Stochastic Neuron Model with Dynamic Synapses and Evolution Equation of Its Density Function

2005 ◽  
pp. 449-455
Author(s):  
Wentao Huang ◽  
Licheng Jiao ◽  
Yuelei Xu ◽  
Maoguo Gong
Keyword(s):  
Evolution Equation ◽  
Density Function ◽  
Neuron Model ◽  
Dynamic Synapses ◽  
Stochastic Neuron

scholarly journals Stimulation Strategies for Tinnitus Suppression in a Neuron Model

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Alessandra Paffi ◽  
Francesca Camera ◽  
Chiara Carocci ◽  
Francesca Apollonio ◽  
Micaela Liberti
Keyword(s):  
Gaussian Noise ◽  
Neuron Model ◽  
Continuous Wave ◽  
Experimental Studies ◽  
Neuronal Firing ◽  
White Gaussian Noise ◽  
Cochlear Prosthesis ◽  
Continuous Waves ◽  
Stochastic Neuron ◽  
Underlying Mechanisms

Tinnitus is a debilitating perception of sound in the absence of external auditory stimuli. It may have either a central or a peripheral origin in the cochlea. Experimental studies evidenced that an electrical stimulation of peripheral auditory fibers may alleviate symptoms but the underlying mechanisms are still unknown. In this work, a stochastic neuron model is used, that mimics an auditory fiber affected by tinnitus, to check the effects, in terms of firing reduction, of different kinds of electric stimulations, i.e., continuous wave signals and white Gaussian noise. Results show that both white Gaussian noise and continuous waves at tens of kHz induce a neuronal firing reduction; however, for the same amplitude of fluctuations, Gaussian noise is more efficient than continuous waves. When contemporary applied, signal and noise exhibit a cooperative effect in retrieving neuronal firing to physiological values. These results are a proof of concept that a combination of signal and noise could be delivered through cochlear prosthesis for tinnitus suppression.

Linear and Nonlinear Electrical Models of Neurons for Hopfield Neural Network

2016 ◽  
Vol 71 (11) ◽  
pp. 995-1002
Author(s):  
Farah Sarwar ◽  
Shaukat Iqbal ◽  
Muhammad Waqar Hussain
Keyword(s):  
Neural Network ◽  
Neuron Model ◽  
Deterministic Model ◽  
Hopfield Neural Network ◽  
Biological Properties ◽  
Operational Amplifiers ◽  
Nonlinear Input ◽  
Stochastic Neuron ◽  
Output Characteristics ◽  
The Stability

AbstractA novel electrical model of neuron is proposed in this presentation. The suggested neural network model has linear/nonlinear input-output characteristics. This new deterministic model has joint biological properties in excellent agreement with the earlier deterministic neuron model of Hopfield and Tank and to the stochastic neuron model of McCulloch and Pitts. It is an accurate portrayal of differential equation presented by Hopfield and Tank to mimic neurons. Operational amplifiers, resistances, capacitor, and diodes are used to design this system. The presented biological model of neurons remains to be advantageous for simulations. Impulse response is studied and conferred to certify the stability and strength of this innovative model. A simple illustration is mapped to demonstrate the exactness of the intended system. Precisely mapped illustration exhibits 100 % accurate results.

scholarly journals A computable evolution equation for the joint response-excitation probability density function of stochastic dynamical systems

2011 ◽  
Vol 468 (2139) ◽  
pp. 759-783 ◽  
Author(s):  
D. Venturi ◽  
T. P. Sapsis ◽  
H. Cho ◽  
G. E. Karniadakis
Keyword(s):  
Probability Density Function ◽  
Evolution Equation ◽  
Probability Density ◽  
Density Function ◽  
Random Noise ◽  
Functional Integral ◽  
Excitation Density ◽  
Numerical Verification ◽  
Markovian Systems ◽  
Excitation Probability

By using functional integral methods, we determine a computable evolution equation for the joint response-excitation probability density function of a stochastic dynamical system driven by coloured noise. This equation can be represented in terms of a superimposition of differential constraints, i.e. partial differential equations involving unusual limit partial derivatives, the first one of which was originally proposed by Sapsis & Athanassoulis. A connection with the classical response approach is established in the general case of random noise with arbitrary correlation time, yielding a fully consistent new theory for non-Markovian systems. We also address the question of computability of the joint response-excitation probability density function as a solution to a boundary value problem involving only one differential constraint. By means of a simple analytical example, it is shown that, in general, such a problem is undetermined, in the sense that it admits an infinite number of solutions. This issue can be overcome by completing the system with additional relations yielding a closure problem, which is similar to the one arising in the standard response theory. Numerical verification of the equations for the joint response-excitation density is obtained for a tumour cell growth model under immune response.

Estimation and Verification of a Stochastic Neuron Model

1986 ◽  
Vol BME-33 (7) ◽  
pp. 654-666 ◽  
Author(s):  
William D. O'Neill ◽  
James C. Lin ◽  
Ying-Chang Ma
Keyword(s):  
Neuron Model ◽  
Stochastic Neuron

Notes on Bell-Sejnowski PDF-Matching Neuron

2002 ◽  
Vol 14 (12) ◽  
pp. 2847-2855 ◽  
Author(s):  
Simone Fiori
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Maximum Entropy ◽  
Density Function ◽  
Single Unit ◽  
Neuron Model ◽  
Maximum Entropy Principle ◽  
Entropy Principle ◽  
Single Input ◽  
Pdf Matching

This article investigates the behavior of a single-input, single-unit neuron model of the Bell-Sejnowski class, which learn through the maximum-entropy principle, in order to understand its probability density function matching ability.

scholarly journals Temporal discrimination from the interaction between dynamic synapses and intrinsic subthreshold oscillations

2019 ◽  
Author(s):  
Joaquin J. Torres ◽  
Fabiano Baroni ◽  
Roberto Latorre ◽  
Pablo Varona
Keyword(s):  
Information Processing ◽  
Neuron Model ◽  
Temporal Discrimination ◽  
Temporal Structure ◽  
Synaptic Strength ◽  
Input Output ◽  
Subthreshold Oscillations ◽  
Dynamic Synapses ◽  
Synaptic Dynamics ◽  
Neuronal Computation

AbstractThe interaction between synaptic and intrinsic dynamics can efficiently shape neuronal input-output relationships in response to temporally structured spike trains. We use a neuron model with subthreshold oscillations receiving inputs through a synapse with short-term depression and facilitation to show that the combination of intrinsic subthreshold and synaptic dynamics leads to channel-specific nontrivial responses and recognition of specific temporal structures. We employ the Generalized Integrate-and-Fire (GIF) model, which can be subjected to analytical characterization. We map the temporal structure of spike input trains to the type of spike response, and show how the emergence of nontrivial input-output preferences is modulated by intrinsic and synaptic parameters in a synergistic manner. We demonstrate that these temporal input discrimination properties are robust to noise and to variations in synaptic strength, suggesting that they likely contribute to neuronal computation in biological circuits. Furthermore, we also illustrate the presence of these input-output relationships in conductance-based models.Author summaryNeuronal subthreshold oscillations underlie key aspects of information processing in single neuron and network dynamics. Dynamic synapses provide a channel-specific temporal modulation of input information. We combine a neuron model that displays subthreshold oscillations and a dynamic synapse to analytically assess their interplay in processing trains of spike-mediated synaptic currents. Our results show that the co-action of intrinsic and synaptic dynamics builds nontrivial input-output relationships, which are resistant to noise and to changes in synaptic strength. The discrimination of a precise temporal structure of the input signal is shaped as a function of the joint interaction of intrinsic oscillations and synaptic dynamics. This interaction can result in channel-specific recognition of precise temporal patterns, hence greatly expanding the flexibility and complexity in information processing achievable by individual neurons with respect to temporal discrimination mechanisms based on intrinsic neuronal dynamics alone.

scholarly journals Some remarks on modelling the PDF of the concentration of a dispersing scalar in turbulence

2002 ◽  
Vol 13 (1) ◽  
pp. 95-108 ◽  
Author(s):  
P. C. CHATWIN
Keyword(s):  
Probability Density Function ◽  
Evolution Equation ◽  
Turbulent Flow ◽  
Probability Density ◽  
Density Function ◽  
Molecular Diffusion ◽  
Concentration Field ◽  
Similarity Solutions ◽  
Small Scale ◽  
Probability Density Function Pdf

The paper deals with the probability density function (PDF) of the concentration of a scalar within a turbulent flow. Following some comments about the overall structure of the PDF, and its approach to a limit at large times, attention focusses on the so-called small scale mixing term in the evolution equation for the PDF. This represents the effect of molecular diffusion in reducing concentration uctuations, eventually to zero. Arguments are presented which suggest that this quantity could, in certain circumstances, depend inversely upon the PDF, and a particular example of this leads to a new closure hypothesis. Consequences of this, especially similarity solutions, are explored for the case when the concentration field is statistically homogeneous.

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