arXiv subjects

Krzysztof Malarz

Publications and source records attributed to Krzysztof Malarz.

At least 37 records · Page 2Linked to original sources

arXiv2021

Comment on `Phase transition in a network model of social balance with Glauber dynamics'

In a recent work [R. Shojaei et al, Physical Review E 100, 022303 (2019)] the Authors calculate numerically the critical temperature $T_c$ of the balanced-imbalanced phase transition in a fully connected graph. According to their findings, $T_c$ decreases with the number of nodes $N$. Here we calculate the same critical temperature using the heat-bath algorithm. We show that $T_c$ increases with $N$ as $N^γ$, with $γ$ close to 0.5 or 1.0. This value depends on the initial fraction of positive bonds.

physics.soc-ph↗

arXiv2020

Site percolation thresholds on triangular lattice with complex neighborhoods

We determine thresholds $p_c$ for random site percolation on a triangular lattice for neighbourhoods containing nearest (NN), next-nearest (2NN), next-next-nearest (3NN), next-next-next-nearest (4NN) and next-next-next-next-nearest (5NN) neighbours, and their combinations forming regular hexagons (3NN+2NN+NN, 5NN+4NN+NN, 5NN+4NN+3NN+2NN, 5NN+4NN+3NN+2NN+NN). We use a fast Monte Carlo algorithm, by Newman and Ziff [M. E. J. Newman and R. M. Ziff, Physical Review E 64, 016706 (2001)], for obtaining the dependence of the largest cluster size on occupation probability. The method is combined with a method, by Bastas et al. [N. Bastas, K. Kosmidis, P. Giazitzidis, and M. Maragakis, Physical Review E 90, 062101 (2014)], of estimating thresholds from low statistics data. The estimated values of percolation thresholds are $p_c(\text{4NN})=0.192410(43)$, $p_c(\text{3NN+2NN})=0.232008(38)$, $p_c(\text{5NN+4NN})=0.140286(5)$, $p_c(\text{3NN+2NN+NN})=0.215484(19)$, $p_c(\text{5NN+4NN+NN})=0.131792(58)$, $p_c(\text{5NN+4NN+3NN+2NN})=0.117579(41)$, $p_c(\text{5NN+4NN+3NN+2NN+NN})=0.115847(21)$. The method is tested on the standard case of site percolation on triangular lattice, where $p_c(\text{NN})=p_c(\text{2NN})=p_c(\text{3NN})=p_c(\text{5NN})=\frac{1}{2}$ is recovered with five digits accuracy $p_c(\text{NN})=0.500029(46)$ by averaging over one thousand lattice realisations only.

cond-mat.stat-mech↗

arXiv2020

Expulsion from structurally balanced paradise

We perform simulations of structural balance evolution on a triangular lattice using the heat-bath algorithm. In contrast to similar approaches---but applied to analysis of complete graphs---the triangular lattice topology successfully prevents the occurrence of even partial Heider balance. Starting with the state of Heider's paradise, it is just a matter of time when the evolution of the system leads to an unbalanced and disordered state. The time of the system relaxation does not depend on the system size. The lack of any signs of a balanced state was not observed in earlier investigated systems dealing with the structural balance.

physics.soc-ph↗

arXiv2020

Are randomness of behavior and information flow important to opinion forming in organization?

We examine how the randomness of behavior and the flow of information between agents affect the formation of opinions. Our main research involves the process of opinion evolution, opinion clusters formation and studying the probability of sustaining opinion. The results show that opinion formation (clustering of opinion) is influenced by both flow of information between agents (interactions outside the closest neighbors) and randomness in adopting opinions.

econ.TH↗

arXiv2020

Ageing of complex networks

Many real-world complex networks arise as a result of a competition between growth and rewiring processes. Usually the initial part of the evolution is dominated by growth while the later one rather by rewiring. The initial growth allows the network to reach a certain size while rewiring to optimise its function and topology. As a model example we consider tree networks which first grow in a stochastic process of node attachment and then age in a stochastic process of local topology changes. The ageing is implemented as a Markov process that preserves the node-degree distribution. We quantify differences between the initial and aged network topologies and study the dynamics of the evolution. We implement two versions of the ageing dynamics. One is based on reshuffling of leaves and the other on reshuffling of branches. The latter one generates much faster ageing due to non-local nature of changes.

cond-mat.stat-mech↗

arXiv2020

Heider balance of a chain of actors as dependent on the interaction range and a thermal noise

The Heider balance is investigated in a chain of actors, with periodic boundary conditions and the neighborhood of range $r$, with $r$ as a parameter. Two model dynamics are applied: a deterministic cellular automaton (Malarz et al, Physica D 411 (2020) 132556) and the heat-bath algorithm, with the density of unbalanced-balanced triads in the role of energy. The outcome is a spectrum of energy in stationary and blinking states and a balanced-unbalanced network transition driven by thermal noise. The critical point $T_c$ increases with the range $r$ and it does not depend on the system size.

physics.soc-ph↗

arXiv2020

Towards the Heider balance with a cellular automaton

The state of structural balance (termed also `Heider balance') of a social network is often discussed in social psychology and sociophysics. In this state, actors at network nodes classify other individuals as enemies or friends. Hence, the network contains two kinds of links: positive and negative. Here a new cellular automaton is designed and investigated, which mimics the time evolution towards the structural balance. The automaton is deterministic and synchronous. The medium is the triangular lattice with some fraction $f$ of links removed. We analyse the number of unbalanced triads (parameterized as `energy'), the frequencies of balanced triads and correlations between them. The time evolution enhances the local correlations of balanced triads. Local configurations of unbalanced triads are found which are blinking with period of two time steps.

physics.soc-ph↗

arXiv2020

Noise induced unanimity and disorder in opinion formation

We propose an opinion dynamics model based on Latané's social impact theory. Actors in this model are heterogeneous and, in addition to opinions, are characterised by their varying levels of persuasion and support. The model is tested for two and three initial opinions randomly distributed among actors. We examine how the noise (randomness of behaviour) and the flow of information among actors affect the formation and spread of opinions. Our main research involves the process of opinion formation and finding phases of the system in terms of parameters describing noise and flow of the information for two and three opinions available in the system. The results show that opinion formation and spread are influenced by both (i) flow of information among actors (effective range of interactions among actors) and (ii) noise (randomness in adopting opinions). The noise not only leads to opinions disorder but also it promotes consensus under certain conditions.

physics.soc-ph↗

arXiv2019

Paradox of integration---Cellular automata approach

We discuss the self-deprecating strategy introduced by Peter Blau as one of stages of the process of social integration. Recently we have introduced a two-dimensional space of status, real and surface one ($A$ and $B$), and we have demonstrated that with this setup, the self-deprecating strategy efficiently prevents the rejection [K. Malarz and K. Kulakowski, International Journal of Modern Physics C 30, 1950040 (2019)]. There, the process of reducing the conflict was described by master equations, i.e. a set of differential equations describing evolution of density $v(A,B)$ of actors of status $(A,B)$. Here we reformulate the problem in terms of probabilistic cellular automata. The obtained results for number $n(A,B)$ of actors of status $(A,B)$ are qualitatively the same as in the previous approach, both for synchronous and asynchronous version of the automaton. Namely, an enhancement of the surface status compensates a deficiency of the real one.

physics.soc-ph↗

arXiv2019

Multi-choice opinion dynamics model based on Latane theory

In this paper Nowak--Szamrej-Latané model is reconsidered. This computerised model of opinion formation bases on Latané theory of social impact. We modify this model to allow for multi (more than two) opinions. With computer simulations we show that in the modified model the signatures of order/disorder phase transition are still observed. The transition may be observed in the average fraction of actors sharing the $i$-th opinion, its variation and also average number of clusters of actors with the same opinion and the average size of the largest cluster of actors sharing the same opinion. Also an influence of model control parameters on simulation results is shortly reviewed. For a homogeneous society with identical actors' supportiveness and persuasiveness the critical social temperature $T_C$ decreases with an increase of available opinions $K$ from $T_C=6.1$ ($K=2$) via 4.7, 4.1 to $T_C=3.6$ for $K=3$, 4, 5, respectively.

physics.soc-ph↗

arXiv2017

Influence of a range of interaction among agents on efficiency and effectiveness of knowledge transfer within an organisation

In this study we examined how the size of non-formal groups between organization members affect the transfer of knowledge in the context of the efficiency and effectiveness of this process. To analyse the dynamics of the transfer of knowledge the cellular automata model was used. The model is based on local interactions between members of the organization, that take place in the nearest neighbourhood. These groups of close neighbours are represented by von Neumann's neighbourhood (four nearest-neighbours) and Moore's neighbourhood (four nearest-neighbours and four next-nearest neighbours) and complex neighbourhood (four nearest neighbours, four next-nearest neighbours and four next-next-neighbours). The results of the simulation show the influence of the size of the neighbourhood on the efficiency of knowledge transfer.

physics.soc-ph↗

arXiv2017

Searching for effective and efficient way of knowledge transfer within an organization

In this paper three models of knowledge transfer in organization are considered. In the first model (A) the transfer of chunks of knowledge among agents is possible only when the sender has exactly one more chunks of knowledge than recipient. This is not dissimilar with bounded confidence model of opinion dynamics. In the second model (B) the knowledge transfer take place when sender is "smarter" than recipient. Finally, in the third scenario (model C) we allow for knowledge transfer also when sender posses the same or greater number of chunks of knowledge as recipient. The simulation bases on cellular automata technique. The organization members occupy nodes of square lattice and they interact only with their nearest neighbors. With computer simulations we show, that the efficiency and the effectiveness of knowledge transfer i) for model C is better than for model B ii) and it is worse for model A than for model B.

physics.soc-ph↗

arXiv2017

Model of knowledge transfer within an organisation

Many studies show that the acquisition of knowledge is the key to build competitive advantage of companies. We propose a simple model of knowledge transfer within the organization and we implement the proposed model using cellular automata technique. In this paper the organisation is considered in the context of complex systems. In this perspective, the main role in organisation is played by the network of informal contacts and the distributed leadership. The goal of this paper is to check which factors influence the efficiency and effectiveness of knowledge transfer. Our studies indicate a significant role of initial concentration of chunks of knowledge for knowledge transfer process, and the results suggest taking action in the organisation to shorten the distance (social distance) between people with different levels of knowledge, or working out incentives to share knowledge.

physics.soc-ph↗

arXiv2015

The working group performance modeled by a bi-layer cellular automaton

The problem `human and work' in a model working group is investigated by means of cellular automata technique. Attitude of members of a group towards work is measured by an indicator of loyalty to the group (the number of agents who carry out their tasks), and lack of loyalty (the number of agents, who give their tasks to other agents). Initially, all agents realize scheduled tasks one-by-one. Agents with the number of scheduled tasks larger than a given threshold change their strategy to unloyal one and start avoiding completing tasks by passing them to their colleagues. Optionally, in some conditions, we allow agents to return to loyal state; hence the rule is hysteretic. Results are presented on an influence of i) the density of tasks, ii) the threshold number of tasks assigned to the agents' forcing him/her for strategy change on the system efficiency. We show that a `black' scenario of the system stacking in a `jammed phase' (with all agents preferring unloyal strategy and having plenty tasks scheduled for realization) may be avoided when return to loyalty is allowed and either i) the number of agents chosen for task realization, or ii) the number of assigned tasks, or iii) the threshold value of assigned tasks, which force the agent to conversion from loyal strategy to unloyal one, or iv) the threshold value of tasks assigned to unloyal agent, which force him/her to task redistribution among his/her neighbors, are smartly chosen.

nlin.CG↗

arXiv2015

Competing contact processes in the Watts-Strogatz network

We investigate two competing contact processes on a set of Watts--Strogatz networks with the clustering coefficient tuned by rewiring. The base for network construction is one-dimensional chain of $N$ sites, where each site $i$ is directly linked to nodes labelled as $i\pm 1$ and $i\pm 2$. So initially, each node has the same degree $k_i=4$. The periodic boundary conditions are assumed as well. For each node $i$ the links to sites $i+1$ and $i+2$ are rewired to two randomly selected nodes so far not-connected to node $i$. An increase of the rewiring probability $q$ influences the nodes degree distribution and the network clusterization coefficient $\mathcal{C}$. For given values of rewiring probability $q$ the set $\mathcal{N}(q)=\{\mathcal{N}_1, \mathcal{N}_2, \cdots, \mathcal{N}_M \}$ of $M$ networks is generated. The network's nodes are decorated with spin-like variables $s_i\in\{S,D\}$. During simulation each $S$ node having a $D$-site in its neighbourhood converts this neighbour from $D$ to $S$ state. Conversely, a node in $D$ state having at least one neighbour also in state $D$-state converts all nearest-neighbours of this pair into $D$-state. The latter is realized with probability $p$. We plot the dependence of the nodes $S$ final density $n_S^T$ on initial nodes $S$ fraction $n_S^0$. Then, we construct the surface of the unstable fixed points in $(\mathcal{C}, p, n_S^0)$ space. The system evolves more often toward $n_S^T=1$ for $(\mathcal{C}, p, n_S^0)$ points situated above this surface while starting simulation with $(\mathcal{C}, p, n_S^0)$ parameters situated below this surface leads system to $n_S^T=0$. The points on this surface correspond to such value of initial fraction $n_S^*$ of $S$ nodes (for fixed values $\mathcal{C}$ and $p$) for which their final density is $n_S^T=\frac{1}{2}$.

physics.soc-ph↗

arXiv2014

Mental ability and common sense in an artificial society

We read newspapers and watch TV every day. There are many issues and many controversies. Since media are free, we can hear arguments from every possible side. How do we decide what is wrong or right? The first condition to accept a message is to understand it; messages that are too sophisticated are ignored. So it seems reasonable to assume that our understanding depends on our ability and our current knowledge. Here we show that the consequences of this statement are surprising and funny.

physics.soc-ph↗

arXiv2011

Bounded confidence model: addressed information maintain diversity of opinions

A community of agents is subject to a stream of messages, which are represented as points on a plane of issues. Messages are sent by media and by agents themselves. Messages from media shape the public opinion. They are unbiased, i.e. positive and negative opinions on a given issue appear with equal frequencies. In our previous work, the only criterion to receive a message by an agent is if the distance between this message and the ones received earlier does not exceed the given value of the tolerance parameter. Here we introduce a possibility to address a message to a given neighbour. We show that this option reduces the unanimity effect, what improves the collective performance.

physics.soc-ph↗

arXiv2011

Simple cubic random-site percolation thresholds for complex neighbourhoods

In this communication with computer simulation we evaluate simple cubic random-site percolation thresholds for neighbourhoods including the nearest neighbours (NN), the next-nearest neighbours (2NN) and the next-next-nearest neighbours (3NN). Our estimations base on finite-size scaling analysis of the percolation probability vs. site occupation probability plots. The Hoshen--Kopelman algorithm has been applied for cluster labelling. The calculated thresholds are 0.1372(1), 0.1420(1), 0.0976(1), 0.1991(1), 0.1036(1), 0.2455(1) for (NN + 2NN), (NN + 3NN), (NN + 2NN + 3NN), 2NN, (2NN + 3NN), 3NN neighbourhoods, respectively. In contrast to the results obtained for a square lattice the calculated percolation thresholds decrease monotonically with the site coordination number z, at least for our inspected neighbourhoods.

math-ph↗