arXiv subjects

Dalibor Štys

Publications and source records attributed to Dalibor Štys.

4 recordsLinked to original sources

arXiv2018

Point Divergence Gain and Multidimensional Data Sequences Analysis

We introduce novel information-entropic variables -- a Point Divergence Gain ($Ω^{(l \rightarrow m)}_α$), a Point Divergence Gain Entropy ($I_α$), and a Point Divergence Gain Entropy Density ($P_α$) -- which are derived from the Rényi entropy and describe spatio-temporal changes between two consecutive discrete multidimensional distributions. The behavior of $Ω^{(l \rightarrow m)}_α$ is simulated for typical distributions and, together with $I_α$ and $P_α$, applied in analysis and characterization of series of multidimensional datasets of computer-based and real images.

physics.data-an↗

arXiv2016

Point Information Gain and Multidimensional Data Analysis

We generalize the Point information gain (PIG) and derived quantities, i.e. Point information entropy (PIE) and Point information entropy density (PIED), for the case of Rényi entropy and simulate the behavior of PIG for typical distributions. We also use these methods for the analysis of multidimensional datasets. We demonstrate the main properties of PIE/PIED spectra for the real data on the example of several images, and discuss possible further utilization in other fields of data processing.

physics.data-an↗

arXiv2016

Multi-state stochastic hotchpotch model gives rise to the observed mesoscopic behaviour in the non-stirred Belousov--Zhabotinsky reaction

Mesoscopic dynamics of self-organized structures is the most important aspect in the description of complex living systems. The Belousov--Zhabotinsky (B--Z) reaction is in this respect a convenient testbed because it represents a prototype of chemical self-organization with a rich variety of emergent wave-spiral patterns. Using a multi-state stochastic hotchpotch model, we show here that the mesoscopic behaviour of the non-stirred B--Z reaction is both qualitatively and quantitatively susceptible to the description in terms of stochastic multilevel cellular automata. This further implies that the mesoscopic dynamics of the non-stirred B--Z reaction results from a delicate interplay between a) a maximal number of available states within the elementary time lag (i.e. a minimal time interval needed for demise of a final state) and b) an imprecision or uncertainty in the definition of state. If either the number of time lags is largely different from 7 or the maximal number of available states is smaller than 20, the physicochemical conditions are inappropriate for a formation of the wave-spiral patterns. Furthermore, a white noise seems to be key for the formation of circular structures (target patterns) which could not be as yet systematically explained in existing models.

nlin.CG↗

arXiv2015

Measurement in biological systems from the self-organisation point of view

Measurement in biological systems became a subject of concern as a consequence of numerous reports on limited reproducibility of experimental results. To reveal origins of this inconsistency, we have examined general features of biological systems as dynamical systems far from not only their chemical equilibrium, but, in most cases, also of their Lyapunov stable states. Thus, in biological experiments, we do not observe states, but distinct trajectories followed by the examined organism. If one of the possible sequences is selected, a minute sub-section of the whole problem is obtained, sometimes in a seemingly highly reproducible manner. But the state of the organism is known only if a complete set of possible trajectories is known. And this is often practically impossible. Therefore, we propose a different framework for reporting and analysis of biological experiments, respecting the view of non-linear mathematics. This view should be used to avoid overoptimistic results, which have to be consequently retracted or largely complemented. An increase of specification of experimental procedures is the way for better understanding of the scope of paths, which the biological system may be evolving. And it is hidden in the evolution of experimental protocols.

q-bio.OT↗