Morse theory for Min-type functions

Min-type Morse theory for configuration spaces of hard spheres

In this paper we study configuration spaces of hard spheres in a bounded region. We develop a general Morse-theoretic framework and show that mechanically balanced configurations play the role of critical points. As an application, we find the precise threshold radius for a configuration space to be homotopy equivalent to the configuration space of points.

Morse theory for analytic functions on surfaces

In this paper we deal with analytic functions f : S → R defined on a compact two dimensional Riemannian surface S whose critical points are semi degenerated (critical points having a non identically vanishing Hessian). To any element p of the set of semi degenerated critical points Q we assign an unique index which can take the values −1, 0 or 1, and prove that Q is made up of finitely many (cr...

Min Morse: Approximability & Applications

In this work, we resolve an open problem posed by Joswig et al. [49] by providing an ̃ O(N ) time, O(log(N )) factor approximation algorithm for the min-Morse unmatched problem (MMUP) Let ⇤ be the no. of critical cells of the optimal discrete Morse function and N be the total no. of cells of a regular cell complex K. The goal of MMUP is to find ⇤ for a given K. To begin with, we apply an approx....

Fuzzy type theory with partial functions

This paper is a study of fuzzy type theory (FTT) with partial functions. Out of several possibilities we decided tointroduce a special value ”∗” that represents ”undefined”. In the interpretation of FTT, this value lays outside of thecorresponding domain. In the syntax it can be naturally represented by the description operator acting on the empty(fuzzy) set, because choosing an element from it...

Morse Theory