对二维分布连接神经网络模型的研究

对二维分布连接神经网络模型的研究帅建伟，陈振湘，刘瑞堂，吴伯僖（厦门大学物理系，厦门３６１００５）在生物神经网络中，神经元间的突触连接不仅具有局域性，而且神经元的某一信号通过不同突触连接对不同神经元的激励强度大小也不同，一般其连接强度与神经元间的距离...     

Biexponential distribution of open times of a toy channel model

The biexponential distributions of open times are observed in various types of ion channels. In this paper, by discussing a simple channel model, we show that there are two different schemes to understand the biexponential distribution of open times. One scheme is mathematically strict based on generator matrix theory, while the other one has a clear physical explanation according to an approximation process with numerical simulation of Markovian channel dynamics. Our comparison results suggest that even for biologically complex channels, in addition to carrying out a stochastic simulation,the strict theoretical analysis should be considered to understand the multiple exponential distributions of open times.     

Dual mechanisms of Bcl-2 regulation in IP3-receptor-mediated Ca2+ release: A computational study

Inositol 1,4,5-trisphosphate receptors (IP₃R)-mediated calcium ion (Ca²⁺) release plays a central role in the regulation of cell survival and death. Bcl-2 limits the Ca²⁺ release function of the IP₃R through a direct or indirect mechanism. However, the two mechanisms are overwhelmingly complex and not completely understood. Here, we convert the mechanisms into a set of ordinary differential equations. We firstly simulate the time evolution of Ca²⁺ concentration under two different levels of Bcl-2 for the direct and indirect mechanism models and compare them with experimental results available in the literature. Secondly, we employ one- and two-parameter bifurcation analysis to demonstrate that Bcl-2 can suppress Ca²⁺ signal from a global point of view both in the direct and indirect mechanism models. We then use mathematical analysis to clarify that the indirect mechanism is more efficient than the direct mechanism in repressing Ca²⁺ signal. Lastly, we predict that the two mechanisms restrict Ca²⁺ signal synergistically. Together, our study provides theoretical insights into Bcl-2 regulation in IP₃R-mediated Ca²⁺ release, which may be instrumental for the successful development of therapies to target Bcl-2 for cancer treatment.     

八元数神经网络模型：256色图像的识别

首次把八元数引入到神经网络中，提出了八元数离散神经网络模型，并用信噪比理论初步考察了模型的稳定性和存贮容量。八元数神经网络模型可应用于高精度的２５６级的灰度图像或２５６值的彩色图像的识别中。     

Modelling Moran Process with Network Dynamics for the Evolution of Cooperation

We introduce a simple model based on the Moran process with network dynamics. Using pair approximation, the cooperation frequencies at equilibrium states are deduced for general interactions. Three usual social dilemmas are discussed in the framework of our model. It is found that they all have a phase transition at the same value of cost-to-benefit ratio. For the prisoner＇s dilemma game, notably it is exactly the simple rule reported in the literature [Nature 441 （2006） 502]. In our model, the simple rule results from the parent-offspring link. Thus the basic mechanism for cooperation enhancement in network reciprocity is in line with the Hamilton rule of kin selection. Our simulations verify the analysis obtained from pair approximation.     

权重连接神经网络的光电实现

在Ｈｏｐｆｉｅｌｄ模型基础上，对具有权重连接的Ｈｏｐｆｉｅｌｄ模型引入连接权重矩阵，这样只要在Ｈｏｐｆｉｅｌｄ内容寻址记忆光电阵更前多加一个连接权重矩阵阵列，则得具有权重连接的神经网络模型的光电实现。     

四元数神经网络模型的计算机模拟研究

用Ｄｉｒａｃ符号表示１６态四元数离散神经网络模型，用计算机模拟讨论了该模型的存贮容量和容错能力，与Ｈｏｐｆｉｅｌｄ模型对比，并进行了计算机１６值灰度或彩色图像识别模拟。     

Bcl-2蛋白抑制钙信号的建模与全局动力学分析

钙离子(Ca~(2+))是生物体内一种"生死攸关"的信号分子,Bcl-2蛋白可以直接或间接调节IP_3R通道释放Ca~(2+)的能力,借此决定细胞命运.本文基于新近的实验成果,针对Bcl-2蛋白间接调控Ca~(2+)的信号通路建立数学模型,得到了与实验数据相符合的结果,从理论上证明了Bcl-2蛋白对钙信号有抑制作用.在对模型进行鲁棒性检验之后,本文对该信号通路中一些关键组分的作用进行了预测.以[IP_3]和[Bcl-2]为双分岔参数分析的结果表明Bcl-2对刺激强度能产生Ca~(2+)振荡的区域有重要影响.以蛋白磷酸酶1[PP1]和蛋白激酶A[PKA]为单分岔参数分析的结果揭示:PP1可以有效地抑制钙信号,而PKA对钙信号的促进作用有一定的局限性.模型结果表明,不同浓度组合的IP_3,Bcl-2和PKA会对钙信号发挥复杂的调控作用.本文不仅对相关生物学实验有一定的指导作用,而且可为治疗因钙信号失调而导致的疾病提供思路.     

Motile parameters of cell migration in anisotropic environment derived by speed power spectrum fitting with double exponential decay

Cell migration through anisotropic microenvironment is critical to a wide variety of physiological and pathological processes.However,adequate analytical tools to derive motile parameters to characterize the anisotropic migration are lacking.Here,we proposed a method to obtain the four motile parameters of migration cells based on the anisotropic persistent random walk model which is described by two persistence times and two migration speeds at perpendicular directions.The key process is to calculate the velocity power spectra of cell migration along intrinsically perpendicular directions respectively,then to apply maximum likelihood estimation to derive the motile parameters from the power spectra fitting with double exponential decay.The simulation results show that the averaged persistence times and the corrected migration speeds can be good estimations for motile parameters of cell migration.     

异步四元数神经网络模型的能量函数研究

本文证明了异步离散四元数神经网络模型在其动力学演化过程中，网络的能量函数单调递减，网络最终将稳定在一个平衡态上，存贮图像在能量函数空间中对应一能量极小点，为网络的稳定吸引子。