Results 31 to 40 of about 1,393 (155)
Discrete morse theory and the cohomology ring [PDF]
Transactions of the American Mathematical Society, 2002 In [5], we presented a discrete Morse Theory that can be applied to general cell complexes. In particular, we defined the notion of a discrete Morse function, along with its associated set of critical cells. We also constructed a discrete Morse cocomplex, built from the critical cells and the gradient paths between them, which has the same cohomology ...
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Topological data analysis with Bregman divergences
Journal of Computational Geometry, 2019 We show that the framework of topological data analysis can be extended from metrics to Bregman divergences, widening the scope of possible applications. Examples are the Kullback-Leibler divergence, which is commonly used for comparing text and images,
Herbert Edelsbrunner, Hubert Wagner
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Birth and death in discrete Morse theory
Journal of Symbolic Computation, 2017 Suppose $M$ is a finite simplicial complex and that for $0=t_0,t_1,...,t_r=1$ we have a discrete Morse function $F_{t_i}:M\to \zr$. In this paper, we study the births and deaths of critical cells for the functions $F_{t_i}$ and present an algorithm for pairing the cells that occur in adjacent slices.
Henry King +2 more
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Graph Reconstruction by Discrete Morse Theory
CoRR, 2018 25 pages, 22 ...
Dey, Tamal K., Wang, Jiayuan, Wang, Yusu
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Memristive Physical Reservoir Computing
Advanced Science, EarlyView.Memristors’ nonlinear dynamics and input‐dependent memory effects make them ideal candidates for high‐performance physical reservoir computing (RC). Based on their conductance modulation, memristors can be classified as electronic or optoelectronic types.
Dian Jiao +9 more
wiley +1 more source
Examples and CounterexamplesRobin Forman’s highly influential 2002 paper A User’s Guide to Discrete Morse Theory presents an overview of the subject in a very readable manner. As a proof of concept, the author determines the topology (homotopy type) of the abstract simplicial ...
Anupam Mondal, Pritam Chandra Pramanik
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Discrete Morse Theory for the Barycentric Subdivision [PDF]
Journal of Mathematical Sciences, 2018 Let $F$ be a discrete Morse function on a simplicial complex $L$. We construct a discrete Morse function $Δ(F)$ on the barycentric subdivision $Δ(L)$. The constructed function $Δ(F)$ "behaves the same way" as $F$, i. e. has the same number of critical simplexes and the same gradient path structure.
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ENERGY &ENVIRONMENTAL MATERIALS, EarlyView.A recyclable triboelectric nanogenerator integrating a pseudo‐honeycomb microstructure with liquid metal doping achieves 120% higher output (122 mW m−2) and >90% retention over seven cycles, enabling self‐powered smart home functions. The performance of single‐electrode triboelectric nanogenerators (SE‐TENGs) is governed by the effective contact area ...
Chencheng Hu +10 more
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Discrete Morse theory for manifolds with boundary [PDF]
Transactions of the American Mathematical Society, 2012 We introduce a version of discrete Morse theory specific for manifolds with boundary. The idea is to consider Morse functions for which all boundary cells are critical. We obtain "Relative Morse Inequalities" relating the homology of the manifold to the number of interior critical cells.
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PLANTS, PEOPLE, PLANET, EarlyView.Banana and plantain are vital for food security and income in West Africa, yet banana bunchy top virus (BBTV) threatens production. This study combined remote sensing, field surveys, modelling and socio‐economic analysis to assess BBTV spread and control strategies in Benin.
Renata Retkute +13 more
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