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.
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.
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 $D=1,2,3,4$.
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.
We investigate the existence and location of the surface phase known as the Surface-Attached Globule (SAG) conjectured previously to exist in lattice models of three-dimensional polymers when they are attached to a wall that has a short range potenti
al. The bulk phase, where the attractive intra-polymer interactions are strong enough to cause a collapse of the polymer into a liquid-like globule and the wall either has weak attractive or repulsive interactions, is usually denoted Desorbed-Collapsed or DC. Recently this DC phase was conjectured to harbour two surface phases separated by a boundary where the bulk free energy is analytic while the surface free energy is singular. The surface phase for more attractive values of the wall interaction is the SAG phase. We discuss more fully the properties of this proposed surface phase and provide Monte Carlo evidence for self-avoiding walks up to length 256 that this surface phase most likely does exist. Importantly, we discuss alternatives for the surface phase boundary. In particular, we conclude that this boundary may lie along the zero wall interaction line and the bulk phase boundaries rather than any new phase boundary curve.
We present results for a lattice model of bio-polymers where the type of $beta$-sheet formation can be controlled by different types of hydrogen bonds depending on the relative orientation of close segments of the polymer. Tuning these different inte
raction strengths leads to low-temperature structures with different types of orientational order. We perform simulations of this model and so present the phase diagram, ascertaining the nature of the phases and the order of the transitions between these phases.
