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	<title>The Pasqualian</title>
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	<link>http://thepasqualian.com</link>
	<description>Mathematics and Poetry by Carlos Pasquali (c) 2008 - 2010</description>
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		<title>On Lanchester&#8217;s Differential Equations and WWII: Modeling the Iwo Jima battle</title>
		<link>http://thepasqualian.com/?p=2088</link>
		<comments>http://thepasqualian.com/?p=2088#comments</comments>
		<pubDate>Thu, 19 Aug 2010 02:57:52 +0000</pubDate>
		<dc:creator>Carlos</dc:creator>
				<category><![CDATA[Combinatorics and Probability]]></category>
		<category><![CDATA[Differential Equations]]></category>
		<category><![CDATA[Linear Algebra]]></category>
		<category><![CDATA[Markov Chains]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[F.W. Lanchester]]></category>
		<category><![CDATA[Lanchester]]></category>
		<category><![CDATA[Lanchester's differential equations]]></category>
		<category><![CDATA[Markov]]></category>
		<category><![CDATA[Markov chain]]></category>
		<category><![CDATA[Markov chains]]></category>
		<category><![CDATA[Markov transition matrix]]></category>

		<guid isPermaLink="false">http://thepasqualian.com/?p=2088</guid>
		<description><![CDATA[Almost at the end of World War II, a battle to the death between US and Japanese forces took place off Japan in the island of Iwo Jima.  We can definitely apply a Lanchesterian analysis to this encounter; in fact, &#8230; <a href="http://thepasqualian.com/?p=2088">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
		<wfw:commentRss>http://thepasqualian.com/?feed=rss2&amp;p=2088</wfw:commentRss>
		<slash:comments>1</slash:comments>
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		<title>On Stochastic Processes</title>
		<link>http://thepasqualian.com/?p=2086</link>
		<comments>http://thepasqualian.com/?p=2086#comments</comments>
		<pubDate>Wed, 11 Aug 2010 15:47:37 +0000</pubDate>
		<dc:creator>Carlos</dc:creator>
				<category><![CDATA[Combinatorics and Probability]]></category>
		<category><![CDATA[Differential Equations]]></category>
		<category><![CDATA[Linear Algebra]]></category>
		<category><![CDATA[Markov Chains]]></category>
		<category><![CDATA[Markov chain]]></category>
		<category><![CDATA[Markov chains]]></category>
		<category><![CDATA[stochastic process]]></category>
		<category><![CDATA[stochastic processes]]></category>

		<guid isPermaLink="false">http://thepasqualian.com/?p=2086</guid>
		<description><![CDATA[Why can&#8217;t I shake the feeling that a stochastic process really&#8230; isn&#8217;t? In previous posts we have been able to frame a deterministic system in terms of its Markov transform matrix, and going backward really doesn&#8217;t seem like a problem. &#8230; <a href="http://thepasqualian.com/?p=2086">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
		<wfw:commentRss>http://thepasqualian.com/?feed=rss2&amp;p=2086</wfw:commentRss>
		<slash:comments>0</slash:comments>
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		<item>
		<title>On Lanchester&#8217;s Differential Equations and their Transform into a Markov Transition Matrix (or, the Markovization of the Lanchester Equations)</title>
		<link>http://thepasqualian.com/?p=2037</link>
		<comments>http://thepasqualian.com/?p=2037#comments</comments>
		<pubDate>Wed, 11 Aug 2010 02:38:49 +0000</pubDate>
		<dc:creator>Carlos</dc:creator>
				<category><![CDATA[Combinatorics and Probability]]></category>
		<category><![CDATA[Differential Equations]]></category>
		<category><![CDATA[Linear Algebra]]></category>
		<category><![CDATA[Markov Chains]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[F.W. Lanchester]]></category>
		<category><![CDATA[Lanchester]]></category>
		<category><![CDATA[Lanchester's differential equations]]></category>
		<category><![CDATA[Markov chain]]></category>
		<category><![CDATA[Markov chains]]></category>
		<category><![CDATA[Markov transition matrix]]></category>
		<category><![CDATA[SIR]]></category>
		<category><![CDATA[SIR model]]></category>

		<guid isPermaLink="false">http://thepasqualian.com/?p=2037</guid>
		<description><![CDATA[I have been very curious as to whether the Markovization of differential equations is applicable to all systems, linear or not.  In the case of the SIR differential equations, Markovization was possible even when the system is both non-linear and &#8230; <a href="http://thepasqualian.com/?p=2037">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
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		<slash:comments>7</slash:comments>
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		<item>
		<title>On the Swine Flu (a Year-and-a-Half Later)</title>
		<link>http://thepasqualian.com/?p=2006</link>
		<comments>http://thepasqualian.com/?p=2006#comments</comments>
		<pubDate>Mon, 09 Aug 2010 05:37:17 +0000</pubDate>
		<dc:creator>Carlos</dc:creator>
				<category><![CDATA[Combinatorics and Probability]]></category>
		<category><![CDATA[Differential Equations]]></category>
		<category><![CDATA[Linear Algebra]]></category>
		<category><![CDATA[Markov Chains]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Accuracy of Euler's Method]]></category>
		<category><![CDATA[Euler's Method]]></category>
		<category><![CDATA[Markov chain]]></category>
		<category><![CDATA[Markov chains]]></category>
		<category><![CDATA[Markov transition matrix]]></category>
		<category><![CDATA[SIR]]></category>
		<category><![CDATA[SIR model]]></category>
		<category><![CDATA[SIRD]]></category>
		<category><![CDATA[swine flu]]></category>
		<category><![CDATA[transition matrix]]></category>

		<guid isPermaLink="false">http://thepasqualian.com/?p=2006</guid>
		<description><![CDATA[This week I have been revisiting the swine flu scare of April 2009.  The Mexican government then was particularly anxious: it suspended regular classes, and many kids were just thrilled that they found themselves suddenly on vacation.  Some schools even &#8230; <a href="http://thepasqualian.com/?p=2006">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
		<wfw:commentRss>http://thepasqualian.com/?feed=rss2&amp;p=2006</wfw:commentRss>
		<slash:comments>0</slash:comments>
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		<title>On the SIR Equations and Their Transform into a Markov Transition Matrix (or, the Markovization of the SIR Model)</title>
		<link>http://thepasqualian.com/?p=1862</link>
		<comments>http://thepasqualian.com/?p=1862#comments</comments>
		<pubDate>Fri, 06 Aug 2010 07:35:10 +0000</pubDate>
		<dc:creator>Carlos</dc:creator>
				<category><![CDATA[Combinatorics and Probability]]></category>
		<category><![CDATA[Differential Equations]]></category>
		<category><![CDATA[Linear Algebra]]></category>
		<category><![CDATA[Markov Chains]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[discretization]]></category>
		<category><![CDATA[Lotka-Volterra]]></category>
		<category><![CDATA[Markov chain]]></category>
		<category><![CDATA[Markov chains]]></category>
		<category><![CDATA[sampling]]></category>
		<category><![CDATA[SIR]]></category>
		<category><![CDATA[SIR model]]></category>
		<category><![CDATA[SIRD]]></category>
		<category><![CDATA[swine flu]]></category>

		<guid isPermaLink="false">http://thepasqualian.com/?p=1862</guid>
		<description><![CDATA[It&#8217;s been a while since I&#8217;ve had the time to write here, mostly for personal reasons.  However this period has not been without very exciting &#8220;discoveries,&#8221; at least in my mathematics understanding. Ever since last year in April with the &#8230; <a href="http://thepasqualian.com/?p=1862">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
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		<slash:comments>0</slash:comments>
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		<title>On Markov Chain Music</title>
		<link>http://thepasqualian.com/?p=1831</link>
		<comments>http://thepasqualian.com/?p=1831#comments</comments>
		<pubDate>Mon, 03 May 2010 17:24:30 +0000</pubDate>
		<dc:creator>Carlos</dc:creator>
				<category><![CDATA[Combinatorics and Probability]]></category>
		<category><![CDATA[Markov Chains]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Music]]></category>
		<category><![CDATA[Markov chain]]></category>
		<category><![CDATA[Markov chains]]></category>
		<category><![CDATA[Mozart]]></category>

		<guid isPermaLink="false">http://thepasqualian.cjacobandco.com/?p=1831</guid>
		<description><![CDATA[Ever wonder what music produced by a Markov chain might sound like?  Yeah, me too! &#8230;and&#8230; wonder no more!  So I went to where the piano is and grabbed the more regular, simple score I could find.  As it turns &#8230; <a href="http://thepasqualian.com/?p=1831">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
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		<slash:comments>1</slash:comments>
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		<item>
		<title>On the Beale Cipher, Part III</title>
		<link>http://thepasqualian.com/?p=1818</link>
		<comments>http://thepasqualian.com/?p=1818#comments</comments>
		<pubDate>Sat, 01 May 2010 21:40:04 +0000</pubDate>
		<dc:creator>Carlos</dc:creator>
				<category><![CDATA[Combinatorics and Probability]]></category>
		<category><![CDATA[Cryptography]]></category>
		<category><![CDATA[Markov Chains]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Beale cipher]]></category>
		<category><![CDATA[Beale cypher]]></category>
		<category><![CDATA[book cipher]]></category>
		<category><![CDATA[book cypher]]></category>
		<category><![CDATA[cipher]]></category>
		<category><![CDATA[cryptography]]></category>
		<category><![CDATA[cypher]]></category>
		<category><![CDATA[Markov chain]]></category>
		<category><![CDATA[Markov chains]]></category>

		<guid isPermaLink="false">http://thepasqualian.cjacobandco.com/?p=1818</guid>
		<description><![CDATA[In this post I&#8217;m including a compressed archive of some results I have obtained by following through on my previous post:  I used the Declaration of Independence transition probability matrix I calculated based on a text I found online, and &#8230; <a href="http://thepasqualian.com/?p=1818">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
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		<slash:comments>0</slash:comments>
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		<item>
		<title>On the Beale Cipher, Part II (and Other Book Ciphers)</title>
		<link>http://thepasqualian.com/?p=1796</link>
		<comments>http://thepasqualian.com/?p=1796#comments</comments>
		<pubDate>Wed, 28 Apr 2010 16:45:42 +0000</pubDate>
		<dc:creator>Carlos</dc:creator>
				<category><![CDATA[Combinatorics and Probability]]></category>
		<category><![CDATA[Cryptography]]></category>
		<category><![CDATA[Markov Chains]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Beale]]></category>
		<category><![CDATA[Beale cipher]]></category>
		<category><![CDATA[Beale cypher]]></category>
		<category><![CDATA[book cipher]]></category>
		<category><![CDATA[book cypher]]></category>
		<category><![CDATA[cipher]]></category>
		<category><![CDATA[cryptography]]></category>
		<category><![CDATA[cypher]]></category>
		<category><![CDATA[Markov chain]]></category>
		<category><![CDATA[Markov chains]]></category>

		<guid isPermaLink="false">http://thepasqualian.cjacobandco.com/?p=1796</guid>
		<description><![CDATA[Last time I talked about extending the usual frequency analysis on the (first) Beale cipher to augment our understanding of the composition of the individual letters the numbers may represent.  I have said before that Markov chains are immensely applicable &#8230; <a href="http://thepasqualian.com/?p=1796">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
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		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>On the Beale Cipher, Part I</title>
		<link>http://thepasqualian.com/?p=1778</link>
		<comments>http://thepasqualian.com/?p=1778#comments</comments>
		<pubDate>Wed, 28 Apr 2010 02:56:39 +0000</pubDate>
		<dc:creator>Carlos</dc:creator>
				<category><![CDATA[Combinatorics and Probability]]></category>
		<category><![CDATA[Cryptography]]></category>
		<category><![CDATA[Markov Chains]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Beale]]></category>
		<category><![CDATA[Beale cipher]]></category>
		<category><![CDATA[Beale cypher]]></category>
		<category><![CDATA[book cipher]]></category>
		<category><![CDATA[book cypher]]></category>
		<category><![CDATA[cipher]]></category>
		<category><![CDATA[cryptography]]></category>
		<category><![CDATA[cypher]]></category>
		<category><![CDATA[Markov chain]]></category>
		<category><![CDATA[Markov chains]]></category>

		<guid isPermaLink="false">http://thepasqualian.cjacobandco.com/?p=1778</guid>
		<description><![CDATA[Ugh, so right now there is construction going on behind my house; an abandoned house got put down and I can only imagine Telecable extending it&#8217;s dominions over.  The street is zoned to be residential, not commercial, but the owner &#8230; <a href="http://thepasqualian.com/?p=1778">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
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		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>On revolutionizing the whole of Linear Algebra, Markov Chain Theory, Group Theory&#8230; and all of Mathematics</title>
		<link>http://thepasqualian.com/?p=1727</link>
		<comments>http://thepasqualian.com/?p=1727#comments</comments>
		<pubDate>Fri, 23 Apr 2010 04:00:21 +0000</pubDate>
		<dc:creator>Carlos</dc:creator>
				<category><![CDATA[Combinatorics and Probability]]></category>
		<category><![CDATA[Group Theory]]></category>
		<category><![CDATA[Linear Algebra]]></category>
		<category><![CDATA[Markov Chains]]></category>
		<category><![CDATA[Beale]]></category>
		<category><![CDATA[Beale cipher]]></category>
		<category><![CDATA[Beale cypher]]></category>
		<category><![CDATA[Chapman-Kolmogorov]]></category>
		<category><![CDATA[cryptography]]></category>
		<category><![CDATA[cypher]]></category>
		<category><![CDATA[Kolmogorov]]></category>
		<category><![CDATA[Markov]]></category>
		<category><![CDATA[Markov chains]]></category>
		<category><![CDATA[probability]]></category>

		<guid isPermaLink="false">http://thepasqualian.cjacobandco.com/?p=1727</guid>
		<description><![CDATA[I have been so remiss about writing here lately!  I&#8217;m so sorry!  There are several good reasons for this, believe me.  Among them: (1) I have been enthralled with deciphering a two hundred-year old code, the Beale cipher part I, &#8230; <a href="http://thepasqualian.com/?p=1727">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
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