Biomedical subjects

B G Giraud

Publications and source records attributed to B G Giraud.

4 recordsLinked to original sources

PubMed2001

Elementary derivative tasks and neural net multiscale analysis of tasks.

Formal neurons implementing wavelets have been shown to build nets that are able to approximate any multidimensional task. In this paper, we use a finite number of formal neurons implementing elementary tasks such as "sombrero" responses or even simpler "window" responses, with adjustable widths. We show this to provide a reasonably efficient, practical and robust, multifrequency analysis of tasks. The translation degree of freedom of wavelets is shown to be unnecessary. A training algorithm, optimizing the output task with respect to the widths of the responses, reveals two distinct training modes. The first mode keeps the formal neurons distinct. The other mode induces some of the formal neurons to become identical, with output weights of equal strengths but opposite signs. Hence this latter mode promotes tasks that are derivatives of the elementary tasks with respect to the width parameter. Such results, obtained from optimizations with respect to a width parameter, can be generalized for any other parameters of the elementary tasks.

Journal Article↗

PubMed1999

Superadditive correlation.

The fact that correlation does not imply causation is well known. Correlation between variables at two sites does not imply that the two sites directly interact, because, e.g., correlation between distant sites may be induced by chaining of correlation between a set of intervening, directly interacting sites. Such "noncausal correlation" is well understood in statistical physics: an example is long-range order in spin systems, where spins which have only short-range direct interactions, e.g., the Ising model, display correlation at a distance. It is less well recognized that such long-range "noncausal" correlations can in fact be stronger than the magnitude of any causal correlation induced by direct interactions. We call this phenomenon superadditive correlation (SAC). We demonstrate this counterintuitive phenomenon by explicit examples in (i) a model spin system and (ii) a model continuous variable system, where both models are such that two variables have multiple intervening pathways of indirect interaction. We apply the technique known as decimation to explain SAC as an additive, constructive interference phenomenon between the multiple pathways of indirect interaction. We also explain the effect using a definition of the collective mode describing the intervening spin variables. Finally, we show that the SAC effect is mirrored in information theory, and is true for mutual information measures in addition to correlation measures. Generic complex systems typically exhibit multiple pathways of indirect interaction, making SAC a potentially widespread phenomenon. This affects, e.g., attempts to deduce interactions by examination of correlations, as well as, e.g., hierarchical approximation methods for multivariate probability distributions, which introduce parameters based on successive orders of correlation.

Journal Article↗

PubMed1999

Independent statistical observables for ultrametric disordered populations.

It is not exceptional that a sample of N random data X(i), i=1,...,N contains ultrametric covariations, namely the matrix C with matrix elements - is ultrametric. We define independent (decorrelated) "collective" observables by diagonalizing this matrix. Symmetry properties of such eigenvectors are discussed. Often also, however, while the existence of an ultrametric tree is known, the degrees of parentage of the data are unknown, because a random perturbation confuses the labeling of the leaves of the tree. We sort out those observables which are more robust with respect to such labeling mistakes.

Genetic Heterogeneity↗

PubMed1993

Effects of collateral inhibition in a model of the immature rat cerebellar cortex: multineuron correlations.

A model of the immature rat cerebellar cortex is used to simulate the effect of the inhibitory recurrent collateral axons of the Purkinje cells on the spike trains in the network. Inhibition induces an important overall change in the statistical characteristics of individual spike trains. It is also instrumental in producing a strong cooperativity between the different neurons. Moreover, a functional spatial anisotropy appears. A specific entropy index is used to analyze levels of information transfer between clustered and faraway neurons in the network. The formatting effect of recurrent collateral inhibition on spike trains and on network functional dynamics is studied by means of a model of the newborn rat cerebellar cortex. This immature structure has simpler morphological characteristics and fewer physiological parameters than the adult one. It is thus a good candidate for the comparison between experimental and theoretical data. The model network is made of 256 formal neurons (FN), arranged in a square lattice. Each neuron is coupled to its eight nearest neighbors by inhibitory links. All the parameters of the different elements of the model--in particular integration of inhibitory and excitatory inputs--are given anatomical and physiological values derived from biological data. Activities of single FNs and correlations between spatially distant ones are analyzed with classical statistical techniques as well as with a specific informational entropy method we introduce. Simulation results indicate that inhibition is instrumental in: (1) the transformation of the spike train characteristics. This includes a lengthening of the mean interspike interval as well as an overall change in the statistical distribution of intervals, with an emergence of long-lasting ones; (2) the functional structuration of the network. Inhibitory connections between nearest neighbors induce a strong cooperativity between FNs. Furthermore a clear spatial anisotropy occurs in the functioning of the network, with inhibitory effects extending beyond local connectivity in preferential directions. We propose an interpretation of this functional structuration in terms of the various routes followed by the inhibition, including relay effects. The parameters of the model (levels of activities, inhibition rules and connectivities) were varied in order to test the robustness of the above results. Finally, the results are compared with those obtained in an experimental situation.

Animals↗