Abstract not found

According to a popular hypothesis, short-term memories are stored as persistent neural activity maintained by synaptic feedback loops. This hypothesis has been formulated mathematically in a number of recurrent network models. Here we study an abstraction of these models, a single neuron with a synapse onto itself, or autapse. This abstraction cannot simulate the way in which persistent activity patterns are distributed over neural populations in the brain. However, with proper tuning of parameters, it does reproduce the continuously graded, or analog, nature of many examples of persistent activity. The conditions for tuning are derived for the dynamics of a conductance-based model neuron with a slow excitatory autapse. The derivation uses the method of averaging to approximate the spiking model with a nonspiking, reduced model. Short-term analog memory storage is possible if the reduced model is approximately linear, and its feedforward bias and autapse strength are precisely...

Cells in several areas of the hippocampal formation show place specific firing patterns, and are thought to form a distributed representation of an animal’s current location in an environment. Experimental results suggest that this representation is continually updated even in complete darkness, indicating the presence of a path integration mechanism in the rat. Adopting the Neural Engineering Framework (NEF) presented by Eliasmith and Anderson (2003) we derive a novel attractor network model of path integration, using heterogeneous spiking neurons. The network we derive incorporates representation and updating of position into a single layer of neurons, eliminating the need for a large external control population, and without making use of multiplicative synapses. An efficient and biologically plausible control mechanism results directly from applying the principles of the NEF. We simulate the network for a variety of inputs, analyze its performance, and give three testable predictions of our model.

In this dissertation I develop both general results on the dynamics of neural oscil-lators and integrators and specific applications of these results to brain areas involved in simple cognitive tasks. The scientific motivation is broad: neural networks inside our brains are able to adapt to changing information processing demands by exercising cognitive control, for example focussing on salient components of noisy sensory inputs when making specific decisions based on these inputs, but relaxing this focus when other needs become prominent. But what free variables or parameters can account for the observed adaptability? And does this adaptation occur optimally, with respect to simple economic metrics and physiological limitations? Here I address these questions via reduced models of neurons and populations near bifurcations, which characterize the dynamics of a brainstem nucleus involved in adaptive cognitive control, and via variational problems arising from neural signal processing, which clarify the role of this nucleus, and other dynamical mechanisms in decision tasks. First, I study and apply nonlinear oscillator dynamics. I develop and extend phase

Theoretical neuroscience has experienced explosive growth over the past 20 years. In addition to bringing new researchers into the field with backgrounds in physics, mathematics, computer science, and engineering, theoretical approaches have helped to introduce new ideas and shape directions of neuroscience research. This review presents some of the developments that have occurred and the lessons they have taught us.

appear in Neural Computation Cortical sensory neurons are known to be highly variable, in the sense that responses evoked by identical stimuli often change dramatically from trial to trial. The origin of this variability is uncertain, but it is usually interpreted as detrimental noise that reduces the computational accuracy of neural circuits. Here we investigate the possibility that such response variability might, in fact, be beneficial, because it may partially compensate for a decrease in accuracy due to stochastic changes in the synaptic strengths of a network. We study the interplay between two kinds of noise, response (or neuronal) noise and synaptic noise, by analyzing their joint influence on the accuracy of neural networks trained to perform various tasks. We find an interesting, generic interaction: when fluctuations in the synaptic connections are proportional to their strengths (multiplicative noise), a certain amount of response noise in the input neurons can significantly improve network performance, compared to the same network without response noise. Performance is enhanced because response noise and multiplicative synaptic noise are in some ways equivalent. So,

We investigated a model for the neural integrator based on hysteretic units connected by positive feedback. Hysteresis is assumed to emerge from the intrinsic properties of the cells. We consider the recurrent networks containing either bistable or multistable neurons. We apply our analysis to the oculomotor velocity-to-position neural integrator that calculates the eye positions from the inputs that carry information about eye angular velocity. Using the analysis of the system in the parameter space we show the following. The direction of hysteresis in the neuronal response may be reversed for the system with recurrent connections compared to the case of unconnected neurons. Thus, for the NMDA receptor based bistability the firing rates after ON saccades may be higher than after OFF saccades for the same eye position. We suggest that this is an emergent property due to the presence of global recurrent feedback. The reversal of hysteresis occurs only when the size of hysteresis differs from neuron to neuron. We also relate the macroscopic leak time-constant of the integrator to the rate of microscopic spontaneous noise-driven transitions in the hysteretic units. Finally, we argue that the presence of neurons with small hysteresis may remove the threshold for integration.

Abstract not found

Thepresen paper studies a feedbackregulation problem that arisesin at least twodi#eren biologicalapplication The feedbackregulation problemunbl conemkVPB:k may beinP:BkT= asan adaptivecontiv problem fortun= bifurcation parameters,an it has ns been studiedin theconzVP literature. The goal of the paper is to formulate this probleman to presen some preliminT results.

The population vector is a linear decoder for an ensemble of neurons, whose response properties are nonlinear functions of the input vector. However, previous analyses of this decoder seem to have missed the obsevation that the population vector can also be used to estimate functions of the input vector. We explore how to use singular value decomposition to delineate the class of functions which are linearly decodable from a given population of noisy neural encoders.