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	<title>2023Seitz Geometric - Revision history</title>
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	<updated>2026-05-24T18:16:12Z</updated>
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	<entry>
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		<title>WikiSysop: Created page with &quot;== Citation ==  Seitz, Evan / Frank, Joachim / Schwander, Peter. Beyond ManifoldEM: geometric relationships between manifold embeddings of a continuum of 3D molecular structur...&quot;</title>
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		<updated>2023-08-22T09:37:25Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;== Citation ==  Seitz, Evan / Frank, Joachim / Schwander, Peter. Beyond ManifoldEM: geometric relationships between manifold embeddings of a continuum of 3D molecular structur...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;== Citation ==&lt;br /&gt;
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Seitz, Evan / Frank, Joachim / Schwander, Peter. Beyond ManifoldEM: geometric relationships between manifold embeddings of a continuum of 3D molecular structures and their 2D projections. 2023. Digital Discovery, Vol. 2, p. 702-717 &lt;br /&gt;
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== Abstract ==&lt;br /&gt;
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ManifoldEM is an established method of geometric machine learning developed to extract information on conformational motions of molecules from their projections obtained by cryogenic electron microscopy (cryo-EM). In a previous work, in-depth analysis of the properties of manifolds obtained for simulated ground-truth data from molecules exhibiting domain motions has led to improvements of this method, as demonstrated in selected applications of single-particle cryo-EM. In the present work this analysis has been extended to investigate the properties of manifolds constructed by embedding data from synthetic models represented by atomic coordinates in motion, or three-dimensional density maps from biophysical experiments other than single-particle cryo-EM, with extensions to cryo-electron tomography and single-particle imaging with a X-ray free-electron laser. Our theoretical analysis revealed interesting relationships between all these manifolds, which can be exploited in future work.&lt;br /&gt;
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== Keywords ==&lt;br /&gt;
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== Links ==&lt;br /&gt;
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https://pubs.rsc.org/en/content/articlehtml/2023/dd/d2dd00128d&lt;br /&gt;
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== Related software ==&lt;br /&gt;
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== Related methods ==&lt;br /&gt;
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== Comments ==&lt;/div&gt;</summary>
		<author><name>WikiSysop</name></author>
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