https://en.formulasearchengine.com/index.php?action=history&feed=atom&title=Square_classSquare class - Revision history2026-04-10T12:29:07ZRevision history for this page on the wikiMediaWiki 1.43.0-wmf.28https://en.formulasearchengine.com/index.php?title=Square_class&diff=27952&oldid=preven>David Eppstein: why the positives2014-02-03T01:35:47Z<p>why the positives</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 03:35, 3 February 2014</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">The adore for branded outfits and extras is not new</del>, <del style="font-weight: bold; text-decoration: none;">but men and females are just in appreciate with shopping branded objects for themselves.<br><br>This </del>is <del style="font-weight: bold; text-decoration: none;">the purpose, why the popularity and desire for designer outfits, footwear and purses have been escalating by just about every passing working day.�</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">In [[mathematics]]</ins>, <ins style="font-weight: bold; text-decoration: none;">a '''statistical manifold''' </ins>is a <ins style="font-weight: bold; text-decoration: none;">[[Riemannian manifold]]</ins>, <ins style="font-weight: bold; text-decoration: none;">each </ins>of <ins style="font-weight: bold; text-decoration: none;">whose points </ins>is a <ins style="font-weight: bold; text-decoration: none;">[[probability distribution]]</ins>. <ins style="font-weight: bold; text-decoration: none;"> Statistical manifolds provide a setting </ins>for the <ins style="font-weight: bold; text-decoration: none;">field </ins>of [<ins style="font-weight: bold; text-decoration: none;">[information geometry]</ins>]. <ins style="font-weight: bold; text-decoration: none;"> </ins>The <ins style="font-weight: bold; text-decoration: none;">[[Fisher information metric]] provides </ins>a <ins style="font-weight: bold; text-decoration: none;">[[Metric (mathematics)|metric]] </ins>on <ins style="font-weight: bold; text-decoration: none;">these manifolds</ins>.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Different trend homes have brought natural beauty and class in the lives of men and women living across the world. When you go out in the marketplace for searching or store online, then you come throughout </del>a <del style="font-weight: bold; text-decoration: none;">substantial range of manufacturers</del>, <del style="font-weight: bold; text-decoration: none;">which are marketing incredible items, but if you chat about sleekness and lovely extras then almost nothing can be improved then Abercrombie and Fitch.�<br></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">This model has been exceedingly rising consideration of guys and girls. The rationale of these types </del>of <del style="font-weight: bold; text-decoration: none;">a sturdy enjoy for the A&F garment and accessories </del>is <del style="font-weight: bold; text-decoration: none;">the way this model fulfills the style demands of guys gals, belonging from various walks of lifestyl<br></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Abercrombie and Fitch outlet has turn out to be </del>a <del style="font-weight: bold; text-decoration: none;">single of the most sought following retailer<br></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">You will get total assortment of branded goods, shelved in an appealing way</del>. <del style="font-weight: bold; text-decoration: none;">Adult males and women of diverse ages have been incredibly glad by the way, Abercrombie and Fitch has been catering their vogue demands. This brand has attained appreciable respect, </del>for <del style="font-weight: bold; text-decoration: none;">it has always been prosperous in going beyond </del>the <del style="font-weight: bold; text-decoration: none;">anticipations </del>of <del style="font-weight: bold; text-decoration: none;">it�s hugely prestigious and esteemed buyer<br><br></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">The extra you devote on the garments of Abercrombie and Fitch, the additional you adorn and improve the value of your clothes and add-ons assortme<br></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">If you are fashion freak human being and do not want to glimpse like they your good friends look, then nothing at all can </del>[<del style="font-weight: bold; text-decoration: none;">http://www.pcs-systems.co.uk/Images/celinebag.aspx http://www.pcs-systems.co.uk/Images/celinebag.aspx</del>] <del style="font-weight: bold; text-decoration: none;">be superior than visiting your nearest Abercrombie and Fitch outlet</del>. <del style="font-weight: bold; text-decoration: none;">You will be astonished to see so many fashionable, trendy and modish solutions available, beneath a person roo<br><br></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Abercrombie and Fitch has been providing some definitely celine bags trendy garments, for adult men and g<br></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">� </del>The <del style="font-weight: bold; text-decoration: none;">demand from customers for the products and solutions of this model is very </del>a <del style="font-weight: bold; text-decoration: none;">lot substantial in younger men and women. This brand name pays sheer attention </del>on <del style="font-weight: bold; text-decoration: none;">building and production the solutions of the optimum top quality</del>. <del style="font-weight: bold; text-decoration: none;">The material, hues, stitching and detailing of the goods of A&F, makes this manufacturer extremely different, novel and styli<br><br></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">It talks about giving decent and innovative merchandise to its pros<br>c</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Examples==</ins></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">.� If you will take a look at Abercrombie and Fitch outlet, then you are undoubtedly going to be tantalized by the products and solutions, for you will get all what you have been longing for. Much more and much more individuals want to phase into the shops of Abercrombie and Fitch, for they have entire have confidence in in the products, which this brand name has been presenting to its highly prestigious<br><br></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>s.<del style="font-weight: bold; text-decoration: none;">� This manufacturer understands </del>the <del style="font-weight: bold; text-decoration: none;">style demands </del>of <del style="font-weight: bold; text-decoration: none;">its buyers</del>. <del style="font-weight: bold; text-decoration: none;">It has been devoted </del>in <del style="font-weight: bold; text-decoration: none;">catering their wants and would like </del>to <del style="font-weight: bold; text-decoration: none;">go further than its customers� anticipations</del>. <del style="font-weight: bold; text-decoration: none;">This </del>is the <del style="font-weight: bold; text-decoration: none;">explanation</del>, <del style="font-weight: bold; text-decoration: none;">why so lots </del>of <del style="font-weight: bold; text-decoration: none;">consumers </del>have <del style="font-weight: bold; text-decoration: none;">constantly been checking out their nearest and closest Abercrombie </del>and [<del style="font-weight: bold; text-decoration: none;">http://Www</del>.<del style="font-weight: bold; text-decoration: none;">reddit.com</del>/<del style="font-weight: bold; text-decoration: none;">r</del>/<del style="font-weight: bold; text-decoration: none;">howto</del>/<del style="font-weight: bold; text-decoration: none;">search?q</del>=<del style="font-weight: bold; text-decoration: none;">Fitch+outlet Fitch ou</del><<del style="font-weight: bold; text-decoration: none;">br</del>><del style="font-weight: bold; text-decoration: none;">et]</del>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The family of all [[normal distribution]]</ins>s<ins style="font-weight: bold; text-decoration: none;">, parametrized by the [[expected value]] ''&mu;'' and the [[variance]] ''σ''<sup>2</sup>&nbsp;≥&nbsp;0, with the [[Riemannian metric]] given by the [[Fisher information]] matrix, is a statistical manifold</ins>. <ins style="font-weight: bold; text-decoration: none;">Its geometry is modeled on [[hyperbolic space]].</ins></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">All </del>the <del style="font-weight: bold; text-decoration: none;">stores </del>of this <del style="font-weight: bold; text-decoration: none;">brand name serve you </del>in the <del style="font-weight: bold; text-decoration: none;">most effective feasible </del>way. <del style="font-weight: bold; text-decoration: none;">It is for absolutely sure </del>that <del style="font-weight: bold; text-decoration: none;">you will get to place your arms on the goods</del>, <del style="font-weight: bold; text-decoration: none;">which are available at standardized charges at all shop of Abercrombie and Fitch.</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">A simple example of a statistical manifold, taken from physics, would be </ins>the <ins style="font-weight: bold; text-decoration: none;">[[canonical ensemble]]: it is a one-dimensional manifold, with the [[temperature]] ''T'' serving as the coordinate on the manifold. For any fixed temperature ''T'', one has a probability space: so, for a gas </ins>of <ins style="font-weight: bold; text-decoration: none;">atoms, it would be the probability distribution of the velocities of the atoms. As one varies the temperature ''T'', the probability distribution varies</ins>. <ins style="font-weight: bold; text-decoration: none;"> </ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Another simple example, taken from medicine, would be the probability distribution of patient outcomes, </ins>in <ins style="font-weight: bold; text-decoration: none;">response </ins>to <ins style="font-weight: bold; text-decoration: none;">the quantity of medicine administered</ins>. <ins style="font-weight: bold; text-decoration: none;"> That is, for a fixed dose, some patients improve, and some do not: this </ins>is the <ins style="font-weight: bold; text-decoration: none;">base probability space. If the dosage is varied</ins>, <ins style="font-weight: bold; text-decoration: none;">then the probability </ins>of <ins style="font-weight: bold; text-decoration: none;">outcomes changes. Thus, the dosage is the coordinate on the manifold. To be a smooth manifold, one would </ins>have <ins style="font-weight: bold; text-decoration: none;">to measure outcomes in response to arbitrarily small changes in dosage; this is not a practically realizable example, unless one has a pre-existing mathematical model of dose-response where the dose can be arbitrarily varied.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">== Definition ==</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Let ''X'' be an [[orientable manifold]], </ins>and <ins style="font-weight: bold; text-decoration: none;">let <math>(X,\Sigma,\mu)</math> be a [</ins>[<ins style="font-weight: bold; text-decoration: none;">measure space|measure]] on ''X''</ins>. <ins style="font-weight: bold; text-decoration: none;">Equivalently, let <math>(\Omega, \mathcal{F},P)<</ins>/<ins style="font-weight: bold; text-decoration: none;">math> be a [[probability space]] on <math>\Omega=X<</ins>/<ins style="font-weight: bold; text-decoration: none;">math>, with [[sigma algebra]] <math>\mathcal{F}=\Sigma<</ins>/<ins style="font-weight: bold; text-decoration: none;">math> and probability <math>P</ins>=<ins style="font-weight: bold; text-decoration: none;">\mu</ins><<ins style="font-weight: bold; text-decoration: none;">/math</ins>>.</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The statistical manifold ''S''(''X'') of ''X'' is defined as </ins>the <ins style="font-weight: bold; text-decoration: none;">space </ins>of <ins style="font-weight: bold; text-decoration: none;">all measures <math>\mu</math> on ''X'' (with the sigma-algebra <math>\Sigma</math> held fixed). Note that </ins>this <ins style="font-weight: bold; text-decoration: none;">space is infinite-dimensional; it is commonly taken to be a [[Fréchet space]]. The points of ''S''(''X'') are measures. </ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Rather than dealing with an infinite-dimensional space ''S''(''X''), it is common to work with a finite-dimensional [[submanifold]], defined by considering a set of [[probability distribution]]s parameterized by some smooth, continuously-varying parameter <math>\theta</math>. That is, one considers only those measures that are selected by the parameter. If the parameter <math>\theta</math> is ''n''-dimensional, then, </ins>in <ins style="font-weight: bold; text-decoration: none;">general, </ins>the <ins style="font-weight: bold; text-decoration: none;">submanifold will be as well. All finite-dimensional statistical manifolds can be understood in this </ins>way.<ins style="font-weight: bold; text-decoration: none;">{{clarify|reason = definition above says </ins>that <ins style="font-weight: bold; text-decoration: none;">all manifolds are infinite-dimensional</ins>, <ins style="font-weight: bold; text-decoration: none;">so there can't be any finite-dimensional ones|date=July 2012}}</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Manifolds]]</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Statistical theory]]</ins></div></td></tr>
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<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">{{geometry-stub}}</ins></div></td></tr>
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</table>en>David Eppsteinhttps://en.formulasearchengine.com/index.php?title=Square_class&diff=270571&oldid=preven>David Eppstein: stub sort2012-08-29T04:44:54Z<p>stub sort</p>
<p><b>New page</b></p><div>The adore for branded outfits and extras is not new, but men and females are just in appreciate with shopping branded objects for themselves.<br><br>This is the purpose, why the popularity and desire for designer outfits, footwear and purses have been escalating by just about every passing working day.�<br />
Different trend homes have brought natural beauty and class in the lives of men and women living across the world. When you go out in the marketplace for searching or store online, then you come throughout a substantial range of manufacturers, which are marketing incredible items, but if you chat about sleekness and lovely extras then almost nothing can be improved then Abercrombie and Fitch.�<br><br />
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