Heavy context dependence---decisions of underground soldiers

An attempt is made to simulate the disclosure of underground soldiers in terms of theory of networks. The coupling mechanism between the network nodes is the possibility that a disclosed soldier is going to disclose also his acquaintances. We calculate the fraction of disclosed soldiers as dependent on the fraction of those who, once disclosed, reveal also their colleagues. The simulation is immersed in the historical context of the Polish Home Army under the communist rule in 1946-49.Comment: 7 pages, 5 figures, for the European Conference on Modelling and Simulation (ECMS 2015

Evacuation in the Social Force Model is not stationary

An evacuation process is simulated within the Social Force Model. Thousand pedestrians are leaving a room by one exit. We investigate the stationarity of the distribution of time lags between instants when two successive pedestrians cross the exit. The exponential tail of the distribution is shown to gradually vanish. Taking fluctuations apart, the time lags decrease in time till there are only about 50 pedestrians in the room, then they start to increase. This suggests that at the last stage the flow is laminar. In the first stage, clogging events slow the evacuation down. As they are more likely for larger crowds, the flow is not stationary. The data are investigated with detrended fluctuation analysis.Comment: 7 pages, 3 figures; PACS numbers: 89.75.Fb, 05.40.-a, 05.45.Tp, 89.40.B

Communication and trust in the bounded confidence model

The communication process in a situation of emergency is discussed within the Scheff theory of shame and pride. The communication involves messages from media and from other persons. Three strategies are considered: selfish (to contact friends), collective (to join other people) and passive (to do nothing). We show that the pure selfish strategy cannot be evolutionarily stable. The main result is that the community structure is statistically meaningful only if the interpersonal communication is weak.Comment: 6 pages, 5 figures, RevTeX, for ICCCI-201

Average distance in growing trees

Two kinds of evolving trees are considered here: the exponential trees, where subsequent nodes are linked to old nodes without any preference, and the Barab\'asi--Albert scale-free networks, where the probability of linking to a node is proportional to the number of its pre-existing links. In both cases, new nodes are linked to $m=1$ nodes. Average node-node distance $d$ is calculated numerically in evolving trees as dependent on the number of nodes $N$. The results for $N$ not less than a thousand are averaged over a thousand of growing trees. The results on the mean node-node distance $d$ for large $N$ can be approximated by $d=2\ln(N)+c_1$ for the exponential trees, and $d=\ln(N)+c_2$ for the scale-free trees, where the $c_i$ are constant. We derive also iterative equations for $d$ and its dispersion for the exponential trees. The simulation and the analytical approach give the same results.Comment: 6 pages, 3 figures, Int. J. Mod. Phys. C14 (2003) - in prin

How pairs of partners emerge in an initially fully connected society

A social group is represented by a graph, where each pair of nodes is connected by two oppositely directed links. At the beginning, a given amount $p(i)$ of resources is assigned randomly to each node $i$. Also, each link $r(i,j)$ is initially represented by a random positive value, which means the percentage of resources of node $i$ which is offered to node $j$. Initially then, the graph is fully connected, i.e. all non-diagonal matrix elements $r(i,j)$ are different from zero. During the simulation, the amounts of resources $p(i)$ change according to the balance equation. Also, nodes reorganise their activity with time, going to give more resources to those which give them more. This is the rule of varying the coefficients $r(i,j)$. The result is that after some transient time, only some pairs $(m,n)$ of nodes survive with non-zero $p(m)$ and $p(n)$, each pair with symmetric and positive $r(m,n)=r(n,m)$. Other coefficients $r(m,i\ne n)$ vanish. Unpaired nodes remain with no resources, i.e. their $p(i)=0$, and they cease to be active, as they have nothing to offer. The percentage of survivors (i.e. those with with $p(i)$ positive) increases with the velocity of varying the numbers $r(i,j)$, and it slightly decreases with the size of the group. The picture and the results can be interpreted as a description of a social algorithm leading to marriages.Comment: 7 pages, 3 figure

New algorithm for the computation of the partition function for the Ising model on a square lattice

A new and efficient algorithm is presented for the calculation of the partition function in the $S=\pm 1$ Ising model. As an example, we use the algorithm to obtain the thermal dependence of the magnetic spin susceptibility of an Ising antiferromagnet for a $8\times 8$ square lattice with open boundary conditions. The results agree qualitatively with the prediction of the Monte Carlo simulations and with experimental data and they are better than the mean field approach results. For the $8\times 8$ lattice, the algorithm reduces the computation time by nine orders of magnitude.Comment: 7 pages, 3 figures, to appear in Int. J. Mod. Phys.

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--R\'enyi directed network.Comment: 8 pages, 2 figures. Some misleading sentences are removed from section

Magnetization reversal in spin patterns with complex geometry

We study field-driven dynamics of spins with antiferromagnetic interaction along the links of a complex substrate geometry, which is modeled by graphs of a controlled connectivity distribution. The magnetization reversal occurs in avalanches of spin flips, which are pinned by the topological constraints of the underlying graph. The hysteresis loop and avalanche sizes are analyzed and classified in terms of graph's connectivity and clustering. The results are relevant for magnets with a hierarchical spatial inhomogeneity and for design of nanoscale magnetic devices.Comment: 4 pages, 3 color figures, revtex

The Galam Model of Minority Opinion Spreading and the Marriage Gap

In 2002, Serge Galam designed a model of a minority opinion spreading. The effect is expected to lead a conservative minority to prevail if the issue is discussed long enough. Here we analyze the marriage gap, i.e. the difference in voting for Bush and Kerry in 2004 between married and unmarried people. It seems possible to interpret this marriage gap in terms of the Galam model.Comment: 6 page