Harmonic entropy: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2017-12-~~27 19~~:57:22 UTC</tt>.<br>

: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2017-12-28 22:49:55 UTC</tt>.<br>

: The original revision id was <tt>~~624270115~~</tt>.<br>

: The original revision id was <tt>624289853</tt>.<br>

: The revision comment was: <tt></tt><br>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>

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[[math]]

where the expression $\left[S \ast K\right]^a(-d)$ represents the convolution of S and K, taken to the a'th power.

where the expression

[[math]]\left[S \ast K\right]^a(-d)[[math]] represents the convolution of S and K, taken to the a'th power.

We have succeeded in representing Harmonic Renyi Entropy in simple terms of two convolution products, each of which can be computed in O(N log N) time.

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--><script type="math/tex">H_a(d) = \frac{1}{1-a} \log_β \left( \frac{\left[S^a \ast K^a\right](-d)}{\left[S \ast K\right]^a(-d)} \right)</script><br />

<br />

where the expression $\left[S \ast K\right]^a(-d)$ represents the convolution of S and K, taken to the a'th power.<br />

where the expression<br />

<br />

<a class="wiki_link" href="/math">math</a>\left[S \ast K\right]^a(-d)<a class="wiki_link" href="/math">math</a> represents the convolution of S and K, taken to the a'th power.<br />

<br />

We have succeeded in representing Harmonic Renyi Entropy in simple terms of two convolution products, each of which can be computed in O(N log N) time.<br />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2017-12-27 19:57:22 UTC</tt>.<br>
+: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2017-12-28 22:49:55 UTC</tt>.<br>
-: The original revision id was <tt>624270115</tt>.<br>
+: The original revision id was <tt>624289853</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 302: / Line 302: @@
 [[math]]
-where the expression $\left[S \ast K\right]^a(-d)$ represents the convolution of S and K, taken to the a'th power.
+where the expression
+[[math]]\left[S \ast K\right]^a(-d)[[math]] represents the convolution of S and K, taken to the a'th power.
 We have succeeded in representing Harmonic Renyi Entropy in simple terms of two convolution products, each of which can be computed in O(N log N) time.
@@ Line 652: / Line 654: @@
   --&gt;&lt;script type="math/tex"&gt;H_a(d) = \frac{1}{1-a} \log_β \left( \frac{\left[S^a \ast K^a\right](-d)}{\left[S \ast K\right]^a(-d)} \right)&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:33 --&gt;&lt;br /&gt;
 &lt;br /&gt;
-where the expression $\left[S \ast K\right]^a(-d)$ represents the convolution of S and K, taken to the a'th power.&lt;br /&gt;
+where the expression&lt;br /&gt;
+&lt;br /&gt;
+&lt;a class="wiki_link" href="/math"&gt;math&lt;/a&gt;\left[S \ast K\right]^a(-d)&lt;a class="wiki_link" href="/math"&gt;math&lt;/a&gt; represents the convolution of S and K, taken to the a'th power.&lt;br /&gt;
 &lt;br /&gt;
 We have succeeded in representing Harmonic Renyi Entropy in simple terms of two convolution products, each of which can be computed in O(N log N) time.&lt;br /&gt;