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Majority-Vote Model on Scale-Free Hypergraphs

100%
Gradowski T., Krawiecki A.
Acta Physica Polonica A
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2015
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vol. 127
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issue 3A
A-55-A-58
EN
Majority-vote models on scale-free hypergraphs are investigated by means of numerical simulations with different variants of system dynamics. Hypergraphs are generalisations of ordinary graphs in which higher order of social organisation is included by introducing hyperedges corresponding to social groups, connecting more than two nodes. In the models under study, opinions of agents (two-state spins) placed in nodes are updated according to a probabilistic rule with control parameter representing social noise. The probability of a single spin flip depends on the average opinion within only one social group (hyperedge) the agent belongs to. This introduces an intermediate level of social interactions, in contrast with the case of networks, where the opinion of an agent usually depends on the average opinion of all neighbours. In all cases under consideration a second-order phase transition to a state with an uniform opinion was found as a function of the social noise, with the critical value of the control parameter and the critical exponents depending on the hypergraph topology and details of the system dynamics (node or hyperedge update).
2
Content available remote

Statistical Properties of the Proportional Voting Process

100%
Gradowski T., Kosiński R.
Acta Physica Polonica A
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2008
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vol. 114
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issue 3
575-580
EN
We propose a model of elections based on the Sznajd model of social interactions in the stochastic Ravasz-Barabási hierarchical network. The results of numerical calculations for the population described by this model were compared with statistical analysis of elections' results to the lower house of Parliament held in Poland in the years of 2001, 2005 and 2007. It is shown that the distribution of votes among candidates for the whole country as well as for the district of Warsaw has the log-normal character. The results from Poland are compared with other countries: Brazil and India. For all the cases log-normal distribution of votes for the candidates from each political party is shown. The probability of gaining a number of votes as a function of the number of the candidate on the list is presented.
3
Content available remote

Majority Vote Model on Multiplex Networks

81%
Krawiecki A., Gradowski T., Siudem G.
Acta Physica Polonica A
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2018
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vol. 133
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issue 6
1433-1440
EN
Majority vote model on multiplex networks with two independently generated layers in the form of scale-free networks is investigated by means of Monte Carlo simulations and heterogeneous mean-field approximation. In a version of the model under study each agent with probability 1-q (0≤q≤1/2) follows the opinions of the majorities of her neighbors within both layers if these opinions are identical; otherwise, she makes decision randomly. The model exhibits second-order ferromagnetic transition as q, the parameter measuring the level of internal noise, is decreased, with critical exponents depending on the details of the degree distributions in the layers. The critical value q_{c} of the parameter q evaluated in the heterogeneous mean-field approximation shows quantitative agreement with that obtained from numerical simulations for a broad range of parameters characterizing the degree distributions of the layers.
4
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Cooperation Model with Costly Punishment

81%
Gradowski T., Mrowinski M., Kosinski R.
Acta Physica Polonica A
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2012
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vol. 121
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issue 2B
B-31-B-33
EN
In recent years the issue of costly punishment in systems where free-riding occurs has been a subject of extensive research in the field of game theory. This issue is present in many areas of human activities like paying taxes, using public transport, wireless Internet or P2P networks. It is one of the most common dilemmas in modern societies. In this work we present a simple model of cooperation with three possible strategies (cooperate, defect or punish). In the model players explore the available strategies according to their interactions with other players. We introduce two groups of parameters. The first group is sociological-like and it describes the social acceptance for the free riding behavior. The other group of parameters describes the economical aspects of the system - the cost and efficiency of punishers. Using differential equations approach, as well as an agent based model, we look for equilibrium properties of the system.
5
Content available remote

Models of Pedestrian Evacuation based on Cellular Automata

81%
Mrowinski M., Gradowski T., Kosinski R.
Acta Physica Polonica A
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2012
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vol. 121
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issue 2B
B-95-B-100
EN
We study two models of pedestrian evacuation based on cellular automata and intelligent agents. We use the static floor field approach and augment it with additional transition rules (random movement and preservation of personal space) in order to model various aspects of human behaviour. Through numerical simulations we investigate pedestrian evacuation from rooms with various geometries (e.g. empty room, classroom). Using heatmaps (density diagrams of pedestrians), average evacuation times, velocity and other parameters we study the effectiveness of evacuation and potential dangers pedestrians may encounter.
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