arXiv subjects

Ljupco Kocarev

Publications and source records attributed to Ljupco Kocarev.

At least 19 recordsLinked to original sources

arXiv2025

Response to an external field of a generalized Langevin equation with stochastic resetting of the memory kernel

We study a generalized Langevin equation (GLE) framework that incorporates stochastic resetting of a truncation power-law memory kernel. The inclusion of stochastic resetting enables the emergence of resonance phenomena even in parameter regimes where conventional settings (without resetting) do not exhibit such behavior. Specifically, we explore the response of the system to an external field under three scenarios: (i) a free particle, (ii) a particle in a harmonic potential, and (iii) the effect of truncation in the memory kernel. In each case, the primary focus is on understanding how the resetting mechanism interacts with standard parameters to induce stochastic resonance. In addition, we explore the effect of resetting on the dielectric loss.

cond-mat.stat-mech↗

arXiv2025

Generalized diffusion process with nonlocal interactions: Continuous time random walk model and stochastic resetting

A space fractional diffusion-like equation is introduced, which embodies the nonlocality in time, represented by the memory kernel and the non-locality in space. A specific example of the nonlocal term is considered in combination with three different forms of the memory kernel. To analyse the probability density function, we utilize the subordination approach. Subsequently, the corresponding continuous time random walk model is presented. Furthermore, we investigate the effects of the stochastic resetting on the dynamics of the process and we showed that in the long time limit the system approaches a nonequilibrium stationary state.

cond-mat.stat-mech↗

arXiv2024

The 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 non-stationary 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. Our analysis uncovers distinct long-term regimes determined by the interplay between the resetting rate, the strength of resource redistribution, and standard geometric Brownian motion parameters: the drift and the noise amplitude. Notably, we identify a critical resetting rate beyond which the self-averaging time becomes effectively infinite. In this regime, the first two moments are stationary, indicating a stabilized distribution of an initially unstable, mean-repulsive process. We demonstrate that optimal resetting can effectively balance growth and redistribution, reducing inequality in the resource distribution. These findings help us understand better the management of resource dynamics in uncertain environments.

cond-mat.stat-mech↗

arXiv2023

Ornstein-Uhlenbeck process and generalizations: particle's 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. Two examples of the generalized Ornstein-Uhlenbeck process are considered. In the first one, we study the Ornstein-Uhlenbeck process on a comb model, as an example of the harmonically bounded random motion in the topologically constrained geometry. The main dynamical characteristics (as the first and the second moments) and the probability density function are studied in the framework of both the Langevin stochastic equation and the Fokker-Planck equation. The second example is devoted to the study of the effects of stochastic resetting on the Ornstein-Uhlenbeck process, including stochastic resetting in the comb geometry. Here, the non-equilibrium stationary state is the main question in task, where the two divergent forces, namely the resetting and the drift towards the mean, lead to compelling results both in the case of the Ornstein-Uhlenbeck process with resetting and its generalization on the two dimensional comb structure.

cond-mat.stat-mech↗

arXiv2022

The fate of the American dream: A first passage under resetting approach to income dynamics

Detailed knowledge of individual income dynamics is crucial for investigating the existence of the American dream: Are we able to improve our income status during our working life? This key question simply boils down to observing individual status and how it moves between two thresholds: the current income and the desired income. Yet, our knowledge of these temporal properties of income remains limited since we rely on estimates coming from transition matrices which simplify income dynamics by aggregating the individual changes into quantiles and thus overlooking significant microscopic variations. Here, we bridge this gap by employing First Passage Time concepts in a baseline stochastic process with resetting used for modeling income dynamics and developing a framework that is able to crucially disaggregate the temporal properties of income to the level of an individual worker. We find analytically and illustrate numerically that our framework is orthogonal to the transition matrix approach and leads to improved and more granular estimates. Moreover, to facilitate empirical applications of the framework, we introduce a publicly available statistical methodology, and showcase the application using the USA income dynamics data. These results help to improve our understanding on the temporal properties of income in real economies and provide a set of tools for designing policy interventions.

econ.GN↗

arXiv2022

Stochastic dynamics with multiplicative dichotomic noise: heterogeneous telegrapher's equation, anomalous crossovers and resetting

We analyze diffusion processes with finite propagation speed in a non-homogeneous medium in terms of the heterogeneous telegrapher's equation. In the diffusion limit of infinite-velocity propagation we recover the results for the heterogeneous diffusion process. The heterogeneous telegrapher's process exhibits a rich variety of diffusion regimes including hyperdiffusion, ballistic motion, superdiffusion, normal diffusion and subdiffusion, and different crossover dynamics characteristic for complex systems in which anomalous diffusion is observed. The anomalous diffusion exponent in the short time limit is twice the exponent in the long time limit, in accordance to the crossover dynamics from ballistic diffusion to normal diffusion in the standard telegrapher's process. We also analyze the finite-velocity heterogeneous diffusion process in presence of stochastic Poissonian resetting. We show that the system reaches a non-equilibrium stationary state. The transition to this non-equilibrium steady state is analysed in terms of the large deviation function.

cond-mat.stat-mech↗

arXiv2022

Non-trivial dynamics in a model of glial membrane voltage driven by open potassium pores

Despite the molecular evidence that close to linear steady state I-V relationship in mammalian astrocytes reflects a total current resulting from more than one differently regulated K+ conductances, detailed ODE models of membrane voltage Vm incorporating multiple conductances are lacking. Repeated results of deregulated expressions of major K+ channels in glia, Kir4.1, in models of disease, as well as their altered rectification when assembling heteromeric Kir4.1/Kir5.1 channels have motivated us to attempt a detailed model adding the weaker potassium K2P current, in addition to Kir4.1, and study the stability of the resting state Vr. We ask whether with a deregulated Kir conductivity the nominal resting state Vr remains stable, and the cell retains a potassium electrode behavior with Vm following E_K. The minimal 2-dimensional model near Vr showed that certain alterations of Kir4.1 current may result in multistability of Vm if the model incorporates the typically observed K+ currents: Kir, K2P, and non-specific potassium leak. More specifically, a decrease or loss of outward Kir4.1 conductance introduces instability of Vr, near E_K. That happens through a fold bifurcation giving birth to a much more depolarized second, stable resting state Vdr>-10 mV. Realistic timeseries were used to perturb the membrane model, from recordings at the glial membrane during electrographic seizures. Simulations of the perturbed system by constant current through GJCs and transient seizure-like discharges as local field potentials led to depolarization of the astrocyte and switching of Vm between the two stable states, in a down-state / up-state manner. If the prolonged depolarizations near Vdr prove experimentally plausible, such catastrophic instability would impact all aspects of the glial function, from metabolic support to membrane transport and practically all neuromodulatory roles assigned to glia.

q-bio.NC↗

arXiv2022

Event-Triggered Optimal Attitude Consensus of Multiple Rigid Body Networks with Unknown Dynamics

In this paper, an event-triggered Reinforcement Learning (RL) method is proposed for the optimal attitude consensus of multiple rigid body networks with unknown dynamics. Firstly, the consensus error is constructed through the attitude dynamics. According to the Bellman optimality principle, the implicit form of the optimal controller and the corresponding Hamilton-Jacobi-Bellman (HJB) equations are obtained. Because of the augmented system, the optimal controller can be obtained directly without relying on the system dynamics. Secondly, the self-triggered mechanism is applied to reduce the computing and communication burden when updating the controller. In order to address the problem that the HJB equations are difficult to solve analytically, a RL method which only requires measurement data at the event-triggered instants is proposed. For each agent, only one neural network is designed to approximate the optimal value function. Each neural network is updated only at the event triggered instants. Meanwhile, the Uniformly Ultimately Bounded (UUB) of the closed-loop system is obtained, and the Zeno behavior is also avoided. Finally, the simulation results on a multiple rigid body network demonstrate the validity of the proposed method.

math.OC↗

arXiv2022

Correlates of the country differences in the infection and mortality rates during the first wave of the COVID-19 pandemic: Evidence from Bayesian model averaging

In the initial wave of the COVID-19 pandemic we observed great discrepancies in both infection and mortality rates between countries. Besides the biological and epidemiological factors, a multitude of social and economic criteria also influence the extent to which these discrepancies appear. Consequently, there is an active debate regarding the critical socio-economic and health factors that correlate with the infection and mortality rates outcome of the pandemic. Here, we leverage Bayesian model averaging techniques and country level data to investigate the potential of 28 variables, describing a diverse set of health and socio-economic characteristics, in being correlates of the final number of infections and deaths during the first wave of the coronavirus pandemic. We show that only few variables are able to robustly correlate with these outcomes. To understand the relationship between the potential correlates in explaining the infection and death rates, we create a Jointness Space. Using this space, we conclude that the extent to which each variable is able to provide a credible explanation for the COVID-19 infections/mortality outcome varies between countries because of their heterogeneous features.

physics.soc-ph↗

arXiv2021

Non-Markovian SIR epidemic spreading model

We introduce non-Markovian SIR epidemic spreading model inspired by the characteristics of the COVID-19, by considering discrete- and continuous-time versions. The incubation period, delayed infectiousness and the distribution of the recovery period are modeled with general functions. By taking corresponding choice of these functions, it is shown that the model reduces to the classical Markovian case. The epidemic threshold is analytically determined for arbitrary functions of infectivity and recovery and verified numerically. The relevance of the model is shown by modeling the first wave of the epidemic in Italy, in the spring, 2020.

physics.soc-ph↗

arXiv2021

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 mobility, the feasibility of an individual to change their position in the income distribution. For this purpose, we explore the properties of an established model for income growth that includes "resetting" as a stabilising force which ensures stationary dynamics. We find that the dynamics of inequality is regime-dependent and 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 ergodic behaviour. Mobility measures, conversely, are always stable over time, but the stationary value is dependent on the regime, suggesting that economies become less mobile in non-ergodic regimes. By fitting the model to empirical data for the dynamics of income share of the top earners in the United States, we provide evidence that the income dynamics in this country is consistently in a regime in which non-ergodicity characterises inequality and immobility dynamics. Our results can serve as a simple rationale for the observed real world income dynamics and as such aid in addressing non-ergodicity in various empirical settings across the globe.

econ.GN↗

arXiv2021

Geometric Brownian Motion under Stochastic Resetting: A Stationary yet Non-ergodic Process

We study the effects of stochastic resetting on geometric Brownian motion (GBM), a canonical stochastic multiplicative process for non-stationary and non-ergodic 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 non-ergodic. Quite surprisingly, the effect of resetting is pivotal in manifesting the non-ergodic behavior. In particular, we observe three different long-time regimes: a quenched state, an unstable and a stable annealed state depending on the resetting strength. Notably, in the last regime, the system is self-averaging and thus the sample average will always mimic ergodic behavior establishing a stand alone feature for GBM under resetting. Crucially, the above-mentioned regimes are well separated by a self-averaging time period which can be minimized by an optimal resetting rate. Our results can be useful to interpret data emanating from stock market collapse or reconstitution of investment portfolios.

q-fin.RM↗

arXiv2021

Autocorrelation functions and ergodicity in diffusion with stochastic resetting

Diffusion with stochastic resetting is a paradigm of resetting processes. Standard renewal or master equation approach are typically used to study steady state and other transport properties such as average, mean squared displacement etc. What remains less explored is the two time point correlation functions whose evaluation is often daunting since it requires the implementation of the exact time dependent probability density functions of the resetting processes which are unknown for most of the problems. We adopt a different approach that allows us to write a stochastic solution in the level of a single trajectory undergoing resetting. Moments and the autocorrelation functions between any two times along the trajectory can then be computed directly using the laws of total expectation. Estimation of autocorrelation functions turns out to be pivotal for investigating the ergodic properties of various observables for this canonical model. In particular, we investigate two observables (i) sample mean which is widely used in economics and (ii) time-averaged-mean-squared-displacement (TAMSD) which is of acute interest in physics. We find that both diffusion and drift-diffusion processes are ergodic at the mean level unlike their reset-free counterparts. In contrast, resetting renders ergodicity breaking in the TAMSD while both the stochastic processes are ergodic when resetting is absent. We quantify these behaviors with detailed analytical study and corroborate with extensive numerical simulations. The current study provides an important baseline that unifies two different approaches, used ubiquitously in economics and physics, for studying the ergodic properties in diffusion with resetting. We believe that our results can be verified in single particle experimental set-ups and thus have strong implications in the field of resetting.

cond-mat.stat-mech↗

arXiv2021

Evolution of cooperation in networked heterogeneous fluctuating environments

Fluctuating environments are situations where the spatio-temporal stochasticity plays a significant role in the evolutionary dynamics. The study of the evolution of cooperation in these environments typically assumes a homogeneous, well mixed population, whose constituents are endowed with identical capabilities. In this paper, we generalize these results by developing a systematic study for the cooperation dynamics in fluctuating environments under the consideration of structured, heterogeneous populations with individual entities subjected to general behavioral rules. Considering complex network topologies, and a behavioral rule based on generalized reciprocity, we perform a detailed analysis of the effect of the underlying interaction structure on the evolutionary stability of cooperation. We find that, in the presence of environmental fluctuations, the cooperation dynamics can lead to the creation of multiple network components, each with distinct evolutionary properties. This is paralleled to the freezing state in the Random Energy Model. We utilize this result to examine the applicability of our generalized reciprocity behavioral rule in a variety of settings. We thereby show that the introduced rule leads to steady state cooperative behavior that is always greater than or equal to the one predicted by the evolutionary stability analysis of unconditional cooperation. As a consequence, the implementation of our results may go beyond explaining the evolution of cooperation. In particular, they can be directly applied in domains that deal with the development of artificial systems able to adequately mimic reality, such as reinforcement learning.

q-bio.PE↗

arXiv2020

Digital me ontology and ethics

This paper addresses ontology and ethics of an AI agent called digital me. We define digital me as autonomous, decision-making, and learning agent, representing an individual and having practically immortal own life. It is assumed that digital me is equipped with the big-five personality model, ensuring that it provides a model of some aspects of a strong AI: consciousness, free will, and intentionality. As computer-based personality judgments are more accurate than those made by humans, digital me can judge the personality of the individual represented by the digital me, other individuals' personalities, and other digital me-s. We describe seven ontological qualities of digital me: a) double-layer status of Digital Being versus digital me, b) digital me versus real me, c) mind-digital me and body-digital me, d) digital me versus doppelganger (shadow digital me), e) non-human time concept, f) social quality, g) practical immortality. We argue that with the advancement of AI's sciences and technologies, there exist two digital me thresholds. The first threshold defines digital me having some (rudimentarily) form of consciousness, free will, and intentionality. The second threshold assumes that digital me is equipped with moral learning capabilities, implying that, in principle, digital me could develop their own ethics which significantly differs from human's understanding of ethics. Finally we discuss the implications of digital me metaethics, normative and applied ethics, the implementation of the Golden Rule in digital me-s, and we suggest two sets of normative principles for digital me: consequentialist and duty based digital me principles.

cs.AI↗

arXiv2020

Generalised geometric Brownian motion: Theory and applications to option pricing

Classical option pricing schemes assume that the value of a financial asset follows a geometric Brownian motion (GBM). However, a growing body of studies suggest that a simple GBM trajectory is not an adequate representation for asset dynamics due to irregularities found when comparing its properties with empirical distributions. As a solution, we develop a generalisation of GBM where the introduction of a memory kernel critically determines the behavior of the stochastic process. We find the general expressions for the moments, log-moments, and the expectation of the periodic log returns, and obtain the corresponding probability density functions by using the subordination approach. Particularly, we consider subdiffusive GBM (sGBM), tempered sGBM, a mix of GBM and sGBM, and a mix of sGBMs. We utilise the resulting generalised GBM (gGBM) to examine the empirical performance of a selected group of kernels in the pricing of European call options. Our results indicate that the performance of a kernel ultimately depends on the maturity of the option and its moneyness.

q-fin.PR↗

arXiv2020

First encounters on Bethe Lattices and Cayley Trees

In this work we consider the first encounter problems between a fixed and/or mobile target A and a moving trap B on Bethe Lattices and Cayley trees. The survival probability (SP) of the target A on the both kinds of structures are analyzed analytically and compared. On Bethe Lattices, the results show that the fixed target will still prolong its survival time, whereas, on Cayley trees, there are some initial positions where the target should move to prolong its survival time. The mean first encounter time (MFET) for mobile target A is evaluated numerically and compared with the mean first passage time (MFPT) for the fixed target A. Different initial settings are addressed and clear boundaries are obtained. These findings are helpful for optimizing the strategy to prolong the survival time of the target or to speed up the search process on Cayley trees, in relation to the target's movement and the initial position configuration of the two walkers. We also present a new method, which uses a small amount of memory, for simulating random walks on Cayley trees.

cond-mat.stat-mech↗

arXiv2020

Random Walk with Memory on Complex Networks

We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs of nodes, for a random walk with a memory of one step. We have analyzed one particular model of random walk, where the transition probabilities depend on the number of paths to the second neighbors. The numerical experiments on paradigmatic complex networks verify the validity of the theoretical expressions, and also indicate that the flattening of the stationary occupation probability accompanies a nearly optimal random search.

physics.soc-ph↗