S A Cannas | PubMed Health

PubMed2001

Long-range effects in granular avalanching.

We introduce a model for granular flow in a one-dimensional rice pile that incorporates rolling effects through a long-range rolling probability for the individual rice grains proportional to r(-rho), r being the distance traveled by a grain in a single toppling event. The exponent rho controls the average rolling distance. We have shown that the crossover from the power law to the stretched exponential behaviors observed experimentally in the granular dynamics of rice piles can be well described as a long-range effect resulting from a change in the transport properties of individual grains. We showed that stretched exponential avalanche distributions can be associated with a long-range regime for 1 2, where the average rolling distance is independent of the system size.

Journal Article↗

PubMed2000

Generalization and selection of examples in feedforward neural networks.

In this work, we study how the selection of examples affects the learning procedure in a boolean neural network and its relationship with the complexity of the function under study and its architecture. We analyze the generalization capacity for different target functions with particular architectures through an analytical calculation of the minimum number of examples needed to obtain full generalization (i.e., zero generalization error). The analysis of the training sets associated with such parameter leads us to propose a general architecture-independent criterion for selection of training examples. The criterion was checked through numerical simulations for various particular target functions with particular architectures, as well as for random target functions in a nonoverlapping receptive field perceptron. In all cases, the selection sampling criterion lead to an improvement in the generalization capacity compared with a pure random sampling. We also show that for the parity problem, one of the most used problems for testing learning algorithms, only the use of the whole set of examples ensures global learning in a depth two architecture. We show that this difficulty can be overcome by considering a tree-structured network of depth 2log2(N)-1.

Algorithms↗