Morse Predecomposition of an Invariant Set.

Motivated by the study of recurrent orbits and dynamics within a Morse set of a Morse decomposition we introduce the concept of Morse predecomposition of an isolated invariant set within the setting of both combinatorial and classical dynamical systems. While Morse decomposition summarizes solely the gradient part of a dynamical system, the developed generalization extends to the recurrent component as well. In particular, a chain recurrent set, which is indecomposable in terms of Morse decomposition, can be represented more finely in the Morse predecomposition framework.

Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces.

We generalize and extend the Conley-Morse-Forman theory for combinatorial multivector fields introduced in Mrozek (Found Comput Math 17(6):1585-1633, 2017). The generalization is threefold. First, we drop the restraining assumption in Mrozek (Found Comput Math 17(6):1585-1633, 2017) that every multivector must have a unique maximal element.

Conley Index Approach to Sampled Dynamics.

The topological method for the reconstruction of dynamics from time series [K. Mischaikow et al., .

Sensitivity and Specificity of Fractal Analysis to Distinguish Between Healthy and Pathologic Rectal Mucosa Microvasculature Seen During Colonoscopy.

Purpose: Conventional endoscopy is limited by human capability to recognize and to differentiate pathology. Fractal analysis of blood vessels has been used in other organs, such as the retina, but never before to supplement colonoscopy. The aim of this study was to assess whether it is possible to differentiate between healthy and pathologic rectal mucosa using fractal analysis of the mucosal microvascular architecture seen during colonoscopic examination (Supplemental Digital Content 1, http://links.

Fractal dimensions of skin microcirculation flow in subjects with familial predisposition or newly diagnosed hypertension.

Background: Fractal analysis has been shown to be capable of characterizing irregular time series generated in non-linear systems. Fluctuations in skin flow signals have a fractal nature, but to date there has been no analysis of subjects with hypertension. The aim of this study is to assess the fractal dimensions of skin microcirculation flows in subjects with a familial predisposition or newly diagnosed hypertension.