diff --git a/ads-1.tex b/ads-1.tex index e83e29f07..ee0d2a245 100644 --- a/ads-1.tex +++ b/ads-1.tex @@ -12489,7 +12489,7 @@ \chapter*{#1}% \end{equation*} % \par -One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this ``decoding'' is quite easy.% +One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this ``decoding'' is quite easy.% \end{example} \begin{example}{Applications of the Gray Code.}{g:example:idm347915442752}% One application of the Gray code was discussed in the Introduction to this book. Another application is in statistics. In a statistical analysis, there is often a variable that depends on several factors, but exactly which factors are significant may not be obvious. For each subset of factors, there would be certain quantities to be calculated. One such quantity is the multiple correlation coefficient for a subset. If the correlation coefficient for a given subset, \(A\), is known, then the value for any subset that is obtained by either deleting or adding an element to \(A\) can be obtained quickly. To calculate the correlation coefficient for each set, we simply travel along \(G_n\), where \(n\) is the number of factors being studied. The first vertex will always be the string of 0's, which represents the empty set. For each vertex that you visit, the set that it corresponds to contains the \(k^{\text{th}}\) factor if the \(k^{\text{th}}\) character is a 1.% @@ -18097,4 +18097,4 @@ \chapter*{#1}% %% Index locators are cross-references, so same font here {\xreffont\printindex} % -\end{document} \ No newline at end of file +\end{document} diff --git a/ads-1_print.tex b/ads-1_print.tex index d913afad8..b9ac26efe 100644 --- a/ads-1_print.tex +++ b/ads-1_print.tex @@ -12494,7 +12494,7 @@ \chapter*{#1}% \end{equation*} % \par -One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this ``decoding'' is quite easy.% +One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this ``decoding'' is quite easy.% \end{example} \begin{example}{Applications of the Gray Code.}{g:example:idm294775519728}% One application of the Gray code was discussed in the Introduction to this book. Another application is in statistics. In a statistical analysis, there is often a variable that depends on several factors, but exactly which factors are significant may not be obvious. For each subset of factors, there would be certain quantities to be calculated. One such quantity is the multiple correlation coefficient for a subset. If the correlation coefficient for a given subset, \(A\), is known, then the value for any subset that is obtained by either deleting or adding an element to \(A\) can be obtained quickly. To calculate the correlation coefficient for each set, we simply travel along \(G_n\), where \(n\) is the number of factors being studied. The first vertex will always be the string of 0's, which represents the empty set. For each vertex that you visit, the set that it corresponds to contains the \(k^{\text{th}}\) factor if the \(k^{\text{th}}\) character is a 1.% @@ -18102,4 +18102,4 @@ \chapter*{#1}% %% Index locators are cross-references, so same font here {\xreffont\printindex} % -\end{document} \ No newline at end of file +\end{document} diff --git a/ads-3-6/knowl/ex-intro-a-to-d-hidden.html b/ads-3-6/knowl/ex-intro-a-to-d-hidden.html index ca991e0fc..a7d02b0a0 100644 --- a/ads-3-6/knowl/ex-intro-a-to-d-hidden.html +++ b/ads-3-6/knowl/ex-intro-a-to-d-hidden.html @@ -76,5 +76,5 @@ \right) \end{equation*} -

One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.

+

One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.

diff --git a/ads-3-6/knowl/ex-intro-a-to-d.html b/ads-3-6/knowl/ex-intro-a-to-d.html index 87e625966..84194cb14 100644 --- a/ads-3-6/knowl/ex-intro-a-to-d.html +++ b/ads-3-6/knowl/ex-intro-a-to-d.html @@ -80,6 +80,6 @@ \right) \end{equation*} -

One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.

in-context +

One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.

in-context diff --git a/ads-3-6/knowl/p-3258.html b/ads-3-6/knowl/p-3258.html index ef9c250bb..0514637ca 100644 --- a/ads-3-6/knowl/p-3258.html +++ b/ads-3-6/knowl/p-3258.html @@ -13,7 +13,7 @@
Paragraph
-

One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.

+

One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.

in-context diff --git a/ads-3-6/s-traversals.html b/ads-3-6/s-traversals.html index 45816e394..057939fda 100644 --- a/ads-3-6/s-traversals.html +++ b/ads-3-6/s-traversals.html @@ -418,7 +418,7 @@

Applied Discrete Stru \right) \end{equation*} -

One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.

+

One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.

Example 9.4.22. Applications of the Gray Code.

One application of the Gray code was discussed in the Introduction to this book. Another application is in statistics. In a statistical analysis, there is often a variable that depends on several factors, but exactly which factors are significant may not be obvious. For each subset of factors, there would be certain quantities to be calculated. One such quantity is the multiple correlation coefficient for a subset. If the correlation coefficient for a given subset, \(A\text{,}\) is known, then the value for any subset that is obtained by either deleting or adding an element to \(A\) can be obtained quickly. To calculate the correlation coefficient for each set, we simply travel along \(G_n\text{,}\) where \(n\) is the number of factors being studied. The first vertex will always be the string of 0's, which represents the empty set. For each vertex that you visit, the set that it corresponds to contains the \(k^{\text{th}}\) factor if the \(k^{\text{th}}\) character is a 1.

diff --git a/ads-3-7/knowl/ex-intro-a-to-d-hidden.html b/ads-3-7/knowl/ex-intro-a-to-d-hidden.html index 014431992..c39a6ef52 100644 --- a/ads-3-7/knowl/ex-intro-a-to-d-hidden.html +++ b/ads-3-7/knowl/ex-intro-a-to-d-hidden.html @@ -76,5 +76,5 @@ \right) \end{equation*} -

One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.

+

One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.

diff --git a/ads-3-7/knowl/ex-intro-a-to-d.html b/ads-3-7/knowl/ex-intro-a-to-d.html index bed2839b6..638a9da41 100644 --- a/ads-3-7/knowl/ex-intro-a-to-d.html +++ b/ads-3-7/knowl/ex-intro-a-to-d.html @@ -80,6 +80,6 @@ \right) \end{equation*} -

One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.

in-context +

One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.

in-context diff --git a/ads-3-7/knowl/p-3277.html b/ads-3-7/knowl/p-3277.html index 0c22c1d53..2f9303093 100644 --- a/ads-3-7/knowl/p-3277.html +++ b/ads-3-7/knowl/p-3277.html @@ -13,7 +13,7 @@

Paragraph
-

One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.

+

One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.

in-context diff --git a/ads-3-7/s-traversals.html b/ads-3-7/s-traversals.html index dd877873f..c941bc66d 100644 --- a/ads-3-7/s-traversals.html +++ b/ads-3-7/s-traversals.html @@ -414,7 +414,7 @@

Applied Discrete Stru \right) \end{equation*} -

One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.

+

One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this “decoding” is quite easy.

Example 9.4.22. Applications of the Gray Code.

One application of the Gray code was discussed in the Introduction to this book. Another application is in statistics. In a statistical analysis, there is often a variable that depends on several factors, but exactly which factors are significant may not be obvious. For each subset of factors, there would be certain quantities to be calculated. One such quantity is the multiple correlation coefficient for a subset. If the correlation coefficient for a given subset, \(A\text{,}\) is known, then the value for any subset that is obtained by either deleting or adding an element to \(A\) can be obtained quickly. To calculate the correlation coefficient for each set, we simply travel along \(G_n\text{,}\) where \(n\) is the number of factors being studied. The first vertex will always be the string of 0's, which represents the empty set. For each vertex that you visit, the set that it corresponds to contains the \(k^{\text{th}}\) factor if the \(k^{\text{th}}\) character is a 1.

diff --git a/ads.tex b/ads.tex index e0aaf6793..bbae36b7e 100644 --- a/ads.tex +++ b/ads.tex @@ -12499,7 +12499,7 @@ \chapter*{#1}% \end{equation*} % \par -One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this ``decoding'' is quite easy.% +One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this ``decoding'' is quite easy.% \end{example} \begin{example}{Applications of the Gray Code.}{g:example:idm40460211632}% One application of the Gray code was discussed in the Introduction to this book. Another application is in statistics. In a statistical analysis, there is often a variable that depends on several factors, but exactly which factors are significant may not be obvious. For each subset of factors, there would be certain quantities to be calculated. One such quantity is the multiple correlation coefficient for a subset. If the correlation coefficient for a given subset, \(A\), is known, then the value for any subset that is obtained by either deleting or adding an element to \(A\) can be obtained quickly. To calculate the correlation coefficient for each set, we simply travel along \(G_n\), where \(n\) is the number of factors being studied. The first vertex will always be the string of 0's, which represents the empty set. For each vertex that you visit, the set that it corresponds to contains the \(k^{\text{th}}\) factor if the \(k^{\text{th}}\) character is a 1.% @@ -31018,4 +31018,4 @@ \chapter*{#1}% %% Index locators are cross-references, so same font here {\xreffont\printindex} % -\end{document} \ No newline at end of file +\end{document} diff --git a/ads_print.tex b/ads_print.tex index 98ed56a3a..3599ad03e 100644 --- a/ads_print.tex +++ b/ads_print.tex @@ -12504,7 +12504,7 @@ \chapter*{#1}% \end{equation*} % \par -One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this ``decoding'' is quite easy.% +One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this ``decoding'' is quite easy.% \end{example} \begin{example}{Applications of the Gray Code.}{g:example:idm172460095776}% One application of the Gray code was discussed in the Introduction to this book. Another application is in statistics. In a statistical analysis, there is often a variable that depends on several factors, but exactly which factors are significant may not be obvious. For each subset of factors, there would be certain quantities to be calculated. One such quantity is the multiple correlation coefficient for a subset. If the correlation coefficient for a given subset, \(A\), is known, then the value for any subset that is obtained by either deleting or adding an element to \(A\) can be obtained quickly. To calculate the correlation coefficient for each set, we simply travel along \(G_n\), where \(n\) is the number of factors being studied. The first vertex will always be the string of 0's, which represents the empty set. For each vertex that you visit, the set that it corresponds to contains the \(k^{\text{th}}\) factor if the \(k^{\text{th}}\) character is a 1.% @@ -31023,4 +31023,4 @@ \chapter*{#1}% %% Index locators are cross-references, so same font here {\xreffont\printindex} % -\end{document} \ No newline at end of file +\end{document} diff --git a/src/S94.xml b/src/S94.xml index a16fba468..a15717f2e 100644 --- a/src/S94.xml +++ b/src/S94.xml @@ -253,7 +253,7 @@ with 0, and then (2) reversing the list of strings in G_n with each strin \end{array} \right)

-

One question might come to mind at this point. If the coatings of the dial no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this decoding is quite easy.

+

One question might come to mind at this point. If the coatings of the dial are no longer in the sequence from 0 to 7, how would you interpret the patterns that are on the back of the dial as numbers from 0 to 7? In Chapter 14 we will see that if the Gray Code is used, this decoding is quite easy.

Applications of the Gray Code

One application of the Gray code was discussed in the Introduction to this book. Another application is @@ -357,4 +357,4 @@ as many times as it loses. Every round-robin tournament graph has a Hamiltonian - \ No newline at end of file +