4,220 research outputs found
Wandering in the state space
We analyse the topology of the state space of two systems: i) N Ising spins
+/-1 with the antiferromagnetic interactions on a triangular lattice, with the
condition of minimum of energy, ii) a roundabout of three access roads and
three exit roads, with up to 2 cars on each road. The state space is
represented by a network, and states - as nodes; two nodes are linked if an
elementary process (spin flip or car shift) transforms the respective states
one into another. Information is collected on the number of neighbours of
states, what allows to distinguish classes and subclasses of states, and on the
cluster structure of the state space. In the Ising systems, the clusters are
characterized by anisotropy of the spin-spin correlation functions. In the case
of a roundabout, the clusters differ by the number of empty or full roads. The
method is general and it provides a basis for applications of the random walk
theory
Communities and classes in symmetric fractals
Two aspects of fractal networks are considered: the community structure and
the class structure, where classes of nodes appear as a consequence of a local
symmetry of nodes. The analysed systems are the networks constructed for two
selected symmetric fractals: the Sierpinski triangle and the Koch curve.
Communities are searched for by means of a set of differential equations.
Overlapping nodes which belong to two different communities are identified by
adding some noise to the initial connectivity matrix. Then, a node can be
characterized by a spectrum of probabilities of belonging to different
communities. Our main goal is that the overlapping nodes with the same spectra
belong to the same class
Combinatorial aspect of fashion
Simulations are performed according to the Axelrod model of culture
dissemination, with modified mechanism of repulsion. Previously, repulsion was
considered by Radillo-Diaz et al (Phys. Rev. E 80 (2009) 066107) as dependent
on a predefined threshold. Here the probabilities of attraction and repulsion
are calculated from the number of cells in the same states. We also investigate
the influence of some homogeneity, introduced to the initial state. As the
result of the probabilistic definition of repulsion, the ordered state
vanishes. A small cluster of a few percent of population is retained only if in
the initial state a set of agents is prepared in the same state. We conclude
that the modelled imitation is successful only with respect to agents, and not
only their features
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