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 calcula
te 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.
Two models of a queue are proposed: a human queue and two lines of vehicles before a narrowing. In both models, a queuer tries to evaluate his waiting time, taking into account the delay caused by intruders who jump to the queue front. As the collect
ed statistics of such events is very limited, the evaluation can give very long times. The results provide an example, when direct observations should be supplemented by an inference from the context.
An order--disorder phase transition is observed for Ising-like systems even for arbitrarily chosen probabilities of spins flips [K. Malarz et al, Int. J. Mod. Phys. C 22, 719 (2011)]. For such athermal dynamics one must define $(z+1)$ spin flips prob
abilities $w(n)$, where $z$ is a number of the nearest-neighbours for given regular lattice and $n=0,cdots,z$ indicates the number of nearest spins with the same value as the considered spin. Recently, such dynamics has been successfully applied for the simulation of a cooperative and competitive strategy selection by pedestrians in crowd [P. Gawronski et al, Acta Phys. Pol. A 123, 522 (2013)]. For the triangular lattice ($z=6$) and flips probabilities dependence on a single control parameter $x$ chosen as $w(0)=1$, $w(1)=3x$, $w(2)=2x$, $w(3)=x$, $w(4)=x/2$, $w(5)=x/4$, $w(6)=x/6$ the ordered phase (where most of pedestrians adopt the same strategy) vanishes for $x>x_Capprox 0.429$. In order to introduce long-range interactions between pedestrians the bonds of triangular lattice are randomly rewired with the probability $p$. The amount of rewired bonds can be interpreted as the probability of communicating by mobile phones. The critical value of control parameter $x_C$ increases monotonically with the number of rewired links $M=pzN/2$ from $x_C(p=0)approx 0.429$ to $x_C(p=1)approx 0.81$.
In an emergency situation, imitation of strategies of neighbours can lead to an order-disorder phase transition, where spatial clusters of pedestrians adopt the same strategy. We assume that there are two strategies, cooperating and competitive, whic
h correspond to a smaller or larger desired velocity. The results of our simulations within the Social Force Model indicate that the ordered phase can be detected as an increase of spatial order of positions of the pedestrians in the crowd.
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), coll
ective (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.
