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The paper introduces a new numerical characteristic of one dimensional stochastic systems. This quantity is a measure of minimal periodicity, can be detected in the process deep differential structure. The claim is that this new measure of…
The examples of rhythmical signals with variable period are considered. The definition of periodic function with the variable period is given as a model of such signals. The examples of such functions are given and their variable periods…
The parameter space of dynamical systems arising in applications is often found to be high-dimensional and difficult to explore. We construct a fast algorithm to numerically analyze "quantitative features" of dynamical systems depending on…
Dimensional analysis is a simple qualitative method for determining essential connections between physical quantities. It is applicable to a multitude of physics problems, many of which canbe introduced early on in a university physics…
(Abbr.) We consider a direct representation of a periodic time-function by means of its zero-crossings. The use of the zero-crossings as the describing parameters is made possible by a singular model of a strongly nonlinear electrical…
Periodically occurring accumulations of events or measured values are present in many time-dependent datasets and can be of interest for analyses. The frequency of such periodic behavior is often not known in advance, making it difficult to…
A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…
The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…
Quantile-based classifiers can classify high-dimensional observations by minimising a discrepancy of an observation to a class based on suitable quantiles of the within-class distributions, corresponding to a unique percentage for all…
Principal component analysis is a useful dimension reduction and data visualization method. However, in high dimension, low sample size asymptotic contexts, where the sample size is fixed and the dimension goes to infinity,a paradox has…
This paper considers a structural-factor approach to modeling high-dimensional time series and space-time data by decomposing individual series into trend, seasonal, and irregular components. For ease in analyzing many time series, we…
We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a…
The problem of the Nature of Time is twofold: whether or not time is a fundamental quantity of Nature, and how does clock time of metrology emerge in the experimental description of dynamics. This work strongly supports the fundamental…
We introduce a simple method to estimate the system parameters in continuous dynamical systems from the time series. In this method, we construct a modified system by introducing some constants (controlling constants) into the given…
We establish a deterministic technique to investigate transport moments of arbitrary order. The theory is applied to the analysis of different kinds of intermittent one-dimensional maps and the Lorentz gas with infinite horizon: the typical…
We describe two different approaches for incorporating systematics into analyses for parameter determination in the physical sciences. We refer to these as the Pragmatic and the Full methods, with the latter coming in two variants: Full…
Periodic point sets model all solid crystalline materials whose structures are determined in a rigid form and should be studied up to rigid motion or isometry preserving inter-point distances. In 2021 H.Edelsbrunner et al. introduced an…
Dynamical systems often contain oscillatory forces or depend on periodic potentials. Time or space periodicity is reflected in the properties of these systems through a dependence on the parameters of their periodic terms. In this paper we…
We are going to introduce a new algebraic, analytic structure that is a kind of generalization of the Hausdorff dimension and measure. We give many examples and study the basic properties and relations of such systems.
We introduce a rigorous, physically appealing, and practical way to measure distances between exchange-only correlations of interacting many-electron systems, which works regardless of their size and inhomogeneity. We show that this…