Catálogo de publicaciones - libros

The hierarchical non-negative matrix factorization (HNMF) is a multilayer generative network for decomposing strictly positive data into strictly positive activations and base vectors in a hierarchical manner. However, the standard hierarchical NMF is not suited for overcomplete representations and does not code efficiently for transformations in the input data. Therefore we extend the standard HNMF by sparsity conditions and transformation-invariance in a natural, straightforward way. The idea is to factorize the input data into several hierarchical layers of activations, base vectors and transformations under sparsity constraints, leading to a less redundant and sparse encoding of the input data.

How can two distant neural assemblies synchronize their firings at zero-lag even in the presence of non-negligible delays in the transfer of information between them? Here we propose a simple network module that naturally accounts for zero-lag neural synchronization for a wide range of temporal delays. In particular, we demonstrate that isochronous (without lag) millisecond precise synchronization between two distant neurons or neural populations can be achieved by relaying their dynamics via a third mediating single neuron or population.

One-layer space-invariant Cellular Neural Networks (CNNs) are widely appreciated for their simplicity and versatility; however, such structures are not able to solve non-linearly separable problems. In this paper we show that a polynomial CNN - that has with a direct VLSI implementation - is capable of dealing with the ‘Game of Life’, a Cellular Automaton with the same computational complexity as a Turing machine. Furthermore, we describe a simple design algorithm that allows to convert the rules of a Cellular Automaton into the weights of a polynomial CNN.

Deterministic nonlinear dynamics has been observed in experimental electrophysiological recordings performed in several areas of the brain. However, little is known about the ability to transmit a complex temporally organized activity through different types of spiking neurons. This study investigates the response of a spiking neuron model representing three archetypical types (regular spiking, thalamo-cortical and resonator) to input spike trains composed of deterministic (chaotic) and stochastic processes with weak background activity. The comparison of the input and output spike trains allows to assess the transmission of information contained in the deterministic nonlinear dynamics. The pattern grouping algorithm (PGA) was applied to the output of the neuron to detect the dynamical attractor embedded in the original input spike train. The results show that the model of the thalamo-cortical neuron can be a better candidate than regular spiking and resonator type neurons in transmitting temporal information in a spatially organized neural network.

We present an artificial neural network used to learn online complex temporal sequences of gestures to a robot. The system is based on a simple temporal sequences learning architecture, neurobiological inspired model using some of the properties of the cerebellum and the hippocampus, plus a diversity generator composed of CTRNN oscillators. The use of oscillators allows to remove the ambiguity of complex sequences. The associations with oscillators allow to build an internal state to disambiguate the observable state. To understand the effect of this learning mechanism, we compare the performance of (i) our model with (ii) simple sequence learning model and with (iii) the simple sequence learning model plus a competitive mechanism between inputs and oscillators. Finally, we present an experiment showing a AIBO robot, which learns and reproduces a sequence of gestures.

Synchrony is a phenomenon present in many complex systems of coupled oscillators. It is often important to cluster those systems into subpopulations of oscillators, and characterise the interactions therein. This article derives the clustering information, based on an eigenvalue decomposition of the complex synchronisation matrix. A phase sensitive post-rotation is proposed, to separate classes of oscillators with similar frequencies, but with no physical interaction.

We have studied the spatiotemporal behaviour of threshold coupled chaotic neurons. We observe that the chaos is controlled by threshold activated coupling, and the system yields synchronized temporally periodic states under the threshold response. Varying the frequency of thresholding provides different higher order periodic behaviors, and can serve as a simple mechanism for stabilising a large range of regular temporal patterns in chaotic systems. Further, we have obtained a transition from spatiotemporal chaos to fixed spatiotemporal profiles, by lengthening the relaxation time scale.

Feedback circuits are important for understanding the emergence of patterns of neural activity. In this contribution we study how a delayed circuit representing a recurrent synaptic connection interferes with neuronal nonlinear dynamics. The neuron is modeled using a Hodgkin-Huxley type model in which the firing pattern depends on subthreshold oscillations, and the feedback is included as a time delayed linear term in the membrane voltage equation. In the regime of subthreshold oscillations the feedback amplifies the oscillation amplitude, inducing threshold crossings and firing activity that is self regularized by the delay. We also study a small neuron ensemble globally coupled through the delayed mean field. We find that the firing pattern is controlled by the delay. Depending on the delay, either all neurons fire spikes, or they all exhibit subthreshold activity, or the ensemble divides into clusters, with some neurons displaying subthreshold activity while others fire spikes.