考虑时间因素的双目标应急召回闭环网络规划

研究产品召回突发情况下的闭环供应链物流网络规划问题,考虑了产品召回紧迫性以及召回应急管理的管理特性,引入时间和召回率两类随机参数,提出了基于成本的召回处理时间反应函数,建立了基于总成本以及总召回处理反应时间的双目标随机混合整数规划模型.采用一类启发式算法对该模型进行求解,并用Matlab6.5软件进行编程求数值解.在数值解的基础上,进行相关参数的敏感件分析,结果表明网络选址结果具有一定的鲁棒性.     

Representation of the bilinear system output by multiple stochastic integrals

Consideration was given to the scalar stochastic differential Ito equation whose drift and diffusion coefficients are affine functions of the phase coordinate. Its solution was represented in terms of the stochastic exponent which plays the part of the equation resolvent. Expansion of the stochastic exponent in series in the Hermit polynomials induces expansion of the solution of the bilinear equation in series in multiple stochastic integrals. Obtained were the moment characteristics of the stochastic integrals solving the problem of statistical analysis of the approximate solutions of the bilinear stochastic systems. A model of the financial (B, S)-market and its optimization in terms of a nonsquare criterion were considered by way of example of a bilinear system.     

Finding the shortest path in stochastic networks

Common network parameters, such as number of nodes and arc lengths are frequently subjected to ambiguity as a result of probability law. A number of authors have discussed the calculation of the shortest path in networks with random variable arc lengths. Generally, only a subset of intermediate nodes chosen in accordance with a given probability law can be used to transition from source node to sink node. The determination of a priori path of the minimal length in an incomplete network is defined as a probabilistic shortest path problem. When arc lengths between nodes are randomly assigned variables in an incomplete network the resulting network is known as an incomplete stochastic network. In this paper, the computation of minimal length in incomplete stochastic networks, when travel times between nodes are allowed to be exponentially distributed random variables, is formulated as a linear programming problem. A practical application of the methodology is demonstrated and the results and process compared to the Kulkarni’s [V.G. Kulkarni, Shortest paths in networks with exponentially distributed arc lengths, Networks 16 (1986) 255–274] method.     

面向全局搜索的自适应领导者樽海鞘群算法

针对实际配送过程中客户需求、车辆服务时间随机可变,提出带软时间窗的随机需求和随机服务时间的车辆路径问题.以配送车辆行驶路径为研究对象,建立基于配送成本、时间惩罚成本、修正成本的配送车辆路径优化模型,并提出一种混合禁忌搜索算法.该算法将最近邻算法和禁忌搜索算法相结合,将时间窗宽度及距离作为最近邻算法中节点选择标准;并对禁忌搜索算法中禁忌长度等构成要素进行自适应调整,引入自适应惩罚系数.实验结果表明,改进后的混合禁忌搜索算法具有较强的寻优能力、较高的鲁棒性,同时算法所得车辆行驶路径受客户需求变动影响较小.     

Modeling variable user mobility with stochastic correlation concept

Analyzing stochastic behavior of user mobility is a basic study for traffic performance analysis in land–mobile cellular communications. Due to the heavy burden in simulation considering significant mobility parameters, many analytical models have been proposed as alternatives. However, analytical approach to figure out the stochastic behavior is so difficult that realistic features can hardly be reflected without simplification. As expected, the effect of variable user mobility (VUM) on traffic performance may not be reasonably analyzed with such simplified models, especially in a case of micro-cellular systems where traffic performance, such as handover rate, is more sensitively affected by user mobility. Thus we are motivated to investigate an improved alternative. This paper has focused on developing a VUM model. Considering VUM in mobility modeling, we figure out its effect on probability distributions of cell dwell time which is basic for traffic performance analysis in land–mobile cellular communications. A new concept on variable characteristics of user mobility called stochastic correlation is introduced for the analysis. Probability distribution of path length during a call is also studied using our model of VUM. We believe that our model with stochastic correlation could be applied to many performance modeling problems in land–mobile cellular systems with mobility sensitive traffic performance.     

Finding Minimum Vertex Covering in Stochastic Graphs: A Learning Automata Approach

Structural and behavioral parameters of many real networks such as social networks are unpredictable, uncertain, and have time-varying parameters, and for these reasons, deterministic graphs for modeling such networks are too restrictive to solve most of the real-network problems. It seems that stochastic graphs, in which weights associated to the vertices are random variables, might be better graph models for real-world networks. Once we use a stochastic graph as the model for a network, every feature of the graph such as path, spanning tree, clique, dominating set, and cover set should be treated as a stochastic feature. For example, choosing a stochastic graph as a graph model of an online social network and defining community structure in terms of clique, the concept of a stochastic clique may be used to study community structures’ properties or define spreading of influence according to the coverage of influential users; the concept of stochastic vertex covering may be used to study spread of influence. In this article, minimum vertex covering in stochastic graphs is first defined, and then four learning, automata-based algorithms are proposed for solving a minimum vertex-covering problem in stochastic graphs where the probability distribution functions of the weights associated with the vertices of the graph are unknown. It is shown that through a proper choice of the parameters of the proposed algorithms, one can make the probability of finding minimum vertex cover in a stochastic graph as close to unity as possible. Experimental results on synthetic stochastic graphs reveal that at a certain confidence level the proposed algorithms significantly outperform the standard sampling method in terms of the number of samples needed to be taken from the vertices of the stochastic graph.     

Probabilistic analysis of some (un)directed animals

Using weak convergence theorems, we analyze stochastic properties of some parameters of directed or undirected animals. For directed column convex animals, with fixed large area, we obtain asymptotic distributions for the number of columns, the internal path length, the trajectories and the right width. For general directed animals, we derive asymptotic densities of the lower width and of some decomposition parameter. The limiting processes are given by Gaussian stochastic processes based on Brownian Motion or stochastic integrals on such.     

概率包标记方法中收敛时间的数学模型

本文建立了概率包标记方法中关于收敛时间的数学模型。该模型通过将概率标记方法中攻击路径重构过程表述为一个收敛的随机过程,推导出平均收敛时间与路径长度、标记概率之间的数学定量关系及其概率分布,得出达到最小平均收敛时间需要满足的数学条件。在此基础上,给出两种传统概率包标记方法中收敛时间的改进数学模型。     

Flow-level models for multipath routing

In this paper we study coordinated multipath routing at the flow-level in networks with routes of length one. As a first step the static case is considered, in which the number of flows is fixed. A clustering pattern in the rate allocation is identified, and we describe a finite algorithm to find this rate allocation and the clustering explicitly. Then we consider the dynamic model, in which there are stochastic arrivals and departures; we do so for models with both streaming and elastic traffic, and where a peak-rate is imposed on the elastic flows (to be thought of as an access rate). Lacking explicit expressions for the equilibrium distribution of the Markov process under consideration, we study its fluid and diffusion limits; in particular, we prove the uniqueness of the equilibrium point. We demonstrate through a specific example how the diffusion limit can be identified; it also reveals structural results about the clustering pattern when the minimal rate is very small and the network grows large.     

Numerical simulation of stochastic replicator models in catalyzed RNA-like polymers

A stochastic model for replicators in catalyzed RNA-like polymers is presented and numerically solved. The model consists of a system of reaction–diffusion equations describing the evolution of a population formed by RNA-like molecules with catalytic capabilities in a prebiotic process. The diffusion effects and the catalytic reactions are deterministic. A stochastic excitation with additive noise is introduced as a force term. To numerically solve the governing equations we apply the stochastic method of lines. A finite-difference reaction–diffusion system is constructed by discretizing the space and the associated stochastic differential system is numerically solved using a class of stochastic Runge–Kutta methods. Numerical experiments are carried out on a prototype of four catalyzed selfreplicator species along with an activated and an inactivated residues. Results are given in two space dimensions.     

Stochastic models for an educational system

A method is presented for determining the parameters of a stochastic model for an educational system, based on the time-series analysis approach. As an example the parameters of such a model are derived for the student population in the Faculty of Engineering at McMaater University     

一类含有随机和模糊参数的规划模型

提出一类模糊机会约束的随机期望值规划模型,该模型同时含有随机和模糊参数.对改进的“报童问题”进行的分析,说明了模型的合理性.运用随机模拟与模糊模拟相结合的技术,给出了求解该规划模型的遗传算法.并对改进的“报童问题”进行了数值求解,同时给出了其它数值例子,进一步说明了所给出模型的适用性和有效性.     

Spike-driven synaptic plasticity: theory, simulation, VLSI implementation

We present a model for spike-driven dynamics of a plastic synapse, suited for aVLSI implementation. The synaptic device behaves as a capacitor on short timescales and preserves the memory of two stable states (efficacies) on long timescales. The transitions (LTP/LTD) are stochastic because both the number and the distribution of neural spikes in any finite (stimulation) interval fluctuate, even at fixed pre- and postsynaptic spike rates. The dynamics of the single synapse is studied analytically by extending the solution to a classic problem in queuing theory (Takacs process). The model of the synapse is implemented in aVLSI and consists of only 18 transistors. It is also directly simulated. The simulations indicate that LTP/LTD probabilities versus rates are robust to fluctuations of the electronic parameters in a wide range of rates. The solutions for these probabilities are in very good agreement with both the simulations and measurements. Moreover, the probabilities are readily manipulable by variations of the chip's parameters, even in ranges where they are very small. The tests of the electronic device cover the range from spontaneous activity (3-4 Hz) to stimulus-driven rates (50 Hz). Low transition probabilities can be maintained in all ranges, even though the intrinsic time constants of the device are short (approximately 100 ms). Synaptic transitions are triggered by elevated presynaptic rates: for low presynaptic rates, there are essentially no transitions. The synaptic device can preserve its memory for years in the absence of stimulation. Stochasticity of learning is a result of the variability of interspike intervals; noise is a feature of the distributed dynamics of the network. The fact that the synapse is binary on long timescales solves the stability problem of synaptic efficacies in the absence of stimulation. Yet stochastic learning theory ensures that it does not affect the collective behavior of the network, if the transition probabilities are low and LTP is balanced against LTD.     

一类允许缺货的易变质物品的随机非线性存贮模型

研究了货物存贮问题．考虑到在仓库出空期间一般人们有耐烦与不耐烦两种反应，研究中假设仓库出空期丢失顾客量服从正态分布，据此建立允许缺货的易变质物品的非线性存贮模型，使模型更接近于实际．并给出数值例子，运用Matlab软件求解最优存贮控制策略，得到近似的最佳进货量和最佳出空期长度．     

考虑乘客感知的公交随机用户均衡配流

针对公交网络的特殊性,提出符合乘客路径选择行为且易于确定的广义路径概念,综合考虑乘客自主选择各路径的关键阻抗,在累积前景理论分析框架下,建立考虑乘客感知的用户均衡配流模型,用以反映乘客的择路行为,并通过算例分析验证了模型的有效性及合理性。该方法改进了传统模型完全理性的基本假设及适用的局限性,有助于对城市复杂公交出行行为及其决策规则的理解。配流结果可作为确定公交设施布局和规划以及评价服务水平的参考,同时还可作为交通诱导强有力的决策支撑。     

STDP突触的双输入信号动力学模型研究*

为了准确地建模突触前刺激引起的谷氨酸信号和突触后刺激引起的峰电位信号,并将这两个信号用于STDP突触模型的验证,提出一种谷氨酸信号和后向传播树突信号的离子通道动力学模型。模型的仿真结果不仅得到了实际生理学机理下的谷氨酸信号和树突信号,而且对STDP突触模型的验证还得到了STDP突触的时间非对称函数波形。仿真结果表明,所设计的双输入信号动力学模型符合实际的STDP神经突触生理学原理,模型产生的信号可用于对STDP突触模型的验证。     

Stochastic DT-MRI connectivity mapping on the GPU

We present a method for stochastic fiber tract mapping from diffusion tensor MRI (DT-MRI) implemented on graphics hardware. From the simulated fibers we compute a connectivity map that gives an indication of the probability that two points in the dataset are connected by a neuronal fiber path. A Bayesian formulation of the fiber model is given and it is shown that the inversion method can be used to construct plausible connectivity. An implementation of this fiber model on the graphics processing unit (GPU) is presented. Since the fiber paths can be stochastically generated independently of one another, the algorithm is highly parallelizable. This allows us to exploit the data-parallel nature of the GPU fragment processors. We also present a framework for the connectivity computation on the GPU. Our implementation allows the user to interactively select regions of interest and observe the evolving connectivity results during computation. Results are presented from the stochastic generation of over 250,000 fiber steps per iteration at interactive frame rates on consumer-grade graphics hardware.     

State feedback stabilization of stochastic nonlinear systems with SiISS inverse dynamics

This paper further considers a more general class of stochastic nonlinear systems with stochastic integral input‐to‐state stability (SiISS) inverse dynamics and drift and diffusion terms depending upon the other states besides stochastic inverse dynamics and the first state. By skillfully choosing the designed functions and the update laws of parameters, and using the important mathematical tools established in IEEE Trans. Automat. Contr. 2010; 55 (2):304–320, a unifying framework of state feedback controller is proposed to guarantee that all the signals of the closed‐loop system are bounded almost surely and the states can be regulated to zero almost surely. A simulation example demonstrates the effectiveness of the control scheme. Copyright © 2011 John Wiley & Sons, Ltd.     

Performance analysis of the auxiliary models based multi-innovation stochastic gradient estimation algorithm for output error systems

This paper combines the multi-innovation identification theory and the auxiliary model identification idea and presents an auxiliary model based multi-innovation stochastic gradient algorithm by expanding the scalar innovation to an innovation vector and introducing the innovation length. Convergence analysis in the stochastic framework indicates that the parameter estimates given by the proposed algorithm can fast converge to their true values. Finally, we illustrate and test the proposed algorithm with an example.