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Search results for: FIRING MAP
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Firing map of an almost periodic input function
PublicationIn mathematical biology and the theory of electric networks the firing map of an integrate-and-fire system is a notion of importance. In order to prove useful properties of this map authors of previous papers assumed that the stimulus function f of the system ẋ = f(t,x) is continuous and usually periodic in the time variable. In this work we show that the required properties of the firing map for the simplified model ẋ = f(t) still...
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Firing map for periodically and almost-periodically driven integrate-and-fire models: a dynamical systems approach
PublicationWe consider the Leaky Integrate-and-Fire and Perfect Integrator models of neuron’s dynamics with the input function being periodic and almost-periodic (in the sense of Stepanov). In particular we analyze properties and dynamics of the so-called firing map, which iterations give timings of consecutive spikes of a neuron. In case of a periodic input function we provide a detailed description of the sequence of interspike-intervals,...
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On the interspike-intervals of periodically-driven integrate-and-fire models
PublicationWe analyze properties of the firing map, which iterations give information about consecutive spikes, for periodically driven linear integrate-and-fire models. By considering locally integrable (thus in general not continuous) input functions, we generalize some results of other authors. In particular, we prove theorems concerning continuous dependence of the firing map on the input in suitable function spaces. Using mathematical...
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Integrate-and-fire models with an almost periodic input function
PublicationWe investigate leaky integrate-and-fire models (LIF models for short) driven by Stepanov and μ-almost periodic functions. Special attention is paid to the properties of the firing map and its displacement, which give information about the spiking behavior of the considered system. We provide conditions under which such maps are well-defined and are uniformly continuous. We show that the LIF models with Stepanov almost periodic...
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Analysis of Interspike-Intervals for the General Class of Integrate-and-Fire Models with Periodic Drive
PublicationWe study one-dimensional integrate-and-fire models of the general type x˙=F (t, x) and analyze properties of the firing map which iterations recover consecutive spike timings. We impose very week constraints for the regularity of the function F (t, x), e.g. often it suffices to assume that F is continuous. If additionally F is periodic in t, using mathematical study of the displacement sequence of an orientation preserving circle...
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Distinct hippocampal-prefrontal neural assemblies coordinate memory encoding, maintenance, and recall
PublicationShort-term memory enables incorporation of recent experience into subsequent decision-making. This processing recruits both the prefrontal cortex and hippocampus, where neurons encode task cues, rules, and outcomes. However, precisely which information is carried when, and by which neurons, remains unclear. Using population decoding of activity in rat medial prefrontal cortex (mPFC) and dorsal hippocampal CA1, we confirm that mPFC...