Supervised Associative Learning in Spiking Neural Network

In this paper, we propose a simple supervised associative learning approach for spiking neural networks. In an excitatory-inhibitory network paradigm with Izhikevich spiking neurons, synaptic plasticity is implemented on excitatory to excitatory synapses dependent on both spike emission rates and spike timings. As results of learning, the network is able to associate not just familiar stimuli but also novel stimuli observed through synchronised activity within the same subpopulation and between two associated subpopulations

Resonance Behavior and Partial Averaging in a Three-Body System with Gravitational Radiation Damping

In a previous investigation, a model of three-body motion was developed which included the effects of gravitational radiation reaction. The aim was to describe the motion of a relativistic binary pulsar that is perturbed by a third mass and look for resonances between the binary and third mass orbits. Numerical integration of an equation of relative motion that approximates the binary gives evidence of such resonances. These $(m:n)$ resonances are defined for the present purposes by the resonance condition, $m\omega=2n\Omega$, where $m$ and $n$ are relatively prime integers and $\omega$ and $\Omega$ are the angular frequencies of the binary orbit and third mass orbit, respectively. The resonance condition consequently fixes a value for the semimajor axis $a$ of the binary orbit for the duration of the resonance because of the Kepler relationship $\omega=a^{-3/2}$. This paper outlines a method of averaging developed by Chicone, Mashhoon, and Retzloff which renders a nonlinear system that undergoes resonance capture into a mathematically amenable form. This method is applied to the present system and one arrives at an analytical solution that describes the average motion during resonance. Furthermore, prominent features of the full nonlinear system, such as the frequency of oscillation and antidamping, accord with their analytically derived formulae.Comment: 19 pages, 4 Postscript figure

Deep Neural Networks - A Brief History

Introduction to deep neural networks and their history.Comment: 14 pages, 14 figure

Investigation of vertical cavity surface emitting laser dynamics for neuromorphic photonic systems

We report an approach based upon vertical cavity surface emitting lasers (VCSELs) to reproduce optically different behaviors exhibited by biological neurons but on a much faster timescale. The technique proposed is based on the polarization switching and nonlinear dynamics induced in a single VCSEL under polarized optical injection. The particular attributes of VCSELs and the simple experimental configuration used in this work offer prospects of fast, reconfigurable processing elements with excellent fan-out and scaling potentials for use in future computational paradigms and artificial neural networks. © 2012 American Institute of Physics

Enhanced entrainability of genetic oscillators by period mismatch

Biological oscillators coordinate individual cellular components so that they function coherently and collectively. They are typically composed of multiple feedback loops, and period mismatch is unavoidable in biological implementations. We investigated the advantageous effect of this period mismatch in terms of a synchronization response to external stimuli. Specifically, we considered two fundamental models of genetic circuits: smooth- and relaxation oscillators. Using phase reduction and Floquet multipliers, we numerically analyzed their entrainability under different coupling strengths and period ratios. We found that a period mismatch induces better entrainment in both types of oscillator; the enhancement occurs in the vicinity of the bifurcation on their limit cycles. In the smooth oscillator, the optimal period ratio for the enhancement coincides with the experimentally observed ratio, which suggests biological exploitation of the period mismatch. Although the origin of multiple feedback loops is often explained as a passive mechanism to ensure robustness against perturbation, we study the active benefits of the period mismatch, which include increasing the efficiency of the genetic oscillators. Our findings show a qualitatively different perspective for both the inherent advantages of multiple loops and their essentiality.Comment: 28 pages, 13 figure

Reliable scaling exponent estimation of long-range correlated noise in the presence of random spikes

Detrended fluctuation analysis (DFA) has been used widely to determine possible long-range correlations in data obtained from diverse settings. In a recent study [1], uncorrelated random spikes superimposed on the long-range correlated noise (LR noise) were found to affect DFA scaling exponent estimates. In this brief communication, singular-value decomposition (SVD) filter is proposed to minimize the effect random spikes superimposed on LR noise, thus facilitating reliable estimation of the scaling exponents. The effectiveness of the proposed approach is demonstrated on random spikes sampled from normal and uniform distributions.Comment: 36 Pages, 20 Figure

Interaction dynamics in small networks of nonlinear elements

We study a small circuit of coupled nonlinear elements to investigate general features of signal transmission through networks. The small circuit itself is perceived as building block for larger networks. Individual dynamics and coupling are motivated by neuronal systems: We consider two types of dynamical modes for an individual element, regular spiking and chattering and each individual element can receive excitatory and/or inhibitory inputs and is subjected to different feedback types (excitatory and inhibitory; forward and recurrent). Both, deterministic and stochastic simulations are carried out to study the input-output relationships of these networks. Major results for regular spiking elements include frequency locking, spike rate amplification for strong synaptic coupling, and inhibition-induced spike rate control which can be interpreted as a output frequency rectification. For chattering elements, spike rate amplification for low frequencies and silencing for large frequencies is characteristi

The Dynamics of Hybrid Metabolic-Genetic Oscillators

The synthetic construction of intracellular circuits is frequently hindered by a poor knowledge of appropriate kinetics and precise rate parameters. Here, we use generalized modeling (GM) to study the dynamical behavior of topological models of a family of hybrid metabolic-genetic circuits known as "metabolators." Under mild assumptions on the kinetics, we use GM to analytically prove that all explicit kinetic models which are topologically analogous to one such circuit, the "core metabolator," cannot undergo Hopf bifurcations. Then, we examine more detailed models of the metabolator. Inspired by the experimental observation of a Hopf bifurcation in a synthetically constructed circuit related to the core metabolator, we apply GM to identify the critical components of the synthetically constructed metabolator which must be reintroduced in order to recover the Hopf bifurcation. Next, we study the dynamics of a re-wired version of the core metabolator, dubbed the "reverse" metabolator, and show that it exhibits a substantially richer set of dynamical behaviors, including both local and global oscillations. Prompted by the observation of relaxation oscillations in the reverse metabolator, we study the role that a separation of genetic and metabolic time scales may play in its dynamics, and find that widely separated time scales promote stability in the circuit. Our results illustrate a generic pipeline for vetting the potential success of a potential circuit design, simply by studying the dynamics of the corresponding generalized model

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

Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling

Small lattices of $N$ nearest neighbor coupled excitable FitzHugh-Nagumo systems, with time-delayed coupling are studied, and compared with systems of FitzHugh-Nagumo oscillators with the same delayed coupling. Bifurcations of equilibria in N=2 case are studied analytically, and it is then numerically confirmed that the same bifurcations are relevant for the dynamics in the case $N>2$. Bifurcations found include inverse and direct Hopf and fold limit cycle bifurcations. Typical dynamics for different small time-lags and coupling intensities could be excitable with a single globally stable equilibrium, asymptotic oscillatory with symmetric limit cycle, bi-stable with stable equilibrium and a symmetric limit cycle, and again coherent oscillatory but non-symmetric and phase-shifted. For an intermediate range of time-lags inverse sub-critical Hopf and fold limit cycle bifurcations lead to the phenomenon of oscillator death. The phenomenon does not occur in the case of FitzHugh-Nagumo oscillators with the same type of coupling.Comment: accepted by Phys.Rev.