We propose an extended local-world evolving network model including a triad formation (TF) step. In the process of network evolution, random fluctuation in the number of new edges is involved. We derive analytical expressions for degree distribution, clustering coefficient and average path...

We propose a deterministic weighted scale-free small-world model for considering pseudofractal web with the co-evolution of topology and weight. Considering the fluctuations in traffic flow constitute a main reason for congestion of packet delivery and poor performance of communication networks,...

We propose a general geometric growth model for pseudofractal scale-free web (PSW), which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks: degree distribution, second moment of degree distribution, degree correlations, distribution of...

We present a training algorithm for multilayer perceptrons which relates to the technique of principal component analysis. The latter is performed with respect to a correlation matrix which is computed from the example inputs and their target outputs. For large networks the novel procedure...

We study the propagation of elastic perturbations in magneto-rheological slurries of iron particles dispersed in glycerine. The complexity of these systems is revealed in the fibrillar structure acquired under the application of a magnetic field. Recently, it has been reported the observation of...

The ground state energy and entropy of the dilute mean field Ising model is computed exactly by a single order parameter as a function of the dilution coefficient. An analogous exact solution is obtained in the presence of a magnetic field with random locations. Results lead to a complete...

We propose a simple algorithm which produces a new category of networks, high-dimensional random Apollonian networks, with small-world and scale-free characteristics. We derive analytical expressions for their degree distributions and clustering coefficients which are determined by the dimension...

Using statistical physics, we study support vector machines (SVMs) learning noisy target rules in cases when the optimal predictor is a polynomial of the inputs. If the kernel of the SVM has sufficiently high order or is transcendental, the scale of the learning curve and the asymptote is...

We consider a new model for invasion in which the mechanism is also dependent on the fluid's filling of neighboring pores. During the invasion process, it is assumed that the resistance of a pore for invasion may be weakened depending on the fluids’ configurations of its nearest-neighbor...

We made a first attempt to associate a probabilistic description of stochastic processes like birth–death processes with spacetime geometry in the Schwarzschild metrics on distance scales from the macro- to the micro-domains. We idealize an ergodic system in which system states communicate...