Nicolas Le Roux | PubMed Health

PubMed2006

Homeostatic control of the excitation-inhibition balance in cortical layer 5 pyramidal neurons.

Homeostatic regulation in the brain is thought to be achieved through a control of the synaptic strength by close interactions between excitation and inhibition in cortical circuits. We recorded in a layer 5 pyramidal neuron of rat cortex the composite response to an electrical stimulation of various layers (2-3, 4 or 6). Decomposition of the global conductance change in its excitatory and inhibitory components permits a direct measurement of excitation-inhibition (E-I) balance. Whatever the stimulated layer was, afferent inputs led to a conductance change consisting of 20% excitation and 80% inhibition. Changing synaptic strengths in cortical networks by using a high-frequency of stimulation (HFS) protocol or a low-frequency of stimulation (LFS) protocol (classically used to induce long-term potentiation or long-term depression at the synaptic level) were checked in order to disrupt this balance. Application of HFS protocols in layers 2-3, 4 or 6, or of LFS protocols in layer 4 induced, respectively, long-term paralleled increases or long-term paralleled decreases in E and I which did not change the E-I balance. LFS protocols in layers 2-3 or 6 decreased E but not I and disrupted the balance. It is proposed that regulatory mechanisms might be mainly sustained by recurrent connectivity between excitatory and inhibitory neuronal circuits and by modulation of shunting GABA(A) inhibition in the layer 5 pyramidal neuron.

Animals↗

PubMed2004

Learning eigenfunctions links spectral embedding and kernel PCA.

In this letter, we show a direct relation between spectral embedding methods and kernel principal components analysis and how both are special cases of a more general learning problem: learning the principal eigenfunctions of an operator defined from a kernel and the unknown data-generating density. Whereas spectral embedding methods provided only coordinates for the training points, the analysis justifies a simple extension to out-of-sample examples (the Nyström formula) for multidimensional scaling (MDS), spectral clustering, Laplacian eigenmaps, locally linear embedding (LLE), and Isomap. The analysis provides, for all such spectral embedding methods, the definition of a loss function, whose empirical average is minimized by the traditional algorithms. The asymptotic expected value of that loss defines a generalization performance and clarifies what these algorithms are trying to learn. Experiments with LLE, Isomap, spectral clustering, and MDS show that this out-of-sample embedding formula generalizes well, with a level of error comparable to the effect of small perturbations of the training set on the embedding.

Algorithms↗