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of 32
pro vyhledávání: '"Henselman‐Petrusek, Gregory"'
Autor:
Kay, Bill, Aksoy, Sinan G., Baird, Molly, Best, Daniel M., Jenne, Helen, Joslyn, Cliff, Potvin, Christopher, Henselman-Petrusek, Gregory, Seppala, Garret, Young, Stephen J., Purvine, Emilie
In this position paper, we argue that when hypergraphs are used to capture multi-way local relations of data, their resulting topological features describe global behaviour. Consequently, these features capture complex correlations that can then serv
Externí odkaz:
http://arxiv.org/abs/2312.00023
The study of persistent homology has contributed new insights and perspectives into a variety of interesting problems in science and engineering. Work in this domain relies on the result that any finitely-indexed persistence module of finite-dimensio
Externí odkaz:
http://arxiv.org/abs/2310.07971
Autor:
Riess, Hans, Henselman-Petrusek, Gregory, Munger, Michael C., Ghrist, Robert, Bell, Zachary I., Zavlanos, Michael M.
Preferences, fundamental in all forms of strategic behavior and collective decision-making, in their raw form, are an abstract ordering on a set of alternatives. Agents, we assume, revise their preferences as they gain more information about other ag
Externí odkaz:
http://arxiv.org/abs/2310.00179
Autor:
Myers, Audun, Bittner, Alyson, Aksoy, Sinan, Best, Daniel M., Henselman-Petrusek, Gregory, Jenne, Helen, Joslyn, Cliff, Kay, Bill, Seppala, Garret, Young, Stephen J., Purvine, Emilie
In this study we synthesize zigzag persistence from topological data analysis with autoencoder-based approaches to detect malicious cyber activity and derive analytic insights. Cybersecurity aims to safeguard computers, networks, and servers from var
Externí odkaz:
http://arxiv.org/abs/2309.08010
Autor:
Wang, Qiquan, García-Redondo, Inés, Faugère, Pierre, Henselman-Petrusek, Gregory, Monod, Anthea
Publikováno v:
Computer Graphics forum, Volume 43 (2024), Number 5
Persistent homology barcodes and diagrams are a cornerstone of topological data analysis that capture the "shape" of a wide range of complex data structures, such as point clouds, networks, and functions. However, their use in statistical settings is
Externí odkaz:
http://arxiv.org/abs/2307.02904
A persistence module is a functor $f: \mathbf{I} \to \mathsf{E}$, where $\mathbf{I}$ is the poset category of a totally ordered set. This work introduces saecular decomposition: a categorically natural method to decompose $f$ into simple parts, calle
Externí odkaz:
http://arxiv.org/abs/2112.04927
Let $K$ be a finite simplicial, cubical, delta or CW complex. The persistence map $\mathrm{PH}$ takes a filter $f:K \rightarrow \mathbb{R}$ as input and returns the barcodes $\mathrm{PH}(f)$ of the associated sublevel set persistent homology modules.
Externí odkaz:
http://arxiv.org/abs/2110.14676
Persistent homology is a leading tool in topological data analysis (TDA). Many problems in TDA can be solved via homological -- and indeed, linear -- algebra. However, matrices in this domain are typically large, with rows and columns numbered in bil
Externí odkaz:
http://arxiv.org/abs/2108.08831
Cycle representatives of persistent homology classes can be used to provide descriptions of topological features in data. However, the non-uniqueness of these representatives creates ambiguity and can lead to many different interpretations of the sam
Externí odkaz:
http://arxiv.org/abs/2105.07025
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