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Article: On Laplacian spectrum of dendrite trees
Title | On Laplacian spectrum of dendrite trees |
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Authors | |
Keywords | Dendrite graphs Eigenvalue distribution Graph Laplacian Retinal ganglion cells Number of spikesSpike eigenvalues |
Issue Date | 2020 |
Publisher | Elsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/laa |
Citation | Linear Algebra and Its Applications, 2020, v. 591, p. 215-234 How to Cite? |
Abstract | For dendrite graphs from biological experiments on mouse's retinal ganglion cells, a paper by Nakatsukasa, Saito and Woei reveals a mysterious phase transition phenomenon in the spectra of the corresponding graph Laplacian matrices. While the bulk of the spectrum can be well understood by structures resembling starlike trees, mysteries about the spikes, that is, isolated eigenvalues outside the bulk spectrum, remain unexplained. In this paper, we bring new insights on these mysteries by considering a class of uniform trees. Exact relationships between the number of such spikes and the number of T-junctions are analyzed in function of the number of vertices separating the T-junctions. Using these theoretical results, predictions are proposed for the number of spikes observed in real-life dendrite graphs. Interestingly enough, these predictions match well the observed numbers of spikes, thus confirm the practical meaningness of our theoretical results. |
Persistent Identifier | http://hdl.handle.net/10722/290985 |
ISSN | 2023 Impact Factor: 1.0 2023 SCImago Journal Rankings: 0.837 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Xu, Y | - |
dc.contributor.author | Yao, J | - |
dc.date.accessioned | 2020-11-02T05:49:55Z | - |
dc.date.available | 2020-11-02T05:49:55Z | - |
dc.date.issued | 2020 | - |
dc.identifier.citation | Linear Algebra and Its Applications, 2020, v. 591, p. 215-234 | - |
dc.identifier.issn | 0024-3795 | - |
dc.identifier.uri | http://hdl.handle.net/10722/290985 | - |
dc.description.abstract | For dendrite graphs from biological experiments on mouse's retinal ganglion cells, a paper by Nakatsukasa, Saito and Woei reveals a mysterious phase transition phenomenon in the spectra of the corresponding graph Laplacian matrices. While the bulk of the spectrum can be well understood by structures resembling starlike trees, mysteries about the spikes, that is, isolated eigenvalues outside the bulk spectrum, remain unexplained. In this paper, we bring new insights on these mysteries by considering a class of uniform trees. Exact relationships between the number of such spikes and the number of T-junctions are analyzed in function of the number of vertices separating the T-junctions. Using these theoretical results, predictions are proposed for the number of spikes observed in real-life dendrite graphs. Interestingly enough, these predictions match well the observed numbers of spikes, thus confirm the practical meaningness of our theoretical results. | - |
dc.language | eng | - |
dc.publisher | Elsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/laa | - |
dc.relation.ispartof | Linear Algebra and Its Applications | - |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.subject | Dendrite graphs | - |
dc.subject | Eigenvalue distribution | - |
dc.subject | Graph Laplacian | - |
dc.subject | Retinal ganglion cells | - |
dc.subject | Number of spikesSpike eigenvalues | - |
dc.title | On Laplacian spectrum of dendrite trees | - |
dc.type | Article | - |
dc.identifier.email | Yao, J: jeffyao@hku.hk | - |
dc.identifier.authority | Yao, J=rp01473 | - |
dc.description.nature | postprint | - |
dc.identifier.doi | 10.1016/j.laa.2019.12.046 | - |
dc.identifier.scopus | eid_2-s2.0-85077792064 | - |
dc.identifier.hkuros | 318130 | - |
dc.identifier.volume | 591 | - |
dc.identifier.spage | 215 | - |
dc.identifier.epage | 234 | - |
dc.identifier.isi | WOS:000517849200014 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 0024-3795 | - |