Searcharxiv⌕ Search

arXiv subjects

Krzysztof Kulakowski

Publications and source records attributed to Krzysztof Kulakowski.

At least 37 records · Page 2Linked to original sources
arXiv2011

Norm breaking in a queue -- athermal phase transition

Standard order-disorder phase transition in the Ising model is described in terms of rates of processes of spin flips. This formulation allows to extend numerous results on phase transition for sciences other than physics of magnetism. We apply it to the problem of norm breaking. Two strategies: to cooperate or to defect, form an analogy to two spin orientations. An example is a crowd at an exit, where to defect means to push others, and to cooperate is to move slowly together.

physics.soc-ph↗
arXiv2010

Probabilistic spreading of information in a spatial network

Spread of information in crowd is analysed in terms of directed percolation in two-dimensional spatial network. We investigate the case when the information transmitted can be incomplete or damaged. The results indicate that for small or moderate probability of errors, it is only the critical connectivity that varies with this probability, but the shape of the transmission velocity curve remains unchanged in a wide range of the probability. The shape of the boundary between those already informed and those yet uninformed becomes complex when the connectivity of agents is small.

physics.soc-ph↗
arXiv2010

Zaller-Deffuant model of mass opinion

Recent formulation of the Zaller model of mass opinion is generalized to include the interaction between agents. The mechanism of interaction is close to the bounded confidence model. The outcome of the simulation is the probability distribution of opinions on a given issue as dependent on the mental capacity of agents. Former result was that a small capacity leads to a strong belief. Here we show that an intensive interaction between agents also leads to a consensus, accepted without doubts.

physics.soc-ph↗
arXiv2009

Indifferents as an interface between Contra and Pro

In most sociophysical simulations on public opinion, only two opinions are allowed: Pro and Contra. However, in all political elections many people do not vote. Here we analyse two models of dynamics of public opinion, taking into account Indifferent voters: {\it i)} the Sznajd model with symmetry Pro-Contra, {\it ii)} the outflow one move voter model, where Contra's are converted to Indifferent by their Pro neighbours. Our results on the Sznajd model are in an overall agreement with the results of the mean field approach and with those known from the initial model formulation. The simulation on the voter model shows that an amount of Contra's who remain after convertion depends on the network topology.

physics.soc-ph↗
arXiv2009

Assortativity in random line graphs

We investigate the degree-degree correlations in the Erdos-Renyi networks, the growing exponential networks and the scale-free networks. We demonstrate that these correlations are the largest for the exponential networks. We calculate also these correlations in the line graphs, formed from the considered networks. Theoretical and numerical results indicate that all the line graphs are assortative, i.e. the degree-degree correlation is positive.

cond-mat.dis-nn↗
arXiv2009

Hate: no choice. Agent simulations

We report our recent simulations on the social processes which -- in our opinion -- lie at the bottom of hate. First simulation deals with the so-called Heider balance where initial purely random preferences split the community into two mutually hostile groups. Second simulation shows that once these groups are formed, the cooperation between them is going to fail. Third simulation provides a numerical illustration of the process of biased learning; the model indicates that lack of objective information is a barrier to new information. Fourth simulation shows that in the presence of a strong conflict between communities hate is unavoidable.

physics.soc-ph↗
arXiv2009

Clustering in random line graphs

We investigate the degree distribution $P(k)$ and the clustering coefficient $C$ of the line graphs constructed on the Erdös-Rényi networks, the exponential and the scale-free growing networks. We show that the character of the degree distribution in these graphs remains Poissonian, exponential and power law, respectively, i.e. the same as in the original networks. When the mean degree $ $ increases, the obtained clustering coefficient $C$ tends to 0.50 for the transformed Erdös-Rényi networks, to 0.53 for the transformed exponential networks and to 0.61 for the transformed scale-free networks. These results are close to theoretical values, obtained with the model assumption that the degree-degree correlations in the initial networks are negligible.

physics.comp-ph↗
arXiv2009

Frustration and collectivity in spatial networks

In random networks decorated with Ising spins, an increase of the density of frustrations reduces the transition temperature of the spin-glass ordering. This result is in contradiction to the Bethe theory. Here we investigate if this effect depends on the small-world property of the network. The results on the specific heat and the spin susceptibility indicate that the effect appears also in spatial networks.

cond-mat.dis-nn↗
arXiv2009

Scaling of spin avalanches in growing networks

Growing networks decorated with antiferromagnetically coupled spins are archetypal examples of complex systems due to the frustration and the multivalley character of their energy landscapes. Here we use the damage spreading method (DS) to investigate the cohesion of spin avalanches in the exponential networks and the scale-free networks. On the contrary to the conventional methods, the results obtained from DS suggest that the avalanche spectra are characterized by the same statistics as the degree distribution in their home networks. Further, the obtained mean range $Z$ of an avalanche, i.e. the maximal distance reached by an avalanche from the damaged site, scales with the avalanche size $s$ as $Z/N^β=f(s/N^α)$, where $α=0.5$ and $β=0.33$. These values are true for both kinds of networks for the number $M$ of nodes to which new nodes are attached between 4 and 10; a check for M=25 confirms these values as well.

cond-mat.dis-nn↗
arXiv2009

To cooperate or to defect? Altruism and reputation

The basic problem in the cooperation theory is to justify the cooperation. Here we propose a new approach, where players are driven by their altruism to cooperate or not. The probability of cooperation depends also on the co-player's reputation. We find that players with positive altruism cooperate and met cooperation. In this approach, payoffs are not relevant. The mechanism is most efficient in the fully connected network.

physics.soc-ph↗
arXiv2008

Magnetism of frustrated regular networks

We consider a regular random network where each node has exactly three neighbours. Ising spins at the network nodes interact antiferromagnetically along the links. The clustering coefficient $C$ is tuned from zero to 1/3 by adding new links. At the same time, the density of geometrically frustrated links increases. We calculate the magnetic specific heat, the spin susceptibility and the Edwards-Anderson order parameter $q$ by means of the heat-bath Monte Carlo simulations. The aim is the transition temperature $T_x$ dependence on the clustering coefficient $C$. The results are compared with the predictions of the Bethe approximation. At C=0, the network is bipartite and the low temperature phase is antiferromagnetic. When $C$ increases, the critical temperature falls down towards the values which are close to the theoretical predictions for the spin-glass phase.

cond-mat.dis-nn↗
arXiv2008

The norm game - how a norm fails

We discuss the simulations of the norm game between players at nodes of a directed random network. The final boldness of the players can vary with the initial one as the $Θ$ function. One of the conditions of this behaviour is that the player who does not punish automatically becomes a defector. The threshold value of the initial boldness can be interpreted as a norm strength. It increases with the punishment and decreases with its cost. Surprisingly, it also decreases with the number of potential punishers. The numerical results are discussed in the context of the statistical data on crimes in Northern Ireland and New Zealand, on divorces in USA, and on the alcohol consumption in Poland.

physics.soc-ph↗
arXiv2008

Opinion polarization in the Receipt-Accept-Sample model

The Zaller theory of opinion formation is reformulated with one free parameter $μ$, which measures the largest possible ideological distance which can be made by a citizen in one mental step. Our numerical results show the transient effects: {\it i)} the political awareness, measured by the number of received messages, increases with time first exponentially, later linearly; {\it ii)} for small $μ$ correlations are present between previously and newly received messages; {\it iii)} these correlation lead to a hyperdiffusion effect in the space of attitudes of messages. Citizens with small $μ$ are more prone to extremal opinions.

physics.soc-ph↗
arXiv2008

Sociophysics - an astriding science

The status of the sociophysics is discussed as placed between the physics and the sociology. In particular we ask if the second law of thermodynamics can be useful in social sciences.

physics.soc-ph↗
arXiv2008

Cops or robbers - a bistable society

The norm game described by Axelrod in 1985 was recently treated with the master equation formalism. Here we discuss the equations, where {\it i)} those who break the norm cannot punish and those who punish cannot break the norm, {\it ii)} the tendency to punish is suppressed if the majority breaks the norm. The second mechanism is new. For some values of the parameters the solution shows the saddle-point bifurcation. Then, two stable solutions are possible, where the majority breaks the norm or the majority punishes. This means, that the norm breaking can be discontinuous, when measured in the social scale. The bistable character is reproduced also with new computer simulations on the Erd{\H o}s--Rényi directed network.

physics.soc-ph↗
arXiv2008

Communities in networks - a continuous approach

A system of differential equations is proposed designed as to identify communities in weighted networks. The input is a symmetric connectivity matrix $A_{ij}$. A priori information on the number of communities is not needed. To verify the dynamics, we prepared sets of separate, fully connected clusters. In this case, the matrix $A$ has a block structure of zeros and units. A noise is introduced as positive random numbers added to zeros and subtracted from units. The task of the dynamics is to reproduce the initial block structure. In this test, the system outperforms the modularity algorithm, if the number of clusters is larger than four.

physics.data-an↗
arXiv2008

When the spatial networks split?

We consider a three dimensional spatial network, where $N$ nodes are randomly distributed within a cube $L\times L\times L$. Each two nodes are connected if their mutual distance does not excess a given cutoff $a$. We analyse numerically the probability distribution of the critical density $ρ_c=N(a_c/L)^3$, where one or more nodes become separated; $ρ_c$ is found to increase with $N$ as $N^{0.105}$, where $N$ is between 20 and 300. The results can be useful for a design of protocols to control sets of wearable sensors.

physics.comp-ph↗