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...

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...

A simple model for the collective behaviour of diverse speculative agents in a competitive market is considered from the point of view of statistical physics. The only information about other agents available to any one is the total trade effected at each time-step. Evidence is presented for...

The Random Field Ising Model (RFIM) following bimodal and Gaussian distributions for the RF is investigated using a finite connectivity technique. We focused on determining the order of the phase transition as well as the existence of a tricritical point as a function of the connectivity c for...