Adaptive Exponential Synchronization for Stochastic Competitive Neural Networks with Time-Varying Leakage Delays and Reaction-Diffusion Terms

We study the exponential synchronization problem for a class of stochastic competitive neural networks with different timescales, as well as spatial diffusion, time-varying leakage delays, and discrete and distributed time-varying delays. By introducing several important inequalities and using Lyapunov functional technique, an adaptive feedback controller is designed to realize the exponential synchronization for the proposed competitive neural networks in terms of p-norm. According to the theoretical results obtained in this paper, the influences of the timescale, external stimulus constants, disposable scaling constants, and controller parameters on synchronization are analyzed. Numerical simulations are presented to show the feasibility of the theoretical results

The Timing of Vision – How Neural Processing Links to Different Temporal Dynamics

In this review, we describe our recent attempts to model the neural correlates of visual perception with biologically inspired networks of spiking neurons, emphasizing the dynamical aspects. Experimental evidence suggests distinct processing modes depending on the type of task the visual system is engaged in. A first mode, crucial for object recognition, deals with rapidly extracting the glimpse of a visual scene in the first 100 ms after its presentation. The promptness of this process points to mainly feedforward processing, which relies on latency coding, and may be shaped by spike timing-dependent plasticity (STDP). Our simulations confirm the plausibility and efficiency of such a scheme. A second mode can be engaged whenever one needs to perform finer perceptual discrimination through evidence accumulation on the order of 400 ms and above. Here, our simulations, together with theoretical considerations, show how predominantly local recurrent connections and long neural time-constants enable the integration and build-up of firing rates on this timescale. In particular, we review how a non-linear model with attractor states induced by strong recurrent connectivity provides straightforward explanations for several recent experimental observations. A third mode, involving additional top-down attentional signals, is relevant for more complex visual scene processing. In the model, as in the brain, these top-down attentional signals shape visual processing by biasing the competition between different pools of neurons. The winning pools may not only have a higher firing rate, but also more synchronous oscillatory activity. This fourth mode, oscillatory activity, leads to faster reaction times and enhanced information transfers in the model. This has indeed been observed experimentally. Moreover, oscillatory activity can format spike times and encode information in the spike phases with respect to the oscillatory cycle. This phenomenon is referred to as “phase-of-firing coding,” and experimental evidence for it is accumulating in the visual system. Simulations show that this code can again be efficiently decoded by STDP. Future work should focus on continuous natural vision, bio-inspired hardware vision systems, and novel experimental paradigms to further distinguish current modeling approaches

Information processing in biological complex systems: a view to bacterial and neural complexity

This thesis is a study of information processing of biological complex systems seen from the perspective of dynamical complexity (the degree of statistical independence of a system as a whole with respect to its components due to its causal structure). In particular, we investigate the influence of signaling functions in cell-to-cell communication in bacterial and neural systems. For each case, we determine the spatial and causal dependencies in the system dynamics from an information-theoretic point of view and we relate it with their physiological capabilities. The main research content is presented into three main chapters. First, we study a previous theoretical work on synchronization, multi-stability, and clustering of a population of coupled synthetic genetic oscillators via quorum sensing. We provide an extensive numerical analysis of the spatio-temporal interactions, and determine conditions in which the causal structure of the system leads to high dynamical complexity in terms of associated metrics. Our results indicate that this complexity is maximally receptive at transitions between dynamical regimes, and maximized for transient multi-cluster oscillations associated with chaotic behaviour. Next, we introduce a model of a neuron-astrocyte network with bidirectional coupling using glutamate-induced calcium signaling. This study is focused on the impact of the astrocyte-mediated potentiation on synaptic transmission. Our findings suggest that the information generated by the joint activity of the population of neurons is irreducible to its independent contribution due to the role of astrocytes. We relate these results with the shared information modulated by the spike synchronization imposed by the bidirectional feedback between neurons and astrocytes. It is shown that the dynamical complexity is maximized when there is a balance between the spike correlation and spontaneous spiking activity. Finally, the previous observations on neuron-glial signaling are extended to a large-scale system with community structure. Here we use a multi-scale approach to account for spatiotemporal features of astrocytic signaling coupled with clusters of neurons. We investigate the interplay of astrocytes and spiking-time-dependent-plasticity at local and global scales in the emergence of complexity and neuronal synchronization. We demonstrate the utility of astrocytes and learning in improving the encoding of external stimuli as well as its ability to favour the integration of information at synaptic timescales to exhibit a high intrinsic causal structure at the system level. Our proposed approach and observations point to potential effects of the astrocytes for sustaining more complex information processing in the neural circuitry

Perspectives on adaptive dynamical systems

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems, such as the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems. We reflect on the notion and terminology of adaptivity in different disciplines and discuss which role adaptivity plays for various fields. We highlight common open challenges and give perspectives on future research directions, looking to inspire interdisciplinary approaches

Neural field model of binocular rivalry waves

We present a neural field model of binocular rivalry waves in visual cortex. For each eye we consider a one–dimensional network of neurons that respond maximally to a particular feature of the corresponding image such as the orientation of a grating stimulus. Recurrent connections within each one-dimensional network are assumed to be excitatory, whereas connections between the two networks are inhibitory (cross-inhibition). Slow adaptation is incorporated into the model by taking the network connections to exhibit synaptic depression. We derive an analytical expression for the speed of a binocular rivalry wave as a function of various neurophysiological parameters, and show how properties of the wave are consistent with the wave–like propagation of perceptual dominance observed in recent psychophysical experiments. In addition to providing an analytical framework for studying binocular rivalry waves, we show how neural field methods provide insights into the mechanisms underlying the generation of the waves. In particular, we highlight the important role of slow adaptation in providing a “symmetry breaking mechanism” that allows waves to propagate

Complex and Adaptive Dynamical Systems: A Primer

An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and small-world networks, a generic introduction to the concepts of dynamical system theory, random Boolean networks, cellular automata and self-organized criticality, the statistical modeling of Darwinian evolution, synchronization phenomena and an introduction to the theory of cognitive systems. It inludes chapter on Graph Theory and Small-World Networks, Chaos, Bifurcations and Diffusion, Complexity and Information Theory, Random Boolean Networks, Cellular Automata and Self-Organized Criticality, Darwinian evolution, Hypercycles and Game Theory, Synchronization Phenomena and Elements of Cognitive System Theory.Comment: unformatted version of the textbook; published in Springer, Complexity Series (2008, second edition 2010

Perspectives on adaptive dynamical systems

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems like the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems. We reflect on the notion and terminology of adaptivity in different disciplines and discuss which role adaptivity plays for various fields. We highlight common open challenges, and give perspectives on future research directions, looking to inspire interdisciplinary approaches.Comment: 46 pages, 9 figure

Mesoscale Systems, Finite Size Effects, and Balanced Neural Networks

Cortical populations are typically in an asynchronous state, sporadically interrupted by brief epochs of coordinated population activity. Current cortical models are at a loss to explain this combination of states. At one extreme are network models where recurrent in- hibition dynamically stabilizes an asynchronous low activity state. While these networks are widely used they cannot produce the coherent population-wide activity that is reported in a variety of datasets. At the other extreme are models where short term synaptic depression between excitatory neurons can generate the epochs of population-wide activity. However, in these networks inhibition plays only a perfunctory role in network stability, which is at odds with many reports across cortex. In this study we analyze spontaneously active in vitro preparations of primary auditory cortex that show dynamics that are emblematic of this mix- ture of states. To capture this complex population activity we consider models where large excitation is balanced by recurrent inhibition yet we include short term synaptic depression dynamics of the excitatory connections. This model gives very rich nonlinear behavior that mimics the core features of the in vitro data, including the possibility of low frequency (2- 12 Hz) rhythmic dynamics within population events. Our study extends balanced network models to account for nonlinear, population-wide correlated activity, thereby providing a critical step in a mechanistic theory of realistic cortical activity. We further investigate an extension of this model that l exhibits clearly non-Arrhenius behavior, whereby lower noise systems may exhibit faster escape from a stable state. We show that this behavior is due to the system size dependent vector field, intrinsically linking noise and dynamics