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dr hab. Paweł Pilarczyk
Employment
- Associate professor at Instytut Matematyki Stosowanej
- 2018 - present at Faculty of Applied Physics and Mathematics
Publications
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total: 32
Catalog Publications
Year 2009
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A Database Schema for the Analysis of Global Dynamics of Multiparameter Systems
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Decomposing Cavities in Digital Volumes into Products of Cycles
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Year 2012
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A dynamical model for plasma confinement transitions
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Combinatorial-topological framework for the analysis of global dynamics
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Global dynamics in a stage-structured discrete-time population model with harvesting
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Year 2020
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A space-efficient algorithm for computing the minimum cycle mean in a directed graph
PublicationAn algorithm is introduced for computing the minimum cycle mean in a strongly connected directed graph with n vertices and m arcs that requires O(n) working space. This is a considerable improvement for sparse graphs in comparison to the classical algorithms that require O(n^2) working space. The time complexity of the algorithm is still O(nm). An implementation in C++ is made publicly available at http://www.pawelpilarczyk.com/cymealg/.
Year 2016
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A study of rigorous ODE integrators for multi-scale set-oriented computations
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Computation of Cubical Steenrod Squares
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Year 2024
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An absorbing set for the Chialvo map
PublicationThe classical Chialvo model, introduced in 1995, is one of the most important models that describe single neuron dynamics. In order to conduct effective numerical analysis of this model, it is necessary to obtain a rigorous estimate for the maximal bounded invariant set. We discuss this problem, and we correct and improve the results obtained by Courbage and Nekorkin (2010). In particular, we provide an explicit formula for an...
Year 2015
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An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds
PublicationFor a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m 4, we provide an algorithm for estimating the values of the topological invariant D^m_r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing D^m_r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013),...
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Computation of cubical homology, cohomology, and (co)homological operations via chain contraction
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Inducing a map on homology from a correspondence
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Year 2002
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Year 2023
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Differentiating patients with obstructive sleep apnea from healthy controls based on heart rate-blood pressure coupling quantified by entropy-based indices
PublicationWe introduce an entropy-based classification method for pairs of sequences (ECPS) for quantifying mutual dependencies in heart rate and beat-to-beat blood pressure recordings. The purpose of the method is to build a classifier for data in which each item consists of two intertwined data series taken for each subject. The method is based on ordinal patterns and uses entropy-like indices. Machine learning is used to select a subset...
Year 2008
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Excision-preserving cubical approach to the algorithmic computation of the discrete Conley index
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Homology algorithm based on acyclic subspace
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Year 2011
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Finite Resolution Dynamics
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Year 2005
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