arXiv subjects

Anna Chmiel

Publications and source records attributed to Anna Chmiel.

18 recordsLinked to original sources

arXiv2026

Dynamics-structure interchangeability in binary opinion models on multiplex networks

We examine the interchangeability between two duplex systems with opinion dynamics: one characterized by different dynamics parameters $a_1$ and $a_2$ on each layer and full node overlap, and the second with the same parameter $a_1$ on both layers but only partial node overlap $r$. We introduce a general framework for identifying the critical line between the ordered and disordered phases, thereby translating one system into another. The description is supported by several examples of opinion dynamics models and a rigorous measure of the distance between the stationary solutions of the rate equations in both settings. Our results show that even large values of $r$ are sufficient to obtain very good correspondence between the two settings.

physics.soc-ph↗

arXiv2025

Temperature-Noise Interplay in a Coupled Model of Opinion Dynamics

We consider a coupled system mimicking opinion formation under the influence of a group of $q$ neighbors ($q$-lobby) that consists of an Ising part governed by temperature-like parameter $T$ and a voter dynamics parameterized by noise probability $p$ (independence of choice). Using rigorous analytical calculations backed by extensive Monte Carlo simulations, we examine the interplay between these two quantities. Based on the theory of phase transitions, we derive the relation between $T$ and $p$ at the critical line dividing the ordered and disordered phases, which takes a very simple and generic form $T(p-a)=b$ in the high temperature limit. For specific lobby sizes, we show where the temperature and noise are balanced, and we hint that for large $q$, the temperature-like dynamics prevails.

cond-mat.stat-mech↗

arXiv2024

q-neighbor Ising model on a polarized network

In this paper, we examine the interplay between the lobby size $q$ in the $q$-neighbor Ising model of opinion formation (Phys. Rev. E 92, 052105) and the level of overlap $v$ of two fully connected graphs. Results suggest that for each lobby size $q \ge 3$, a specific level of overlap $v^*$ exists, which destroys initially polarized clusters of opinions. By performing Monte-Carlo simulations, backed by an analytical approach, we show that the dependence of the $v^*$ on the lobby size $q$ is far from trivial in the absence of temperature, showing consecutive maximum and minimum, that additionally depends on the parity of $q$. The temperature is, in general, a destructive factor; its increase leads to the collapse of polarized clusters for smaller values of $v$ and additionally brings a substantial decrease in the level of polarization. However, we show that this behavior is counter-intuitively inverted for specific lobby sizes and temperature ranges.

cond-mat.stat-mech↗

arXiv2020

A veritable zoology of successive phase transitions in the asymmetric $q$-voter model on multiplex networks

We analyze a nonlinear $q$-voter model with stochastic noise, interpreted in the social context as independence, on a duplex network. The size of the lobby $q$ (i.e., the pressure group) is a crucial parameter that changes the behavior of the system. The $q$-voter model has been applied on multiplex networks in a previous work [Phys. Rev E. 92. 052812. (2015)], and it has been shown that the character of the phase transition depends on the number of levels in the multiplex network as well as the value of $q$. Here we study phase transition character in the case when on each level of the network the lobby size is different, resulting in two parameters $q_1$ and $q_2$. We find evidence of successive phase transitions when a continuous phase transition is followed by a discontinuous one or two consecutive discontinuous phases appear, depending on the parameter. When analyzing this system, we even encounter mixed-order (or hybrid) phase transition. We perform simulations and obtain supporting analytical solutions on a simple multiplex case - a duplex clique, which consists of two fully overlapped complete graphs (cliques).

cond-mat.stat-mech↗

arXiv2019

Truncated Lévy Walks and Superdiffusion in Boltzmann-Gibbs Equilibrium of the Hamiltonian Mean-Field Model

The Hamiltonian Mean-Field (HMF) model belongs to a broad class of statistical physics models with non-additive Hamiltonians that reveal many non-trivial properties, such as non-equivalence of statistical ensembles, ergodicity breaking, and negative specific heat. With this paper, we add to this set another intriguing feature, which is that of super-diffusive equilibrium dynamics. Using molecular dynamics techniques, we compare the diffusive properties of the HMF model in the quasi-stationary metastable state (QSS) and in the Boltzmann-Gibbs (BG) regime. In contrast to the current state of knowledge, we show that Lévy walks underlying super-diffusion in QSS do not disappear when the system settles in the thermodynamic equilibrium. We demonstrate that it is extremely difficult to distinguish QSS from the BG regime, by only examining the statistics of Lévy walks in HMF particle trajectories. We construct a simple stochastic model based on the truncated Lévy walks with rests that quantitatively resembles diffusion behavior observed in both stages of the HMF dynamics.

cond-mat.stat-mech↗

arXiv2017

Tricriticality in the $q$-neighbor Ising model on a partially duplex clique

We analyze a modified kinetic Ising model, so called $q$-neighbor Ising model, with Metropolis dynamics, [Phys. Rev. E 92, 052105], on a duplex clique and a partially duplex clique. In the $q$-neighbor Ising model each spin interacts only with $q$ spins randomly chosen from its whole neighborhood. In the case of a duplex clique the change of a spin is allowed only if both levels simultaneously induce this change. Due to the mean-field like nature of the model we are able to derive the analytic form of transition probabilities and solve the corresponding master equation. The existence of the second level changes dramatically the character of the phase transition. In the case of the monoplex clique, the $q$-neighbor Ising model exhibits continuous phase transition for $q=3$, discontinuous phase transition for $q \ge 4$ and for $q=1$ and $q=2$ the phase transition is not observed. On the other hand, in the case of the duplex clique continuous phase transitions are observed for all values of $q$, even for $q=1$ and $q=2$. Subsequently we introduce a partially duplex clique, parametrized by $r \in [0,1]$, which allows us to tune the network from monoplex ($r=0$) to duplex ($r=1$). Such a generalized topology, in which a fraction $r$ of all nodes appear on both levels, allows to obtain the critical value of $r=r^*(q)$ at which a tricriticality (switch from continuous to discontinuous phase transition) appears.

cond-mat.stat-mech↗

arXiv2017

Quantifying layer similarity in multiplex networks: a systematic study

Computing layer similarities is an important way of characterizing multiplex networks because various static properties and dynamic processes depend on the relationships between layers. We provide a taxonomy and experimental evaluation of approaches to compare layers in multiplex networks. Our taxonomy includes, systematizes and extends existing approaches, and is complemented by a set of practical guidelines on how to apply them.

cs.SI↗

arXiv2017

Exact combinatorial approach to finite coagulating systems

The paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete, and the binary aggregation alone governs the time evolution of the systems. By considering the growth histories of all possible clusters, the exact expression is derived for the probability of a coagulating system with an arbitrary kernel being found in a given cluster configuration when monodisperse initial conditions are applied. Then, this probability is used to calculate the time-dependent distribution for the number of clusters of a given size, the average number of such clusters and that average's standard deviation. The correctness of our general expressions is proved based on the (analytical and numerical) results obtained for systems with the constant kernel. In addition, the results obtained are compared with the results arising from the solutions to the mean-field Smoluchowski coagulation equation, indicating its weak points. The paper closes with a brief discussion on the extensibility to other systems of the approach presented herein, emphasizing the issue of arbitrary initial conditions.

cond-mat.stat-mech↗

arXiv2017

Kinetic Ising models with various single-spin flip dynamics on quenched and annealed random regular graphs

We investigate a kinetic Ising model with several single-spin flip dynamics (including Metropolis and heat-bath) on quenched and annealed random regular graphs. As expected, on the quenched structures all proposed algorithms reproduce the same results since the conditions for the detailed balance and the Boltzmann distribution in an equilibrium are satisfied. However, on the annealed graphs situation is far less clear -- the network annealing disturbs the equilibrium moving the system away from it. Consequently, distinct dynamics lead to different steady states. We show that some algorithms are more resistant to the annealed disorder, which causes only small quantitative changes in the model behavior. On the other hand, there are dynamics for which the influence of annealing on the system is significant, and qualitative changes arise like switching the type of phase transition from continuous to discontinuous one. We try to identify features of the proposed dynamics which are responsible for the above phenomenon.

cond-mat.stat-mech↗

arXiv2016

Temporal Taylor's scaling of facial electromyography and electrodermal activity in the course of emotional stimulation

High frequency psychophysiological data create a challenge for quantitative modeling based on Big Data tools since they reflect the complexity of processes taking place in human body and its responses to external events. Here we present studies of fluctuations in facial electromyography (fEMG) and electrodermal activity (EDA) massive time series and changes of such signals in the course of emotional stimulation. Zygomaticus major (ZYG, "smiling" muscle) activity, corrugator supercilii (COR, "frowning"bmuscle) activity, and phasic skin conductance (PHSC, sweating) levels of 65 participants were recorded during experiments that involved exposure to emotional stimuli (i.e., IAPS images, reading and writing messages on an artificial online discussion board). Temporal Taylor's fluctuations scaling were found when signals for various participants and during various types of emotional events were compared. Values of scaling exponents were close to 1, suggesting an external origin of system dynamics and/or strong interactions between system's basic elements (e.g., muscle fibres). Our statistical analysis shows that the scaling exponents enable identification of high valence and arousal levels in ZYG and COR signals.

q-bio.NC↗

arXiv2015

Oscillating hysteresis in the q-neighbor Ising model

We modify the kinetic Ising model with Metropolis dynamics, allowing each spin to interact only with $q$ spins randomly chosen from the whole system, which corresponds to the topology of a complete graph. We show that the model with $q \ge 3$ exhibits a phase transition between ferromagnetic and paramagnetic phases at temperature $T^*$, which linearly increases with $q$. Moreover, we show that for $q=3$ the phase transition is continuous and discontinuous for larger values of $q$. For $q>3$ the hysteresis exhibits oscillatory behavior -- expanding for even values of $q$ and shrinking for odd values of $q$. If only simulation results were taken into account, this phenomenon could be mistakenly interpreted as switching from discontinuous to continuous phase transitions or even as evidence of the so-called mixed phase transitions. Due to the mean-field like nature of the model we are able to calculate analytically not only the stationary value of the order parameter but also precisely determine the hysteresis and the effective potential showing stable, unstable and metastable steady states. The main message is that in case of non-equilibrium systems the hysteresis can behave in an odd way and computer simulations alone may mistakenly lead to incorrect conclusions.

cond-mat.stat-mech↗

arXiv2015

Phase transitions in the q-voter model with noise on a duplex clique

We study a nonlinear q-voter model with stochastic noise, interpreted in the social context as independence, on a duplex network. To study the role of the multi-levelness we propose three methods of transferring the model from a mono- to a multiplex network. They take into account two criteria -- one related to the status of independence (LOCAL vs. GLOBAL) and one related to peer pressure (AND vs. OR). In order to examine the influence of the presence of more than one level in the social network, we perform simulations on a particularly simple multiplex -- a duplex clique, which consists of two fully overlapped complete graphs (cliques). Solving numerically the rate equation and simultaneously conducting Monte Carlo simulations, we provide evidence that even a simple rearrangement into a duplex topology may lead to significant changes in the observed behavior. However, qualitative changes in the phase transitions can be observed for only one of the considered rules -- LOCAL&AND. For this rule the phase transition becomes discontinuous for q=5, whereas for a monoplex such a behavior is observed for q=6. Interestingly, only this rule admits construction of realistic variants of the model, in line with recent social experiments.

physics.soc-ph↗

arXiv2014

Spreading of diseases through comorbidity networks across life and gender

The state of health of patients is typically not characterized by a single disease alone but by multiple (comorbid) medical conditions. These comorbidities may depend strongly on age and gender. We propose a specific phenomenological comorbidity network of human diseases that is based on medical claims data of the entire population of Austria. The network is constructed from a two-layer multiplex network, where in one layer the links represent the conditional probability for a comorbidity, and in the other the links contain the respective statistical significance. We show that the network undergoes dramatic structural changes across the lifetime of patients.Disease networks for children consist of a single, strongly inter-connected cluster. During adolescence and adulthood further disease clusters emerge that are related to specific classes of diseases, such as circulatory, mental, or genitourinary disorders.For people above 65 these clusters start to merge and highly connected hubs dominate the network. These hubs are related to hypertension, chronic ischemic heart diseases, and chronic obstructive pulmonary diseases. We introduce a simple diffusion model to understand the spreading of diseases on the disease network at the population level. For the first time we are able to show that patients predominantly develop diseases which are in close network-proximity to disorders that they already suffer. The model explains more than 85 % of the variance of all disease incidents in the population. The presented methodology could be of importance for anticipating age-dependent disease-profiles for entire populations, and for validation and of prevention schemes.

physics.med-ph↗

arXiv2013

Quantifying age- and gender-related diabetes comorbidity risks using nation-wide big claims data

Currently emerging "big data" techniques are reshaping medical science into a data science. Medical claims data allow assessing an entire nation's health state in a quantitative way, in particular with regard to the occurrences and consequences of chronic and pandemic diseases like diabetes. We develop a quantitative, statistical approach to test for associations between the incidence of type 1 or type 2 diabetes and any possible other disease as provided by the ICD10 diagnosis codes using a complete set of Austrian inpatient data. With a new co-occurrence analysis the relative risks for each possible comorbidity are studied as a function of patient age and gender, a temporal analysis investigates whether the onset of diabetes typically precedes or follows the onset of the other disease. The samples is always of maximal size, i.e. contains all patients with that comorbidity within the country. The present study is an equivalent of almost 40,000 studies, all with maximum patient number available. Out of more than thousand possible associations, 123 comorbid diseases for type 1 or type 2 diabetes are identified at high significance levels. Well known diabetic comorbidities are recovered, such as retinopathies, hypertension, chronic kidney diseases, etc. This validates the method. Additionally, a number of comorbidities are identified which have only been recognized to a lesser extent, for example epilepsy, sepsis, or mental disorders. The temporal evolution, age, and gender-dependence of these comorbidities are discussed. The new statistical-network methodology developed here can be readily applied to other chronic diseases.

stat.AP↗

arXiv2012

Dynamical phase transition due to preferential cluster growth of collective emotions in online communities

We consider a preferential cluster growth in a one-dimensional stochastic model describing the dynamics of a binary chain with long-range memory. The model is driven by data corresponding to emotional patterns observed during online communities' discussions. The system undergoes a dynamical phase transition. For low values of the preference exponent, both states are observed during the string evolution in the majority of simulated discussion threads. When the exponent crosses a critical value, in the majority of threads an ordered phase emerges, i.e. from a certain time moment only one state is represented. The transition becomes discontinuous in the thermodynamical limit when the discussions are infinitely long and even an infinitely small preference exponent leads to the ordering behavior in every discussion thread. Numerical simulations are in a good agreement with approximated analytical formula.

physics.soc-ph↗

arXiv2011

Collective emotions online and their influence on community life

E-communities, social groups interacting online, have recently become an object of interdisciplinary research. As with face-to-face meetings, Internet exchanges may not only include factual information but also emotional information - how participants feel about the subject discussed or other group members. Emotions are known to be important in affecting interaction partners in offline communication in many ways. Could emotions in Internet exchanges affect others and systematically influence quantitative and qualitative aspects of the trajectory of e-communities? The development of automatic sentiment analysis has made large scale emotion detection and analysis possible using text messages collected from the web. It is not clear if emotions in e-communities primarily derive from individual group members' personalities or if they result from intra-group interactions, and whether they influence group activities. We show the collective character of affective phenomena on a large scale as observed in 4 million posts downloaded from Blogs, Digg and BBC forums. To test whether the emotions of a community member may influence the emotions of others, posts were grouped into clusters of messages with similar emotional valences. The frequency of long clusters was much higher than it would be if emotions occurred at random. Distributions for cluster lengths can be explained by preferential processes because conditional probabilities for consecutive messages grow as a power law with cluster length. For BBC forum threads, average discussion lengths were higher for larger values of absolute average emotional valence in the first ten comments and the average amount of emotion in messages fell during discussions. Our results prove that collective emotional states can be created and modulated via Internet communication and that emotional expressiveness is the fuel that sustains some e-communities.

physics.soc-ph↗

arXiv2011

Negative emotions boost users activity at BBC Forum

We present an empirical study of user activity in online BBC discussion forums, measured by the number of posts written by individual debaters and the average sentiment of these posts. Nearly 2.5 million posts from over 18 thousand users were investigated. Scale free distributions were observed for activity in individual discussion threads as well as for overall activity. The number of unique users in a thread normalized by the thread length decays with thread length, suggesting that thread life is sustained by mutual discussions rather than by independent comments. Automatic sentiment analysis shows that most posts contain negative emotions and the most active users in individual threads express predominantly negative sentiments. It follows that the average emotion of longer threads is more negative and that threads can be sustained by negative comments. An agent based computer simulation model has been used to reproduce several essential characteristics of the analyzed system. The model stresses the role of discussions between users, especially emotionally laden quarrels between supporters of opposite opinions, and represents many observed statistics of the forum.

cs.HC↗

arXiv2010

Flow of emotional messages in artificial social networks

Models of message flows in an artificial group of users communicating via the Internet are introduced and investigated using numerical simulations. We assumed that messages possess an emotional character with a positive valence and that the willingness to send the next affective message to a given person increases with the number of messages received from this person. As a result, the weights of links between group members evolve over time. Memory effects are introduced, taking into account that the preferential selection of message receivers depends on the communication intensity during the recent period only. We also model the phenomenon of secondary social sharing when the reception of an emotional e-mail triggers the distribution of several emotional e-mails to other people.

physics.soc-ph↗