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	<title>De Rerum Natura &#187; Mathematics</title>
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	<link>http://www.corrada.com/blog</link>
	<description>Randomness, entropy, pattern matching, maps, geometry, knots, and scientific readings</description>
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		<title>Unpacking and Euclid&#8217;s Geometry</title>
		<link>http://www.corrada.com/blog/2011/08/07/unpacking-and-euclids-geometry/</link>
		<comments>http://www.corrada.com/blog/2011/08/07/unpacking-and-euclids-geometry/#comments</comments>
		<pubDate>Sun, 07 Aug 2011 15:47:48 +0000</pubDate>
		<dc:creator>Andrés</dc:creator>
				<category><![CDATA[Geometry]]></category>
		<category><![CDATA[Illustration]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Scientific Readings]]></category>

		<guid isPermaLink="false">http://www.corrada.com/blog/?p=179</guid>
		<description><![CDATA[Engaged once more in the bittersweet act of unpacking books after a move, I hit upon Oliver Byrne&#8217;s 19th century refashioning of Euclid&#8217;s Elements. The first two lines of its preface reading: The arts and sciences have become so extensive, that to facilitate their acquirement is of as much importance as to extend their boundaries. [...]]]></description>
		<wfw:commentRss>http://www.corrada.com/blog/2011/08/07/unpacking-and-euclids-geometry/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>ICML accepts precision error via L1 minimization paper</title>
		<link>http://www.corrada.com/blog/2008/04/09/icml-accepts-precision-error-via-l1-minimization-paper/</link>
		<comments>http://www.corrada.com/blog/2008/04/09/icml-accepts-precision-error-via-l1-minimization-paper/#comments</comments>
		<pubDate>Wed, 09 Apr 2008 10:48:02 +0000</pubDate>
		<dc:creator>Andrés</dc:creator>
				<category><![CDATA[Compressed Sensing]]></category>
		<category><![CDATA[Fourier Analysis]]></category>
		<category><![CDATA[Group Theory]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[MathML]]></category>
		<category><![CDATA[Randomness]]></category>
		<category><![CDATA[Scientific Readings]]></category>

		<guid isPermaLink="false">http://www.corrada.com/blog/?p=69</guid>
		<description><![CDATA[Our technical report on how to recover precision error estimates with $\ell_1$-minimization has been accepted by the 2008 International Conference on Machine Learning. The paper originally got three anonymous reviews. Two were positive, one strongly negative. In our response to the reviews, we agreed with the general criticism by the reviewers that one experimental demonstration [...]]]></description>
		<wfw:commentRss>http://www.corrada.com/blog/2008/04/09/icml-accepts-precision-error-via-l1-minimization-paper/feed/</wfw:commentRss>
		<slash:comments>2</slash:comments>
		</item>
		<item>
		<title>Precision error for parse trees</title>
		<link>http://www.corrada.com/blog/2008/04/01/precision-error-for-parse-trees/</link>
		<comments>http://www.corrada.com/blog/2008/04/01/precision-error-for-parse-trees/#comments</comments>
		<pubDate>Tue, 01 Apr 2008 05:20:21 +0000</pubDate>
		<dc:creator>Andrés</dc:creator>
				<category><![CDATA[Error Theory]]></category>
		<category><![CDATA[Graph Theory]]></category>
		<category><![CDATA[Natural Language Processing]]></category>
		<category><![CDATA[parse trees]]></category>

		<guid isPermaLink="false">http://www.corrada.com/blog/?p=68</guid>
		<description><![CDATA[The precision error equations require that &#8220;ground truth&#8221; cancel out. It is easy to see what that means for elevations in a map. What does it mean for parse trees in a natural language processing task like sentence parsing? One way to define distance between trees is to consider the total number of reverse operations [...]]]></description>
		<wfw:commentRss>http://www.corrada.com/blog/2008/04/01/precision-error-for-parse-trees/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Variations in student responses to a multiple exam for latent group discovery</title>
		<link>http://www.corrada.com/blog/2008/03/13/variations-in-student-responses-to-a-multiple-exam-for-latent-group-discovery/</link>
		<comments>http://www.corrada.com/blog/2008/03/13/variations-in-student-responses-to-a-multiple-exam-for-latent-group-discovery/#comments</comments>
		<pubDate>Fri, 14 Mar 2008 00:03:37 +0000</pubDate>
		<dc:creator>Andrés</dc:creator>
				<category><![CDATA[Error Theory]]></category>
		<category><![CDATA[Fourier Analysis]]></category>
		<category><![CDATA[Group Theory]]></category>
		<category><![CDATA[Machine Learning]]></category>
		<category><![CDATA[latent labels]]></category>

		<guid isPermaLink="false">http://www.corrada.com/blog/2008/03/13/variations-in-student-responses-to-a-multiple-exam-for-latent-group-discovery/</guid>
		<description><![CDATA[Questions in an exam are detectors of student competency. Students are detectors of the correct answers in a test. What is the variation in the student&#8217;s model of the correct exam? The precision error equations can be used to construct a covariance matrix for the students instead of the questions. What makes the difference is [...]]]></description>
		<wfw:commentRss>http://www.corrada.com/blog/2008/03/13/variations-in-student-responses-to-a-multiple-exam-for-latent-group-discovery/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Geometry in the dark</title>
		<link>http://www.corrada.com/blog/2008/02/19/geometry-in-the-dark/</link>
		<comments>http://www.corrada.com/blog/2008/02/19/geometry-in-the-dark/#comments</comments>
		<pubDate>Tue, 19 Feb 2008 12:46:21 +0000</pubDate>
		<dc:creator>Andrés</dc:creator>
				<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Scientific Readings]]></category>
		<category><![CDATA[diagrams]]></category>
		<category><![CDATA[geometry]]></category>

		<guid isPermaLink="false">http://www.corrada.com/blog/2008/02/19/geometry-in-the-dark/</guid>
		<description><![CDATA[In a previous post I erroneously claimed that the mathematician Hilbert advocated teaching geometry in the dark. Hilbert&#8217;s &#8220;Foundations of Geometry&#8221; axiomatized the subject and carried out its exposition without a single diagram. I found the correct attribution yesterday while re-reading Hofstadter&#8217;s foreword to &#8220;King of Infinite Space&#8221;, a biography of geometer David Coxeter. Hofstadter [...]]]></description>
		<wfw:commentRss>http://www.corrada.com/blog/2008/02/19/geometry-in-the-dark/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>To err is human, to study your errors is glorious</title>
		<link>http://www.corrada.com/blog/2008/02/17/to-err-is-human-to-study-your-errors-is-glorious/</link>
		<comments>http://www.corrada.com/blog/2008/02/17/to-err-is-human-to-study-your-errors-is-glorious/#comments</comments>
		<pubDate>Mon, 18 Feb 2008 01:59:33 +0000</pubDate>
		<dc:creator>Andrés</dc:creator>
				<category><![CDATA[Error Theory]]></category>
		<category><![CDATA[Fourier Analysis]]></category>
		<category><![CDATA[Group Theory]]></category>
		<category><![CDATA[Machine Learning]]></category>
		<category><![CDATA[Maps]]></category>
		<category><![CDATA[Randomness]]></category>
		<category><![CDATA[error estimation]]></category>
		<category><![CDATA[model precision]]></category>

		<guid isPermaLink="false">http://www.corrada.com/blog/2008/02/17/to-err-is-human-to-study-your-errors-is-glorious/</guid>
		<description><![CDATA[I&#8217;ve been sick all week but today has been the worst. In between my sleeping hallucinations I have been thinking a lot about a proposal I&#8217;m currently writing on the use of non-commutative harmonic analysis to study mapping error patterns. It has become clear that the approach we are advocating at the AIRS lab is [...]]]></description>
		<wfw:commentRss>http://www.corrada.com/blog/2008/02/17/to-err-is-human-to-study-your-errors-is-glorious/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Diagrams in Greek mathematics</title>
		<link>http://www.corrada.com/blog/2008/02/05/diagrams-in-greek-mathematics/</link>
		<comments>http://www.corrada.com/blog/2008/02/05/diagrams-in-greek-mathematics/#comments</comments>
		<pubDate>Tue, 05 Feb 2008 22:02:59 +0000</pubDate>
		<dc:creator>Andrés</dc:creator>
				<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Scientific Readings]]></category>
		<category><![CDATA[Archimedes]]></category>
		<category><![CDATA[diagrams]]></category>
		<category><![CDATA[Euclid]]></category>
		<category><![CDATA[visual proofs]]></category>

		<guid isPermaLink="false">http://www.corrada.com/blog/2008/02/05/diagrams-in-greek-mathematics/</guid>
		<description><![CDATA[The Archimedes Codex is turning out to be a great read on the importance of diagrams in Greek mathematics, the transmission of ancient knowledge to present times and modern document forensic techniques. The book is written by two principals of the Archimedes Palimpsest Project. I just finished reading Reviel Netz&#8217;s explanation of why visual thinking [...]]]></description>
		<wfw:commentRss>http://www.corrada.com/blog/2008/02/05/diagrams-in-greek-mathematics/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>X-raying the geometric precision error of DEMs with Fourier analysis</title>
		<link>http://www.corrada.com/blog/2008/02/02/x-raying-the-geometric-precision-error-of-dems-with-fourier-analysis/</link>
		<comments>http://www.corrada.com/blog/2008/02/02/x-raying-the-geometric-precision-error-of-dems-with-fourier-analysis/#comments</comments>
		<pubDate>Sat, 02 Feb 2008 18:10:32 +0000</pubDate>
		<dc:creator>Andrés</dc:creator>
				<category><![CDATA[Compressed Sensing]]></category>
		<category><![CDATA[Error Theory]]></category>
		<category><![CDATA[Fourier Analysis]]></category>
		<category><![CDATA[Group Theory]]></category>
		<category><![CDATA[Machine Learning]]></category>
		<category><![CDATA[Randomness]]></category>
		<category><![CDATA[DEMs]]></category>
		<category><![CDATA[symmetry group]]></category>
		<category><![CDATA[theory of geometric errors]]></category>

		<guid isPermaLink="false">http://www.corrada.com/blog/2008/02/02/x-raying-the-geometric-precision-error-of-dems-with-fourier-analysis/</guid>
		<description><![CDATA[In a previous post I mentioned a way of Fourier analyzing the geometric precision error of DEMs. Today I realized that the scheme I proposed can only account for part of the error signal. The approach I proposed is correct but it can only capture one particular aspect of the total error. The simplest way [...]]]></description>
		<wfw:commentRss>http://www.corrada.com/blog/2008/02/02/x-raying-the-geometric-precision-error-of-dems-with-fourier-analysis/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Error covariance matrices as images</title>
		<link>http://www.corrada.com/blog/2008/02/02/error-covariance-matrices-as-images/</link>
		<comments>http://www.corrada.com/blog/2008/02/02/error-covariance-matrices-as-images/#comments</comments>
		<pubDate>Sat, 02 Feb 2008 17:29:30 +0000</pubDate>
		<dc:creator>Andrés</dc:creator>
				<category><![CDATA[Compressed Sensing]]></category>
		<category><![CDATA[Error Theory]]></category>
		<category><![CDATA[Maps]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[covariance matrix]]></category>
		<category><![CDATA[DEMs]]></category>

		<guid isPermaLink="false">http://www.corrada.com/blog/2008/02/02/error-covariance-matrices-as-images/</guid>
		<description><![CDATA[I submitted my paper on autonomous precision error estimation in 3-D models to the 2008 International Conference on Machine Learning yesterday. One week early, too, a first for me! The format for the paper is the standard double column format and this makes it very hard to have complex equations in the paper. One mathematical [...]]]></description>
		<wfw:commentRss>http://www.corrada.com/blog/2008/02/02/error-covariance-matrices-as-images/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Fourier theory of DEM precision errors</title>
		<link>http://www.corrada.com/blog/2008/01/29/fourier-theory-of-dem-precision-errors/</link>
		<comments>http://www.corrada.com/blog/2008/01/29/fourier-theory-of-dem-precision-errors/#comments</comments>
		<pubDate>Tue, 29 Jan 2008 18:09:58 +0000</pubDate>
		<dc:creator>Andrés</dc:creator>
				<category><![CDATA[Error Theory]]></category>
		<category><![CDATA[Fourier Analysis]]></category>
		<category><![CDATA[Group Theory]]></category>
		<category><![CDATA[Maps]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[DEMs]]></category>
		<category><![CDATA[symmetry group]]></category>

		<guid isPermaLink="false">http://www.corrada.com/blog/?p=29</guid>
		<description><![CDATA[I&#8217;ve finished the experiments with different reconstruction matrices for the DEM precision error and I get a rock solid result independent of which reconstruction matrix I use. So my hypothesis that randomness may be used to increase the precision error was wrong. In the process, however, I have finally understood how to use the symmetry [...]]]></description>
		<wfw:commentRss>http://www.corrada.com/blog/2008/01/29/fourier-theory-of-dem-precision-errors/feed/</wfw:commentRss>
		<slash:comments>0</slash:comments>
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