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Gautam Kumar
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Journal Articles
Publisher: Journals Gateway
Neural Computation (2016) 28 (9): 1889–1926.
Published: 01 September 2016
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A well-known phenomenon in sensory perception is desensitization, wherein behavioral responses to persistent stimuli become attenuated over time. In this letter, our focus is on studying mechanisms through which desensitization may be mediated at the network level and, specifically, how sensitivity changes arise as a function of long-term plasticity. Our principal object of study is a generic isoinhibitory motif: a small excitatory-inhibitory network with recurrent inhibition. Such a motif is of interest due to its overrepresentation in laminar sensory network architectures. Here, we introduce a sensitivity analysis derived from control theory in which we characterize the fixed-energy reachable set of the motif. This set describes the regions of the phase-space that are more easily (in terms of stimulus energy) accessed, thus providing a holistic assessment of sensitivity. We specifically focus on how the geometry of this set changes due to repetitive application of a persistent stimulus. We find that for certain motif dynamics, this geometry contracts along the stimulus orientation while expanding in orthogonal directions. In other words, the motif not only desensitizes to the persistent input, but heightens its responsiveness (sensitizes) to those that are orthogonal. We develop a perturbation analysis that links this sensitization to both plasticity-induced changes in synaptic weights and the intrinsic dynamics of the network, highlighting that the effect is not purely due to weight-dependent disinhibition. Instead, this effect depends on the relative neuronal time constants and the consequent stimulus-induced drift that arises in the motif phase-space. For tightly distributed (but random) parameter ranges, sensitization is quite generic and manifests in larger recurrent E-I networks within which the motif is embedded.
Journal Articles
Publisher: Journals Gateway
Neural Computation (2013) 25 (12): 3183–3206.
Published: 01 December 2013
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We derive conditions for continuous differentiability of inter-spike intervals (ISIs) of spiking neurons with respect to parameters (decision variables) of an external stimulating input current that drives a recurrent network of synaptically connected neurons. The dynamical behavior of individual neurons is represented by a class of discontinuous single-neuron models. We report here that ISIs of neurons in the network are continuously differentiable with respect to decision variables if (1) a continuously differentiable trajectory of the membrane potential exists between consecutive action potentials with respect to time and decision variables and (2) the partial derivative of the membrane potential of spiking neurons with respect to time is not equal to the partial derivative of their firing threshold with respect to time at the time of action potentials. Our theoretical results are supported by showing fulfillment of these conditions for a class of known bidimensional spiking neuron models.