The concept of magnetic susceptibility in the Ising model is used to identify the social temperature as the rate of random changes of strategy for a set of agents playing two different strategies.
Algorithms for search of communities in networks usually consist discrete variations of links. Here we discuss a flow method, driven by a set of differential equations. Two examples are demonstrated in detail. First is a partition of a signed graph i
nto two parts, where the proposed equations are interpreted in terms of removal of a cognitive dissonance by agents placed in the network nodes. There, the signs and values of links refer to positive or negative interpersonal relationships of different strength. Second is an application of a method akin to the previous one, dedicated to communities identification, to the Sierpinski triangle of finite size. During the time evolution, the related graphs are weighted; yet at the end the discrete character of links is restored. In the case of the Sierpinski triangle, the method is supplemented by adding a small noise to the initial connectivity matrix. By breaking the symmetry of the network, this allows to a successful handling of overlapping nodes.
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.
A set of $N$ points is chosen randomly in a $D$-dimensional volume $V=a^D$, with periodic boundary conditions. For each point $i$, its distance $d_i$ is found to its nearest neighbour. Then, the maximal value is found, $d_{max}=max(d_i, i=1,...,N)$.
Our numerical calculations indicate, that when the density $N/V$=const, $d_{max}$ scales with the linear system size as $d^2_{max}propto a^phi$, with $phi=0.24pm0.04$ for $D=1,2,3,4$.
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.
