Morse and Morse-Smale complexes have been recognized as a suitable tool for modeling the topology of a manifold M through a decomposition of M induced by a scalar field f defined over M. We consider here the problem of representing, constructing and simplifying Morse and Morse-Smale complexes in 3D. We first describe and compare two data structures for encoding 3D Morse and Morse-Smale complexe...

This report provides theoretical justification for the use of discrete Morse theory for the computation of homology and persistent homology, an overview of the state of the art for the computation of discrete Morse matchings and motivation for an interest in these computations, particularly from the point of view of topological data analysis. Additionally, a new simulated annealing based method...

Morse theory was originally due to Marston Morse [5]. It gives us a method to study the topology of a manifold using the information of the critical points of a Morse function defined on the manifold. Based on the same idea, Morse homology was introduced by Thom, Smale, Milnor, and Witten in various forms. This paper is a survey of some work in this direction. The first part of the paper focuse...

We improve the best known lower bounds on the distance between two points of a Morse cluster in R, with ρ ∈ [4.967, 15]. Our method is a generalization of the one applied to the Lennard-Jones potential in [2], and it also leads to improvements of lower bounds for the energy of a Morse cluster. Some of the numerical results have been announced in [1].

our study performed upon an extended series of 28 compounds of 1,2,4-triazole derivativesthat demonstrate substantial in vitro antimicrobial activities by serial plate dilution method,using quantitative structure-activity relationship (qsar) methods that imply analysis ofcorrelations and multiple linear regression (mlr); a significant collection of moleculardescriptors was used e.g., edge adjac...

In this paper, in order to numerically solve for multiple positive solutions to a singularly perturbed Neumann boundary value problem in mathematical biology and other applications, a local minimax method is modified with new local mesh refinement and other strategies. Algorithm convergence and other related properties are verified. Motivated by the numerical algorithm and convinced by the nume...

For Morse-Smale pairs on a smooth, closed manifold the MorseSmale-Witten chain complex can be defined. The associated Morse homology is isomorphic to the singular homology of the manifold and yields the classical Morse relations for Morse functions. A similar approach can be used to define homological invariants for isolated invariant sets of flows on a smooth manifold, which gives an analogue ...

Terrain visualization has been an interesting issue for graphics people for long, and there have been a lot of attempts in various ways for more e cient visualization. In most of the works the terrain data was considered as a triangular mesh as it is, or as an implicit surface in which the original shape(topology) of the terrain can be slightly changed. Recently, the Morse Theory, [1, 2], has b...