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pro vyhledávání: '"Beers, David"'
Autor:
Nartallo-Kaluarachchi, Ramón, Expert, Paul, Beers, David, Strang, Alexander, Kringelbach, Morten L., Lambiotte, Renaud, Goriely, Alain
Disentangling irreversible and reversible forces from random fluctuations is a challenging problem in the analysis of stochastic trajectories measured from real-world dynamical systems. We present an approach to approximate the dynamics of a stationa
Externí odkaz:
http://arxiv.org/abs/2409.07479
Autor:
Beers, David, Leygonie, Jacob
Consider the space of continuous functions on a geometric tree $X$ whose persistent homology gives rise to a finite generic barcode $D$. We show that there are exactly as many path connected components in this space as there are merge trees whose bar
Externí odkaz:
http://arxiv.org/abs/2303.16176
Autor:
Marsh, Lewis, Beers, David
The Euler characteristic transform (ECT) is a signature from topological data analysis (TDA) which summarises shapes embedded in Euclidean space. Compared with other TDA methods, the ECT is fast to compute and it is a sufficient statistic for a broad
Externí odkaz:
http://arxiv.org/abs/2303.13200
The topological morphology descriptor of a neuron is a multiset of intervals associated to the shape of the neuron represented as a tree. In practice, topological morphology descriptors are vectorized using persistence images, which can help classify
Externí odkaz:
http://arxiv.org/abs/2211.09058
Autor:
Goodbrake, Christian, Beers, David, Thompson, Travis B., Harrington, Heather A., Goriely, Alain
We propose a topological framework to study the evolution of Alzheimer's disease, the most common neurodegenerative disease. The modeling of this disease starts with the representation of the brain connectivity as a graph and the seeding of a toxic p
Externí odkaz:
http://arxiv.org/abs/2208.12748
The geometry of neurons is known to be important for their functions. Hence, neurons are often classified by their morphology. Two recent methods, persistent homology and the topological morphology descriptor, assign a morphology descriptor called a
Externí odkaz:
http://arxiv.org/abs/2204.03348
Autor:
Leygonie, Jacob, Beers, David
Let $f$ be a Morse function on a smooth compact manifold $M$ with boundary. The path component $\mathrm{PH}_f^{-1}(D)$ containing $f$ of the space of Morse functions giving rise to the same Persistent Homology $D=\mathrm{PH}(f))$ is shown to be the s
Externí odkaz:
http://arxiv.org/abs/2108.07512
Autor:
Beers, David, Szczesny, Matt
Publikováno v:
Involve 12 (2019) 1379-1397
We study commutative ring structures on the integral span of rooted trees and $n$-dimensional skew shapes. The multiplication in these rings arises from the smash product operation on monoid representations in pointed sets. We interpret these as Grot
Externí odkaz:
http://arxiv.org/abs/1812.04937
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