Optimal system size for complex dynamics in random neural networks near criticality

In this Letter, we consider a model of dynamical agents coupled through a random connectivity matrix, as introduced in [Sompolinsky et. al, 1988] in the context of random neural networks. It is known that increasing the disorder parameter induces a phase transition leading to chaotic dynamics. We observe and investigate here a novel phenomenon in the subcritical regime : the probability of observing complex dynamics is maximal for an intermediate system size when the disorder is close enough to criticality. We give a more general explanation of this type of system size resonance in the framework of extreme values theory for eigenvalues of random matrices.Comment: 11 pages, 2 figure

A genetic-algorithms based evolutionary computational neural network for modelling spatial interaction data

Building a feedforward computational neural network model (CNN) involves two distinct tasks: determination of the network topology and weight estimation. The specification of a problem adequate network topology is a key issue and the primary focus of this contribution. Up to now, this issue has been either completely neglected in spatial application domains, or tackled by search heuristics (see Fischer and Gopal 1994). With the view of modelling interactions over geographic space, this paper considers this problem as a global optimization problem and proposes a novel approach that embeds backpropagation learning into the evolutionary paradigm of genetic algorithms. This is accomplished by interweaving a genetic search for finding an optimal CNN topology with gradient-based backpropagation learning for determining the network parameters. Thus, the model builder will be relieved of the burden of identifying appropriate CNN-topologies that will allow a problem to be solved with simple, but powerful learning mechanisms, such as backpropagation of gradient descent errors. The approach has been applied to the family of three inputs, single hidden layer, single output feedforward CNN models using interregional telecommunication traffic data for Austria, to illustrate its performance and to evaluate its robustness.

Photometric redshift estimation based on data mining with PhotoRApToR

Photometric redshifts (photo-z) are crucial to the scientific exploitation of modern panchromatic digital surveys. In this paper we present PhotoRApToR (Photometric Research Application To Redshift): a Java/C++ based desktop application capable to solve non-linear regression and multi-variate classification problems, in particular specialized for photo-z estimation. It embeds a machine learning algorithm, namely a multilayer neural network trained by the Quasi Newton learning rule, and special tools dedicated to pre- and postprocessing data. PhotoRApToR has been successfully tested on several scientific cases. The application is available for free download from the DAME Program web site.Comment: To appear on Experimental Astronomy, Springer, 20 pages, 15 figure