تقرير
Analyzing Multifiltering Functions Using Multiparameter Discrete Morse Theory
| العنوان: | Analyzing Multifiltering Functions Using Multiparameter Discrete Morse Theory |
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| المؤلفون: | Brouillette, Guillaume |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Geometric Topology, Computer Science - Computational Geometry, 57Z25 (Primary), 52-08, 55N31, 57Q70 (Secondary) |
| الوصف: | A multiparameter filtration, or a multifiltration, may in many cases be seen as the collection of sublevel sets of a vector function, which we call a multifiltering function. The main objective of this paper is to obtain a better understanding of such functions through multiparameter discrete Morse (MDM) theory, which is an extension of Morse-Forman theory to vector-valued functions. Notably, we prove algorithmically that any multifiltering function defined on a simplicial complex can always be approximated by a compatible MDM function. Moreover, we define the Pareto set of a discrete multifiltering function and show that the concept links directly to that of critical simplices of a MDM function. Finally, we experiment with these notions using triangular meshes. Comment: 43 pages, 18 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.09537 |
| رقم الأكسشن: | edsarx.2406.09537 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |