We study the implications of social interactions and individual learning features on consumer demand in a simple market model. We consider a social system of interacting heterogeneous agents with learning abilities. Given a fixed price, agents repeatedly decide whether or not to buy a unit of a...

In this paper, we consider a discrete choice model where heterogeneous agents are subject to mutual influences. We explore some consequences on the market's behaviour, in the simplest case of a uniform willingness to pay distribution. We exhibit a first-order phase transition in the profit...

We introduce a simple agent-based model which allows us to analyze three stylized facts: a fat-tailed size distribution of companies, a ‘tent-shaped’ growth rate distribution, the scaling relation of the growth rate variance with firm size, and the causality between them. This is achieved...

Statistical mechanics is used to derive a new learning rule for a feed-forward neural network with one hidden layer. Generalization to multilayer neural networks is straightforward, and proceeds in the same way as backpropagation.

We consider the properties of multi-class neural networks, where each neuron can be in several different states. The motivations for considering such systems are manifold. In image processing for example, the different states correspond to the different grey tone levels. Another multi-class...