Perceived state of self during motion can differentially modulate numerical magnitude allocation.

Although a direct relationship between numerical-allocation and spatial-attention has been proposed, recent research suggests these processes are not directly coupled. In keeping with this, spatial attention shifts induced either via visual or vestibular motion can modulate numerical allocation in some circumstances but not in others. In addition to shifting spatial attention, visual or vestibular motion-paradigms also (i) elicit compensatory eye-movements which themselves can influence numerical-processing and (ii) alter the perceptual-state of-"self", inducing changes in bodily self-consciousness impacting upon cognitive mechanisms. Thus, the precise mechanism by which motion modulates numerical-allocation remains unknown. We sought to investigate the influence that different perceptual experiences of motion have upon numerical magnitude allocation whilst controlling for both eye-movements and task-related effects. We first used optokinetic visual-motion stimulation (OKS) to elicit the perceptual experience of either "visual world" or "self"-motion during which eye movements were identical. In a second experiment we used a vestibular protocol examining the effects of perceived and subliminal angular rotations in darkness, which also provoked identical eye movements. We observed that during the perceptual experience of "visual-world" motion, rightward OKS biased judgments towards smaller numbers, whereas leftward OKS biased judgments towards larger numbers. During the perceptual experience of "self-motion", judgments were biased towards larger numbers irrespective of the OKS direction. Contrastingly, vestibular motion perception was found not to modulate numerical magnitude allocation, nor was there any differential modulation when comparing "perceived" versus "subliminal" rotations. We provide a novel demonstration that magnitude-allocation can be differentially modulated by the perceptual state of-self during visual-motion. This article is protected by copyright. All rights reserved

Synchronized dynamics of cortical neurons with time-delay feedback

The dynamics of three mutually coupled cortical neurons with time delays in the coupling are explored numerically and analytically. The neurons are coupled in a line, with the middle neuron sending a somewhat stronger projection to the outer neurons than the feedback it receives, to model for instance the relay of a signal from primary to higher cortical areas. For a given coupling architecture, the delays introduce correlations in the time series at the time-scale of the delay. It was found that the middle neuron leads the outer ones by the delay time, while the outer neurons are synchronized with zero lag times. Synchronization is found to be highly dependent on the synaptic time constant, with faster synapses increasing both the degree of synchronization and the firing rate. Analysis shows that presynaptic input during the interspike interval stabilizes the synchronous state, even for arbitrarily weak coupling, and independent of the initial phase. The finding may be of significance to synchronization of large groups of cells in the cortex that are spatially distanced from each other.Comment: 21 pages, 11 figure

Spreading, Nonergodicity, and Selftrapping: a puzzle of interacting disordered lattice waves

Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transitions, the quantum Hall effect, light propagation in photonic crystals, and dynamics of ultra-cold atoms in optical arrays, to name just a few examples. Large intensity light can induce nonlinear response, ultracold atomic gases can be tuned into an interacting regime, which leads again to nonlinear wave equations on a mean field level. The interplay between disorder and nonlinearity, their localizing and delocalizing effects is currently an intriguing and challenging issue in the field of lattice waves. In particular it leads to the prediction and observation of two different regimes of destruction of Anderson localization - asymptotic weak chaos, and intermediate strong chaos, separated by a crossover condition on densities. On the other side approximate full quantum interacting many body treatments were recently used to predict and obtain a novel many body localization transition, and two distinct phases - a localization phase, and a delocalization phase, both again separated by some typical density scale. We will discuss selftrapping, nonergodicity and nonGibbsean phases which are typical for such discrete models with particle number conservation and their relation to the above crossover and transition physics. We will also discuss potential connections to quantum many body theories.Comment: 13 pages in Springer International Publishing Switzerland 2016 1 M. Tlidi and M. G. Clerc (eds.), Nonlinear Dynamics: Materials, Theory and Experiment, Springer Proceedings in Physics 173. arXiv admin note: text overlap with arXiv:1405.112

Suppression of growth by multiplicative white noise in a parametric resonant system

The author studied the growth of the amplitude in a Mathieu-like equation with multiplicative white noise. The approximate value of the exponent at the extremum on parametric resonance regions was obtained theoretically by introducing the width of time interval, and the exponents were calculated numerically by solving the stochastic differential equations by a symplectic numerical method. The Mathieu-like equation contains a parameter $\alpha$ that is determined by the intensity of noise and the strength of the coupling between the variable and the noise. The value of $\alpha$ was restricted not to be negative without loss of generality. It was shown that the exponent decreases with $\alpha$, reaches a minimum and increases after that. It was also found that the exponent as a function of $\alpha$ has only one minimum at $\alpha \neq 0$ on parametric resonance regions of $\alpha = 0$. This minimum value is obtained theoretically and numerically. The existence of the minimum at $\alpha \neq 0$ indicates the suppression of the growth by multiplicative white noise.Comment: The title and the description in the manuscript are change

Desynchronizing effect of high-frequency stimulation in a generic cortical network model

Transcranial Electrical Stimulation (TCES) and Deep Brain Stimulation (DBS) are two different applications of electrical current to the brain used in different areas of medicine. Both have a similar frequency dependence of their efficiency, with the most pronounced effects around 100Hz. We apply superthreshold electrical stimulation, specifically depolarizing DC current, interrupted at different frequencies, to a simple model of a population of cortical neurons which uses phenomenological descriptions of neurons by Izhikevich and synaptic connections on a similar level of sophistication. With this model, we are able to reproduce the optimal desynchronization around 100Hz, as well as to predict the full frequency dependence of the efficiency of desynchronization, and thereby to give a possible explanation for the action mechanism of TCES.Comment: 9 pages, figs included. Accepted for publication in Cognitive Neurodynamic

Signal Propagation in Feedforward Neuronal Networks with Unreliable Synapses

In this paper, we systematically investigate both the synfire propagation and firing rate propagation in feedforward neuronal network coupled in an all-to-all fashion. In contrast to most earlier work, where only reliable synaptic connections are considered, we mainly examine the effects of unreliable synapses on both types of neural activity propagation in this work. We first study networks composed of purely excitatory neurons. Our results show that both the successful transmission probability and excitatory synaptic strength largely influence the propagation of these two types of neural activities, and better tuning of these synaptic parameters makes the considered network support stable signal propagation. It is also found that noise has significant but different impacts on these two types of propagation. The additive Gaussian white noise has the tendency to reduce the precision of the synfire activity, whereas noise with appropriate intensity can enhance the performance of firing rate propagation. Further simulations indicate that the propagation dynamics of the considered neuronal network is not simply determined by the average amount of received neurotransmitter for each neuron in a time instant, but also largely influenced by the stochastic effect of neurotransmitter release. Second, we compare our results with those obtained in corresponding feedforward neuronal networks connected with reliable synapses but in a random coupling fashion. We confirm that some differences can be observed in these two different feedforward neuronal network models. Finally, we study the signal propagation in feedforward neuronal networks consisting of both excitatory and inhibitory neurons, and demonstrate that inhibition also plays an important role in signal propagation in the considered networks.Comment: 33pages, 16 figures; Journal of Computational Neuroscience (published

Thermal conductivity of nonlinear waves in disordered chains

We present computational data on the thermal conductivity of nonlinear waves in disordered chains. Disorder induces Anderson localization for linear waves and results in a vanishing conductivity. Cubic nonlinearity restores normal conductivity, but with a strongly temperature-dependent conductivity $\kappa(T)$. We find indications for an asymptotic low-temperature $\kappa \sim T^4$ and intermediate temperature $\kappa \sim T^2$ laws. These findings are in accord with theoretical studies of wave packet spreading, where a regime of strong chaos is found to be intermediate, followed by an asymptotic regime of weak chaos (EPL 91 (2010) 30001).Comment: 8 pages, 3 figure

Analysing Dynamical Behavior of Cellular Networks via Stochastic Bifurcations

The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types

Maintaining extensivity in evolutionary multiplex networks

In this paper, we explore the role of network topology on maintaining the extensive property of entropy. We study analytically and numerically how the topology contributes to maintaining extensivity of entropy in multiplex networks, i.e. networks of subnetworks (layers), by means of the sum of the positive Lyapunov exponents, HKS, a quantity related to entropy. We show that extensivity relies not only on the interplay between the coupling strengths of the dynamics associated to the intra (short-range) and inter (long-range) interactions, but also on the sum of the intra-degrees of the nodes of the layers. For the analytically treated networks of size N, among several other results, we show that if the sum of the intra-degrees (and the sum of inter-degrees) scales as N?+1, ? > 0, extensivity can be maintained if the intra-coupling (and the inter-coupling) strength scales as N??, when evolution is driven by the maximisation of HKS. We then verify our analytical results by performing numerical simulations in multiplex networks formed by electrically and chemically coupled neurons