The time course of perceptual choice is discussed in a model based on gradual and stochastic accumulation of information in non-linear decision units with leakage (or decay of activation) and competition through lateral inhibition. In special cases, the model becomes equivalent to a classical diffusion process, but leakage and mutual inhibition work together to address several challenges to existing diffusion, random-walk, and accumulator models. The model provides a good account of data from choice tasks using both time-controlled (e.g., deadline or response signal) and standard reaction time paradigms and its overall adequacy compares favorably with that of other approaches. An experimental paradigm that explicitly controls the timing of information supporting different choice alternatives provides further support. The model captures flexible choice behavior regardless of the number of alternatives, accounting for the linear slowing of reaction time as a function of the log of the number of alternatives (Hick’s law) and explains a complex pattern of visual and contextual priming effects in visual word identification. Perceptual Choice 2 When an experience presents itself to the senses, the need often arises to determine its identity or to make some other judgment about it. In experimental paradigms, the time course of this judgment process is

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An integral equation describing the time evolution of the population activity in a homogeneous pool of spiking neurons of the integrate-and-fire type is discussed. It is analytically shown that transients from a state of incoherent firing can be immediate. The stability of incoherent firing is analyzed in terms of the noise level and transmission delay and a bifurcation diagram is derived. The response of a population of noisy integrate-and-fire neurons to an input current of small amplitude is calculated and characterized by a linear filter L. The stability of perfectly synchronized `locked' solutions is analyzed.

Bifurcation mechanisms involved in the generation of action potentials (spikes) by neurons are reviewed here. We show how the type of bifurcation determines the neuro-computational properties of the cells. For example, when the rest state is near a saddle-node bifurcation, the cell can fire all-or-none spikes with an arbitrary low frequency, it has a well-defined threshold manifold, and it acts as an integrator; i.e. the higher the frequency of incoming pulses, the sooner it fires. In contrast, when the rest state is near an Andronov–Hopf bifurcation, the cell fires in a certain frequency range, its spikes are not all-or-none, it does not have a well-defined threshold manifold, it can fire in response to an inhibitory pulse, and it acts as a resonator; i.e. it responds preferentially to a certain (resonant) frequency of the input. Increasing the input frequency may actually delay or terminate its firing. We also describe the phenomenon of neural bursting, and we use geometric bifurcation theory to extend the existing classification of bursters, including many new types. We discuss how the type of burster defines its neuro-computational properties, and we show that different bursters can interact, synchronize and process information differently.

Transmission across neocortical synapses depends on the frequency of presynaptic activity (Thomson & Deuchars 1994). Inter-pyramidal synapses in layer V exhibit fast depression of synaptic transmission while other types of synapses exhibit facilitation of transmission. To study the role of dynamic synapses in network computation, we propose a unified phenomenological model which allows computation of the post-synaptic current generated by both types of synapses when driven by an arbitrary pattern of action potential (AP) activity in a presynaptic population. Using this formalism we analyze different regimes of synaptic transmission and demonstrate that dynamic synapses transmit different aspects of the presynaptic activity depending on the average presynaptic frequency. The model also allows for derivation of mean-field equations which govern the activity of large interconnected networks. We show that dynamics of synaptic transmission results in complex sets of regular and irregular...

The nature and origin of the temporal irregularity in the electrical activity of cortical neurons in vivo are still not well understood. We consider the hypothesis that this irregularity is due to a balance of excitatory and inhibitory currents into the cortical cells. We study a network model with excitatory and inhibitory populations of simple binary units. The internal feedback is mediated by relatively large synaptic strengths, so that the magnitude of the total excitatory as well as inhibitory feedback is much larger than the neuronal threshold. The connectivity is random and sparse. The mean number of connections per unit is large but small compared to the total number of cells in the network. The network also receives a large, temporally regular input from external sources. An analytical solution of the mean-field theory of this model which is exact in the limit of large network size is presented. This theory reveals a new cooperative stationary state of large networks, which we term a balanced state. In this state, a balance between the excitatory and inhibitory inputs emerges dynamically for a wide range of parameters, resulting in a net input whose temporal fluctuations are of the same order as its mean. The internal synaptic inputs act as a strong negative feedback, which linearizes the population responses to the external drive despite the strong nonlinearity of the individual cells. This feedback also greatly stabilizes 1 the system's state and enables it to track a time-dependent input on time scales much shorter than the time constant of a single cell. The spatio-temporal statistics of the balanced state is calculated. It is shown that the auto-correlations decay on a short time scale yielding an approximate Poissonian temporal s...

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Introduction In standard neural network theory, neurons are described in terms of mean firing rates. The analog input variable I is mapped via a nonlinear gain function g to an analog output variable = g(I) which may be interpreted as the mean firing rate. If the input consists of output rates j of other neurons weighted by a factor w ij , we arrive at the standard formula i = g( X j w ij j ) (10.1) which is the starting point of most neural network theories. As we have seen in Chapter 1, the firing rate defined by a temporal average over many spikes of a single neuron is a concept which works well if the input is constant or changes on a time scale which is slow with respect to the size of the temporal averaging window. Sensory inpu

To the best of my knowledge, this thesis contains no copy or paraphrase of work published by another person, except where duly acknowledged in the text. This thesis contains no material which has been presented for a degree at the University of Sydney or any other university.