimePowerQ PrimeQ Primes PrimeZetaP PrimitiveRoot PrincipalComponents PrincipalValue Print PrintAction PrintForm PrintingCopies PrintingOptions PrintingPageRange PrintingStartingPageNumber PrintingStyleEnvironment PrintPrecision PrintTemporary Prism PrismBox PrismBoxOptions PrivateCellOptions PrivateEvaluationOptions PrivateFontOptions PrivateFrontEndOptions PrivateNotebookOptions PrivatePaths Probability ProbabilityDistribution ProbabilityPlot ProbabilityPr ProbabilityScalePlot ProbitModelFit ProcessEstimator ProcessParameterAssumptions ProcessParameterQ ProcessStateDomain ProcessTimeDomain Product ProductDistribution ProductLog ProgressIndicator ProgressIndicatorBox ProgressIndicatorBoxOptions Projection Prolog PromptForm Properties Property PropertyList PropertyValue Proportion Proportional Protect Protected ProteinData Pruning PseudoInverse Purple Put PutAppend Pyramid PyramidBox PyramidBoxOptions QBinomial QFactorial QGamma QHypergeometricPFQ QPochhammer QPolyGamma QRDecomposition QuadraticIrrationalQ Quantile QuantilePlot Quantity QuantityForm QuantityMagnitude QuantityQ QuantityUnit Quartics QuartileDeviation Quartiles QuartileSkewness QueueingNetworkProcess QueueingProcess QueueProperties Quiet Quit Quotient QuotientRemainder RadialityCentrality RadicalBox RadicalBoxOptions RadioButton RadioButtonBar RadioButtonBox RadioButtonBoxOptions Radon RamanujanTau RamanujanTauL RamanujanTauTheta RamanujanTauZ Random RandomChoice RandomComplex RandomFunction RandomGraph RandomImage RandomInteger RandomPermutation RandomPrime RandomReal RandomSample RandomSeed RandomVariate RandomWalkProcess Range RangeFilter RangeSpecification RankedMax RankedMin Raster Raster3D Raster3DBox Raster3DBoxOptions RasterArray RasterBox RasterBoxOptions Rasterize RasterSize Rational RationalFunctions Rationalize Rationals Ratios Raw RawArray RawBoxes RawData RawMedium RayleighDistribution Re Read ReadList ReadProtected Real RealBlockDiagonalForm RealDigits RealExponent Reals Reap Record RecordLists RecordSeparators Rectangle RectangleBox RectangleBoxOptions RectangleChart RectangleChart3D RecurrenceFilter RecurrenceTable RecurringDigitsForm Red Reduce RefBox ReferenceLineStyle ReferenceMarkers ReferenceMarkerStyle Refine ReflectionMatrix ReflectionTransform Refresh RefreshRate RegionBinarize RegionFunction RegionPlot RegionPlot3D RegularExpression Regularization Reinstall Release ReleaseHold ReliabilityDistribution ReliefImage ReliefPlot Remove RemoveAlphaChannel RemoveAsynchronousTask Removed RemoveInputStreamMethod RemoveOutputStreamMethod RemoveProperty RemoveScheduledTask RenameDirectory RenameFile RenderAll RenderingOptions RenewalProcess RenkoChart Repeated RepeatedNull RepeatedString Replace ReplaceAll ReplaceHeldPart ReplaceImageValue ReplaceList ReplacePart ReplacePixelValue ReplaceRepeated Resampling Rescale RescalingTransform ResetDirectory ResetMenusPacket ResetScheduledTask Residue Resolve Rest Resultant ResumePacket Return ReturnExpressionPacket ReturnInputFormPacket ReturnPacket ReturnTextPacket Reverse ReverseBiorthogonalSplineWavelet ReverseElement ReverseEquilibrium ReverseGraph ReverseUpEquilibrium RevolutionAxis RevolutionPlot3D RGBColor RiccatiSolve RiceDistribution RidgeFilter RiemannR RiemannSiegelTheta RiemannSiegelZ Riffle Right RightArrow RightArrowBar RightArrowLeftArrow RightCosetRepresentative RightDownTeeVector RightDownVector RightDownVectorBar RightTee RightTeeArrow RightTeeVector RightTriangle RightTriangleBar RightTriangleEqual RightUpDownVector RightUpTeeVector RightUpVector RightUpVectorBar RightVector RightVectorBar RiskAchievementImportance RiskReductionImportance RogersTanimotoDissimilarity Root RootApproximant RootIntervals RootLocusPlot RootMeanSquare RootOfUnityQ RootReduce Roots RootSum Rotate RotateLabel RotateLeft RotateRight RotationAction RotationBox RotationBoxOptions RotationMatrix RotationTransform Round RoundImplies RoundingRadius Row RowAlignments RowBackgrounds RowBox RowHeights RowLines RowMinHeight RowReduce RowsEqual RowSpacings RSolve RudvalisGroupRu Rule RuleCondition RuleDelayed RuleForm RulerUnits Run RunScheduledTask RunThrough RuntimeAttributes RuntimeOptions RussellRaoDissimilarity SameQ SameTest SampleDepth SampledSoundFunction SampledSoundList SampleRate SamplingPeriod SARIMAProcess SARMAProcess SatisfiabilityCount SatisfiabilityInstances SatisfiableQ Saturday Save Saveable SaveAutoDelete SaveDefinitions SawtoothWave Scale Scaled ScaleDivisions ScaledMousePosition ScaleOrigin ScalePadding ScaleRanges ScaleRangeStyle ScalingFunctions ScalingMatrix ScalingTransform Scan ScheduledTaskActiveQ ScheduledTaskData ScheduledTaskObject ScheduledTasks SchurDecomposition ScientificForm ScreenRectangle ScreenStyleEnvironment ScriptBaselineShifts ScriptLevel ScriptMinSize ScriptRules ScriptSizeMultipliers Scrollbars ScrollingOptions ScrollPosition Sec Sech SechDistribution SectionGrouping SectorChart SectorChart3D SectorOrigin SectorSpacing SeedRandom Select Selectable SelectComponents SelectedCells SelectedNotebook Selection SelectionAnimate SelectionCell SelectionCellCreateCell SelectionCellDefaultStyle SelectionCellParentStyle SelectionCreateCell SelectionDebuggerTag SelectionDuplicateCell SelectionEvaluate SelectionEvaluateCreateCell SelectionMove SelectionPlaceholder SelectionSetStyle SelectWithContents SelfLoops SelfLoopStyle SemialgebraicComponentInstances SendMail Sequence SequenceAlignment SequenceForm SequenceHold SequenceLimit Series SeriesCoefficient SeriesData SessionTime Set SetAccuracy SetAlphaChannel SetAttributes Setbacks SetBoxFormNamesPacket SetDelayed SetDirectory SetEnvironment SetEvaluationNotebook SetFileDate SetFileLoadingContext SetNotebookStatusLine SetOptions SetOptionsPacket SetPrecision SetProperty SetSelectedNotebook SetSharedFunction SetSharedVariable SetSpeechParametersPacket SetStreamPosition SetSystemOptions Setter SetterBar SetterBox SetterBoxOptions Setting SetValue Shading Shallow ShannonWavelet ShapiroWilkTest Share Sharpen ShearingMatrix ShearingTransform ShenCastanMatrix Short ShortDownArrow Shortest ShortestMatch ShortestPathFunction ShortLeftArrow ShortRightArrow ShortUpArrow Show ShowAutoStyles ShowCellBracket ShowCellLabel ShowCellTags ShowClosedCellArea ShowContents ShowControls ShowCursorTracker ShowGroupOpenCloseIcon ShowGroupOpener ShowInvisibleCharacters ShowPageBreaks ShowPredictiveInterface ShowSelection ShowShortBoxForm ShowSpecialCharacters ShowStringCharacters ShowSyntaxStyles ShrinkingDelay ShrinkWrapBoundingBox SiegelTheta SiegelTukeyTest Sign Signature SignedRankTest SignificanceLevel SignPadding SignTest SimilarityRules SimpleGraph SimpleGraphQ Simplify Sin Sinc SinghMaddalaDistribution SingleEvaluation SingleLetterItalics SingleLetterStyle SingularValueDecomposition SingularValueList SingularValuePlot SingularValues Sinh SinhIntegral SinIntegral SixJSymbol Skeleton SkeletonTransform SkellamDistribution Skewness SkewNormalDistribution Skip SliceDistribution Slider Slider2D Slider2DBox Slider2DBoxOptions SliderBox SliderBoxOptions SlideView Slot SlotSequence Small SmallCircle Smaller SmithDelayCompensator SmithWatermanSimilarity SmoothDensityHistogram SmoothHistogram SmoothHistogram3D SmoothKernelDistribution SocialMediaData Socket SokalSneathDissimilarity Solve SolveAlways SolveDelayed Sort SortBy Sound SoundAndGraphics SoundNote SoundVolume Sow Space SpaceForm Spacer Spacings Span SpanAdjustments SpanCharacterRounding SpanFromAbove SpanFromBoth SpanFromLeft SpanLineThickness SpanMaxSize SpanMinSize SpanningCharacters SpanSymmetric SparseArray SpatialGraphDistribution Speak SpeakTextPacket SpearmanRankTest SpearmanRho Spectrogram SpectrogramArray Specularity SpellingCorrection SpellingDictionaries SpellingDictionariesPath SpellingOptions SpellingSuggestionsPacket Sphere SphereBox SphericalBesselJ SphericalBesselY SphericalHankelH1 SphericalHankelH2 SphericalHarmonicY SphericalPlot3D SphericalRegion SpheroidalEigenvalue SpheroidalJoiningFactor SpheroidalPS SpheroidalPSPrime SpheroidalQS SpheroidalQSPrime SpheroidalRadialFactor SpheroidalS1 SpheroidalS1Prime SpheroidalS2 SpheroidalS2Prime Splice SplicedDistribution SplineClosed SplineDegree SplineKnots SplineWeights Split SplitBy SpokenString Sqrt SqrtBox SqrtBoxOptions Square SquaredEuclideanDistance SquareFreeQ SquareIntersection SquaresR SquareSubset SquareSubsetEqual SquareSuperset SquareSupersetEqual SquareUnion SquareWave StabilityMargins StabilityMarginsStyle StableDistribution Stack StackBegin StackComplete StackInhibit StandardDeviation StandardDeviationFilter StandardForm Standardize StandbyDistribution Star StarGraph StartAsynchronousTask StartingStepSize StartOfLine StartOfString StartScheduledTask StartupSound StateDimensions StateFeedbackGains StateOutputEstimator StateResponse StateSpaceModel StateSpaceRealization StateSpaceTransform StationaryDistribution StationaryWaveletPacketTransform StationaryWaveletTransform StatusArea StatusCentrality StepMonitor StieltjesGamma StirlingS1 StirlingS2 StopAsynchronousTask StopScheduledTask StrataVariables StratonovichProcess StreamColorFunction StreamColorFunctionScaling StreamDensityPlot StreamPlot StreamPoints StreamPosition Streams StreamScale StreamStyle String StringBreak StringByteCount StringCases StringCount StringDrop StringExpression StringForm StringFormat StringFreeQ StringInsert StringJoin StringLength StringMatchQ StringPosition StringQ StringReplace StringReplaceList StringReplacePart StringReverse StringRotateLeft StringRotateRight StringSkeleton StringSplit StringTake StringToStream StringTrim StripBoxes StripOnInput StripWrapperBoxes StrokeForm StructuralImportance StructuredArray StructuredSelection StruveH StruveL Stub StudentTDistribution Style StyleBox StyleBoxAutoDelete StyleBoxOptions StyleData StyleDefinitions StyleForm StyleKeyMapping StyleMenuListing StyleNameDialogSettings StyleNames StylePrint StyleSheetPath Subfactorial Subgraph SubMinus SubPlus SubresultantPolynomialRemainders SubresultantPolynomials Subresultants Subscript SubscriptBox SubscriptBoxOptions Subscripted Subset SubsetEqual Subsets SubStar Subsuperscript SubsuperscriptBox SubsuperscriptBoxOptions Subtract SubtractFrom SubValues Succeeds SucceedsEqual SucceedsSlantEqual SucceedsTilde SuchThat Sum SumConvergence Sunday SuperDagger SuperMinus SuperPlus Superscript SuperscriptBox SuperscriptBoxOptions Superset SupersetEqual SuperStar Surd SurdForm SurfaceColor SurfaceGraphics SurvivalDistribution SurvivalFunction SurvivalModel SurvivalModelFit SuspendPacket SuzukiDistribution SuzukiGroupSuz SwatchLegend Switch Symbol SymbolName SymletWavelet Symmetric SymmetricGroup SymmetricMatrixQ SymmetricPolynomial SymmetricReduction Symmetrize SymmetrizedArray SymmetrizedArrayRules SymmetrizedDependentComponents SymmetrizedIndependentComponents SymmetrizedReplacePart SynchronousInitialization SynchronousUpdating Syntax SyntaxForm SyntaxInformation SyntaxLength SyntaxPacket SyntaxQ SystemDialogInput SystemException SystemHelpPath SystemInformation SystemInformationData SystemOpen SystemOptions SystemsModelDelay SystemsModelDelayApproximate SystemsModelDelete SystemsModelDimensions SystemsModelExtract SystemsModelFeedbackConnect SystemsModelLabels SystemsModelOrder SystemsModelParallelConnect SystemsModelSeriesConnect SystemsModelStateFeedbackConnect SystemStub Tab TabFilling Table TableAlignments TableDepth TableDirections TableForm TableHeadings TableSpacing TableView TableViewBox TabSpacings TabView TabViewBox TabViewBoxOptions TagBox TagBoxNote TagBoxOptions TaggingRules TagSet TagSetDelayed TagStyle TagUnset Take TakeWhile Tally Tan Tanh TargetFunctions TargetUnits TautologyQ TelegraphProcess TemplateBox TemplateBoxOptions TemplateSlotSequence TemporalData Temporary TemporaryVariable TensorContract TensorDimensions TensorExpand TensorProduct TensorQ TensorRank TensorReduce TensorSymmetry TensorTranspose TensorWedge Tetrahedron TetrahedronBox TetrahedronBoxOptions TeXForm TeXSave Text Text3DBox Text3DBoxOptions TextAlignment TextBand TextBoundingBox TextBox TextCell TextClipboardType TextData TextForm TextJustification TextLine TextPacket TextParagraph TextRecognize TextRendering TextStyle Texture TextureCoordinateFunction TextureCoordinateScaling Therefore ThermometerGauge Thick Thickness Thin Thinning ThisLink ThompsonGroupTh Thread ThreeJSymbol Threshold Through Throw Thumbnail Thursday Ticks TicksStyle Tilde TildeEqual TildeFullEqual TildeTilde TimeConstrained TimeConstraint Times TimesBy TimeSeriesForecast TimeSeriesInvertibility TimeUsed TimeValue TimeZone Timing Tiny TitleGrouping TitsGroupT ToBoxes ToCharacterCode ToColor ToContinuousTimeModel ToDate ToDiscreteTimeModel ToeplitzMatrix ToExpression ToFileName Together Toggle ToggleFalse Toggler TogglerBar TogglerBox TogglerBoxOptions ToHeldExpression ToInvertibleTimeSeries TokenWords Tolerance ToLowerCase ToNumberField TooBig Tooltip TooltipBox TooltipBoxOptions TooltipDelay TooltipStyle Top TopHatTransform TopologicalSort ToRadicals ToRules ToString Total TotalHeight TotalVariationFilter TotalWidth TouchscreenAutoZoom TouchscreenControlPlacement ToUpperCase Tr Trace TraceAbove TraceAction TraceBackward TraceDepth TraceDialog TraceForward TraceInternal TraceLevel TraceOff TraceOn TraceOriginal TracePrint TraceScan TrackedSymbols TradingChart TraditionalForm TraditionalFunctionNotation TraditionalNotation TraditionalOrder TransferFunctionCancel TransferFunctionExpand TransferFunctionFactor TransferFunctionModel TransferFunctionPoles TransferFunctionTransform TransferFunctionZeros TransformationFunction TransformationFunctions TransformationMatrix TransformedDistribution TransformedField Translate TranslationTransform TransparentColor Transpose TreeForm TreeGraph TreeGraphQ TreePlot TrendStyle TriangleWave TriangularDistribution Trig TrigExpand TrigFactor TrigFactorList Trigger TrigReduce TrigToExp TrimmedMean True TrueQ TruncatedDistribution TsallisQExponentialDistribution TsallisQGaussianDistribution TTest Tube TubeBezierCurveBox TubeBezierCurveBoxOptions TubeBox TubeBSplineCurveBox TubeBSplineCurveBoxOptions Tuesday TukeyLambdaDistribution TukeyWindow Tuples TuranGraph TuringMachine Transparent UnateQ Uncompress Undefined UnderBar Underflow Underlined Underoverscript UnderoverscriptBox UnderoverscriptBoxOptions Underscript UnderscriptBox UnderscriptBoxOptions UndirectedEdge UndirectedGraph UndirectedGraphQ UndocumentedTestFEParserPacket UndocumentedTestGetSelectionPacket Unequal Unevaluated UniformDistribution UniformGraphDistribution UniformSumDistribution Uninstall Union UnionPlus Unique UnitBox UnitConvert UnitDimensions Unitize UnitRootTest UnitSimplify UnitStep UnitTriangle UnitVector Unprotect UnsameQ UnsavedVariables Unset UnsetShared UntrackedVariables Up UpArrow UpArrowBar UpArrowDownArrow Update UpdateDynamicObjects UpdateDynamicObjectsSynchronous UpdateInterval UpDownArrow UpEquilibrium UpperCaseQ UpperLeftArrow UpperRightArrow UpperTriangularize Upsample UpSet UpSetDelayed UpTee UpTeeArrow UpValues URL URLFetch URLFetchAsynchronous URLSave URLSaveAsynchronous UseGraphicsRange Using UsingFrontEnd V2Get ValidationLength Value ValueBox ValueBoxOptions ValueForm ValueQ ValuesData Variables Variance VarianceEquivalenceTest VarianceEstimatorFunction VarianceGammaDistribution VarianceTest VectorAngle VectorColorFunction VectorColorFunctionScaling VectorDensityPlot VectorGlyphData VectorPlot VectorPlot3D VectorPoints VectorQ Vectors VectorScale VectorStyle Vee Verbatim Verbose VerboseConvertToPostScriptPacket VerifyConvergence VerifySolutions VerifyTestAssumptions Version VersionNumber VertexAdd VertexCapacity VertexColors VertexComponent VertexConnectivity VertexCoordinateRules VertexCoordinates VertexCorrelationSimilarity VertexCosineSimilarity VertexCount VertexCoverQ VertexDataCoordinates VertexDegree VertexDelete VertexDiceSimilarity VertexEccentricity VertexInComponent VertexInDegree VertexIndex VertexJaccardSimilarity VertexLabeling VertexLabels VertexLabelStyle VertexList VertexNormals VertexOutComponent VertexOutDegree VertexQ VertexRenderingFunction VertexReplace VertexShape VertexShapeFunction VertexSize VertexStyle VertexTextureCoordinates VertexWeight Vertical VerticalBar VerticalForm VerticalGauge VerticalSeparator VerticalSlider VerticalTilde ViewAngle ViewCenter ViewMatrix ViewPoint ViewPointSelectorSettings ViewPort ViewRange ViewVector ViewVertical VirtualGroupData Visible VisibleCell VoigtDistribution VonMisesDistribution WaitAll WaitAsynchronousTask WaitNext WaitUntil WakebyDistribution WalleniusHypergeometricDistribution 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-                
-                
    
-                    
-                
    
-
             
    
 		
    
 
diff --git a/doc/pub/DimRed/html/reveal.js/plugin/markdown/example.md b/doc/pub/DimRed/html/reveal.js/plugin/markdown/example.md
index 89c75345e..6f6f577a1 100644
--- a/doc/pub/DimRed/html/reveal.js/plugin/markdown/example.md
+++ b/doc/pub/DimRed/html/reveal.js/plugin/markdown/example.md
@@ -29,8 +29,3 @@ Content 3.1
 ## External 3.2
 
 Content 3.2
-
-
-## External 3.3
-
-![External Image](https://s3.amazonaws.com/static.slid.es/logo/v2/slides-symbol-512x512.png)
diff --git a/doc/pub/DimRed/html/reveal.js/plugin/markdown/markdown.js b/doc/pub/DimRed/html/reveal.js/plugin/markdown/markdown.js
index aa08ee5ed..15e3b40b3 100644
--- a/doc/pub/DimRed/html/reveal.js/plugin/markdown/markdown.js
+++ b/doc/pub/DimRed/html/reveal.js/plugin/markdown/markdown.js
@@ -4,26 +4,33 @@
  * of external markdown documents.
  */
 (function( root, factory ) {
-	if (typeof define === 'function' && define.amd) {
-		root.marked = require( './marked' );
-		root.RevealMarkdown = factory( root.marked );
-		root.RevealMarkdown.initialize();
-	} else if( typeof exports === 'object' ) {
+	if( typeof exports === 'object' ) {
 		module.exports = factory( require( './marked' ) );
-	} else {
+	}
+	else {
 		// Browser globals (root is window)
 		root.RevealMarkdown = factory( root.marked );
 		root.RevealMarkdown.initialize();
 	}
 }( this, function( marked ) {
 
+	if( typeof marked === 'undefined' ) {
+		throw 'The reveal.js Markdown plugin requires marked to be loaded';
+	}
+
+	if( typeof hljs !== 'undefined' ) {
+		marked.setOptions({
+			highlight: function( lang, code ) {
+				return hljs.highlightAuto( lang, code ).value;
+			}
+		});
+	}
+
 	var DEFAULT_SLIDE_SEPARATOR = '^\r?\n---\r?\n$',
-		DEFAULT_NOTES_SEPARATOR = 'notes?:',
+		DEFAULT_NOTES_SEPARATOR = 'note:',
 		DEFAULT_ELEMENT_ATTRIBUTES_SEPARATOR = '\\\.element\\\s*?(.+?)$',
 		DEFAULT_SLIDE_ATTRIBUTES_SEPARATOR = '\\\.slide:\\\s*?(\\\S.+?)$';
 
-	var SCRIPT_END_PLACEHOLDER = '__SCRIPT_END__';
-
 
 	/**
 	 * Retrieves the markdown contents of a slide section
@@ -31,15 +38,11 @@
 	 */
 	function getMarkdownFromSlide( section ) {
 
-		// look for a ' );
-
 		var leadingWs = text.match( /^\n?(\s*)/ )[1].length,
 			leadingTabs = text.match( /^\n?(\t*)/ )[1].length;
 
@@ -109,13 +112,9 @@
 		var notesMatch = content.split( new RegExp( options.notesSeparator, 'mgi' ) );
 
 		if( notesMatch.length === 2 ) {
-			content = notesMatch[0] + '';
+			content = notesMatch[0] + '';
 		}
 
-		// prevent script end tags in the content from interfering
-		// with parsing
-		content = content.replace( /<\/script>/g, SCRIPT_END_PLACEHOLDER );
-
 		return '';
 
 	}
@@ -178,7 +177,7 @@
 				markdownSections += '
    ';
 
 				sectionStack[i].forEach( function( child ) {
-					markdownSections += '
    ' + createMarkdownSlide( child, options ) + '
    ';
+					markdownSections += '
    ' +  createMarkdownSlide( child, options ) + '
    ';
 				} );
 
 				markdownSections += '
    ';
@@ -380,24 +379,6 @@
 	return {
 
 		initialize: function() {
-			if( typeof marked === 'undefined' ) {
-				throw 'The reveal.js Markdown plugin requires marked to be loaded';
-			}
-
-			if( typeof hljs !== 'undefined' ) {
-				marked.setOptions({
-					highlight: function( code, lang ) {
-						return hljs.highlightAuto( code, [lang] ).value;
-					}
-				});
-			}
-
-			var options = Reveal.getConfig().markdown;
-
-			if ( options ) {
-				marked.setOptions( options );
-			}
-
 			processSlides();
 			convertSlides();
 		},
diff --git a/doc/pub/DimRed/html/reveal.js/plugin/markdown/marked.js b/doc/pub/DimRed/html/reveal.js/plugin/markdown/marked.js
index 555c1dc1d..70af29bf9 100644
--- a/doc/pub/DimRed/html/reveal.js/plugin/markdown/marked.js
+++ b/doc/pub/DimRed/html/reveal.js/plugin/markdown/marked.js
@@ -3,4 +3,4 @@
  * Copyright (c) 2011-2014, Christopher Jeffrey. (MIT Licensed)
  * https://github.com/chjj/marked
  */
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Error("Tokens array requires a `links` property.")}if(this.options.gfm){if(this.options.breaks){this.rules=inline.breaks}else{this.rules=inline.gfm}}else if(this.options.pedantic){this.rules=inline.pedantic}}InlineLexer.rules=inline;InlineLexer.output=function(src,links,options){var inline=new InlineLexer(links,options);return inline.output(src)};InlineLexer.prototype.output=function(src){var 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r.lex(t)},e.prototype.lex=function(e){return e=e.replace(/\r\n|\r/g,"\n").replace(/\t/g,"    ").replace(/\u00a0/g," ").replace(/\u2424/g,"\n"),this.token(e,!0)},e.prototype.token=function(e,t,n){for(var r,s,i,l,o,h,a,u,c,e=e.replace(/^ +$/gm,"");e;)if((i=this.rules.newline.exec(e))&&(e=e.substring(i[0].length),i[0].length>1&&this.tokens.push({type:"space"})),i=this.rules.code.exec(e))e=e.substring(i[0].length),i=i[0].replace(/^ {4}/gm,""),this.tokens.push({type:"code",text:this.options.pedantic?i:i.replace(/\n+$/,"")});else if(i=this.rules.fences.exec(e))e=e.substring(i[0].length),this.tokens.push({type:"code",lang:i[2],text:i[3]});else if(i=this.rules.heading.exec(e))e=e.substring(i[0].length),this.tokens.push({type:"heading",depth:i[1].length,text:i[2]});else if(t&&(i=this.rules.nptable.exec(e))){for(e=e.substring(i[0].length),h={type:"table",header:i[1].replace(/^ *| *\| *$/g,"").split(/ *\| */),align:i[2].replace(/^ *|\| *$/g,"").split(/ *\| */),cells:i[3].replace(/\n$/,"").split("\n")},u=0;u ?/gm,""),this.token(i,t,!0),this.tokens.push({type:"blockquote_end"});else if(i=this.rules.list.exec(e)){for(e=e.substring(i[0].length),l=i[2],this.tokens.push({type:"list_start",ordered:l.length>1}),i=i[0].match(this.rules.item),r=!1,c=i.length,u=0;c>u;u++)h=i[u],a=h.length,h=h.replace(/^ *([*+-]|\d+\.) +/,""),~h.indexOf("\n ")&&(a-=h.length,h=this.options.pedantic?h.replace(/^ {1,4}/gm,""):h.replace(new RegExp("^ {1,"+a+"}","gm"),"")),this.options.smartLists&&u!==c-1&&(o=p.bullet.exec(i[u+1])[0],l===o||l.length>1&&o.length>1||(e=i.slice(u+1).join("\n")+e,u=c-1)),s=r||/\n\n(?!\s*$)/.test(h),u!==c-1&&(r="\n"===h.charAt(h.length-1),s||(s=r)),this.tokens.push({type:s?"loose_item_start":"list_item_start"}),this.token(h,!1,n),this.tokens.push({type:"list_item_end"});this.tokens.push({type:"list_end"})}else if(i=this.rules.html.exec(e))e=e.substring(i[0].length),this.tokens.push({type:this.options.sanitize?"paragraph":"html",pre:"pre"===i[1]||"script"===i[1]||"style"===i[1],text:i[0]});else if(!n&&t&&(i=this.rules.def.exec(e)))e=e.substring(i[0].length),this.tokens.links[i[1].toLowerCase()]={href:i[2],title:i[3]};else if(t&&(i=this.rules.table.exec(e))){for(e=e.substring(i[0].length),h={type:"table",header:i[1].replace(/^ *| *\| *$/g,"").split(/ *\| */),align:i[2].replace(/^ *|\| *$/g,"").split(/ *\| */),cells:i[3].replace(/(?: *\| *)?\n$/,"").split("\n")},u=0;u])/,autolink:/^<([^ >]+(@|:\/)[^ >]+)>/,url:o,tag:/^|^<\/?\w+(?:"[^"]*"|'[^']*'|[^'">])*?>/,link:/^!?\[(inside)\]\(href\)/,reflink:/^!?\[(inside)\]\s*\[([^\]]*)\]/,nolink:/^!?\[((?:\[[^\]]*\]|[^\[\]])*)\]/,strong:/^__([\s\S]+?)__(?!_)|^\*\*([\s\S]+?)\*\*(?!\*)/,em:/^\b_((?:__|[\s\S])+?)_\b|^\*((?:\*\*|[\s\S])+?)\*(?!\*)/,code:/^(`+)\s*([\s\S]*?[^`])\s*\1(?!`)/,br:/^ {2,}\n(?!\s*$)/,del:o,text:/^[\s\S]+?(?=[\\?(?:\s+['"]([\s\S]*?)['"])?\s*/,u.link=l(u.link)("inside",u._inside)("href",u._href)(),u.reflink=l(u.reflink)("inside",u._inside)(),u.normal=h({},u),u.pedantic=h({},u.normal,{strong:/^__(?=\S)([\s\S]*?\S)__(?!_)|^\*\*(?=\S)([\s\S]*?\S)\*\*(?!\*)/,em:/^_(?=\S)([\s\S]*?\S)_(?!_)|^\*(?=\S)([\s\S]*?\S)\*(?!\*)/}),u.gfm=h({},u.normal,{escape:l(u.escape)("])","~|])")(),url:/^(https?:\/\/[^\s<]+[^<.,:;"')\]\s])/,del:/^~~(?=\S)([\s\S]*?\S)~~/,text:l(u.text)("]|","~]|")("|","|https?://|")()}),u.breaks=h({},u.gfm,{br:l(u.br)("{2,}","*")(),text:l(u.gfm.text)("{2,}","*")()}),t.rules=u,t.output=function(e,n,r){var s=new t(n,r);return s.output(e)},t.prototype.output=function(e){for(var t,n,r,i,l="";e;)if(i=this.rules.escape.exec(e))e=e.substring(i[0].length),l+=i[1];else if(i=this.rules.autolink.exec(e))e=e.substring(i[0].length),"@"===i[2]?(n=this.mangle(":"===i[1].charAt(6)?i[1].substring(7):i[1]),r=this.mangle("mailto:")+n):(n=s(i[1]),r=n),l+=this.renderer.link(r,null,n);else if(this.inLink||!(i=this.rules.url.exec(e))){if(i=this.rules.tag.exec(e))!this.inLink&&/^    /i.test(i[0])&&(this.inLink=!1),e=e.substring(i[0].length),l+=this.options.sanitize?s(i[0]):i[0];else if(i=this.rules.link.exec(e))e=e.substring(i[0].length),this.inLink=!0,l+=this.outputLink(i,{href:i[2],title:i[3]}),this.inLink=!1;else if((i=this.rules.reflink.exec(e))||(i=this.rules.nolink.exec(e))){if(e=e.substring(i[0].length),t=(i[2]||i[1]).replace(/\s+/g," "),t=this.links[t.toLowerCase()],!t||!t.href){l+=i[0].charAt(0),e=i[0].substring(1)+e;continue}this.inLink=!0,l+=this.outputLink(i,t),this.inLink=!1}else if(i=this.rules.strong.exec(e))e=e.substring(i[0].length),l+=this.renderer.strong(this.output(i[2]||i[1]));else if(i=this.rules.em.exec(e))e=e.substring(i[0].length),l+=this.renderer.em(this.output(i[2]||i[1]));else if(i=this.rules.code.exec(e))e=e.substring(i[0].length),l+=this.renderer.codespan(s(i[2],!0));else if(i=this.rules.br.exec(e))e=e.substring(i[0].length),l+=this.renderer.br();else if(i=this.rules.del.exec(e))e=e.substring(i[0].length),l+=this.renderer.del(this.output(i[1]));else if(i=this.rules.text.exec(e))e=e.substring(i[0].length),l+=s(this.smartypants(i[0]));else if(e)throw new Error("Infinite loop on byte: "+e.charCodeAt(0))}else e=e.substring(i[0].length),n=s(i[1]),r=n,l+=this.renderer.link(r,null,n);return l},t.prototype.outputLink=function(e,t){var n=s(t.href),r=t.title?s(t.title):null;return"!"!==e[0].charAt(0)?this.renderer.link(n,r,this.output(e[1])):this.renderer.image(n,r,s(e[1]))},t.prototype.smartypants=function(e){return this.options.smartypants?e.replace(/--/g,"—").replace(/(^|[-\u2014/(\[{"\s])'/g,"$1‘").replace(/'/g,"’").replace(/(^|[-\u2014/(\[{\u2018\s])"/g,"$1“").replace(/"/g,"”").replace(/\.{3}/g,"…"):e},t.prototype.mangle=function(e){for(var t,n="",r=e.length,s=0;r>s;s++)t=e.charCodeAt(s),Math.random()>.5&&(t="x"+t.toString(16)),n+="&#"+t+";";return n},n.prototype.code=function(e,t,n){if(this.options.highlight){var r=this.options.highlight(e,t);null!=r&&r!==e&&(n=!0,e=r)}return t?'
    '+(n?e:s(e,!0))+"\n
    \n":"
    "+(n?e:s(e,!0))+"\n
    "},n.prototype.blockquote=function(e){return"
    \n"+e+"
    \n"},n.prototype.html=function(e){return e},n.prototype.heading=function(e,t,n){return"'+e+"\n"},n.prototype.hr=function(){return this.options.xhtml?"
    \n":"
    \n"},n.prototype.list=function(e,t){var n=t?"ol":"ul";return"<"+n+">\n"+e+"\n"},n.prototype.listitem=function(e){return"
  • "+e+"
    • \n"},n.prototype.paragraph=function(e){return"
    "+e+"
    \n"},n.prototype.table=function(e,t){return"\n\n"+e+"\n\n"+t+"\n
    \n"},n.prototype.tablerow=function(e){return"\n"+e+"\n"},n.prototype.tablecell=function(e,t){var n=t.header?"th":"td",r=t.align?"<"+n+' style="text-align:'+t.align+'">':"<"+n+">";return r+e+"\n"},n.prototype.strong=function(e){return""+e+""},n.prototype.em=function(e){return""+e+""},n.prototype.codespan=function(e){return""+e+""},n.prototype.br=function(){return this.options.xhtml?"
    ":"
    "},n.prototype.del=function(e){return""+e+""},n.prototype.link=function(e,t,n){if(this.options.sanitize){try{var r=decodeURIComponent(i(e)).replace(/[^\w:]/g,"").toLowerCase()}catch(s){return""}if(0===r.indexOf("javascript:")||0===r.indexOf("vbscript:"))return""}var l='    "},n.prototype.image=function(e,t,n){var r=''+n+'":">"},r.parse=function(e,t,n){var s=new r(t,n);return s.parse(e)},r.prototype.parse=function(e){this.inline=new t(e.links,this.options,this.renderer),this.tokens=e.reverse();for(var n="";this.next();)n+=this.tok();return n},r.prototype.next=function(){return this.token=this.tokens.pop()},r.prototype.peek=function(){return this.tokens[this.tokens.length-1]||0},r.prototype.parseText=function(){for(var e=this.token.text;"text"===this.peek().type;)e+="\n"+this.next().text;return this.inline.output(e)},r.prototype.tok=function(){switch(this.token.type){case"space":return"";case"hr":return this.renderer.hr();case"heading":return this.renderer.heading(this.inline.output(this.token.text),this.token.depth,this.token.text);case"code":return this.renderer.code(this.token.text,this.token.lang,this.token.escaped);case"table":var e,t,n,r,s,i="",l="";for(n="",e=0;ebody{font-family: sans-serif;}
    reveal.js multiplex server.
    Generate token');
-		res.end();
-	});
-	stream.on('readable', function() {
-		stream.pipe(res);
-	});
+	fs.createReadStream(opts.baseDir + '/index.html').pipe(res);
 });
 
 app.get("/token", function(req,res) {
@@ -55,7 +47,7 @@ var createHash = function(secret) {
 };
 
 // Actually listen
-server.listen( opts.port || null );
+app.listen(opts.port || null);
 
 var brown = '\033[33m',
 	green = '\033[32m',
diff --git a/doc/pub/DimRed/html/reveal.js/plugin/multiplex/master.js b/doc/pub/DimRed/html/reveal.js/plugin/multiplex/master.js
index 7f4bf4511..b6a7eb7dc 100644
--- a/doc/pub/DimRed/html/reveal.js/plugin/multiplex/master.js
+++ b/doc/pub/DimRed/html/reveal.js/plugin/multiplex/master.js
@@ -1,34 +1,51 @@
 (function() {
-
 	// Don't emit events from inside of notes windows
 	if ( window.location.search.match( /receiver/gi ) ) { return; }
 
 	var multiplex = Reveal.getConfig().multiplex;
 
-	var socket = io.connect( multiplex.url );
+	var socket = io.connect(multiplex.url);
 
-	function post() {
+	var notify = function( slideElement, indexh, indexv, origin ) {
+		if( typeof origin === 'undefined' && origin !== 'remote' ) {
+			var nextindexh;
+			var nextindexv;
 
-		var messageData = {
-			state: Reveal.getState(),
-			secret: multiplex.secret,
-			socketId: multiplex.id
-		};
+			var fragmentindex = Reveal.getIndices().f;
+			if (typeof fragmentindex == 'undefined') {
+				fragmentindex = 0;
+			}
 
-		socket.emit( 'multiplex-statechanged', messageData );
+			if (slideElement.nextElementSibling && slideElement.parentNode.nodeName == 'SECTION') {
+				nextindexh = indexh;
+				nextindexv = indexv + 1;
+			} else {
+				nextindexh = indexh + 1;
+				nextindexv = 0;
+			}
 
+			var slideData = {
+				indexh : indexh,
+				indexv : indexv,
+				indexf : fragmentindex,
+				nextindexh : nextindexh,
+				nextindexv : nextindexv,
+				secret: multiplex.secret,
+				socketId : multiplex.id
+			};
+
+			socket.emit('slidechanged', slideData);
+		}
+	}
+
+	Reveal.addEventListener( 'slidechanged', function( event ) {
+		notify( event.currentSlide, event.indexh, event.indexv, event.origin );
+	} );
+
+	var fragmentNotify = function( event ) {
+		notify( Reveal.getCurrentSlide(), Reveal.getIndices().h, Reveal.getIndices().v, event.origin );
 	};
 
-	// post once the page is loaded, so the client follows also on "open URL".
-	window.addEventListener( 'load', post );
-
-	// Monitor events that trigger a change in state
-	Reveal.addEventListener( 'slidechanged', post );
-	Reveal.addEventListener( 'fragmentshown', post );
-	Reveal.addEventListener( 'fragmenthidden', post );
-	Reveal.addEventListener( 'overviewhidden', post );
-	Reveal.addEventListener( 'overviewshown', post );
-	Reveal.addEventListener( 'paused', post );
-	Reveal.addEventListener( 'resumed', post );
-
-}());
+	Reveal.addEventListener( 'fragmentshown', fragmentNotify );
+	Reveal.addEventListener( 'fragmenthidden', fragmentNotify );
+}());
\ No newline at end of file
diff --git a/doc/pub/DimRed/html/reveal.js/plugin/notes-server/client.js b/doc/pub/DimRed/html/reveal.js/plugin/notes-server/client.js
index 00b277baf..628586ffb 100644
--- a/doc/pub/DimRed/html/reveal.js/plugin/notes-server/client.js
+++ b/doc/pub/DimRed/html/reveal.js/plugin/notes-server/client.js
@@ -41,15 +41,10 @@
 	}
 
 	// When a new notes window connects, post our current state
-	socket.on( 'new-subscriber', function( data ) {
+	socket.on( 'connect', function( data ) {
 		post();
 	} );
 
-	// When the state changes from inside of the speaker view
-	socket.on( 'statechanged-speaker', function( data ) {
-		Reveal.setState( data.state );
-	} );
-
 	// Monitor events that trigger a change in state
 	Reveal.addEventListener( 'slidechanged', post );
 	Reveal.addEventListener( 'fragmentshown', post );
diff --git a/doc/pub/DimRed/html/reveal.js/plugin/notes-server/index.js b/doc/pub/DimRed/html/reveal.js/plugin/notes-server/index.js
index b95f07188..df917f112 100644
--- a/doc/pub/DimRed/html/reveal.js/plugin/notes-server/index.js
+++ b/doc/pub/DimRed/html/reveal.js/plugin/notes-server/index.js
@@ -1,40 +1,37 @@
-var http      = require('http');
 var express   = require('express');
 var fs        = require('fs');
 var io        = require('socket.io');
+var _         = require('underscore');
 var Mustache  = require('mustache');
 
-var app       = express();
+var app       = express.createServer();
 var staticDir = express.static;
-var server    = http.createServer(app);
 
-io = io(server);
+io            = io.listen(app);
 
 var opts = {
 	port :      1947,
 	baseDir :   __dirname + '/../../'
 };
 
-io.on( 'connection', function( socket ) {
+io.sockets.on( 'connection', function( socket ) {
 
-	socket.on( 'new-subscriber', function( data ) {
-		socket.broadcast.emit( 'new-subscriber', data );
+	socket.on( 'connect', function( data ) {
+		socket.broadcast.emit( 'connect', data );
 	});
 
 	socket.on( 'statechanged', function( data ) {
-		delete data.state.overview;
 		socket.broadcast.emit( 'statechanged', data );
 	});
 
-	socket.on( 'statechanged-speaker', function( data ) {
-		delete data.state.overview;
-		socket.broadcast.emit( 'statechanged-speaker', data );
-	});
-
 });
 
-[ 'css', 'js', 'images', 'plugin', 'lib' ].forEach( function( dir ) {
-	app.use( '/' + dir, staticDir( opts.baseDir + dir ) );
+app.configure( function() {
+
+	[ 'css', 'js', 'images', 'plugin', 'lib' ].forEach( function( dir ) {
+		app.use( '/' + dir, staticDir( opts.baseDir + dir ) );
+	});
+
 });
 
 app.get('/', function( req, res ) {
@@ -55,7 +52,7 @@ app.get( '/notes/:socketId', function( req, res ) {
 });
 
 // Actually listen
-server.listen( opts.port || null );
+app.listen( opts.port || null );
 
 var brown = '\033[33m',
 	green = '\033[32m',
@@ -65,5 +62,5 @@ var slidesLocation = 'http://localhost' + ( opts.port ? ( ':' + opts.port ) : ''
 
 console.log( brown + 'reveal.js - Speaker Notes' + reset );
 console.log( '1. Open the slides at ' + green + slidesLocation + reset );
-console.log( '2. Click on the link in your JS console to go to the notes page' );
+console.log( '2. Click on the link your JS console to go to the notes page' );
 console.log( '3. Advance through your slides and your notes will advance automatically' );
diff --git a/doc/pub/DimRed/html/reveal.js/plugin/notes-server/notes.html b/doc/pub/DimRed/html/reveal.js/plugin/notes-server/notes.html
index ab8c5b17a..72d0317f1 100644
--- a/doc/pub/DimRed/html/reveal.js/plugin/notes-server/notes.html
+++ b/doc/pub/DimRed/html/reveal.js/plugin/notes-server/notes.html
@@ -8,7 +8,6 @@
 		
@@ -247,7 +152,7 @@
 	
 
 		
    
-		
    Upcoming
    
+		
    UPCOMING:
    
 		
    
 			
    
 				
    Time Click to Reset
    
@@ -265,10 +170,6 @@
 				
    
 			
    
 		
    
-		
    
-			
-			
-		
    
 
 		
 		
@@ -281,20 +182,11 @@
 				currentState,
 				currentSlide,
 				upcomingSlide,
-				layoutLabel,
-				layoutDropdown,
 				connected = false;
 
 			var socket = io.connect( window.location.origin ),
 				socketId = '{{socketId}}';
 
-			var SPEAKER_LAYOUTS = {
-				'default': 'Default',
-				'wide': 'Wide',
-				'tall': 'Tall',
-				'notes-only': 'Notes only'
-			};
-
 			socket.on( 'statechanged', function( data ) {
 
 				// ignore data from sockets that aren't ours
@@ -303,6 +195,7 @@
 				if( connected === false ) {
 					connected = true;
 
+					setupIframes( data );
 					setupKeyboard();
 					setupNotes();
 					setupTimer();
@@ -313,28 +206,13 @@
 
 			} );
 
-			setupLayout();
-
-			// Load our presentation iframes
-			setupIframes();
-
-			// Once the iframes have loaded, emit a signal saying there's
-			// a new subscriber which will trigger a 'statechanged'
-			// message to be sent back
 			window.addEventListener( 'message', function( event ) {
 
 				var data = JSON.parse( event.data );
 
 				if( data && data.namespace === 'reveal' ) {
 					if( /ready/.test( data.eventName ) ) {
-						socket.emit( 'new-subscriber', { socketId: socketId } );
-					}
-				}
-
-				// Messages sent by reveal.js inside of the current slide preview
-				if( data && data.namespace === 'reveal' ) {
-					if( /slidechanged|fragmentshown|fragmenthidden|overviewshown|overviewhidden|paused|resumed/.test( data.eventName ) && currentState !== JSON.stringify( data.state ) ) {
-						socket.emit( 'statechanged-speaker', { state: data.state } );
+						socket.emit( 'connect', { socketId: socketId } );
 					}
 				}
 
@@ -389,7 +267,7 @@
 			/**
 			 * Creates the preview iframes.
 			 */
-			function setupIframes() {
+			function setupIframes( data ) {
 
 				var params = [
 					'receiver',
@@ -399,8 +277,9 @@
 					'backgroundTransition=none'
 				].join( '&' );
 
-				var currentURL = '/?' + params + '&postMessageEvents=true';
-				var upcomingURL = '/?' + params + '&controls=false';
+				var hash = '#/' + data.state.indexh + '/' + data.state.indexv;
+				var currentURL = '/?' + params + '&postMessageEvents=true' + hash;
+				var upcomingURL = '/?' + params + '&controls=false' + hash;
 
 				currentSlide = document.createElement( 'iframe' );
 				currentSlide.setAttribute( 'width', 1280 );
@@ -472,74 +351,6 @@
 
 			}
 
-			/**
-				 * Sets up the speaker view layout and layout selector.
-				 */
-				function setupLayout() {
-
-					layoutDropdown = document.querySelector( '.speaker-layout-dropdown' );
-					layoutLabel = document.querySelector( '.speaker-layout-label' );
-
-					// Render the list of available layouts
-					for( var id in SPEAKER_LAYOUTS ) {
-						var option = document.createElement( 'option' );
-						option.setAttribute( 'value', id );
-						option.textContent = SPEAKER_LAYOUTS[ id ];
-						layoutDropdown.appendChild( option );
-					}
-
-					// Monitor the dropdown for changes
-					layoutDropdown.addEventListener( 'change', function( event ) {
-
-						setLayout( layoutDropdown.value );
-
-					}, false );
-
-					// Restore any currently persisted layout
-					setLayout( getLayout() );
-
-				}
-
-				/**
-				 * Sets a new speaker view layout. The layout is persisted
-				 * in local storage.
-				 */
-				function setLayout( value ) {
-
-					var title = SPEAKER_LAYOUTS[ value ];
-
-					layoutLabel.innerHTML = 'Layout' + ( title ? ( ': ' + title ) : '' );
-					layoutDropdown.value = value;
-
-					document.body.setAttribute( 'data-speaker-layout', value );
-
-					// Persist locally
-					if( window.localStorage ) {
-						window.localStorage.setItem( 'reveal-speaker-layout', value );
-					}
-
-				}
-
-				/**
-				 * Returns the ID of the most recently set speaker layout
-				 * or our default layout if none has been set.
-				 */
-				function getLayout() {
-
-					if( window.localStorage ) {
-						var layout = window.localStorage.getItem( 'reveal-speaker-layout' );
-						if( layout ) {
-							return layout;
-						}
-					}
-
-					// Default to the first record in the layouts hash
-					for( var id in SPEAKER_LAYOUTS ) {
-						return id;
-					}
-
-				}
-
 			function zeroPadInteger( num ) {
 
 				var str = '00' + parseInt( num );
diff --git a/doc/pub/DimRed/html/reveal.js/plugin/notes/notes.html b/doc/pub/DimRed/html/reveal.js/plugin/notes/notes.html
index 4c5b799b5..0cc8cf612 100644
--- a/doc/pub/DimRed/html/reveal.js/plugin/notes/notes.html
+++ b/doc/pub/DimRed/html/reveal.js/plugin/notes/notes.html
@@ -8,7 +8,6 @@