Understanding the dynamical behavior of infectious disease propagation within enclosed spaces is crucial for effectively establishing control measures. In this article, we present a modeling approach to analyze dynamics individuals in spaces, where such are comprised different chambers. Our focus on capturing movement and their infection status using an open Markov chain framework. Unlike ordinary chains, accounts entering leaving system. We categorize system into three groups: susceptible,...

In this work, we experimentally investigate the narrow escape problem using self-propelled camphor-infused discs, which have possibility to from a bounded circular domain through an opening in boundary. To analyze statistical properties of problem, proposed two experimental protocols: first, control setup within closed where disc encounters target simulating on boundary, and second real is placed boundary domain. These setups allow us compare how differ between simulated (or fictitious)...

In this work we transform the deterministic dynamics of an overdamped tilting ratchet into a discrete dynamical map by looking stroboscopically at continuous motion originally ruled differential equations. We show that, for simple and widely used case periodic dichotomous driving forces, resulting belongs to class circle homeomorphisms. This approach allows us apply well-known properties such maps derive necessary sufficient conditions that potential must satisfy in order have vanishing...

We study the diffusion of an ensemble overdamped particles sliding over a tilted random poten- tial (produced by interaction particle with polymer) long-range correlations. found that properties such system are closely related to correlation function corresponding potential. model substrate as symbolic trajectory shift space which enables us obtain general formula for coefficient when normal occurs. The total time takes travel through n monomers can be seen ergodic sum we apply central limit...

In this work we study the transport properties of non-interacting overdamped particles, moving on tilted disordered potentials, subjected to Gaussian white noise. We give exact formulas for drift and diffusion coefficients case random potentials resulting from interaction a particle with "random polymer". our model polymer" is made up, by means some stochastic process, monomers that can be taken finite or countable infinite set possible monomer types. For uncorrelated polymers found...

In this work, we introduce a method for estimating the entropy rate and production from finite symbolic time series. From point of view statistics, series can be interpreted as problem parameters distribution with censored or truncated sample. We use to give estimations rate, assuming that they are (limit) distribution. The last statement is actually consequence fact obtained recurrence-time statistics satisfies central limit theorem. test our using coming Markov chain models, discrete-time...

We analyze the conditions for existence of current reversals in overdamped deterministic tilting ratchets under symmetric forcing. To this end, we use and extend formalism recently introduced R. Salgado-García, M. Aldana, G. Martínez-Mekler [Phys. Rev. Lett. 96, 134101 (2006)] to transform equations motion ratchet into discrete circle maps. For a periodic dichotomous forcing show that phenomenon reversal is not uncommon exists nonzero measure set parameter space. Additionally, numerically...

We consider the motion of overdamped particles over random potentials subjected to a Gaussian white noise and time-dependent periodic external forcing. The potential is modeled as resulting from interaction point particle with polymer. polymer made up, by means some stochastic process, finite set possible monomer types. process assumed reach nonequilibrium stationary state, which that every realization can be considered an out-of-equilibrium structure. show net flux this medium nonvanishing...

We introduce a method for estimating the complexity function (which counts number of observable words given length) finite symbolic sequence, which we use to estimate coding DNA sequences several species Hominidae family. In all cases, obtained complexities show same characteristic behavior: exponential growth small word lengths, followed by linear larger lengths. The consider exhibit systematic trend in correspondence with phylogenetic tree. Using our method, some known evolution models,...

We study one-dimensional lattice systems with pair-wise interactions of infinite range. show projective convergence Markov measures to the unique equilibrium state. For this purpose we impose a slightly stronger condition than summability variations on regularity interaction. With our are able explicitly obtain stretched exponential bounds for rate mixing Finally entropy that state via their topological pressure.

We introduce a simple model of deterministic particles in weakly disordered media which exhibits transition from normal to anomalous diffusion.The consists set non-interacting overdamped moving on potential.The potential can be thought as substrate having some "defects" scattered along one-dimensional line.The distance between two contiguous defects is assumed have heavy-tailed distribution with given exponent α, means that the are scarce if α small.We prove this system diffusion when...

In this work we study the diffusion of non-interacting overdamped particles, moving on unbiased disordered correlated potentials, subjected to Gaussian white noise.We obtain an exact expression for coefficient which allows us prove that particles a random polymer does not depend correlations potentials.This universal behavior diffusivity is direct consequence validity Einstein relation and decay polymer.We test independence polymers produced by two different stochastic processes, one-step...

In this work we introduce a scheme for the calculation of an approximate closed expression time-dependent probability density function overdamped particles in tilted periodic potentials. Our derivation is based on ansatz solution corresponding Fokker-Planck equation and self-consistent cumulant calculation. The high accuracy our exhibited by comparisons with Langevin dynamics simulations exact analytic results drift diffusion coefficients. Good agreement found both, large intermediate times.

In this work, we implement the so-called matching-time estimators for estimating entropy rate as well production symbolic sequences. These are based on recurrence properties of system, which have been shown to be appropriate testing irreversibility, especially when sequences large correlations or memory. Based limit theorems matching times, derive a maximum likelihood estimator by assuming that set moderately short time series finite random duration. We show proposed has several make it...

In this work, we present a method to assess irreversibility in real-valued time series. Our approach introduces novel measure based on the statistics of what term “trend patterns.” By dividing series into subsequences that exhibit either increasing or decreasing trends, define distributions representing duration uptrend and downtrend subsequences. When process is reversible, these should coincide. Consequently, quantify degree by measuring statistical deviations between them. findings...

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Abstract In this work we propose a transfer entropy approach to discern time-delay couplings within non-linear and stochastic coupled systems. We introduce the concept of ‘time-wise entropy’, which quantifies reduction in future uncertainty for process Y by considering values processes X at specific past moment. The key advantage our is number parameters required estimation when compared other methodologies. Our proposed time-wise not only lends itself effective from actual data but also...

In this work, we perform experimental and numerical investigations on the dynamics of camphor-infused discs, well-established as active particles in their behavior. Our analysis focuses examining individual these discs within a confined circular domain, revealing that they exhibit characteristics akin to chiral particles. To characterize behavior effectively, introduce methodology for estimating key model parameter values from our experiments, including linear velocity, angular noise...

The time-dependent probability density function of the order parameter a system evolving toward stationary state exhibits an oscillatory behavior if eigenvalues corresponding evolution operator are complex. frequencies ${\ensuremath{\omega}}_{n}$, with which reaches its state, correspond to imaginary part such eigenvalues. If (at state) is further driven by small and oscillating perturbation given frequency $\ensuremath{\omega}$, we formally prove that linear response enhanced when...

In this work we propose a simple example of one-dimensional thermodynamic system where non-interacting particles are allowed to move over the $[0,1]$ interval, which influenced by potential with fractal structure. We prove that exhibits phase transition at finte temperature, is characterized fact Gibbs-Boltzmann probability measure passes from being absolutely continuous respect Lebesgue (at high temperature) singular low temperatures). below critical temperature (when continuous) supported...

In this work we propose a model for open Markov chains that can be interpreted as system of non-interacting particles evolving according to the rules chain. The number in is not constant, because allow arrive or leave state space prescribed protocols. We describe by looking at population on every establishing time-evolution distribution particles. show it possible over through corresponding moment generating function. This description given dynamics ruling behavior such function and prove...