First-passage times for generalized heterogeneous telegrapher's processes.

We consider two different fractional generalizations of the heterogeneous telegrapher's process with and without stochastic resetting. Both governing fractional heterogeneous telegrapher's equations can be obtained from the corresponding standard heterogeneous telegrapher's equations by using the subordination approach. The first-passage time problems are solved analytically for both models by finding the survival probabilities, the first-passage time densities, and the mean first-passage times.

Impact of stochastic resetting on resource allocation: The case of reallocating geometric Brownian motion.

We study the effects of stochastic resetting on the reallocating geometric Brownian motion (RGBM), an established model for resource redistribution relevant to systems such as population dynamics, evolutionary processes, economic activity, and even cosmology. The RGBM model is inherently nonstationary and non-ergodic, leading to complex resource redistribution dynamics. By introducing stochastic resetting, which periodically returns the system to a predetermined state, we examine how this mechanism modifies RGBM behavior.

A resetting particle embedded in a viscoelastic bath.

We examine the behavior of a colloidal particle immersed in a viscoelastic bath undergoing stochastic resetting at a rate r. Microscopic probes suspended in a viscoelastic environment do not follow the classical theory of Brownian motion. This is primarily because the memory from successive collisions between the medium particles and the probes does not necessarily decay instantly as opposed to the classical Langevin equation.

Bernoulli trial under subsystem restarts: Two competing searchers looking for a target.

We study a pair of independent searchers competing for a target under restarts and find that introduction of restarts tends to enhance the search efficiency of an already efficient searcher. As a result, the difference between the search probabilities of the individual searchers increases when the system is subject to restarts. This result holds true independent of the identity of individual searchers or the specific details of the distribution of restart times.

Fractional heterogeneous telegraph processes: Interplay between heterogeneity, memory, and stochastic resetting.

Fractional heterogeneous telegraph processes are considered in the framework of telegrapher's equations accompanied by memory effects. The integral decomposition method is developed for the rigorous treating of the problem. Exact solutions for the probability density functions and the mean squared displacements are obtained.

Fractional Telegrapher's Equation under Resetting: Non-Equilibrium Stationary States and First-Passage Times.

We consider two different time fractional telegrapher's equations under stochastic resetting. Using the integral decomposition method, we found the probability density functions and the mean squared displacements. In the long-time limit, the system approaches non-equilibrium stationary states, while the mean squared displacement saturates due to the resetting mechanism.

Bernoulli trial under restarts: A comparative study of resetting transitions.

A Bernoulli trial describing the escape behavior of a lamb to a safe haven in pursuit by a lion is studied under restarts. The process ends in two ways: either the lamb makes it to the safe haven (success) or is captured by the lion (failure). We study the first passage properties of this Bernoulli trial and find that only mean first passage time exists.

Random Walks on Comb-like Structures under Stochastic Resetting.

We study the long-time dynamics of the mean squared displacement of a random walker moving on a comb structure under the effect of stochastic resetting. We consider that the walker's motion along the backbone is diffusive and it performs short jumps separated by random resting periods along fingers. We take into account two different types of resetting acting separately: global resetting from any point in the comb to the initial position and resetting from a finger to the corresponding backbone.

Sensitivity analysis of shock distributions in the world economy.

With the ever increasing interconnectedness among countries and industries, globalization has empowered economies and promoted international trade, capital flow and labor mobility, leading to improved products and services. However, the growing interdependence has also propelled an inherent reliance on joint cooperation which has considerably influenced the complexity of global value chains (GVCs). This plays a significant role in policy decisions, raising questions about trade risks that originate from such interdependence.

Ornstein-Uhlenbeck process and generalizations: Particle dynamics under comb constraints and stochastic resetting.

The Ornstein-Uhlenbeck process is interpreted as Brownian motion in a harmonic potential. This Gaussian Markov process has a bounded variance and admits a stationary probability distribution, in contrast to the standard Brownian motion. It also tends to a drift towards its mean function, and such a process is called mean reverting.

Random Walks on Networks with Centrality-Based Stochastic Resetting.

We introduce a refined way to diffusely explore complex networks with stochastic resetting where the resetting site is derived from node centrality measures. This approach differs from previous ones, since it not only allows the random walker with a certain probability to jump from the current node to a deliberately chosen resetting node, rather it enables the walker to jump to the node that can reach all other nodes faster. Following this strategy, we consider the resetting site to be the geometric center, the node that minimizes the average travel time to all the other nodes.

General approach to stochastic resetting.

We address the effect of stochastic resetting on diffusion and subdiffusion process. For diffusion we find that mean square displacement relaxes to a constant only when the distribution of reset times possess finite mean and variance. In this case, the leading order contribution to the probability density function (PDF) of a Gaussian propagator under resetting exhibits a cusp independent of the specific details of the reset time distribution.

The influence of atrial flutter in automated detection of atrial arrhythmias - are we ready to go into clinical practice?".

Objective: To investigate the impact of atrial flutter (A) in the atrial arrhythmias classification task. We additionally advocate the use of a subject-based split for future studies in the field in order to avoid within-subject correlation which may lead to over-optimistic inferences. Finally, we demonstrate the effectiveness of the classifiers outside of the initially studied circumstances, by performing an inter-dataset model evaluation of the classifiers in data from different sources.

Endemic state equivalence between non-Markovian SEIS and Markovian SIS model in complex networks.

In the light of several major epidemic events that emerged in the past two decades, and emphasized by the COVID-19 pandemics, the non-Markovian spreading models occurring on complex networks gained significant attention from the scientific community. Following this interest, in this article, we explore the relations that exist between the mean-field approximated non-Markovian SEIS (Susceptible-Exposed-Infectious-Susceptible) and the classical Markovian SIS, as basic reoccurring virus spreading models in complex networks. We investigate the similarities and seek for equivalences both for the discrete-time and the continuous-time forms.

Income inequality and mobility in geometric Brownian motion with stochastic resetting: theoretical results and empirical evidence of non-ergodicity.

We explore the role of non-ergodicity in the relationship between income inequality, the extent of concentration in the income distribution, and income mobility, the feasibility of an individual to change their position in the income rankings. For this purpose, we use the properties of an established model for income growth that includes 'resetting' as a stabilizing force to ensure stationary dynamics. We find that the dynamics of inequality is regime-dependent: it may range from a strictly non-ergodic state where this phenomenon has an increasing trend, up to a stable regime where inequality is steady and the system efficiently mimics ergodicity.

Ergodicity breaking in wealth dynamics: The case of reallocating geometric Brownian motion.

A growing body of empirical evidence suggests that the dynamics of wealth within a population tends to be nonergodic, even after rescaling the individual wealth with the population average. Despite these discoveries, the way in which nonergodicity manifests itself in models of economic interactions remains an open issue. Here we shed valuable insight on these properties by studying the nonergodicity of the population average wealth in a simple model for wealth dynamics in a growing and reallocating economy called reallocating geometric Brownian motion (RGBM).

Geometric Brownian motion under stochastic resetting: A stationary yet nonergodic process.

We study the effects of stochastic resetting on geometric Brownian motion with drift (GBM), a canonical stochastic multiplicative process for nonstationary and nonergodic dynamics. Resetting is a sudden interruption of a process, which consecutively renews its dynamics. We show that, although resetting renders GBM stationary, the resulting process remains nonergodic.

Continuous time random walks under Markovian resetting.

We investigate the effects of Markovian resetting events on continuous time random walks where the waiting times and the jump lengths are random variables distributed according to power-law probability density functions. We prove the existence of a nonequilibrium stationary state and finite mean first arrival time. However, the existence of an optimum reset rate is conditioned to a specific relationship between the exponents of both power-law tails.

Hitting times in turbulent diffusion due to multiplicative noise.

We study a distribution of times of the first arrivals to absorbing targets in turbulent diffusion, which is due to a multiplicative noise. Two examples of dynamical systems with a multiplicative noise are studied. The first one is a random process according to inhomogeneous diffusion, which is also known as a geometric Brownian motion in the Black-Scholes model.

Generalized Cattaneo (telegrapher's) equations in modeling anomalous diffusion phenomena.

We study generalized Cattaneo (telegrapher's) equations involving memory effects introduced by smearing the time derivatives. Consistency conditions where the smearing functions obey restrict freedom in their choice but the proposed scheme goes beyond the approach based on using fractional derivatives. We find conditions under which solutions of the equations considered so far can be recognized as probability distributions, i.

Reaction and ultraslow diffusion on comb structures.

A two-dimensional (2D) comb model is proposed to characterize reaction-ultraslow diffusion of tracers both in backbones (x direction) and side branches (y direction) of the comblike structure with two memory kernels. The memory kernels include Dirac delta, power-law, and logarithmic and inverse Mittag-Leffler (ML) functions, which can also be considered as the structural functions in the time structural derivative. Based on the comb model, ultraslow diffusion on a fractal comb structure is also investigated by considering spatial fractal geometry of the backbone volume.

Quenched and annealed disorder mechanisms in comb models with fractional operators.

Recent experimental findings on anomalous diffusion have demanded novel models that combine annealed (temporal) and quenched (spatial or static) disorder mechanisms. The comb model is a simplified description of diffusion on percolation clusters, where the comblike structure mimics quenched disorder mechanisms and yields a subdiffusive regime. Here we extend the comb model to simultaneously account for quenched and annealed disorder mechanisms.

Bayesian consensus clustering in multiplex networks.

Multiplex networks are immanently characterized with heterogeneous relations among vertices. In this paper, we develop Bayesian consensus stochastic block modeling for multiplex networks. The posterior distribution of the model is approximated via Markov chain Monte Carlo, and a Gibbs sampler is derived in detail.

Reliability of Poisson-Nernst-Planck Anomalous Models for Impedance Spectroscopy.

We investigate possible connections between two different implementations of the Poisson-Nernst-Planck (PNP) anomalous models used to analyze the electrical response of electrolytic cells. One of them is built in the framework of the fractional calculus and considers integro-differential boundary conditions also formulated by using fractional derivatives; the other one is an extension of the standard PNP model presented by Barsoukov and Macdonald, which can also be related to equivalent circuits containing constant phase elements (CPEs). Both extensions may be related to an anomalous diffusion with subdiffusive characteristics through the electrical conductivity and are able to describe the experimental data presented here.

Economic complexity unfolded: Interpretable model for the productive structure of economies.

Economic complexity reflects the amount of knowledge that is embedded in the productive structure of an economy. It resides on the premise of hidden capabilities-fundamental endowments underlying the productive structure. In general, measuring the capabilities behind economic complexity directly is difficult, and indirect measures have been suggested which exploit the fact that the presence of the capabilities is expressed in a country's mix of products.