Synchronization dynamics of two coupled neural oscillators receiving shared and unshared noisy stimuli

The response of neurons to external stimuli greatly depends on the intrinsic dynamics of the network. Here, the intrinsic dynamics are modeled as coupling and the external input is modeled as shared and unshared noise. We assume the neurons are repetitively firing action potentials (i.e., neural oscillators), are weakly and identically coupled, and the external noise is weak. Shared noise can induce bistability between the synchronous and anti-phase states even though the anti-phase state is the only stable state in the absence of noise. We study the Fokker-Planck equation of the system and perform an asymptotic reduction ρ ₀. The ρ ₀ solution is more computationally efficient than both the Monte Carlo simulations and the 2D Fokker-Planck solver, and agrees remarkably well with the full system with weak noise and weak coupling. With moderate noise and coupling, ρ ₀ is still qualitatively correct despite the small noise and coupling assumption in the asymptotic reduction. Our phase model accurately predicts the behavior of a realistic synaptically coupled Morris-Lecar system.

Modeling brain dynamics using computational neurogenetic approach

The paper introduces a novel computational approach to brain dynamics modeling that integrates dynamic gene–protein regulatory networks with a neural network model. Interaction of genes and proteins in neurons affects the dynamics of the whole neural network. Through tuning the gene–protein interaction network and the initial gene/protein expression values, different states of the neural network dynamics can be achieved. A generic computational neurogenetic model is introduced that implements this approach. It is illustrated by means of a simple neurogenetic model of a spiking neural network of the generation of local field potential. Our approach allows for investigation of how deleted or mutated genes can alter the dynamics of a model neural network. We conclude with the proposal how to extend this approach to model cognitive neurodynamics.

Synchronization properties of networks of electrically coupled neurons in the presence of noise and heterogeneities

We investigate how synchrony can be generated or induced in networks of electrically coupled integrate-and-fire neurons subject to noisy and heterogeneous inputs. Using analytical tools, we find that in a network under constant external inputs, synchrony can appear via a Hopf bifurcation from the asynchronous state to an oscillatory state. In a homogeneous net work, in the oscillatory state all neurons fire in synchrony, while in a heterogeneous network synchrony is looser, many neurons skipping cycles of the oscillation. If the transmission of action potentials via the electrical synapses is effectively excitatory, the Hopf bifurcation is supercritical, while effectively inhibitory transmission due to pronounced hyperpolarization leads to a subcritical bifurcation. In the latter case, the network exhibits bistability between an asynchronous state and an oscillatory state where all the neurons fire in synchrony. Finally we show that for time-varying external inputs, electrical coupling enhances the synchronization in an asynchronous network via a resonance at the firing-rate frequency.

The influence of sodium and potassium dynamics on excitability,seizures, and the stability of persistent states: II. Network and glial dynamics

In these companion papers, we study how the interrelated dynamics of sodium and potassium affect the excitability of neurons, the occurrence of seizures, and the stability of persistent states of activity. We seek to study these dynamics with respect to the following compartments: neurons, glia, and extracellular space. We are particularly interested in the slower time-scale dynamics that determine overall excitability, and set the stage for transient episodes of persistent oscillations, working memory, or seizures. In this second of two companion papers, we present an ionic current network model composed of populations of Hodgkin–Huxley type excitatory and inhibitory neurons embedded within extracellular space and glia, in order to investigate the role of micro-environmental ionic dynamics on the stability of persistent activity. We show that these networks reproduce seizure-like activity if glial cells fail to maintain the proper micro-environmental conditions surrounding neurons, and produce several experimentally testable predictions. Our work suggests that the stability of persistent states to perturbation is set by glial activity, and that how the response to such perturbations decays or grows may be a critical factor in a variety of disparate transient phenomena such as working memory, burst firing in neonatal brain or spinal cord, up states, seizures, and cortical oscillations.

Hierarchical analysis of piecewise affine models of gene regulatory networks

A key point in the analysis of dynamical models of biological systems is to handle systems of relatively high dimensions. In the present paper we propose a method to hierarchically organize a certain type of piecewise affine (PWA) differential systems. This specific class of systems has been extensively studied for the past few years, as it provides a good framework to model gene regulatory networks. The method, shown on several examples, allows a qualitative analysis of the asymptotic behavior of a PWA system, decomposing it into several smaller subsystems. This technique, based on the well-known strongly connected components decomposition, is not new. However, its adaptation to the non-smooth PWA differential equations turns out to be quite relevant because of the strong discrete structure underlying these equations. Its biological relevance is shown on a 7-dimensional PWA system modeling the gene network responsible for the carbon starvation response in Escherichia coli.

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The connectionist framework for gene regulation

I show that gene regulation networks are qualitatively consistent and therefore sufficiently similar to linearly seperable connectionist networks to warrant that the connectionist framework be applied to gene regulation. On this view, natural selection designs gene regulation networks to overcome the difficulty of development. I offer some general lessons about their evolvability that can be learned by examining the generic features of connectionist networks.

A queueing model for predicting message latency in uni-directional <Emphasis Type="Italic">k</Emphasis>-ary <Emphasis Type="Italic">n</Emphasis>-cubes with deterministic routing and non-uniform traffic

The interconnection network is one of the key architectural components in any parallel computer. The distribution of the traffic injected into the network is among the factors that greatly influences network performance. The uniform traffic pattern has been adopted in many existing network performance evaluation studies due to the tractability of the resulting analytical modelling approach. However, many real applications exhibit non-uniform traffic patterns such as hot-spot traffic. K-ary n-cubes have been the mostly widely used in the implementation of practical parallel systems. Extensive research studies have been conducted on the performance modelling and evaluation of these networks. Nonetheless, most of these studies have been confined to uniform traffic distributions and have been based on software simulation. The present paper proposes a new stochastic model to predict message latency in k-ary n-cubes with deterministic routing in the presence of hot-spot traffic. The model has been validated through simulation experiments and has shown a close agreement with simulation results.

Benchmarking the effects of operating system interference on extreme-scale parallel machines

We investigate operating system noise, which we identify as one of the main reasons for a lack of synchronicity in parallel applications. Using a microbenchmark, we measure the noise on several contemporary platforms and find that, even with a general-purpose operating system, noise can be limited if certain precautions are taken. We then inject artificially generated noise into a massively parallel system and measure its influence on the performance of collective operations. Our experiments indicate that on extreme-scale platforms, the performance is correlated with the largest interruption to the application, even if the probability of such an interruption on a single process is extremely small. We demonstrate that synchronizing the noise can significantly reduce its negative influence.

Spectral plots and the representation and interpretation of biological data

It is basic question in biology and other fields to identify the characteristic properties that on one hand are shared by structures from a particular realm, like gene regulation, protein–protein interaction or neural networks or foodwebs, and that on the other hand distinguish them from other structures. We introduce and apply a general method, based on the spectrum of the normalized graph Laplacian, that yields representations, the spectral plots, that allow us to find and visualize such properties systematically. We present such visualizations for a wide range of biological networks and compare them with those for networks derived from theoretical schemes. The differences that we find are quite striking and suggest that the search for universal properties of biological networks should be complemented by an understanding of more specific features of biological organization principles at different scales.

Adaptationism and the adaptive landscape

Debates over adaptationism can be clarified and partially resolved by careful consideration of the ‘grain’ at which evolutionary processes are described. The framework of ‘adaptive landscapes’ can be used to illustrate and facilitate this investigation. We argue that natural selection may have special status at an intermediate grain of analysis of evolutionary processes. The cases of sickle-cell disease and genomic imprinting are used as case studies.

Causal networks in simulated neural systems

Neurons engage in causal interactions with one another and with the surrounding body and environment. Neural systems can therefore be analyzed in terms of causal networks, without assumptions about information processing, neural coding, and the like. Here, we review a series of studies analyzing causal networks in simulated neural systems using a combination of Granger causality analysis and graph theory. Analysis of a simple target-fixation model shows that causal networks provide intuitive representations of neural dynamics during behavior which can be validated by lesion experiments. Extension of the approach to a neurorobotic model of the hippocampus and surrounding areas identifies shifting causal pathways during learning of a spatial navigation task. Analysis of causal interactions at the population level in the model shows that behavioral learning is accompanied by selection of specific causal pathways—“causal cores”—from among large and variable repertoires of neuronal interactions. Finally, we argue that a causal network perspective may be useful for characterizing the complex neural dynamics underlying consciousness.

Is it a revolution?

Jablonka and Lamb's claim that evolutionary biology is undergoing a ‘revolution’ is queried. But the very concept of revolutionary change has uncertain application to a field organized in the manner of contemporary biology. The explanatory primacy of sequence properties is also discussed.

Objects limit human comprehension

This paper demonstrates that the human visual system, the primary sensory conduit for primates, processes ambient energy in a way that obligatorily constructs the objects that we ineluctably perceive. And since our perceptual apparatus processes information only in terms of objects (along with the properties and movements of objects), we are limited in our ability to comprehend ‘what is’ when we move beyond our ordinary world of midsize objects—as, for example, when we address the micro microworld of quantum physics.

Consistency principle in biological dynamical systems

We propose a principle of consistency between different hierarchical levels of biological systems. Given a consistency between molecule replication and cell reproduction, universal statistical laws on cellular chemical abundances are derived and confirmed experimentally. They include a power law distribution of gene expressions, a lognormal distribution of cellular chemical abundances over cells, and embedding of the power law into the network connectivity distribution. Second, given a consistency between genotype and phenotype, a general relationship between phenotype fluctuations by genetic variation and isogenic phenotypic fluctuation by developmental noise is derived. Third, we discuss the chaos mechanism for stem cell differentiation with autonomous regulation, resulting from a consistency between cell reproduction and growth of the cell ensemble.

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Engineering-approach accelerates computational understanding of V1–V2 neural properties

We present two computational models (i) long-range horizontal connections and the nonlinear effect in V1 and (ii) the filling-in process at the blind spot. Both models are obtained deductively from standard regularization theory to show that physiological evidence of V1 and V2 neural properties is essential for efficient image processing. We stress that the engineering approach should be imported to understand visual systems computationally, even though this approach usually ignores physiological evidence and the target is neither neurons nor the brain.

Realistic threshold policy with hysteresis to control predator–prey continuous dynamics

This paper introduces a threshold policy with hysteresis (TPH) for the control of one-predator one-prey models. The models studied are the Lotka–Volterra and Rosenzweig–MacArthur two species density-dependent predator–prey models and the Arditi–Ginzburg nondimensional ratio-dependent model. The proposed policy (TPH) changes the dynamics of the system in such a way that a bounded oscillation is achieved confined to a region that does not allow extinction of either species. The policy can be designed by a suitable choice of so called virtual equilibrium points in a simple and intuitive manner.

Towards dynamical system models of language-related brain potentials

Event-related brain potentials (ERP) are important neural correlates of cognitive processes. In the domain of language processing, the N400 and P600 reflect lexical-semantic integration and syntactic processing problems, respectively. We suggest an interpretation of these markers in terms of dynamical system theory and present two nonlinear dynamical models for syntactic computations where different processing strategies correspond to functionally different regions in the system’s phase space.