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Philip Holmes
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Journal Articles
Publisher: Journals Gateway
Neural Computation (2012) 24 (8): 2078–2118.
Published: 01 August 2012
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We study the dynamics of a quadratic integrate-and-fire model of a single-compartment neuron with a slow recovery variable, as input current and parameters describing timescales, recovery variable, and postspike reset change. Analysis of a codimension 2 bifurcation reveals that the domain of attraction of a stable hyperpolarized rest state interacts subtly with reset parameters, which reposition the system state after spiking. We obtain explicit approximations of instantaneous firing rates for fixed values of the recovery variable, and use the averaging theorem to obtain asymptotic firing rates as a function of current and reset parameters. Along with the different phase-plane geometries, these computations provide explicit tools for the interpretation of different spiking patterns and guide parameter selection in modeling different cortical cell types.
Includes: Supplementary data
Journal Articles
Publisher: Journals Gateway
Neural Computation (2009) 21 (9): 2407–2436.
Published: 01 September 2009
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Performance on serial tasks is influenced by first- and higher-order sequential effects, respectively, due to the immediately previous and earlier trials. As response-to-stimulus interval (RSI) increases, the pattern of reaction times transits from a benefit-only mode, traditionally ascribed to automatic facilitation (AF), to a cost-benefit mode, due to strategic expectancy (SE). To illuminate the sources of such effects, we develop a connectionist network of two mutually inhibiting neural decision units subject to feedback from previous trials. A study of separate biasing mechanisms shows that residual decision unit activity can lead to only first-order AF, but higher-order AF can result from strategic priming mediated by conflict monitoring, which we instantiate in two distinct versions. A further mechanism mediates expectation-related biases that grow during RSI toward saturation levels determined by weighted repetition (or alternation) sequence lengths. Equipped with these mechanisms, the network, consistent with known neurophysiology, accounts for several sets of behavioral data over a wide range of RSIs. The results also suggest that practice speeds up all the mechanisms rather than adjusting their relative strengths.
Includes: Supplementary data
Journal Articles
Publisher: Journals Gateway
Neural Computation (2009) 21 (6): 1520–1553.
Published: 01 June 2009
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The Eriksen task is a classical paradigm that explores the effects of competing sensory inputs on response tendencies and the nature of selective attention in controlling these processes. In this task, conflicting flanker stimuli interfere with the processing of a central target, especially on short reaction time trials. This task has been modeled by neural networks and more recently by a normative Bayesian account. Here, we analyze the dynamics of the Bayesian models, which are nonlinear, coupled discrete time dynamical systems, by considering simplified, approximate systems that are linear and decoupled. Analytical solutions of these allow us to describe how posterior probabilities and psychometric functions depend on model parameters. We compare our results with numerical simulations of the original models and derive fits to experimental data, showing that agreements are rather good. We also investigate continuum limits of these simplified dynamical systems and demonstrate that Bayesian updating is closely related to a drift-diffusion process, whose implementation in neural network models has been extensively studied. This provides insight into how neural substrates can implement Bayesian computations.
Journal Articles
Publisher: Journals Gateway
Neural Computation (2008) 20 (2): 345–373.
Published: 01 February 2008
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We analyze a neural network model of the Eriksen task: a two-alternative forced-choice task in which subjects must correctly identify a central stimulus and disregard flankers that may or may not be compatible with it. We linearize and decouple the model, deriving a reduced drift-diffusion process with variable drift rate that describes the accumulation of net evidence in favor of either alternative, and we use this to analytically describe how accuracy and response time data depend on model parameters. Such analyses both assist parameter tuning in network models and suggest explanations of changing drift rates in terms of attention. We compare our results with numerical simulations of the full nonlinear model and with empirical data and show good fits to both with fewer parameters.
Journal Articles
Publisher: Journals Gateway
Neural Computation (2004) 16 (4): 673–715.
Published: 01 April 2004
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We undertake a probabilistic analysis of the response of repetitively firing neural populations to simple pulselike stimuli. Recalling and extending results from the literature, we compute phase response curves (PRCs) valid near bifurcations to periodic firing for Hindmarsh-Rose, Hodgkin-Huxley, Fitz Hugh-Nagumo, and Morris-Lecar models, encompassing the four generic (codimension one) bifurcations. Phase density equations are then used to analyze the role of the bifurcation, and the resulting PRC, in responses to stimuli. In particular, we explore the interplay among stimulus duration, baseline firing frequency, and population-level response patterns. We interpret the results in terms of the signal processing measure of gain and discuss further applications and experimentally testable predictions.