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Is there chaos in the brain? II. Experimental evidence and related models
 C. R. Biol
, 2003
"... The search for chaotic patterns has occupied numerous investigators in neuroscience, as in many other fields of science. Their results and main conclusions are reviewed in the light of the most recent criteria that need to be satisfied since the first descriptions of the surrogate strategy. The meth ..."
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The search for chaotic patterns has occupied numerous investigators in neuroscience, as in many other fields of science. Their results and main conclusions are reviewed in the light of the most recent criteria that need to be satisfied since the first descriptions of the surrogate strategy. The methods used in each of these studies have almost invariably combined the analysis of experimental data with simulations using formal models, often based on modified Huxley and Hodgkin equations and/or of the Hindmarsh and Rose models of bursting neurons. Due to technical limitations, the results of these simulations have prevailed over experimental ones in studies on the nonlinear properties of large cortical networks and higher brain functions. Yet, and although a convincing proof of chaos (as defined mathematically) has only been obtained at the level of axons, of single and coupled cells, convergent results can be interpreted as compatible with the notion that signals in the brain are distributed according to chaotic patterns at all levels of its various forms of hierarchy. This chronological account of the main landmarks of nonlinear neurosciences follows an earlier publication [Faure, Korn, C. R. Acad. Sci. Paris, Ser. III 324 (2001) 773–793] that was focused on the basic concepts of nonlinear dynamics and methods of investigations which allow chaotic processes to be distinguished from stochastic ones and on the rationale for envisioning their control using external perturbations. Here we present the data and main arguments that support the existence of chaos at all levels from the simplest to the most complex forms of organization of the nervous system.
Model Dependence in Quantification of Spike Interdependence by Joint PeriStimulus Time Histogram
 Neural Computation
"... Multineuronal recordings have enabled us to examine contextdependent changes in the relationship between the activities of multiple cells. The Joint PeriStimulus Time Histogram (JPSTH) is a muchused method for investigating the dynamics of the interdependence of spike events between pairs of cell ..."
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Cited by 13 (1 self)
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Multineuronal recordings have enabled us to examine contextdependent changes in the relationship between the activities of multiple cells. The Joint PeriStimulus Time Histogram (JPSTH) is a muchused method for investigating the dynamics of the interdependence of spike events between pairs of cells. Its results are often taken as an estimate of interaction strength between cells, independent of modulations in the cells' firing rates. Weevaluate the adequacy of this estimate by examining the mathematical structure of how the JPSTH quantifies an interaction strength after excluding the contribution of firing rates. We introduce a simple probabilistic model of interacting point processes to generate simulated spike data, and show that the normalized JPSTH incorrectly infers the temporal structure of variations in the interaction parameter strength. This occurs because, in our model, the correct normalization of firing rate contributions is different to that used in Aertsen et al.'s "eff...
Activation and coherence in memory processes: revisiting the Parallel Distributed Processing approach to retrieval
"... Abstract. Connectionist models based on activation spreading and attractor dynamics are functionally limited by representational and processing flexibility constraints, the ‘feature binding problem ’ and the need to balance accurately activation and inhibition. We suggest an alternative approach, in ..."
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Abstract. Connectionist models based on activation spreading and attractor dynamics are functionally limited by representational and processing flexibility constraints, the ‘feature binding problem ’ and the need to balance accurately activation and inhibition. We suggest an alternative approach, in which network units are characterized by two variables: activation and phase. Whereas activation evolves according to a ‘classical ’ connectionist rule, the phase variable is characterized by a chaotic evolution. We present a model of memory retrieval with reference to the paradigmatic McClelland’s 1981 ‘Jets and Sharks ’ model. The model solves the ‘multiple reinstantiation problem’, i.e. the problem of retrieval of multiple items with overlapping features, implied by its classical predecessor. In our network, multiple pattern reinstantiation in terms of activation spreading is disambiguate through selective and differential coherence patterns. The system �exibly represents pattern similarity and feature relationships by means of graded and intermittent synchrony. The domaingeneral implications of this approach for connectionist ‘interactive activation models ’ and its neurophysiological plausibility are discussed.
Estimating statistics of neuronal dynamics via Markov chains
, 2000
"... We present an ecient computational method for estimating the mean and variance of interspike intervals dened by the timing of spikes in typical orbits of onedimensional neuronal maps. This is equivalent to nding the mean and variance of return times of orbits to particular regions of phase spac ..."
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Cited by 1 (0 self)
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We present an ecient computational method for estimating the mean and variance of interspike intervals dened by the timing of spikes in typical orbits of onedimensional neuronal maps. This is equivalent to nding the mean and variance of return times of orbits to particular regions of phase space. Rather than computing estimates directly from time series, the system is modelled as a nite state Markov chain to extract stationary behaviour in the form of invariant measures and average absorption times. Ergodictheoretic formulae are then applied to produce the estimates without the need to directly generate orbits. The approach may be applied to both deterministic and randomly forced systems. Research supported by a Japan Society for the Promotion of Science Postdoctoral Fellowship (research grant from the Ministry of Education, Science, and Culture No. 0997004) and the Deutsche Forschungsgemeinschaft under Grant De 448/54. 1 1 Introduction It is well known that spik...
Unsupervised Learning of SubMillisecond Temporal Coded Sequence By a Network of "coincidence Detector" Neurons
, 1998
"... In this paper, we examine unsupervised learning for sequence of submillisecond temporal coded information in a network of neurons, which are assumed to have high temporal resolution. The learning scheme is based on a spatially and temporally local one, i.e., unsupervised Hebbian learning. The input ..."
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In this paper, we examine unsupervised learning for sequence of submillisecond temporal coded information in a network of neurons, which are assumed to have high temporal resolution. The learning scheme is based on a spatially and temporally local one, i.e., unsupervised Hebbian learning. The input sequence is temporal information that needs an accuracy on the order of submilliseconds. Through the learning, segregation of the synaptic connections occurs to form systematic structures in the network. Namely, the network develops in a selforganizing manner. The trained network works like an "associative memory" of the learned sequence, namely, the network responds when a newly input sequence is similar to the learned sequence. Consequently, the assembly of neurons is able to learn and distinguish an input sequence that carries information on the order of submilliseconds, although the spike emission intervals of the neurons are on the order of milliseconds. Unsupervised network learn...
A Neural Model of Preattentional and Attentional Visual Search
, 1997
"... Visual processes do not amount to a simple filtering process performed by a series of hierarchical modules. They allow to select the items immediately useful for the current action from the information included in the external scene. To perform this selection, attentional topdown controls must comb ..."
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Visual processes do not amount to a simple filtering process performed by a series of hierarchical modules. They allow to select the items immediately useful for the current action from the information included in the external scene. To perform this selection, attentional topdown controls must combine with bottomup information issued from the retina. In the prospect to understand how these informations are fused together, a computational model of the first steps of the visual process able to account for the preattentional and attentional mechanisms involved in visual search has been developed. This model, called Competitive Search, integrates the dynamical aspects of a local dynamical architecture. It accounts for 'popout' and attentional phenomena involved in the search for conjunctive targets without introducing ad hoc hypothetical mechanisms such as the attentional spotlight hypothesis. It suggests that such metaphors, issued from the conventional cognitive psychology, may in fa...
Multiobjective Topology Optimization of Structures Using NNOC Algorithms*
"... Abstract. Topology optimization problem, which involves many design variables, is commonly solved by finite element method, a method must recalculate structurestiffness matrix each time of analysis. OC method is a good way to solve topology optimization problem, nevertheless, it can not solve multi ..."
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Abstract. Topology optimization problem, which involves many design variables, is commonly solved by finite element method, a method must recalculate structurestiffness matrix each time of analysis. OC method is a good way to solve topology optimization problem, nevertheless, it can not solve multiobjective topology optimization problems. This paper introduces an effective solution to Multiobjective topology optimization problems by using Neural Network algorithms to improve the traditional OC method. Specifically, in each iteration, calculate the new neural network link weight vector by using the previous link weight vector in the last iteration and the compliance vector in the last time of optimization, then work out the impact factor of each optimization objective on the overall objective of the optimization in order to determine the optimal direction of each design variable. 1
Connects/s AER Hardware Sensory–Processing– Learning–Actuating System for HighSpeed Visual Object Recognition and Tracking
, 2008
"... Abstract—This paper describes CAVIAR, a massively parallel hardware implementation of a spikebased sensing–processing–learning–actuating system inspired by the physiology of the nervous system. CAVIAR uses the asychronous address–event representation (AER) communication framework and was developed ..."
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Abstract—This paper describes CAVIAR, a massively parallel hardware implementation of a spikebased sensing–processing–learning–actuating system inspired by the physiology of the nervous system. CAVIAR uses the asychronous address–event representation (AER) communication framework and was developed in the context of a European Union funded project. It has four custom mixedsignal AER chips, five custom digital AER interface components, 45k neurons (spiking cells), up to 5M synapses, performs 12G synaptic operations per second, and achieves millisecond object recognition and tracking latencies.
Configuring Spiking Neural Networks for Given SpatioTemporal Patterns
"... We developed a general framework to configure a spiking neuronal network so that it can precisely generate a desired spatiotemporal pattern of spikes. The unit of spiking neuronal networks employed here is a leaky integrateandfire model. Robustness of configured spiking neuronal network is discus ..."
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We developed a general framework to configure a spiking neuronal network so that it can precisely generate a desired spatiotemporal pattern of spikes. The unit of spiking neuronal networks employed here is a leaky integrateandfire model. Robustness of configured spiking neuronal network is discussed, which leads us to use some routine methods in linearprogramming to solve the set of inequalities and gives the desirable configuration of spiking neural network. Numerical examples with randomly generated patterns are extensively explored and included to demonstrate the application of our approach.