Hardware design of LIF with Latency neuron model with memristive STDP synapses

In this paper, the hardware implementation of a neuromorphic system is presented. This system is composed of a Leaky Integrate-and-Fire with Latency (LIFL) neuron and a Spike-Timing Dependent Plasticity (STDP) synapse. LIFL neuron model allows to encode more information than the common Integrate-and-Fire models, typically considered for neuromorphic implementations. In our system LIFL neuron is implemented using CMOS circuits while memristor is used for the implementation of the STDP synapse. A description of the entire circuit is provided. Finally, the capabilities of the proposed architecture have been evaluated by simulating a motif composed of three neurons and two synapses. The simulation results confirm the validity of the proposed system and its suitability for the design of more complex spiking neural network

Splitting physics-informed neural networks for inferring the dynamics of integer- and fractional-order neuron models

We introduce a new approach for solving forward systems of differential equations using a combination of splitting methods and physics-informed neural networks (PINNs). The proposed method, splitting PINN, effectively addresses the challenge of applying PINNs to forward dynamical systems and demonstrates improved accuracy through its application to neuron models. Specifically, we apply operator splitting to decompose the original neuron model into sub-problems that are then solved using PINNs. Moreover, we develop an $L^1$ scheme for discretizing fractional derivatives in fractional neuron models, leading to improved accuracy and efficiency. The results of this study highlight the potential of splitting PINNs in solving both integer- and fractional-order neuron models, as well as other similar systems in computational science and engineering

Linear response for spiking neuronal networks with unbounded memory

We establish a general linear response relation for spiking neuronal networks, based on chains with unbounded memory. This relation allows us to predict the influence of a weak amplitude time-dependent external stimuli on spatio-temporal spike correlations, from the spontaneous statistics (without stimulus) in a general context where the memory in spike dynamics can extend arbitrarily far in the past. Using this approach, we show how linear response is explicitly related to neuronal dynamics with an example, the gIF model, introduced by M. Rudolph and A. Destexhe. This example illustrates the collective effect of the stimuli, intrinsic neuronal dynamics, and network connectivity on spike statistics. We illustrate our results with numerical simulations.Comment: 60 pages, 8 figure

Time Fractional Cable Equation And Applications in Neurophysiology

We propose an extension of the cable equation by introducing a Caputo time fractional derivative. The fundamental solutions of the most common boundary problems are derived analitically via Laplace Transform, and result be written in terms of known special functions. This generalization could be useful to describe anomalous diffusion phenomena with leakage as signal conduction in spiny dendrites. The presented solutions are computed in Matlab and plotted.Comment: 10 figures. arXiv admin note: substantial text overlap with arXiv:1702.0532