<div class="csl-bib-body">
<div class="csl-entry">Wallner, M. (2023, September 7). <i>Stretched exponentials in the asymptotics of phylogenetic networks</i> [Presentation]. Mathematics of Evolution-Phylogenetic Trees and Networks Workshop 2023, Singapur, Singapore.</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/191569
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dc.description.abstract
Let c_n be the number of objects, such as phylogenetic networks, of size n. We are interested in the asymptotics of this sequence, i.e., a "simpler" sequence a_n such that the quotient c_n/a_n converges to 1 (or is bounded) for n to infinity. In particular, we will focus on stretched exponential term m^(n^(s)) with m>0 and 0<s<1. The presence of such a term is not common, although recently more and more examples emerge. It is generally quite difficult to prove that a sequence has such a stretched exponential, which is partly due to the observation that such a sequence cannot be "very nice", as, e.g., its generating function cannot be algebraic. Previously, the saddle point method was the only generic method for proving such a phenomenon, which, however, requires detailed information on the generating function. Recently, together with Andrew Elvey Price and Wenjie Fang, we have developed a new method on the level of recurrences to prove stretched exponentials. I will introduce the basics of this method and show how we used it together with Yu-Sheng Chang, Michael Fuchs, Hexuan Liu, and Guan-Ru Yu to prove such a phenomenon for d-combining tree-child networks, i.e. networks in which every reticulation node has exactly d parents.
en
dc.language.iso
en
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dc.subject
Stretched exponentials
en
dc.subject
phylogenetic networks
en
dc.subject
Asymptotics
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dc.title
Stretched exponentials in the asymptotics of phylogenetic networks
en
dc.type
Presentation
en
dc.type
Vortrag
de
dc.type.category
Presentation
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tuw.publication.invited
invited
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tuw.researchTopic.id
A3
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tuw.researchTopic.name
Fundamental Mathematics Research
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tuw.researchTopic.value
100
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tuw.publication.orgunit
E104-05 - Forschungsbereich Kombinatorik und Algorithmen
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tuw.author.orcid
0000-0001-8581-449X
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tuw.event.name
Mathematics of Evolution-Phylogenetic Trees and Networks Workshop 2023
en
tuw.event.startdate
06-09-2023
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tuw.event.enddate
08-09-2023
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tuw.event.online
On Site
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tuw.event.type
Event for scientific audience
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tuw.event.place
Singapur
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tuw.event.country
SG
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tuw.event.institution
Institute for Mathematical Sciences National University of Singapore
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tuw.event.presenter
Wallner, Michael
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tuw.event.track
Single Track
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
100
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item.languageiso639-1
en
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item.openairetype
conference presentation
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item.grantfulltext
none
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item.fulltext
no Fulltext
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item.cerifentitytype
Publications
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item.openairecristype
http://purl.org/coar/resource_type/R60J-J5BD
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crisitem.author.dept
E104 - Institut für Diskrete Mathematik und Geometrie
