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In transport phenomena, perturbation waves are a result of interaction of molecules in gases and liquids, charged particles (ions, electrons) in plasma, conduction electrons and phonons in solid bodies. General statistical theory of the…
We develop a definition of rate-induced tipping (R-tipping) in discrete-time dynamical systems (maps) and prove results giving conditions under which R-tipping will or will not happen. Specifically, we study (possibly non-invertible) maps…
Cumulant mapping has been recently suggested [Frasinski, Phys. Chem. Chem. Phys. 24, 207767 (2022)] as an efficient approach to observing multi-particle fragmentation pathways, while bypassing the restrictions of the usual…
This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques to establish properties of such random…
When testing a set of data for randomness according to a probability distribution that depends on a parameter, access to this parameter can be considered as a computational resource. We call a randomness test Hippocratic if it is not…
We proposed the deep zoom analysis of the composition of the logistic map and the tent map, which are well-known discrete unimodal chaotic maps. The deep zoom technique transforms each point of a given chaotic orbit by removing its first…
Probabilistic sampling methods have become very popular to solve single-shot path planning problems. Rapidly-exploring Random Trees (RRTs) in particular have been shown to be efficient in solving high dimensional problems. Even though…
The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed in which extremal properties are obtained through suitably defined rate equations. A variety…
Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some…
Regression models for supervised learning problems with a continuous target are commonly understood as models for the conditional mean of the target given predictors. This notion is simple and therefore appealing for interpretation and…
We describe a mechanism for transport of energy in a mechanical system consisting of a pendulum and a rotator subject to a random perturbation. The perturbation that we consider is the product of a Hamiltonian vector field and a scalar,…
For words of length $n$, generated by independent geometric random variables, we consider the mean and variance of the number of inversions and of a parameter of Knuth from permutation in situ. In this way, $q$--analogues for these…
We study families of open chaotic maps that classically share the same asymptotic properties -- forward and backwards trapped sets, repeller dimensions, escape rate -- but differ in their short time behavior. When these maps are quantized…
We study the RPA equations in their most general form by taking the matrix elements appearing in the RPA equations as random. This yields either a unitarily or an orthogonally invariant random-matrix model which is not of the Cartan type.…
Consider the random hypercube $H_2^n(p_n)$ obtained from the hypercube $H_2^n$ by deleting any given edge with probabilty $1-p_n$, independently of all the other edges. A diameter path in $H_2^n$ is a longest geodesic path in $H_2^n$.…
Recent studies demonstrate that trends in indicators extracted from measured time series can indicate approaching to an impending transition. Kendall's {\tau} coefficient is often used to study the trend of statistics related to the…
By the methods of multitype branching processes in random environment counted by random characteristics we study the tail distribution of busy periods and some other characteristics of the branching type polling systems in which the service…
Granular convergence is a property of a granular pack as it is repeatedly sheared in a cyclic, quasistatic fashion, as the packing configuration changes via discrete events. Under suitable conditions the set of microscopic configurations…
When considering a graph problem from a parameterized point of view, the parameter chosen is often the size of an optimal solution of this problem (the "standard" parameter). A natural subject for investigation is what happens when we…
Path planning is a classic problem for autonomous robots. To ensure safe and efficient point-to-point navigation an appropriate algorithm should be chosen keeping the robot's dimensions and its classification in mind. Autonomous robots use…