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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Dear all,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Today we have a semi-external speaker: Otto Sumray will speak at 11:00 in Maryam. Title and abstract below.
<o:p></o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Best,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Thomas<o:p></o:p></span></p>
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<b><span style="font-size:11.5pt;font-family:Helvetica;color:black;mso-ligatures:none"> Quiver Laplacians and Data<o:p></o:p></span></b></p>
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<span style="font-size:9.0pt;font-family:Helvetica;color:black;mso-ligatures:none">Analysing the topology or geometry of data is a common task in data analysis, using methods such as clustering, networks, and persistent homology. Often, however, we wish to
embellish data with extra local information, which mathematically can take the form of a quiver representation or cellular sheaf. One example of this enriched data comes from analysis of single-cell epigenetics, and this situation can be further abstracted
to a question about local versus global feature selection.<br>
Graph Laplacians have had great success in the analysis of networks. We introduce the quiver Laplacian as an analogue of the graph Laplacian for quiver representations, and formulate a pipeline for its application to local versus global feature selection.<br>
Applying it to our case study in single-cell epigenetics, we show that the eigenvalues of the quiver Laplacian can aid in feature selection to recover biologically meaningful results. To show stability of this method, we provide explicit bounds on how the spectrum
of a quiver Laplacian changes when the representation and the underlying quiver are modified in certain natural ways.<o:p></o:p></span></p>
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