Alicia D'Anjou

FEEDBACK SYNCHRONIZATION OF CHAOTIC SYSTEMS

Feedback coupling through an interaction term proportional to the difference in the value of some behavioral characteristics of two systems is a very common structural setting that leads to synchronization of the behavior of both systems. The degree of synchronization attained depends on the strength of the interaction term and on the mutual interdependency of the structures of both systems. In this paper, we show that two chaotic systems linked through a feedback coupling interaction term of gain parameter k reach a synchronized regime characterized by a vector of variable errors which tends towards zero with parameter k while the interaction term tends towards a finite nonzero permanent regime. This means that maintaining a certain degree of synchronization has a cost. In the limit, complete synchronization occurs at a finite limit cost. We show that feedback coupling in itself brings about conditions permitting that systems with a degree of structural parameter flexibility evolve close towards each other structures in order to facilitate the maintenance of the synchronized regime. In this paper, we deduce parameter adaptive laws for any family of homochaotic systems provided they are previously forced to work, via feedback coupling, within an appropriate degree of synchronization. The laws are global in the space of parameters and lead eventually to identical synchronization at no interaction cost. We illustrate this point with homochaotic systems from the Lorenz, Rossler and Chua families.

Energy and information in Hodgkin-Huxley neurons.

The generation of spikes by neurons is energetically a costly process and the evaluation of the metabolic energy required to maintain the signaling activity of neurons a challenge of practical interest. Neuron models are frequently used to represent the dynamics of real neurons but hardly ever to evaluate the electrochemical energy required to maintain that dynamics. This paper discusses the interpretation of a Hodgkin-Huxley circuit as an energy model for real biological neurons and uses it to evaluate the consumption of metabolic energy in the transmission of information between neurons coupled by electrical synapses, i.e., gap junctions. We show that for a single postsynaptic neuron maximum energy efficiency, measured in bits of mutual information per molecule of adenosine triphosphate (ATP) consumed, requires maximum energy consumption. For groups of parallel postsynaptic neurons we determine values of the synaptic conductance at which the energy efficiency of the transmission presents clear maxima at relatively very low values of metabolic energy consumption. Contrary to what could be expected, the best performance occurs at a low energy cost.

Linked multi-component mobile robots: Modeling, simulation and control

The Linked Multi-Component Robotic Systems (L-MCRS) consists of a group of mobile robots carrying a passive uni-dimensional object (a hose or a wire). It is a recently identified unexplored and unexploited category of multi-robot systems. In this paper we report the first effort on the modeling, control and visual servoing of L-MCRS. Modeling has been tackled from geometrical and dynamical points of view. The passive element is modeled by splines, and the dynamical modeling is achieved by the appropriate extension of Geometrically Exact Dynamic Splines (GEDS). The systems modeling allows realistic simulation, which can be used as a test bed for the evaluation of control strategies. In this paper we evaluate two such control strategies: a baseline global controller, and a fuzzy local controller based on the observation of the hose segment between two robots. Finally, we have performed physical experiments on a team of robots carrying a wire under a visual servoing scheme that provides the perceptual information about the hose for the fuzzy local controller. Visual servoing robust image segmentation is grounded in the Dichromatic Reflection Model (DRM).

Cost of synchronizing different chaotic systems

Feedback coupling provides a general scheme for synchronizing two oscillatory chaotic systems through the intervention of a term of interaction that accounts for the difference of behaviors. We define a cost of synchronization based on a measure of the interaction term. Synchronizing different systems is not cost free and the cost increases with the requirements imposed on the synchronized behavior. We prove that many systems can reach a regime of complete synchronization at a limited, and a priory computable, cost. For identical systems, the cost of complete synchronization is zero. Some different systems can also keep a completely synchronized behavior in some of their variables at zero cost. We propose to reserve the name identical synchronization for complete synchronization at zero cost. We compute the cost for different stages of synchronization between two systems as different as the Rossler and Lorenz systems and for homochaotic cases of both families. If the response system is flexible enough to adapt to the structure of the driving system, lower synchronization cost or, eventually, identical synchronization will be possible. In this paper, we deduce adaptation laws to reach identical synchronization for any family of homochaotic systems, and we illustrate their application for the Rossler and Lorenz cases.

On the application of Associative Morphological Memories to Hyperspectral Image Analysis

We propose a spectrum selection procedure from hyperspectral images, which uses the Autoassociative Morphological Memories (AMM) as detectors of morphological independence conditions. Selected spectra may be used as endmembers for spectral unmixing. Endmember spectra lie in the vertices of a convex region that covers the image pixel spectra. Therefore, morphological independence is a necessary condition for these vertices. The selective sensitivity of AMMs to erosive and dilative noise allows their use as morphological independence detectors.

An analysis of the GLVQ algorithm

Generalized learning vector quantization (GLVQ) has been proposed in as a generalization of the simple competitive learning (SCL) algorithm. The main argument of GLVQ proposal is its superior insensitivity to the initial values of the weights (code vectors). In this paper we show that the distinctive characteristics of the definition of GLVQ disappear outside a small domain of applications. GLVQ becomes identical to SCL when either the number of code vectors grows or the size of the input space is large. Besides that, the behavior of GLVQ is inconsistent for problems defined on very small scale input spaces. The adaptation rules fluctuate between performing descent and ascent searches on the gradient of the distortion function.

The high-order Boltzmann machine: learned distribution and topology

In this paper we give a formal definition of the high-order Boltzmann machine (BM), and extend the well-known results on the convergence of the learning algorithm of the two-order BM. From the Bahadur-Lazarsfeld expansion we characterize the probability distribution learned by the high order BM. Likewise a criterion is given to establish the topology of the BM depending on the significant correlations of the particular probability distribution to be learned.

Energy demands of diverse spiking cells from the neocortex, hippocampus, and thalamus

It has long been known that neurons in the brain are not physiologically homogeneous. In response to current stimulus, they can fire several distinct patterns of action potentials that are associated with different physiological classes ranging from regular-spiking cells, fast-spiking cells, intrinsically bursting cells, and low-threshold cells. In this work we show that the high degree of variability in firing characteristics of action potentials among these cells is accompanied with a significant variability in the energy demands required to restore the concentration gradients after an action potential. The values of the metabolic energy were calculated for a wide range of cell temperatures and stimulus intensities following two different approaches. The first one is based on the amount of Na+ load crossing the membrane during a single action potential, while the second one focuses on the electrochemical energy functions deduced from the dynamics of the computational neuron models. The results show that the thalamocortical relay neuron is the most energy-efficient cell consuming between 7 and 18 nJ/cm2 for each spike generated, while both the regular and fast spiking cells from somatosensory cortex and the intrinsically-bursting cell from a cat visual cortex are the least energy-efficient, and can consume up to 100 nJ/cm2 per spike. The lowest values of these energy demands were achieved at higher temperatures and high external stimuli.

Solving satisfiability via Boltzmann machines

Boltzmann machines (BMs) are proposed as a computational model for the solution of the satisfiability (SAT) problem in the propositional calculus setting. Conditions that guarantee consensus function maxima for configurations of the BM associated with solutions to the satisfaction problem are given. Experimental results that show a linear behavior of BMs solving the satisfiability problem are presented and discussed. >

Metabolic efficiency with fast spiking in the squid axon

Fundamentally, action potentials in the squid axon are consequence of the entrance of sodium ions during the depolarization of the rising phase of the spike mediated by the outflow of potassium ions during the hyperpolarization of the falling phase. Perfect metabolic efficiency with a minimum charge needed for the change in voltage during the action potential would confine sodium entry to the rising phase and potassium efflux to the falling phase. However, because sodium channels remain open to a significant extent during the falling phase, a certain overlap of inward and outward currents is observed. In this work we investigate the impact of ion overlap on the number of the adenosine triphosphate (ATP) molecules and energy cost required per action potential as a function of the temperature in a Hodgkin–Huxley model. Based on a recent approach to computing the energy cost of neuronal action potential generation not based on ion counting, we show that increased firing frequencies induced by higher temperatures imply more efficient use of sodium entry, and then a decrease in the metabolic energy cost required to restore the concentration gradients after an action potential. Also, we determine values of sodium conductance at which the hydrolysis efficiency presents a clear minimum.