Proof of the WARM whisker conjecture for neuronal connections.
Identifieur interne : 000539 ( Main/Exploration ); précédent : 000538; suivant : 000540Proof of the WARM whisker conjecture for neuronal connections.
Auteurs : Mark Holmes [Australie] ; Victor Kleptsyn [France]Source :
- Chaos (Woodbury, N.Y.) [ 1089-7682 ] ; 2017.
Abstract
This paper is devoted to the study of the so-called WARM reinforcement models that are generalisations of Pólya's urn. We show that in the graph setting, once the exponent α of the reinforcement function is greater than 2, the stable and critical equilibria can be supported only on spanning forests, and once α>25, on spanning whisker forests. Thus, we prove the whisker forests conjecture from Hofstad et al. [Ann. Appl. Probab. 26(4), 2494-2539 (2016)].
DOI: 10.1063/1.4978683
PubMed: 28456154
Affiliations:
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We show that in the graph setting, once the exponent α of the reinforcement function is greater than 2, the stable and critical equilibria can be supported only on spanning forests, and once α>25, on spanning whisker forests. Thus, we prove the whisker forests conjecture from Hofstad et al. [Ann. Appl. Probab. 26(4), 2494-2539 (2016)].</div></front></TEI><affiliations><list><country><li>Australie</li><li>France</li></country><region><li>Région Bretagne</li><li>Victoria (État)</li></region><settlement><li>Melbourne</li><li>Rennes</li></settlement><orgName><li>Université de Melbourne</li></orgName></list><tree><country name="Australie"><region name="Victoria (État)"><name sortKey="Holmes, Mark" sort="Holmes, Mark" uniqKey="Holmes M" first="Mark" last="Holmes">Mark Holmes</name></region></country><country name="France"><region name="Région Bretagne"><name sortKey="Kleptsyn, Victor" sort="Kleptsyn, Victor" uniqKey="Kleptsyn V" first="Victor" last="Kleptsyn">Victor Kleptsyn</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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