Computing The Cubical Cohomology Ring (Extended Abstract)

The goal of this work is to establish a new algorithm for computing the cohomology ring of cubical complexes. The cubical structure enables an explicit recurrence formula for the cup product. We derive this formula and, next, show how to extend the Mrozek and Batko [7] homology coreduction algorithm to the cohomology ring structure. The implementation of the algorithm is a work in progress. This research is aimed at applications in electromagnetism and in image processing, among other fields

Linking combinatorial and classical dynamics : Conley index and Morse decompositions

We prove that every combinatorial dynamical system in the sense of Forman, defined on a family of simplices of a simplicial complex, gives rise to a multivalued dynamical system F on the geometric realization of the simplicial complex. Moreover, F may be chosen in such a way that the isolated invariant sets, Conley indices, Morse decompositions and Conley–Morse graphs of the combinatorial vector field give rise to isomorphic objects in the multivalued map case

CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems

We present the CAPD::DynSys library for rigorous numerical analysis of dynamical systems. The basic interface is described together with several interesting case studies illustrating how it can be used for computer-assisted proofs in dynamics of ODEs.Comment: 25 pages, 4 figures, 11 full C++ example

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. Methods: A four-minutes rest flow (RF), minimal flow (BZ) during three-minutes ischemia and eight-minutes heat flow (HF) were recorded (using laser Doppler flowmetry) in patients with untreated hypertension, and in normotensives with no [NT(-)] or with a familial predisposition to hypertension [NT(+)]. Average one-minute surface areas under the curve of flow records and box dimensions (D) were calculated. Anova Kruskall-Wallis, c2 statistic and multivariate reverse regression analysis were used for calculation. Results: We studied 70 people (average age 36.1 ± 10.3 years, 39 men). Hypertensives (n = 31) had significantly higher values of both clinical blood pressure and 24-hour ambulatory blood pressure, body mass index, glucose, triglycerides and insulin than the NT(-), (n = 17) and NT(+), (n = 22) groups. Mean values of flows and surface area under the curve of RF, BZ, HF records, D RF and D HF were comparable in studied groups, but D BZ differed (1.13 ± ± 0.05 vs 1.15 ± 0.05 vs 1.11 ± 0.05, respectively; p = 0.04). A family history of hypertension, insulin level and variability of 24-hour diastolic blood pressure were significant predictors of D BZ lower values in the multiple regression model. Conclusions: Subjects with a familial predisposition to hypertension reveal altered homeodynamics of microvascular flow, with diminished chaotic ischemic flow. (Cardiol J 2011; 18, 1: 26-32

Phylogeny and systematics of the "Pronophila clade," with 2 new genera to resolve the formerly polyphyletic genus Pseudomaniola (Lepidoptera: Nymphalidae: Satyrinae)

Analysis of a target enrichment molecular dataset confirms the monophyly of the Neotropical montane butterfly group known as the Pronophila Westwood clade, 1 of 2 major lineages of the satyrine subtribe Pronophilina. The Pronophila clade comprises 18-20 recognized genera and some 125 species. Within this group, the genus Pseudomaniola Röber appears as paraphyletic, and is split here into 3 genera, Pseudomaniola sensu novum with 6 species, including 4 previously considered as subspecies of P. phaselis (Hewitson), the monobasic Fahraeusia Pyrcz n. gen. for Catargynnis asuba Thieme, n. comb., and Boyeriana Pyrcz, Espeland & Willmott n. gen., with 9 species. The adults of all 3 genera can be recognized by their wing color patterns, but the strongest synapomorphies are found in the genitalia, especially those of the male, supporting the above systematic de cisions. Notable differences are also found in scale organization and morphology. A divergence time analysis suggests that Fahraeusia diverged from Pseudomaniola + Boyeriana in the mid-Miocene, around 12 Mya, and the subsequent separation of the last 2 genera occurred at the start of the Pliocene at around 5 Mya