typo

Author: mhjensen

doc/LectureNotes/week44.ipynb

@@ -652,50 +652,6 @@ <h2 id="mathematics-of-cnns">Mathematics of CNNs </h2>
 <p>How can we use this? And what does it mean? Let us study some familiar examples first.</p>
 </section>
 
-<section>
-<h2 id="mathematics-of-cnns">Mathematics of CNNs </h2>
-
-<p>The mathematics of CNNs is based on the mathematical operation of
-<b>convolution</b>.  In mathematics (in particular in functional analysis),
-convolution is represented by mathematical operations (integration,
-summation etc) on two functions in order to produce a third function
-that expresses how the shape of one gets modified by the other.
-Convolution has a plethora of applications in a variety of
-disciplines, spanning from statistics to signal processing, computer
-vision, solutions of differential equations,linear algebra,
-engineering, and yes, machine learning.
-</p>
-
-<p>Mathematically, convolution is defined as follows (one-dimensional example):
-Let us define a continuous function \( y(t) \) given by
-</p>
-<p>&nbsp;<br>
-$$
-y(t) = \int x(a) w(t-a) da,
-$$
-<p>&nbsp;<br>
-
-<p>where \( x(a) \) represents a so-called input and \( w(t-a) \) is normally called the weight function or kernel.</p>
-
-<p>The above integral is written in  a more compact form as</p>
-<p>&nbsp;<br>
-$$
-y(t) = \left(x * w\right)(t).
-$$
-<p>&nbsp;<br>
-
-<p>The discretized version reads</p>
-<p>&nbsp;<br>
-$$
-y(t) = \sum_{a=-\infty}^{a=\infty}x(a)w(t-a).
-$$
-<p>&nbsp;<br>
-
-<p>Computing the inverse of the above convolution operations is known as deconvolution and the process is commutative.</p>
-
-<p>How can we use this? And what does it mean? Let us study some familiar examples first.</p>
-</section>
-
 <section>
 <h2 id="convolution-examples-polynomial-multiplication">Convolution Examples: Polynomial multiplication </h2>
 

doc/pub/week44/html/._week44-bs000.html

@@ -108,7 +108,6 @@
                'how-to-do-image-compression-before-the-era-of-deep-learning'),
               ('The SVD example', 2, None, 'the-svd-example'),
               ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
-              ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
               ('Convolution Examples: Polynomial multiplication',
                2,
                None,
@@ -676,43 +675,6 @@ <h2 id="the-svd-example">The SVD example </h2>
 </div>
 
 
-<!-- !split --><br><br><br><br><br><br><br><br><br><br>
-<h2 id="mathematics-of-cnns">Mathematics of CNNs </h2>
-
-<p>The mathematics of CNNs is based on the mathematical operation of
-<b>convolution</b>.  In mathematics (in particular in functional analysis),
-convolution is represented by mathematical operations (integration,
-summation etc) on two functions in order to produce a third function
-that expresses how the shape of one gets modified by the other.
-Convolution has a plethora of applications in a variety of
-disciplines, spanning from statistics to signal processing, computer
-vision, solutions of differential equations,linear algebra,
-engineering, and yes, machine learning.
-</p>
-
-<p>Mathematically, convolution is defined as follows (one-dimensional example):
-Let us define a continuous function \( y(t) \) given by
-</p>
-$$
-y(t) = \int x(a) w(t-a) da,
-$$
-
-<p>where \( x(a) \) represents a so-called input and \( w(t-a) \) is normally called the weight function or kernel.</p>
-
-<p>The above integral is written in  a more compact form as</p>
-$$
-y(t) = \left(x * w\right)(t).
-$$
-
-<p>The discretized version reads</p>
-$$
-y(t) = \sum_{a=-\infty}^{a=\infty}x(a)w(t-a).
-$$
-
-<p>Computing the inverse of the above convolution operations is known as deconvolution and the process is commutative.</p>
-
-<p>How can we use this? And what does it mean? Let us study some familiar examples first.</p>
-
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="mathematics-of-cnns">Mathematics of CNNs </h2>
 

doc/pub/week44/html/._week44-bs001.html

@@ -185,7 +185,6 @@
                'how-to-do-image-compression-before-the-era-of-deep-learning'),
               ('The SVD example', 2, None, 'the-svd-example'),
               ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
-              ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
               ('Convolution Examples: Polynomial multiplication',
                2,
                None,
@@ -753,43 +752,6 @@ <h2 id="the-svd-example">The SVD example </h2>
 </div>
 
 
-<!-- !split --><br><br><br><br><br><br><br><br><br><br>
-<h2 id="mathematics-of-cnns">Mathematics of CNNs </h2>
-
-<p>The mathematics of CNNs is based on the mathematical operation of
-<b>convolution</b>.  In mathematics (in particular in functional analysis),
-convolution is represented by mathematical operations (integration,
-summation etc) on two functions in order to produce a third function
-that expresses how the shape of one gets modified by the other.
-Convolution has a plethora of applications in a variety of
-disciplines, spanning from statistics to signal processing, computer
-vision, solutions of differential equations,linear algebra,
-engineering, and yes, machine learning.
-</p>
-
-<p>Mathematically, convolution is defined as follows (one-dimensional example):
-Let us define a continuous function \( y(t) \) given by
-</p>
-$$
-y(t) = \int x(a) w(t-a) da,
-$$
-
-<p>where \( x(a) \) represents a so-called input and \( w(t-a) \) is normally called the weight function or kernel.</p>
-
-<p>The above integral is written in  a more compact form as</p>
-$$
-y(t) = \left(x * w\right)(t).
-$$
-
-<p>The discretized version reads</p>
-$$
-y(t) = \sum_{a=-\infty}^{a=\infty}x(a)w(t-a).
-$$
-
-<p>Computing the inverse of the above convolution operations is known as deconvolution and the process is commutative.</p>
-
-<p>How can we use this? And what does it mean? Let us study some familiar examples first.</p>
-
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="mathematics-of-cnns">Mathematics of CNNs </h2>