Ascending and descending Morse complexes are defined by the critical points and integral lines of a scalar field f defined on a manifold M . They induce a subdivision of M into regions of uniform gradient flow, thus providing a compact description of the topology of M and of the behavior of f over M . We represent the ascending and descending Morse complexes of f as a graph, that we call the Mo...

1) We introduce random discrete Morse theory as a computational scheme to measure the complicatedness of a triangulation. The idea is to try to quantify the frequence of discrete Morse matchings with few critical cells. Our measure will depend on the topology of the space, but also on how nicely the space is triangulated. (2) The scheme we propose looks for optimal discrete Morse functions with...

of a Delay-Di erential Equation Tom a s Gedeon1 Department of Mathematical Sciences, Montana State University, Bozeman,MT 59717 [email protected] Gwendolen Hines2 Department of Mathematics and Statistics, University of Nebraska, Lincoln, NE 68588 [email protected] In this paper, we consider a discrete delay problem with negative feedback _ x(t) = f(x(t); x(t 1)) along with a ce...

Morse theory is a powerful tool in its applications to computational topology, computer graphics and geometric modeling. It was originally formulated for smooth manifolds. Recently, Robin Forman formulated a version of this theory for discrete structures such as cell complexes. It opens up several categories of interesting objects (particularly meshes) to applications of Morse theory. Once a Mo...

Objective: To evaluate the safety of hospitalized older adults as for the risk of falls according to the parameters of the Morse Fall Scale. Method: Epidemiological, cross-sectional, prospective and descriptive study with n=75. Results: Average age of 71.3 years (SD±8.2); 58.7% male; 44% with low educational level; 38.7% hospitalized for cardiovascular diseases; average hospitalization of 1...