Analysis,Simulation, and Optimization of Stochastic Vesicle Dynamics in Synaptic Transmission

Synaptic transmission is the mechanism of information transfer from one neuron to another (or from a neuron to a muscle or to an endocrine cell). An important step in this physiological process is the stochastic release of neurotransmitter from vesicles that fuse with the presynaptic membrane and spill their contents into the synaptic cleft. We are concerned here with the formulation, analysis, and simulation of a mathematical model that describes the stochastic docking, undocking, and release of synaptic vesicles and their effect on synaptic signal transmission. The focus of this paper is on the parameter p₀, the probability of release for each docked vesicle when an action potential arrives. We study the influence of this parameter on the statistics of the release process and on the theoretical capability of the model synapse in reconstructing various desired outputs based on the timing and amount of neurotransmitter release. This theoretical capability is assessed by formulating and solving an optimal filtering problem. Methods for parameter identification are proposed and applied to simulated data. © 2019 Wiley Periodicals, Inc.     

Spatial Dynamics of Multilayer Cellular Neural Networks

The purpose of this work is to study the spatial dynamics of one-dimensional multilayer cellular neural networks. We first establish the existence of rightward and leftward spreading speeds of the model. Then we show that the spreading speeds coincide with the minimum wave speeds of the traveling wave fronts in the right and left directions. Moreover, we obtain the asymptotic behavior of the traveling wave fronts when the wave speeds are positive and greater than the spreading speeds. According to the asymptotic behavior and using various kinds of comparison theorems, some front-like entire solutions are constructed by combining the rightward and leftward traveling wave fronts with different speeds and a spatially homogeneous solution of the model. Finally, various qualitative features of such entire solutions are investigated.     

Low Dimension Models of Continuously Variable Transmission Dynamics

The paper considers low dimension models describing the dynamics of a continuously variable transmission. Unlike other models, they are aimed primarily on the computer simulation of global dynamics, rather than on the reconstruction of detailed stressed and deformed state. Due to the low dimension of the models, simulation times are much less than those for large models. Therefore, the models proposed can be used for real-time or faster simulations.     

Approximation of Neural Network Dynamics by Reaction-Diffusion Equations

The equations of the Hopfield network, without the constraint of symmetry, can have complex behaviours. Cottet borrowed techniques from particle methods to show that a class of such networks with symmetric, translation-invariant connection matrices may be approximated by a reaction–diffusion equation. This idea is extended to a wider class of network connections yielding a slightly more complex reaction–diffusion equation. It is also shown that the approximation holds rigorously only in certain spatial regions (even for Cottet's special case) but the small regions where it fails, namely within transition layers between regions of high and low activity, are not likely to be critical.     

The Effects of Migration on the Transmission Dynamics of Sickle Cell Anaemia

Among the factors which should be considered in the formulation of a model representing a phenomenon in population dynamics, migration has always been the most difficult to treat mathematically and, hence, it has not been given prominence by researchers over the years. Nevertheless, in this paper we shall analyze its role in the transmission dynamics of a genetically transmitted disease, the Sickle-Cell Anaemia.     

Dynamics about Neural Array with Simple Lateral Inhibitory Connections

Lateral inhibitory effect is a well-known feature of information processing in neural systems. This paper presents a neural array model with simple lateral inhibitory connections. After detailed examining into the dynamics of this kind of neural array, the author gives the sufficient conditions under which the outputs of the network will tend to a special stable pattern called spatial sparse pattern in which if the output of a neuron is 1, then the outputs of the neurons in its neighborhood are 0. This ability called spatial sparse coding plays an important role in self-coding, self-organization and associative memory for patterns and pattern sequences. The main conclusions about the dynamics of this kind of neural array which is related to spatial sparse coding are introduced.     

具有交互神经传递时滞的神经网络的稳定性

本文研究了具有交互神经传递时滞的神经网络模型ｘ′ｉ（ｔ）＝－ｂｉｘｉ（ｔ）＋∑ｎｊ＝１ωｉｊｆｊ（ｘｊ（ｔ－τｊ））＋ｐｉ（ｔ＞０；ｉ＝１，２，…，ｎ）平衡点的全局渐近稳定性，并获得了若干充分条件·     

在时间尺度上研究带有脉冲的泄漏时滞细胞神经网络反周期解的动态特征

在时间尺度上,通过使用叠合度理论中的连续定理和微分不等式技巧,研究带有脉冲的时变泄漏时滞细胞神经网络模型的反周期解,获得了一些使带有脉冲的时变泄漏时滞细胞神经网络模型的反周期解存在和全局指数稳定的充分条件,并将以前的结论在时间尺度上做了扩展.     

On the Dynamics of Bundled Conductors in Overhead Transmission Lines

The Energy Balance Principle (EBP) is well established for estimating the vibration levels of wind induced oscillations of single overhead transmission lines. The mathematical model, wherein a conductor is treated as a continuous system, results in a transcendental eigenvalue problem (EVP), which gives numerical difficulties in the case of bundled conductors. In this paper, different approaches for solving transcendental EVP and their relative merits are discussed. A new method named continuous spectrum approach provides a good engineering solution. Results from different approaches are compared. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)