arXiv subjects

Krzysztof Kułakowski

Publications and source records attributed to Krzysztof Kułakowski.

At least 19 recordsLinked to original sources

arXiv2026

Heider balance in square versus triangular lattices under an external field

We discuss the Heider model in the presence of an external social field. This field breaks the possible symmetry between the probabilities of hostile and friendly relationships. We consider the system in the presence of fluctuations generated by thermal noise and present the results of a comparative study of two-dimensional triangular and square networks with periodic boundary conditions. The results were obtained using three different methods: exact calculations for small systems ($3 \times 3$ square lattice and $2 \times 2$ triangular lattice), Monte Carlo simulations of medium-sized systems ($16 \times 16$ lattices), and exact calculations in the thermodynamic limit (corresponding to infinite size) of certain limiting cases for which analytical solutions are possible. In particular, we exploit the recently discovered equivalence between structurally balanced systems and the Ising model to derive an exact form of the edge magnetization susceptibility for systems in Heider equilibrium.

cond-mat.stat-mech↗

arXiv2026

Relationship between Heider links and Ising spins

We show that the Heider model with an external field is equivalent, in the limit of structural balance, to the Ising model with nearest-neighbor interactions without an external field. More precisely, we claim that the signs of the Heider relations that maintain structural equilibrium in the system can be represented as nearest neighbor Ising spin products. We demonstrate this explicitly for a complete graph and provide a general argument for an arbitrary graph. A consequence of the equivalence is that the system of balanced Heider states undergoes a phase transition, inherited from the Ising model, at a critical value of the social field at which the fluctuations of edge magnetization are maximal.

cond-mat.stat-mech↗

arXiv2025

Heider balance on Archimedean lattices and cliques

We investigate the work function $U(T)$ for the Heider balance, driven by a thermal noise $T$, on several planar networks that contain separated triangles, pairs of triangles, chains of triangles and complex structures of triangles. In simulations, the heat-bath algorithm is applied. Two schemes of link values updating are considered: synchronous and asynchronous (sequential). The latter results are compared with analytical calculations for small cliques. We argue that the actual shape of $U(T)$ is a consequence of a local topology rather than of a macroscopic ordering. Finally, we present the mathematical proof that for any planar lattice, perfect structural (Heider) balance is unreachable at $T>0$.

physics.soc-ph↗

arXiv2022

Status achieved in an organization -- rank dynamics

A new model of an evolution of ranks of employees due to staff turnover in an organization is designed. If the rank is determined only by the performance, the rank shift of incumbents due to the turnover is proportional to the initial rank: the status of high staff is reduced only slightly. This effect that has been observed in the literature. However, if the status also depends on some other variable, the positions of high staff may be greatly deteriorated. In that case, the effect depends nonlinearly on the time $τ$ between subsequent replacements of staff.

physics.soc-ph↗

arXiv2022

Instability of oscillations in the Rosenzweig-MacArthur model of one consumer and two resources

The system of two resources $R_1$, $R_2$ and one consumer $C$ is investigated within the Rosenzweig-MacArthur model with Holling type II functional response. The rates $β_i$ of consumption of resources $i=1,2$ are coupled by the condition $β_1+β_2=1$. The dynamic switching is introduced by a maximization of $C$: $dβ_1/dt=(1/τ) dC/dβ_1$, where the characteristic time $τ$ is large but finite. The space of parameters where both resources coexist is explored numerically. The results indicate that oscillations of $C$ and mutually synchronized $R_i$ which appear at $β_i=0.5$ are destabilized for $β_i$ larger or smaller. Then, the system is driven to one of fixed points where either $β_1>0.5$ and $R_1<R_2$ or the opposite. This behaviour is explained as an inability of the consumer to change the preferred resource, once it is chosen.

physics.soc-ph↗

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

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↗

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↗

arXiv2017

Coupling of link- and node-ordering in the coevolving voter model

We consider the process of reaching the final state in the coevolving voter model. There is a coevolution of state dynamics, where a node can copy a state from a random neighbor with probabilty $1-p$ and link dynamics, where a node can re-wire its link to another node of the same state with probability $p$. That exhibits an absorbing transition to a frozen phase above a critical value of rewiring probability. Our analytical and numerical studies show that in the active phase mean values of magnetization of nodes $n$ and links $m$ tend to the same value that depends on initial conditions. In a similar way mean degrees of spins up and spins down become equal. The system obeys a special statistical conservation law since a linear combination of both types magnetizations averaged over many realizations starting from the same initial conditions is a constant of motion: $Λ\equiv (1-p)μm(t)+pn(t) = const$, where $μ$ is the mean node degree. The final mean magnetization of nodes and links in the active phase is proportional to $Λ$ while the final density of active links is a square function of $Λ$. If the rewiring probability is above a critical value and the system separates into disconnected domains, then the values of nodes and links magnetizations are not the same and final mean degrees of spins up and spins down can be different.

physics.soc-ph↗

arXiv2016

Gain and loss of esteem, direct reciprocity and Heider balance

The effect of gain and loss of esteem is introduced into the equations of time evolution of social relations, hostile or friendly, in a group of actors. The equations allow for asymmetric relations. We prove that in the presence of this asymmetry, the majority of stable solutions are jammed states, i.e. the Heider balance is not attained there. A phase diagram is constructed with three phases: the jammed phase, the balanced phase with two mutually hostile groups, and the phase of so-called paradise, where all relations are friendly.

physics.soc-ph↗

arXiv2015

Simulated hysteresis loop of a bent Fe-rich glass-covered wire

We present new micromagnetic simulations, where an influence of the wire shape on the spatial distribution of internal magnetoelastic stress is taken into account. Local magnetoelastic anisotropy is approximated to be uniaxial, with spatial dependence due to the stress distribution. The hysteresis loop is calculated with the $mumax^3$ software for the wire volume and separately for selected parts of the wire, including the surface. The bistability of the calculated surface hysteresis loops depends on the behaviour of the neighboring part of the inner core, most close to the surface element where the surface loop is measured.

cond-mat.mtrl-sci↗

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

Heider balance, asymmetric ties, and gender segregation

To remove a cognitive dissonance in interpersonal relations, people tend to divide our acquaintances into friendly and hostile parts, both groups internally friendly and mutually hostile. This process is modeled as an evolution towards the Heider balance. A set of differential equations have been proposed and validated (Kulakowski {\it et al}, IJMPC 16 (2005) 707) to model the Heider dynamics of this social and psychological process. Here we generalize the model by including the initial asymmetry of the interprersonal relations and the direct reciprocity effect which removes this asymmetry. Our model is applied to the data on enmity and friendship in 37 school classes and 4 groups of teachers in México. For each class, a stable balanced partition is obtained into two groups. The gender structure of the groups reveals stronger gender segregation in younger classes, i.e. of age below 12 years, a fact consistent with other general empirical results.

physics.soc-ph↗

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↗

arXiv2012

Deterministic ants in labirynth -- information gained by map sharing

A few of ant robots are dropped to a labirynth, formed by a square lattice with a small number of nodes removed. Ants move according to a deterministic algorithm designed to explore all corridors. Each ant remembers the shape of corridors which she has visited. Once two ants met, they share the information acquired. We evaluate how the time of getting a complete information by an ant depends on the number of ants, and how the length known by an ant depends on time. Numerical results are presented in the form of scaling relations.

physics.data-an↗

arXiv2010

Line graphs as social networks

The line graphs are clustered and assortative. They share these topological features with some social networks. We argue that this similarity reveals the cliquey character of the social networks. In the model proposed here, a social network is the line graph of an initial network of families, communities, interest groups, school classes and small companies. These groups play the role of nodes, and individuals are represented by links between these nodes. The picture is supported by the data on the LiveJournal network of about 8 x 10^6 people. In particular, sharp maxima of the observed data of the degree dependence of the clustering coefficient C(k) are associated with cliques in the social network.

physics.soc-ph↗