scholarly journals A Result of Metastability for an Infinite System of Spiking Neurons

2019 ◽  
Vol 177 (5) ◽  
pp. 984-1008 ◽  
Author(s):  
Morgan André
Keyword(s):  
Infinite System ◽  
Spiking Neurons

scholarly journals Discrete Nonlinear Schrödinger Systems for Periodic Media with Nonlocal Nonlinearity: The Case of Nematic Liquid Crystals

2021 ◽  
Vol 11 (10) ◽  
pp. 4420
Author(s):  
Panayotis Panayotaros
Keyword(s):  
Differential Equation ◽  
Infinite System ◽  
Linear Part ◽  
Optical Power ◽  
Explicit Construction ◽  
Translation Invariance ◽  
Nonlocal Nonlinearity ◽  
Wannier Functions ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrödinger Systems

We study properties of an infinite system of discrete nonlinear Schrödinger equations that is equivalent to a coupled Schrödinger-elliptic differential equation with periodic coefficients. The differential equation was derived as a model for laser beam propagation in optical waveguide arrays in a nematic liquid crystal substrate and can be relevant to related systems with nonlocal nonlinearities. The infinite system is obtained by expanding the relevant physical quantities in a Wannier function basis associated to a periodic Schrödinger operator appearing in the problem. We show that the model can describe stable beams, and we estimate the optical power at different length scales. The main result of the paper is the Hamiltonian structure of the infinite system, assuming that the Wannier functions are real. We also give an explicit construction of real Wannier functions, and examine translation invariance properties of the linear part of the system in the Wannier basis.

scholarly journals Using a Low-Power Spiking Continuous Time Neuron (SCTN) for Sound Signal Processing

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1065
Author(s):  
Moshe Bensimon ◽  
Shlomo Greenberg ◽  
Moshe Haiut
Keyword(s):  
Neural Network ◽  
Network Structure ◽  
Analog Circuits ◽  
Continuous Time ◽  
Spiking Neurons ◽  
Spiking Neural Network ◽  
Sound Classification ◽  
Classification Framework ◽  
Neural Network Structure ◽  
Simple Analog

This work presents a new approach based on a spiking neural network for sound preprocessing and classification. The proposed approach is biologically inspired by the biological neuron’s characteristic using spiking neurons, and Spike-Timing-Dependent Plasticity (STDP)-based learning rule. We propose a biologically plausible sound classification framework that uses a Spiking Neural Network (SNN) for detecting the embedded frequencies contained within an acoustic signal. This work also demonstrates an efficient hardware implementation of the SNN network based on the low-power Spike Continuous Time Neuron (SCTN). The proposed sound classification framework suggests direct Pulse Density Modulation (PDM) interfacing of the acoustic sensor with the SCTN-based network avoiding the usage of costly digital-to-analog conversions. This paper presents a new connectivity approach applied to Spiking Neuron (SN)-based neural networks. We suggest considering the SCTN neuron as a basic building block in the design of programmable analog electronics circuits. Usually, a neuron is used as a repeated modular element in any neural network structure, and the connectivity between the neurons located at different layers is well defined. Thus, generating a modular Neural Network structure composed of several layers with full or partial connectivity. The proposed approach suggests controlling the behavior of the spiking neurons, and applying smart connectivity to enable the design of simple analog circuits based on SNN. Unlike existing NN-based solutions for which the preprocessing phase is carried out using analog circuits and analog-to-digital conversion, we suggest integrating the preprocessing phase into the network. This approach allows referring to the basic SCTN as an analog module enabling the design of simple analog circuits based on SNN with unique inter-connections between the neurons. The efficiency of the proposed approach is demonstrated by implementing SCTN-based resonators for sound feature extraction and classification. The proposed SCTN-based sound classification approach demonstrates a classification accuracy of 98.73% using the Real-World Computing Partnership (RWCP) database.

Pulse Inputs Affect Timings of Spikes in Neurons with or Without Time Delays

2019 ◽  
Vol 20 (3-4) ◽  
pp. 257-267
Author(s):  
Jiaoyan Wang ◽  
Xiaoshan Zhao ◽  
Chao Lei
Keyword(s):  
Time Delays ◽  
Single Neuron ◽  
Spiking Neurons ◽  
Phase Resetting ◽  
Subthreshold Oscillations ◽  
Weak Pulse

AbstractInputs can change timings of spikes in neurons. But it is still not clear how input’s parameters for example injecting time of inputs affect timings of neurons. HR neurons receiving both weak and strong inputs are considered. How pulse inputs affecting neurons is studied by using the phase-resetting curve technique. For a single neuron, weak pulse inputs may advance or delay the next spike, while strong pulse inputs may induce subthreshold oscillations depending on parameters such as injecting timings of inputs. The behavior of synchronization in a network with or without coupling delays can be predicted by analysis in a single neuron. Our results can be used to predict the effects of inputs on other spiking neurons.

scholarly journals Differential Games for an Infinite 2-Systems of Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1467
Author(s):  
Muminjon Tukhtasinov ◽  
Gafurjan Ibragimov ◽  
Sarvinoz Kuchkarova ◽  
Risman Mat Hasim
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Differential Games ◽  
Differential Game ◽  
Infinite System ◽  
The State ◽  
Geometric Constraints ◽  
Control Parameters ◽  
Systems Of Differential Equations ◽  
Pursuit And Evasion

A pursuit differential game described by an infinite system of 2-systems is studied in Hilbert space l2. Geometric constraints are imposed on control parameters of pursuer and evader. The purpose of pursuer is to bring the state of the system to the origin of the Hilbert space l2 and the evader tries to prevent this. Differential game is completed if the state of the system reaches the origin of l2. The problem is to find a guaranteed pursuit and evasion times. We give an equation for the guaranteed pursuit time and propose an explicit strategy for the pursuer. Additionally, a guaranteed evasion time is found.

scholarly journals Solvability of an infinite system of integral equations on the real half-axis

2020 ◽  
Vol 10 (1) ◽  
pp. 202-216
Author(s):  
Józef Banaś ◽  
Weronika Woś
Keyword(s):  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Main Tool ◽  
Supremum Norm ◽  
Nonlinear Integral Equations ◽  
Measures Of Noncompactness ◽  
System Of Integral Equations ◽  
The Real ◽  
Half Axis

Abstract The aim of the paper is to investigate the solvability of an infinite system of nonlinear integral equations on the real half-axis. The considerations will be located in the space of function sequences which are bounded at every point of the half-axis. The main tool used in the investigations is the technique associated with measures of noncompactness in the space of functions defined, continuous and bounded on the real half-axis with values in the space l∞ consisting of real bounded sequences endowed with the standard supremum norm. The essential role in our considerations is played by the fact that we will use a measure of noncompactness constructed on the basis of a measure of noncompactness in the mentioned sequence space l∞. An example illustrating our result will be included.

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