WebBirth and death in discrete Morse theory. Birth and death in discrete Morse theory Henry King Kevin Knudson Neža Mramor Kosta. 1. Introduction. The purpose of this paper is to study the discrete analogue of the following phenomenon in … WebThe birth–death process (or birth-and-death process) is a special case of continuous-time Markov process where the state transitions are of only two types: "births", which increase the state variable by one and "deaths", which decrease the state by one. It was introduced by William Feller. The model's name comes from a common application, the use of such …

TOPOLOGY FOR DATA SCIENCE: MORSE THEORY AND …

WebWhereas standard Morse theory studies smooth functions on a di erentiable manifold, discrete Morse theory considers cell complexes equipped with a discrete function assigning a single value to each cell. Many results in Morse theory have discrete analogues, and I hope to explain these results by example. I will follow \A User’s Guide to ... http://acat2012.dm.unibo.it/slides/mramorkosta.pdf tshirteo

The realization problem for discrete Morse functions on trees

WebSmooth Morse functions Discrete Morse functions Applications References References: I Milnor, Morse theory, 1963 I R. Forman, Morse Theory for Cell Complexes Advances in Math., vol. 134, pp. 90-145, 1998 I R. Forman, User’s guide to discrete Morse theory, I Kozlov, Combinatorial algebraic topology, chapter 11 Ne za Mramor Discrete Morse … WebAs observed in Knudson (2008), births and deaths in multi-parameter persistent homology do not necessarily happen due to the entrance of “real” critical cells in the multi-filtration, … WebMorse theory, discrete Morse theory and its applications in computer graphics. It is important to point out that the use of TDA in removing noise is not new. In [7], Bremer et al. used persistence guided simplification of Morse–Smale ... birth and death of homology classes. Each homology class philosophy 106 final