小鼠视觉感受区电位信号(LFP)与视觉刺激之间关系研究

针对小鼠脑电波与行为之间关系研究中涉及弱脑电波信号处理、成分分离及提取、脑电波与对应行为分析等问题,首先处理了脑电波信号,根据呼吸机理建立了"呼"、"吸"动作电位触发下的脑电波模型.其次,通过独立分量分析方法获得睡眠状态小鼠视觉感受区LFP信号模型,采用区间估计和Rayleigh熵检验结合讨论了提取的相关脑电波与呼吸信号的锁相性,分析了LFP信号的周期性,建立了多元线性回归模型,用最小二乘法从理论上讨论了其线性关系,并检验了所建二次模型周期变化的相关性.然后,通过平均经验模态分解及基于互相关性的伪分量检验算法,改善了模态混叠,建立了完整的脑电波信号分离模型.最后,分析图形因素的图像特征,通过提取视觉刺激曲线、功率谱相关频段,采用叠加平均信号法,以LFP节律随视觉信号锁相程度判断不同视觉刺激引起的LFP成分变化.     

用运动变化的观点思考数学问题

运动是永恒的,静止是相对的,用运动变化的观点看事物,往往最能把握事物间的本质联系．运动变化的观点就是动态的、联系的,因而也就是辨证的观点．在教学中引导学生运用运动变化的观点思考问题,尤其是那些与运动有关的问题,不仅可增强直观形象性,而且还可改变学生的思维模式．     

两类带有确定潜伏期的SEIS传染病模型的分析

通过研究两类带有确定潜伏期的SEIS传染病模型,发现对种群的常数输入和指数输入会使疾病的传播过程产生本质的差异．对于带有常数输入的情形,找到了地方病平衡点存在及局部渐近稳定的阈值,证明了地方病平衡点存在时一定局部渐近稳定,并且疾病一致持续存在．对于带有指数输入的情形,发现地方病平衡点当潜伏期充分小时是局部渐近稳定的,当潜伏期充分大时是不稳定的．     

探寻动态图形问题的解题途径

在高考命题中,常涉及几何图形中一些元素的运动变化问题,这类问题形式新颖,小巧灵活,多以小题出现．解决这类问题的关键在于把握动态图形中有关元素的运动变化规律．本文通过2009年的高考试题,谈谈如何探寻动态图形的运动变化规律,以拓展这类问题的解决途径．     

非对称视角下技术创新网络社群结构涌现及其对双元创新的影响研究

针对介于全局网络与自中心网络间的社群现象及其网络结构的创新悖论,分析了不同层面网络社群结构的涌现特征,从组织间关系的非对称视角,探究网络社群动态变化对双元创新的差异性影响。利用高科技生物制药行业的合作与专利数据,使用快速压缩社群识别算法和多元回归模型进行实证检验。研究结果表明:宏观层面的全局网络存在显著“抱团”的多社群巨元组结构;中观层面的网络社群存在选择偏好的核心-边缘结构;微观层面社群组织动态的跨社群运动和成员流动二维变化加剧;社群动态的二维变化对突破式创新具有正向影响,与渐进式创新呈现倒U型关系;位置非对称性正向调节社群动态对双元创新的影响,技术非对称性的调节作用不显著。研究结论有助于揭示技术创新网络社群的合作创新模式,对提升组织创新能力,维持创新网络平稳运行具有重要意义。     

短距离竞技游泳运动的推进力最优化分析初探

通过建立竞技游泳运动的动力学模型和能量转换模型,并运用最优控制理论对于在给定时间内所游进的路程进行了最优化分析,结合奥运会记录和前人实验结果推导出在一定假设和限制条件下推进力的最优解,得到了与实际情况吻合的最佳速度和体能分配方案．     

基于SPCP解析的平均移动距离和城市交通模式

SPCP是一项关于以评估城市内部道路交通网络各段拥挤度,来反映相应道路在该城市道路网中所占重要程度的研究．在通过对于包括东京在内的日本一些城市的应用,其实用性已得到了广泛验证．本论文从理论上揭示了SPCP所近似反映的一种城市交通模式,从而为其为何能够在现实城市中被应用提供了理论性依据．此外在本文中,基于被展示的城市交通模型和SPCP,我们还推导计算出了一项经常用于衡量城市道路交通有效性的尺度-城市内道路交通移动所需平均距离．     

周期激励下的前包钦格呼吸神经元的簇振荡现象研究

研究周期激励作用下的非自治前包钦格呼吸神经元模型,结果表明当外界激励频率与系统固有频率存在着量级差距时,系统可以产生典型的簇放电模式.由于激励频率远小于系统的固有频率,因此将整个周期激励项视为慢变参数,从而可以利用稳定性分析理论研究慢变参数变化下的平衡点的分岔类型,进一步应用快慢动力学分析方法给出簇模式产生的动力学机理.本文的结果说明外界激励对神经元的动力学行为有着重要影响,为进一步揭示呼吸节律的产生机制提供了重要帮助.     

具有增益的概率网络金融计划模型

本文绘出一类具有增益的概率网络金融计划模型．许多多阶段金融计划问题可纳入这类模型．在这类模型中,随机变量的分布函数与Alexander过滤交易规则密切联系在一起,金融市场交易信号由神经网络产生,目标函数的最优值按其期望值计算．文中提出临界流和临界路的概念,给出目标函数下界等于其期望值的充分必要条件和期望最优解的求解方法．     

破冰船航行状态在海冰作用下的运动响应分析

通过MOSES软件建立了多用途破冰工作船的数值模型;分析破冰船破冰过程的机理,建立起破冰船正向与冰排作用过程中的复合式冰排断裂模式,指出船艏冰排径向裂纹的扩展这一关键影响因子;推衍出作用于破冰船船艏的冰力函数;对破冰船在航行时与海冰作用的过程进行了模拟计算,重点考察了破冰船逆流与顺流航行状态下的运动响应差别,发现随着相对冰速的变化,这种运动响应的差别是规律性变化的.     

Statistical analysis of brain waves from randomly interconnected neural nets

A statistical analysis of brain waves from randomly connected neural nets is presented here based to our previous work. The most important findings from this analysis is that several neural networks have the ability to create periods of spontaneous rhythmic activity similar to those observed in animals and human thalamus, cerebral cortex and hippocampus.     

Reciprocity between the cerebellum and the cerebral cortex: Nonlinear dynamics in microscopic modules for generating voluntary motor commands

The cerebellum and basal ganglia are reciprocally connected with the cerebral cortex, forming many loops that function as distributed processing modules. Here we present a detailed model of one microscopic loop between the motor cortex and the cerebellum, and we show how small arrays of these microscopic loops (CB modules) can be used to generate biologically plausible motor commands for controlling movement. A fundamental feature of CB modules is the presence of positive feedback loops between the cerebellar nucleus and the motor cortex. We use nonlinear dynamics to model one microscopic loop and to investigate its bistable properties. Simulations demonstrate an ability to program a motor command well in advance of command generation and an ability to vary command duration. However, control of command intensity is minimal, which could interfere with the control of movement velocity. To assess these hypotheses, we use a minimal nonlinear model of the neuromuscular (NM) system that translates motor commands into actual movements. Simulations of the combined CB‐NM modular model indicate that movement duration is readily controlled, whereas velocity is poorly controlled. We then explore how an array of eight CB‐NM modules can be used to control the direction and endpoint of a planar movement. In actuality, thousands of such microscopic loops function together as an array of adjustable pattern generators for programming and regulating the composite motor commands that control limb movements. We discuss the biological plausibility and limitations of the model. We also discuss ways in which an agent‐based representation can take advantage of the modularity in order to model this complex system. © 2008 Wiley Periodicals, Inc. Complexity, 2008     

Neuron phase shift adaptive to time delay in locomotor control

Based on neurophysiological evidence, theoretical studies have shown that walking can be generated by mutual entrainment of oscillations of a central pattern generator (CPG) and a body. However, it has also been shown that the time delay in the sensorimotor loop destabilizes mutual entrainment, and results in the failure to walk. Recently, it has been reported that if (a) the neuron model used to construct the CPG is replaced by physiologically faithful neuron model (Bonhoeffer–Van der Pol type) and (b) the mechanical impedance of the body (muscle viscoelasticity) is controlled depending on the angle between two legs, the phase relationship between CPG activity and body motion could be flexibly locked according to the loop delay and, therefore, mutual entrainment can be stabilized. That is, locomotor control adaptive to the loop delay can emerge from the coupling between CPG and body. Here, we call this mechanism flexible-phase locking. In this paper, we construct a system of coupled oscillators as a simplified model of a walking system to theoretically investigate the mechanism of flexible-phase locking, and to analyze the simplified model. The analysis suggests that the following are required as the essential mechanism: (i) an asymptotically stable limit cycle of the coupling system of CPG and body and (ii) a sign difference between afferent and efferent coupling coefficients.     

政府调控下的能源供需系统动力学分析

依据一个经济时期内能源需求、能源供应和政府调控之间相互依存、相互制约的演化关系为背景建立了一个新的能源供需模型.模型中引入市场自身调节的闽值,政府调控的阈值,政府调控对能源需求和能源供应的影响系数等参数,通过参数的调整,分析了政府调控在能源供需中的作用.通过平衡点稳定性、系统的耗散性、Lyapunov指数谱等的分析,研究了系统的基本动力学行为,利用数值模拟的方法给出了系统的动力演化行为;给出了模型中参数估计的方式,对模型所反映的现实意义进行了解释,给出了数值模拟结果,验证了理论分析的正确性.     

市场与规制双重不确定下企业环境投资行为选择

通过主体适应性规则构建企业环境投资行为模型,从政府环境规制和市场波动等方面刻画企业环境投资决策面临的不确定性,基于计算实验方法探寻企业在基准、震荡、上涨与下跌等4种情景下的环境投资行为规律。研究发现:政府规制强度越强,企业环境投资越充分,但投资偏差现象越明显。在震荡情景中,企业的环境投资行为表现出非理性状态,在上涨情景中,企业环境投资表现出过度反应。当市场产品价格波动处在单边行情,政府可以通过较为宽松的环境规制实现目标,而当市场产品价格处在震荡波动时,政府需要通过较为严格的环境规制刺激企业进行环境投资。企业的环境投资受到政府规制与市场信号的共同影响,政府的环境规制稳定的持续刺激并不会让企业盲目投资,但政府环境规制的频繁变动却会使企业无所适从。     

Bandwidth allocation and access control in high-speed networks

The problem of bandwidth allocation and access regulation arises in the congestion control of Broadband ISDN networks. This paper assumes that a single user, described by an on-off fluid model, is connected to the network via a leaky bucket access control mechanism. The bandwidth allocated to this user and the leaky bucket parameters are to be selected so as to guarantee a negotiated level of delay probability at the access point and packet loss probability in the network which is modelled as an output buffer. The design problem is to minimize the allocated bandwidth subject to service guarantees and stability conditions for the input and output buffers. We provide a desirable feasible solution to the design problem. The paper studies the effect of non-conforming users on the network performance using the leaky bucket access control corresponding to this feasible solution. We provide expressions that quantify the impact of the leaky bucket parameters in access regulation and the worst-case queueing behavior at the output buffer. Finally, we discuss the extension of this methodology to the multiple leaky buckets case.This research was supported in part by IBM Research Contract No. 1374.     

基于内生参考点的交通网络均衡模型

应用累积前景理论研究了随机交通网络中出行者有限理性的路径选择行为,选择期望 超额出行时间作为参考点,反映出行者同时考虑出行时间的可靠性和不可靠性,建立了基于累积前景理论的随机网络均衡及其等价的变分不等式模型,运用基于连续平均法的启发式算法求解,并给出算例验证了该模型和算法,最后分析了有限理性的假设和内生的参考点对出行者路径选择行为和随机网络均衡的影响．