arXiv subjects

Aleksejus Kononovicius

Publications and source records attributed to Aleksejus Kononovicius.

At least 19 recordsLinked to original sources

arXiv2025

Mean First Passage Time of the Symmetric Noisy Voter Model with Arbitrary Initial and Boundary Conditions

Models of imitation and herding behavior often underestimate the role of individualistic actions and assume symmetric boundary conditions. However, real-world systems (e.g., electoral processes) frequently involve asymmetric boundaries. In this study, we explore how arbitrarily placed boundary conditions influence the mean first passage time in the symmetric noisy voter model, and how individualistic behavior amplifies this asymmetry. We derive exact analytical expressions for mean first passage time that accommodate any initial condition and two types of boundary configurations: (i) both boundaries absorbing, and (ii) one absorbing and one reflective. In both scenarios, mean first passage time exhibits a clear asymmetry with respect to the initial condition, shaped by the boundary placement and the rate of independent transitions. Symmetry in mean first passage time emerges only when absorbing boundaries are equidistant from the midpoint. Additionally, we show that Kramers' law holds in both configurations when the rate of independent transitions is large. Our analytical results are in excellent agreement with numerical simulations, reinforcing the robustness of our findings.

cond-mat.stat-mech↗

arXiv2024

$1/f$ noise in semiconductors arising from the heterogeneous detrapping process of individual charge carriers

We propose a model of $1/f$ noise in semiconductors based on the drift of individual charge carriers and their interaction with the trapping centers. We assume that the trapping centers are homogeneously distributed in the material. The trapping centers are assumed to be heterogeneous and have unique detrapping rates. We show that uniform detrapping rate distribution emerges as a natural consequence of the vacant trap depths following the Boltzmann distribution, and the detrapping process obeying Arrhenius law. When these laws apply, and if the trapping rate is low in comparison to the maximum detrapping rate, $1/f$ noise in the form of Hooge's relation is recovered. Hooge's parameter, $α_{H}$, is shown to be a ratio between the characteristic trapping rate and the maximum detrapping rate. The proposed model implies that $1/f$ noise arises from the temporal charge carrier number fluctuations, not from the spatial mobility fluctuations.

math.PR↗

arXiv2024

Delayed interactions in the noisy voter model through the periodic polling mechanism

We investigate the effects of delayed interactions on the stationary distribution of the noisy voter model. We assume that the delayed interactions occur through the periodic polling mechanism and replace the original instantaneous two-agent interactions. In our analysis, we require that the polling period aligns with the delay in announcing poll outcomes. As expected, when the polling period is relatively short, the model with delayed interactions is almost equivalent to the original model. As the polling period increases, oscillatory behavior emerges, but the model with delayed interactions still converges to stationary distribution. The stationary distribution resembles a Beta-binomial distribution, with its shape parameters scaling with the polling period. The observed scaling behavior is non-monotonic. Namely, the shape parameters peak at some intermediate polling period.

physics.soc-ph↗

arXiv2024

Scaling of variability measures in hierarchical demographic data

Demographic heterogeneity is often studied through the geographical lens. Therefore it is considered at a predetermined spatial resolution, which is a suitable choice to understand scalefull phenomena. Spatial autocorrelation indices are well established for this purpose. Yet complex systems are often scale-free, and thus studying the scaling behavior of demographic heterogeneity may provide valuable insights. Furthermore, migration processes are not necessarily influenced by the physical landscape, which is accounted for by the spatial autocorrelation indices. The migration process may be more influenced by the socio-economic landscape, which is better reflected by the hierarchical demographic data. Here we explore the scaling behavior of variability measures in the United Kingdom 2011 census data set. As expected, all of the considered variability measures decrease as the hierarchical scale becomes coarser. Though the non-monotonicity is observed, it can be explained by accounting for the imperfect hierarchical relationships. We show that the scaling behavior of variability measures can be qualitatively understood in terms of Schelling's segregation model and Kawasaki-Ising

physics.soc-ph↗

arXiv2024

Immediate recapture in the trapping-detrapping process of a single charge carrier

Previously we have shown that pure 1/f noise arises from the trapping-detrapping process when traps are heterogeneous. Namely, the trapping-detrapping process relies on the assumption that detrapping rates of individual trapping centers in the condensed matter are random and uniformly distributed. Another assumption underlying the trapping-detrapping process was that both trapping and detrapping times need to have non-zero duration. Here we violate the latter assumption by introducing immediate recapture of the charge carrier. We show that 1/f noise will still be observed, though the range of frequencies over which it will be observed shifts to the lower frequency range as the immediate recapture probability increases.

cond-mat.stat-mech↗

arXiv2024

Short research review: Applications of statistical physics investigating financial and other social systems

Physics research complements traditional approaches, such as mathematical (stochastic) finance and econometrics in quantitative economics and finance. In the early years of this millennium, we embarked on an interdisciplinary research endeavor in Lithuania, applying concepts from statistical physics to understand complex financial and social systems. Here, we provide a short review of investigations in Lithuania, spanning from 2008 to 2022, undertaken by our research group.

physics.soc-ph↗

arXiv2023

$1/f$ noise from the sequence of nonoverlapping rectangular pulses

We analyze the power spectral density of a signal composed of nonoverlapping rectangular pulses. First, we derive a general formula for the power spectral density of a signal constructed from the sequence of nonoverlapping pulses. Then we perform a detailed analysis of the rectangular pulse case. We show that pure $1/f$ noise can be observed until extremely low frequencies when the characteristic pulse (or gap) duration is long in comparison to the characteristic gap (or pulse) duration, and gap (or pulse) durations are power-law distributed. The obtained results hold for the ergodic and weakly nonergodic processes.

cond-mat.stat-mech↗

arXiv2023

Anomalous diffusion and long-range memory in the scaled voter model

We analyze the scaled voter model, which is a generalization of the noisy voter model with time-dependent herding behavior. We consider the case when the intensity of herding behavior grows as a power-law function of time. In this case, the scaled voter model reduces to the usual noisy voter model, but it is driven by the scaled Brownian motion. We derive analytical expressions for the time evolution of the first and second moments of the scaled voter model. In addition, we have derived an analytical approximation of the first passage time distribution. By numerical simulation, we confirm our analytical results as well as show that the model exhibits long-range memory indicators despite being a Markov model. The proposed model has steady-state distribution consistent with the bounded fractional Brownian motion, thus we expect it to be a good substitute model for the bounded fractional Brownian motion.

cond-mat.stat-mech↗

arXiv2022

Resemblance of the power-law scaling behavior of a non-Markovian and nonlinear point processes

We analyze the statistical properties of a temporal point process driven by a confined fractional Brownian motion. The event count distribution and power spectral density of this non--Markovian point process exhibit power--law scaling. We show that a nonlinear Markovian point process can reproduce the same scaling behavior. This result indicates a possible link between nonlinearity and apparent non--Markovian behavior.

cond-mat.stat-mech↗

arXiv2022

Anomalous diffusion in nonlinear transformations of the noisy voter model

Voter models are well known in the interdisciplinary community, yet they haven't been studied from the perspective of anomalous diffusion. In this paper we show that the original voter model exhibits ballistic regime. Non-linear transformations of the observation variable and time scale allows us to observe other regimes of anomalous diffusion as well as normal diffusion. We show that numerical simulation results coincide with derived analytical approximations describing the temporal evolution of the raw moments.

cond-mat.stat-mech↗

arXiv2021

Understanding the nature of the long-range memory phenomenon in socioeconomic systems

In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long-range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations and agent-based models. Reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first-passage time distributions. Research has lead us to question whether the observed long-range memory is a result of actual long-range memory process or just a consequence of non-linearity of Markov processes. As our most recent result we discuss the long-range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the ARFIMA sample series. Our newly obtained results seem indicate that new estimators of self-similarity and long-range memory for analyzing systems with non-Gaussian distributions have to be developed.

physics.soc-ph↗

arXiv2019

Bessel-like birth-death process

We consider models of the population or opinion dynamics which result in the non-linear stochastic differential equations (SDEs) exhibiting the spurious long-range memory. In this context, the correspondence between the description of the birth-death processes as the continuous-time Markov chains and the continuous SDEs is of high importance for the alternatives of modeling. We propose and generalize the Bessel-like birth-death process having clear representation by the SDEs. The new process helps to integrate the alternatives of description and to derive the equations for the probability density function (PDF) of the burst and inter-burst duration of the proposed continuous time birth-death processes.

physics.soc-ph↗

arXiv2019

Compartmental voter model

Numerous models in opinion dynamics focus on the temporal dynamics within a single electoral unit (e.g., country). The empirical observations, on the other hand, are often made across multiple electoral units (e.g., polling stations) at a single point in time (e.g., elections). Aggregates of these observations, while quite useful in many applications, neglect the underlying heterogeneity in opinions. To address this issue we build a simple agent-based model in which all agents have fixed opinions, but are able to change their electoral units. We demonstrate that this model is able to generate rank-size distributions consistent with the empirical data.

physics.soc-ph↗

arXiv2019

Empirical Survival Jensen-Shannon Divergence as a Goodness-of-Fit Measure for Maximum Likelihood Estimation and Curve Fitting

The coefficient of determination, known as $R^2$, is commonly used as a goodness-of-fit criterion for fitting linear models. $R^2$ is somewhat controversial when fitting nonlinear models, although it may be generalised on a case-by-case basis to deal with specific models such as the logistic model. Assume we are fitting a parametric distribution to a data set using, say, the maximum likelihood estimation method. A general approach to measure the goodness-of-fit of the fitted parameters, which is advocated herein, is to use a nonparametric measure for comparison between the empirical distribution, comprising the raw data, and the fitted model. In particular, for this purpose we put forward the Survival Jensen-Shannon divergence ($SJS$) and its empirical counterpart (${\cal E}SJS$) as a metric which is bounded, and is a natural generalisation of the Jensen-Shannon divergence. We demonstrate, via a straightforward procedure making use of the ${\cal E}SJS$, that it can be used as part of maximum likelihood estimation or curve fitting as a measure of goodness-of-fit, including the construction of a confidence interval for the fitted parametric distribution. Furthermore, we show the validity of the proposed method with simulated data, and three empirical data sets.

stat.ME↗

arXiv2019

Order book model with herd behavior exhibiting long-range memory

In this work, we propose an order book model with herd behavior. The proposed model is built upon two distinct approaches: a recent empirical study of the detailed order book records by Kanazawa et al. [Phys. Rev. Lett. 120, 138301] and financial herd behavior model. Combining these approaches allows us to propose a model that replicates the long-range memory of absolute returns and trading activity. We compare the statistical properties of the model against the empirical statistical properties of the Bitcoin exchange rates and New York stock exchange tickers. We also show that the fracture in the spectral density of the high-frequency absolute return time series might be related to the mechanism of convergence towards the equilibrium price.

q-fin.ST↗

arXiv2019

Approximation of the first passage time distribution for the birth-death processes

We propose a general method to obtain approximation of the first passage time distribution for the birth-death processes. We rely on the general properties of birth-death processes, Keilson's theorem and the concept of Riemann sum to obtain closed-form expressions. We apply the method to the three selected birth-death processes and the sophisticated order-book model exhibiting long-range memory. We discuss how our approach contributes to the competition between spurious and true long-range memory models.

q-fin.ST↗

arXiv2018

Illusion of persistence in NBA 1995-2018 regular season data

Among the sports fans beliefs about "hot hands" and "winning streaks" are widely spread, while the scientific debate about these effects is still ongoing. Recently in a paper by P. Ferreira [Physica A 500: 92-96] detrended fluctuation analysis was applied to the NBA teams' win records. It was shown that 28 considered NBA teams exhibit persistence in the win record time series. In this paper we take the same data set and compare the obtained results against various random models. We find that the empirical results are consistent with the results obtained from various simple random models.

physics.soc-ph↗

arXiv2018

The consentaneous model of the financial markets exhibiting spurious nature of long-range memory

It is widely accepted that there is strong persistence in the volatility of financial time series. The origin of the observed persistence, or long-range memory, is still an open problem as the observed phenomenon could be a spurious effect. Earlier we have proposed the consentaneous model of the financial markets based on the non-linear stochastic differential equations. The consentaneous model successfully reproduces empirical probability and power spectral densities of volatility. This approach is qualitatively different from models built using fractional Brownian motion. In this contribution we investigate burst and inter-burst duration statistics of volatility in the financial markets employing the consentaneous model. Our analysis provides an evidence that empirical statistical properties of burst and inter-burst duration can be explained by non-linear stochastic differential equations driving the volatility in the financial markets. This serves as an strong argument that long-range memory in finance can have spurious nature.

q-fin.ST↗