dr hab. Paweł Pilarczyk
Employment
- Associate professor at Instytut Matematyki Stosowanej
- 2018 - present at Faculty of Applied Physics and Mathematics
Publications
Filters
total: 32
Catalog Publications
Year 2007
Year 2016
Year 2023
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Topological-numerical analysis of a two-dimensional discrete neuron model
PublicationWe conduct computer-assisted analysis of a two-dimensional model of a neuron introduced by Chialvo in 1995 [Chaos, Solitons Fractals 5, 461–479]. We apply the method of rigorous analysis of global dynamics based on a set-oriented topological approach, introduced by Arai et al. in 2009 [SIAM J. Appl. Dyn. Syst. 8, 757–789] and improved and expanded afterward. Additionally, we introduce a new algorithm to analyze the return times...
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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 2002
Year 2014
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Shadowing is generic---a continuous map case
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Year 2020
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Rigorous numerics for critical orbits in the quadratic family
PublicationWe develop algorithms and techniques to compute rigorous bounds for finite pieces of orbits of the critical points, for intervals of parameter values, in the quadratic family of one-dimensional maps fa(x)=a−x2. We illustrate the effectiveness of our approach by constructing a dynamically defined partition P of the parameter interval Ω=[1.4,2] into almost 4 million subintervals, for each of which we compute to high precision the...
Year 2015
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Rich Bifurcation Structure in a Two-Patch Vaccination Model
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Inducing a map on homology from a correspondence
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Year 2009
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Recent development in rigorous computational methods in dynamical systems
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Decomposing Cavities in Digital Volumes into Products of Cycles
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Year 2008
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Quantitative hyperbolicity estimates in one-dimensional dynamics
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Homology algorithm based on acyclic subspace
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Excision-preserving cubical approach to the algorithmic computation of the discrete Conley index
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Year 2021
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Persistent homology as a new method of the assessment of heart rate variability
PublicationHeart rate variability (hrv) is a physiological phenomenon of the variation in the length of the time interval between consecutive heartbeats. In many cases it could be an indicator of the development of pathological states. The classical approach to the analysis of hrv includes time domain methods and frequency domain methods. However, attempts are still being made to define new and more effective hrv assessment tools. Persistent...
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Nilpotent singularities and chaos: Tritrophic food chains
PublicationLocal bifurcation theory is used to prove the existence of chaotic dynamics in two well-known models of tritrophic food chains. To the best of our knowledge, the simplest technique to guarantee the emergence of strange attractors in a given family of vector fields consists of finding a 3-dimensional nilpotent singularity of codimension 3 and verifying some generic algebraic conditions. We provide the essential background regarding...
Year 2010
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Parallelization Method for a Continuous Property
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Year 2005
Year 2012
Year 2011
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Finite Resolution Dynamics
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