arXiv subjects

Tomasz Gubiec

Publications and source records attributed to Tomasz Gubiec.

14 recordsLinked to original sources

arXiv2025

Impact of homophily in adherence to anti-epidemic measures on the spread of infectious diseases in social networks

We investigate how homophily in adherence to anti-epidemic measures affects the final size of epidemics in social networks. Using a modified SIR model, we divide agents into two behavioral groups-compliant and non-compliant-and introduce transmission probabilities that depend asymmetrically on the behavior of both the infected and susceptible individuals. We simulate epidemic dynamics on two types of synthetic networks with tunable inter-group connection probability: stochastic block models (SBM) and networks with triadic closure (TC) that better capture local clustering. Our main result reveals a counterintuitive effect: under conditions where compliant infected agents significantly reduce transmission, increasing the separation between groups may lead to a higher fraction of infections in the compliant population. This paradoxical outcome emerges only in networks with clustering (TC), not in SBM, suggesting that local network structure plays a crucial role. These findings highlight that increasing group separation does not always confer protection, especially when behavioral traits amplify within-group transmission.

physics.soc-ph↗

arXiv2020

The new face of multifractality: Multi-branchedness and the phase transitions in time series of mean inter-event times

Empirical time series of inter-event or waiting times are investigated using a modified Multifractal Detrended Fluctuation Analysis operating on fluctuations of mean detrended dynamics. The core of the extended multifractal analysis is the non-monotonic behavior of the generalized Hurst exponent $h(q)$ -- the fundamental exponent in the study of multifractals. The consequence of this behavior is the non-monotonic behavior of the coarse Hölder exponent $α(q)$ leading to multi-branchedness of the spectrum of dimensions. The Legendre-Fenchel transform is used instead of the routinely used canonical Legendre (single-branched) contact transform. Thermodynamic consequences of the multi-branched multifractality are revealed. These are directly expressed in the language of phase transitions between thermally stable, metastable, and unstable phases. These phase transitions are of the first and second orders according to Mandelbrot's modified Ehrenfest classification. The discovery of multi-branchedness is tantamount in significance to extending multifractal analysis.

q-fin.ST↗

arXiv2020

Continuous Time Random Walk with correlated waiting times. The crucial role of inter-trade times in volatility clustering

In many physical, social or economical phenomena we observe changes of a studied quantity only in discrete, irregularly distributed points in time. The stochastic process used by physicists to describe this kind of variables is the Continuous Time Random Walk (CTRW). Despite the popularity of this type of stochastic processes and strong empirical motivation, models with a long-term memory within the sequence of time intervals between observations are missing. Here, we fill this gap by introducing a new family of CTRWs. The memory is introduced to the model by the assumption that many consecutive time intervals can be the same. Surprisingly, in this process we can observe a slowly decaying nonlinear autocorrelation function without a fat-tailed distribution of time intervals. Our model applied to high-frequency stock market data can successfully describe the slope of decay of nonlinear autocorrelation function of stock market returns. The model achieves this result with no dependence between consecutive price changes. It proves the crucial role of inter-event times in the volatility clustering phenomenon observed in all stock markets.

q-fin.ST↗

arXiv2019

Multi-phase long-term autocorrelated diffusion: Stationary continuous-time Weierstrass walk vs. flight

In this paper we are examining diffusion properties of stationary continuous-time Weierstrass walk (CTWW). We are showing it is a multi-phase representation of the Lévy walk. The hierarchical spatial-temporal coupling, combined with coupling between dynamic variables define the CTWW process. The walker moves here with a piecewise constant velocity between trajectory turning points. We have found the diffusion phase diagram of the CTWW consisting not only of anomalous non-Gaussian or non-fBm phases but also Brownian yet non-Gaussian ones. We compare the diffusion phase diagram of the stationary CTWW with the corresponding hierarchical continuous-time Weierstress flight (CTWF). The instantaneous jumps between trajectory turning points preceded by waiting define the CTWF process. It is a hierarchical representation of the Lévy flight. We have found the diffusion phase diagram of the CTWF to be a small part of the corresponding CTWW one.

cond-mat.stat-mech↗

arXiv2018

Directed Continuous-Time Random Walk with memory

We propose a new Directed Continuous-Time Random Walk (CTRW) model with memory. As CTRW trajectory consists of spatial jumps preceded by waiting times, in Directed CTRW, we consider the case with only positive spatial jumps. Moreover, we consider the memory in the model as each spatial jump depends on the previous one. Our model is motivated by the financial application of the CTRW presented in [Phys. Rev. E 82:046119][Eur. Phys. J. B 90:50]. As CTRW can successfully describe the short term negative autocorrelation of returns in high-frequency financial data (caused by the bid-ask bounce phenomena), we asked ourselves to what extent the observed long-term autocorrelation of absolute values of returns can be explained by the same phenomena. It turned out that the bid-ask bounce can be responsible only for the small fraction of the memory observed in the high-frequency financial data.

q-fin.ST↗

arXiv2018

Statistical mechanics of coevolving spin system

We propose a statistical mechanics approach to a coevolving spin system with an adaptive network of interactions. The dynamics of node states and network connections is driven by both spin configuration and network topology. We consider a Hamiltonian that merges the classical Ising model and the statistical theory of correlated random networks. As a result, we obtain rich phase diagrams with different phase transitions both in the state of nodes and in the graph topology. We argue that the coupling between the spin dynamics and the structure of the network is crucial in understanding the complex behavior of real-world systems and omitting one of the approaches renders the description incomplete.

physics.soc-ph↗

arXiv2017

Predicting language diversity with complex network

Evolution and propagation of the world's languages is a complex phenomenon, driven, to a large extent, by social interactions. Multilingual society can be seen as a system of interacting agents, where the interaction leads to a modification of the language spoken by the individuals. Two people can reach the state of full linguistic compatibility due to the positive interactions, like transfer of loanwords. But, on the other hand, if they speak entirely different languages, they will separate from each other. These simple observations make the network science the most suitable framework to describe and analyze dynamics of language change. Although many mechanisms have been explained, we lack a qualitative description of the scaling behavior for different sizes of a population. Here we address the issue of the language diversity in societies of different sizes, and we show that local interactions are crucial to capture characteristics of the empirical data. We propose a model of social interactions, extending the idea from, that explains the growth of the language diversity with the size of a population of country or society. We argue that high clustering and network disintegration are the most important characteristics of models properly describing empirical data. Furthermore, we cancel the contradiction between previous models and the Solomon Islands case. Our results demonstrate the importance of the topology of the network, and the rewiring mechanism in the process of language change.

cs.SI↗

arXiv2016

Coevolving complex networks in the model of social interactions

We analyze Axelrod's model of social interactions on coevolving complex networks. We introduce four extensions with different mechanisms of edge rewiring. The models are intended to catch two kinds of interactions - preferential attachment, which can be observed in scientists or actors collaborations, and local rewiring, which can be observed in friendship formation in everyday relations. Numerical simulations show that proposed dynamics can lead to the power-law distribution of nodes' degree and high value of the clustering coefficient, while still retaining the small-world effect in three models. All models are characterized by two phase transitions of a different nature. In case of local rewiring we obtain order-disorder discontinuous phase transition even in the thermodynamic limit, while in case of long-distance switching discontinuity disappears in the thermodynamic limit, leaving one continuous phase transition. In addition, we discover a new and universal characteristic of the second transition point - an abrupt increase of the clustering coefficient, due to formation of many small complete subgraphs inside the network.

physics.soc-ph↗

arXiv2016

Continuous-Time Random Walk with multi-step memory: An application to market dynamics

A novel version of the Continuous-Time Random Walk (CTRW) model with memory is developed. This memory means the dependence between arbitrary number of successive jumps of the process, while waiting times between jumps are considered as i.i.d. random variables. The dependence was found by analysis of empirical histograms for the stochastic process of a single share price on a market within the high frequency time scale, and justified theoretically by considering bid-ask bounce mechanism containing some delay characteristic for any double-auction market. Our model turns out to be exactly analytically solvable, which enables a direct comparison of its predictions with their empirical counterparts, for instance, with empirical velocity autocorrelation function. Thus this paper significantly extends the capabilities of the CTRW formalism.

physics.data-an↗

arXiv2016

Can banks default overnight? Modeling endogenous contagion on O/N interbank market

We propose a new model of the liquidity driven banking system focusing on overnight interbank loans. This significant branch of the interbank market is commonly neglected in the banking system modeling and systemic risk analysis. We construct a model where banks are allowed to use both the interbank and the securities markets to manage their liquidity demand and supply as driven by prudential requirements in a volatile environment. The network of interbank loans is dynamic and simulated every day. We show how only the intrasystem cash fluctuations, without any external shocks, may lead to systemic defaults, what may be a symptom of the self-organized criticality of the system. We also analyze the impact of different prudential regulations and market conditions on the interbank market resilience. We confirm that central bank's asset purchase programs, limiting the declines in government bond prices, can successfully stabilize bank's liquidity demand. The model can be used to analyze the interbank market impact of macroprudential tools.

econ.GN↗

arXiv2015

Universality of market superstatistics

We use a continuous-time random walk (CTRW) to model market fluctuation data from times when traders experience excessive losses or excessive profits. We analytically derive "superstatistics" that accurately model empirical market activity data (supplied by Bogachev, Ludescher, Tsallis, and Bunde)that exhibit transition thresholds. We measure the interevent times between excessive losses and excessive profits, and use the mean interevent time as a control variable to derive a universal description of empirical data collapse. Our superstatistic value is a weighted sum of two components, (i) a powerlaw corrected by the lower incomplete gamma function, which asymptotically tends toward robustness but initially gives an exponential, and (ii) a powerlaw damped by the upper incomplete gamma function, which tends toward the power-law only during short interevent times. We find that the scaling shape exponents that drive both components subordinate themselves and a "superscaling" configuration emerges. We use superstatistics to describe the hierarchical activity when component (i) reproduces the negative feedback and component (ii) reproduces the stylized fact of volatility clustering. Our results indicate that there is a functional (but not literal) balance between excessive profits and excessive losses that can be described using the same body of superstatistics, but different calibration values and driving parameters.

q-fin.ST↗

arXiv2014

Universality of Tsallis q-exponential of interoccurrence times within the microscopic model of cunning agents

We proposed the agent-based model of financial markets where agents (or traders) are represented by three-state spins located on the plane lattice or social network. The spin variable represents only the individual opinion (advice) that each trader gives to his nearest neighbors. In the model the agents can be considered as cunning. For instance, although agent having currently a maximal value of the spin advises his nearest neighbors to buy some stocks he, perfidiously, will sell some stocks in the next Monte Carlo step or will occupy a neutral position. In general, the trader has three possibilities: he can buy some stocks if his opinion change within a single time step is positive, sell some stocks if this change is negative, or remain inactive if his opinion is unchanged. The predictions of our model, found by simulations, well agree with the empirical universal distribution of interoccurrence times between daily losses below negative thresholds following the Tsallis q-exponential.

q-fin.ST↗

arXiv2013

Reinterpretation of Sieczka-Hołyst financial market model

In this work we essentially reinterpreted the Sieczka-Hołyst (SH) model to make it more suited for description of real markets. For instance, this reinterpretation made it possible to consider agents as crafty. These agents encourage their neighbors to buy some stocks if agents have an opportunity to sell these stocks. Also, agents encourage them to sell some stocks if agents have an opposite opportunity. Furthermore, in our interpretation price changes respond only to the agents' opinions change. This kind of respond protects the stock market dynamics against the paradox (present in the SH model), where all agents e.g. buy stocks while the corresponding prices remain unchanged. In this work we found circumstances, where distributions of returns (obtained for quite different time scales) either obey power-law or have at least fat tails. We obtained these distributions from numerical simulations performed in the frame of our approach.

q-fin.ST↗

arXiv2010

Super-extreme event's influence on a Weierstrass-Mandelbrot Continuous-Time Random Walk

Two utmost cases of super-extreme event's influence on the velocity autocorrelation function (VAF) were considered. The VAF itself was derived within the hierarchical Weierstrass-Mandelbrot Continuous-Time Random Walk (WM-CTRW) formalism, which is able to cover a broad spectrum of continuous-time random walks. Firstly, we studied a super-extreme event in a form of a sustained drift, whose duration time is much longer than that of any other event. Secondly, we considered a super-extreme event in the form of a shock with the size and velocity much larger than those corresponding to any other event. We found that the appearance of these super-extreme events substantially changes the results determined by extreme events (the so called "black swans") that are endogenous to the WM-CTRW process. For example, changes of the VAF in the latter case are in the form of some instability and distinctly differ from those caused in the former case. In each case these changes are quite different compared to the situation without super-extreme events suggesting the possibility to detect them in natural system if they occur.

physics.data-an↗