Abdelmalik Moujahid

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.

Energy efficiency of information transmission by electrically coupled neurons.

The generation of spikes by neurons is energetically a costly process. This paper studies the consumption of energy and the information entropy in the signalling activity of a model neuron both when it is supposed isolated and when it is coupled to another neuron by an electrical synapse. The neuron has been modelled by a four-dimensional Hindmarsh-Rose type kinetic model for which an energy function has been deduced. For the isolated neuron values of energy consumption and information entropy at different signalling regimes have been computed. For two neurons coupled by a gap junction we have analyzed the roles of the membrane and synapse in the contribution of the energy that is required for their organized signalling. Computational results are provided for cases of identical and nonidentical neurons coupled by unidirectional and bidirectional gap junctions. One relevant result is that there are values of the coupling strength at which the organized signalling of two neurons induced by the gap junction takes place at relatively low values of energy consumption and the ratio of mutual information to energy consumption is relatively high. Therefore, communicating at these coupling values could be energetically the most efficient option.

Facial expression recognition using tracked facial actions: Classifier performance analysis

In this paper, we address the analysis and recognition of facial expressions in continuous videos. More precisely, we study classifiers performance that exploit head pose independent temporal facial action parameters. These are provided by an appearance-based 3D face tracker that simultaneously provides the 3D head pose and facial actions. The use of such tracker makes the recognition pose- and texture-independent. Two different schemes are studied. The first scheme adopts a dynamic time warping technique for recognizing expressions where training data are given by temporal signatures associated with different universal facial expressions. The second scheme models temporal signatures associated with facial actions with fixed length feature vectors (observations), and uses some machine learning algorithms in order to recognize the displayed expression. Experiments quantified the performance of different schemes. These were carried out on CMU video sequences and home-made video sequences. The results show that the use of dimension reduction techniques on the extracted time series can improve the classification performance. Moreover, these experiments show that the best recognition rate can be above 90%.

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.

Efficient synchronization of structurally adaptive coupled Hindmarsh–Rose neurons

Abstract The use of spikes to carry information between brain areas implies complete or partial synchronization of the neurons involved. The degree of synchronization reached by two coupled systems and the energy cost of maintaining their synchronized behavior is highly dependent on the nature of the systems. For non-identical systems the maintenance of a synchronized regime is energetically a costly process. In this work, we study conditions under which two non-identical electrically coupled neurons can reach an efficient regime of synchronization at low energy cost. We show that the energy consumption required to keep the synchronized regime can be spontaneously reduced if the receiving neuron has adaptive mechanisms able to bring its biological parameters closer in value to the corresponding ones in the sending neuron.

Building detection from orthophotos using a machine learning approach

Automatic building detection in orthophotos via a machine learning approach.Flexible framework that exploits supervised learning.Applying the covariance descriptor to the building detection problem.An extended performance study of several combination segmentation-descriptor.Classification performance is obtained with K-NN, Partial Least Square and SVM. Building detection from aerial images has many applications in fields like urban planning, real-estate management, and disaster relief. In the last two decades, a large variety of methods on automatic building detection have been proposed in the remote sensing literature. Many of these approaches make use of local features to classify each pixel or segment to an object label, therefore involving an extra step to fuse pixelwise decisions. This paper presents a generic framework that exploits recent advances in image segmentation and region descriptors extraction for the automatic and accurate detection of buildings on aerial orthophotos. The proposed solution is supervised in the sense that appearances of buildings are learnt from examples. For the first time in the context of building detection, we use the matrix covariance descriptor, which proves to be very informative and compact. Moreover, we introduce a principled evaluation that allows selecting the best pair segmentation algorithm-region descriptor for the task of building detection. Finally, we provide a performance evaluation at pixel level using different classifiers. This evaluation is conducted over 200 buildings using different segmentation algorithms and descriptors. The performance analysis quantifies the quality of both the image segmentation and the descriptor used. The proposed approach presents several advantages in terms of scalability, suitability and simplicity with respect to the existing methods. Furthermore, the proposed scheme (detection chain and evaluation) can be deployed for detecting multiple object categories that are present in images and can be used by intelligent systems requiring scene perception and parsing such as intelligent unmanned aerial vehicle navigation and automatic 3D city modeling.

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.

ENERGY-LIKE FUNCTIONS FOR SOME DISSIPATIVE CHAOTIC SYSTEMS

Functions of the phase space variables that can considered as possible energy functions for a given family of dissipative chaotic systems are discussed. This kind of functions are interesting due to their use as an energy-like quantitative measure to characterize different aspects of dynamic behavior of associated chaotic systems. We have calculated quadratic energy-like functions for the cases of Lorenz, Chen, Lu–Chen and Chua, and show the patterns of dissipation of energy on their respective attractors. We also show that in the case of the Rossler system at least a fourth-order polynomial is required to properly represent its energy.

Nonzero error synchronization of chaotic systems via dynamic coupling

Abstract When feedback coupling is used to synchronize arbitrary chaotic systems large enough constant interaction gains lead to nearly complete synchronization at quasi-zero error. This forced oscillatory regime takes place in a region of phase space that, although natural for the guiding system, can result to be impracticable as an operating region for the guided system. However, we show that a dynamic feedback coupling with the appropriate variable gain can lead to a fully synchronized regime at a given nonzero synchronization error, that is, with the guided system operating on a desired region of the phase space. Computational results for oscillators of the Lorenz and Rossler families are shown. The cost of maintaining a couple of oscillatory Lorenz systems synchronized at different constant values of the synchronization error has been evaluated. To do so, an energy-like function associated to the state of the guided system has been defined.