Analytical and simulation results for the stochastic spatial Fitzhugh-Nagumo model neuron

For the Fitzhugh-Nagumo system with space-time white noise, we use numerical methods to consider the generation of action potentials and the reliability of transmission in the presence of noise. The accuracy of simulated solutions is verified by comparison with known exact analytical results. Noise of small amplitude may prevent transmission directly, whereas larger-amplitude noise may also interfere by producing secondary nonlocal responses. The probability of transmission as a function of noise amplitude is found for both uniform noise and noise restricted to a patch. For certain parameter ranges, the recovery variable may be neglected to give a single-component nonlinear diffusion with space-time white noise. In this case, analytical results are obtained for small perturbations and noise, which agree well with simulation results. For the voltage variable, expressions are given for the mean, covariance, and variance and their steady-state forms. The spectral density of the voltage is also obtained. Numerical examples are given of the difference between the properties of nonlinear and linear cables, and the validity of the expressions obtained for the statistical properties is investigated as a function of noise amplitude. For given parameters, analytical results are in good agreement with simulation until a certain critical noise amplitude is reached, which can be estimated. The role of trigger zones in increasing the reliability of transmission is discussed.     

Interspike interval statistics in the stochastic Hodgkin-Huxley model: coexistence of gamma frequency bursts and highly irregular firing

When the classical Hodgkin-Huxley equations are simulated with Na- and K-channel noise and constant applied current, the distribution of interspike intervals is bimodal: one part is an exponential tail, as often assumed, while the other is a narrow gaussian peak centered at a short interspike interval value. The gaussian arises from bursts of spikes in the gamma-frequency range, the tail from the interburst intervals, giving overall an extraordinarily high coefficient of variation--up to 2.5 for 180,000 Na channels when I approximately 7 microA/cm(2). Since neurons with a bimodal ISI distribution are common, it may be a useful model for any neuron with class 2 firing. The underlying mechanism is due to a subcritical Hopf bifurcation, together with a switching region in phase-space where a fixed point is very close to a system limit cycle. This mechanism may be present in many different classes of neurons and may contribute to widely observed highly irregular neural spiking.     

Multi-objective supply planning for two-level assembly systems with stochastic lead times

This paper considers two-level assembly systems whose lead times of components are stochastic with known discrete random distributions. In such a system, supply planning requires determination of release dates of components at level 2 in order to minimize expected holding cost and to maximize customer service. Hnaien et al. [Hnaien F, Delorme X, Dolgui A. Multi-objective optimization for inventory control in two-level assembly systems under uncertainty of lead times. Computers and Operations Research 2010; 37:1835-43] have recently examined this problem, trying to solve it through multi-objective genetic algorithms. However, some reconsideration in their paper is unavoidable. The main problem with Hnaien et al. proposal is their wrong mathematical model. In addition, the proposed algorithms do not work properly in large-scale instances. In the current paper, this model is corrected and solved via a new approach based on NSGA-II that is called Guided NSGA-II. This approach tries to guide search toward preferable regions in the solution space. According to the statistical analyses, the guided NSGA-II has the higher performance in comparison with the basic NSGA-II used by Hnaien et al. Moreover, the wrongly reported characteristics of the Pareto front shape provided by Hnaien et al. are modified.     

The optimum stochastic control for a problem with random cost incursion times

A sequential stochastic control problem is considered in which the performance criterion cost is incremented periodically at random times. Although these cost incursion times are unknown, they are governed by a known prior probability density function. The optimum Bayesian control decision strategy is obtained by solving the stochastic dynamic programming equation. As anticipated, the solution exhibits a type of separation principle.     

Risk-sensitivity conditions for stochastic uncertain model validation

The paper presents sufficient and necessary conditions that verify the relevance of an assumed linear stochastic system model for problems in which probabilistic characteristics of the plant are not known exactly. The approach is to establish the existence of an admissible probability space on which the output of the candidate stochastic system model is consistent (in a stochastic sense) with the noisy output of the plant.     

A stochastic model for the throughput of non-persistent TCP flows

The general aim of this paper is to analyze the throughput of a HTTP flow. For this, we introduce a simplified model of such a flow which consists of a succession of idle and download periods. The file downloads are subject to a fixed packet loss probability. The same TCP connection is possibly used for the download of a random number of files, for which the effect of the slow start is taken into account. For this stochastic model, we derive a closed form formula for the stationary throughput obtained by a flow. We also derive closed form expressions for the mean time to transfer a file and for the distribution of the throughput. Several laws of file sizes and idle times are considered including heavy tailed distributions. We also briefly discuss how the formulas can be applied to predict bandwidth sharing among competing HTTP flows.     

Rescheduling of parallel machines with stochastic processing and setup times

This paper tackles rescheduling for the unrelated parallel machine problem with sequence dependent setup times and different rates of breakdowns or urgent jobs arrivals. The jobs’ processing and setup times are stochastic for better depiction of the real world. A new repair rule which will be referred to as Minimum Weighted C_max Difference (MWCD) is developed and compared to existing algorithms using simulation.     

Identification of MIMO time-varying stochastic systems with unknown dead times

This paper presents a new on-line procedure for identifying MIMO time-varying stochastic dynamic systems. It is based on a decomposition model derived from the state-space representation. This scheme gives an estimated model with a minimal number of parameters. The parameters of the MIMO system are identified from short records with unknown dead times. Extended recursive least-squares and fixed-lag smoothing identification algorithms are applied to identify the validity of the model structure. Artificial and hydrological records are used to illustrate the efficiency of the proposed procedure.     

Linear-nonlinear neuronal model for shape from shading

The goal of shape from shading (SFS) is to recover a relative depth map from the variations of image intensity associated to changes in surface shape. There have been very few attempts at developing biologically plausible solutions to this problem, and a sound neurophysiological basis is still missing. Here we present a biologically inspired approach to SFS, formulated in terms of the well-known linear-nonlinear model of neuronal responses. Without resorting to the image irradiance equation, which is at the heart of the traditional SFS algorithms, we submit the input image to a linear filter followed by nonlinear transformations modelled on the tuning curves of the disparity-selective binocular neurons. This yields plausible shape estimates, without requiring information regarding surface reflectance or illumination.     

A mathematical stochastic model for the particles diffusion in atmosphere

A mathematical model for the analysis of the random diffusion and dispersion of solid particles with arbitrary shape in a steady state flow defined is here proposed. In particular a mathematical model for the drag coefficient C_D is defined including a scalar random parameter suitable to describe the fluctuations of the physical conditions of the gas surface system. The equation of the dynamics of the particles, which is, in the proposed model, a random non-linear differential equation is qualitatively discussed and some quasi-analytical solutions are obtained with the perturbations techniques. Some numerical experiments visualize the gap between the results obtained by the proposed model and the ones obtained by the corresponding deterministic model.     

Irregular firing of isolated cortical interneurons in vitro driven by intrinsic stochastic mechanisms

Pharmacologically isolated GABAergic irregular spiking and stuttering interneurons in the mouse visual cortex display highly irregular spike times, with high coefficients of variation approximately 0.9-3, in response to a depolarizing, constant current input. This is in marked contrast to cortical pyramidal cells, which spike quite regularly in response to the same current injection. We applied time-series analysis methods to show that the irregular behavior of the interneurons was not a consequence of low-dimensional, deterministic processes. These methods were also applied to the Hindmarsh and Rose neuronal model to confirm that the methods are adequate for the types of data under investigation. This result has important consequences for the origin of fluctuations observed in the cortex in vivo.     

The firing of an excitable neuron in the presence of stochastic trains of strong synaptic inputs

We consider a fast-slow excitable system subject to a stochastic excitatory input train and show that under general conditions, its long-term behavior is captured by an irreducible Markov chain with a limiting distribution. This limiting distribution allows for the analytical calculation of the system's probability of firing in response to each input, the expected number of response failures between firings, and the distribution of slow variable values between firings. Moreover, using this approach, it is possible to understand why the system will not have a stationary distribution and why Monte Carlo simulations do not converge under certain conditions. The analytical calculations involved can be performed whenever the distribution of interexcitation intervals and the recovery dynamics of the slow variable are known. The method can be extended to other models that feature a single variable that builds up to a threshold where an instantaneous spike and reset occur. We also discuss how the Markov chain analysis generalizes to any pair of input trains, excitatory or inhibitory and synaptic or not, such that the frequencies of the two trains are sufficiently different from each other. We illustrate this analysis on a model thalamocortical (TC) cell subject to two example distributions of excitatory synaptic inputs in the cases of constant and rhythmic inhibition. The analysis shows a drastic drop in the likelihood of firing just after inhibitory onset in the case of rhythmic inhibition, relative even to the case of elevated but constant inhibition. This observation provides support for a possible mechanism for the induction of motor symptoms in Parkinson's disease and for their relief by deep brain stimulation, analyzed in Rubin and Terman (2004).     

A stochastic policy search model for matching behavior

The matching law is one of the basic empirical laws in decision theory,and it states that a subject’s preference to optional targets depends on which choices are reinforced.In this paper,we study the possible mechanisms that explain why subjects’ decisions often obey this law.On the basis of reinforcement learning theory,we put forward a decision-making model in which the policy is updated by a policy parameter,and the model might be implemented in the brain through the prefrontal cortex and the basal gangl...     

Stabilization for T-S model based uncertain stochastic systems

This paper considers the stabilization problem of a class of uncertain Itô stochastic fuzzy systems driven by a multidimensional Wiener process. The uncertainty modeled in the systems is of the linear fractional type which includes the norm-bounded uncertainty as a special case. The objective is to design a state-feedback fuzzy controller such that the closed-loop system is robustly asymptotically stable under a stochastic setting. By using a stochastic Lyapunov approach, sufficiency conditions for the stability and stabilization of this class of systems are established based on a novel matrix decomposition technique. The derived stability conditions are then employed to design controllers which stabilize the uncertain Itô stochastic fuzzy systems. Two simulation examples are given to illustrate the effectiveness of the approaches proposed.     

A stochastic optimization model for real-time ambulance redeployment

When ambulances are engaged in responding to emergency calls, the ability to respond quickly to future calls is considerably compromised. The available ambulances are typically relocated to reestablish maximal coverage. We present a two-stage stochastic optimization model for the ambulance redeployment problem that minimizes the number of relocations over a planning horizon while maintaining an acceptable service level. We conduct computational testing based on the real historical data from the Region of Waterloo Emergency Medical Services. The results show that the optimal relocation strategies can be computed within 40 s of computational time for a desired service level of 90%.     

A two-asset stochastic model for long-term portfolio selection

In mean–variance (M–V) analysis, an investor with a holding period [0,T] operates in a two-dimensional space—one is the mean and the other is the variance. At time 0, he/she evaluates alternative portfolios based on their means and variances, and holds a combination of the market portfolio (e.g., an index fund) and the risk-free asset to maximize his/her expected utility at time T. In our continuous-time model, we operate in a three-dimensional space—the first is the spot rate, the second is the expected return on the risky asset (e.g., an index fund), and the third is time. At various times over [0,T], we determine, for each combination of the spot rate and expected return, the optimum fractions invested in the risky and risk-free assets to maximize our expected utility at time T. Hence, unlike those static M–V models, our dynamic model allows investors to trade at any time in response to changes in the market conditions and the length of their holding period. Our results show that (1) the optimum fraction y*(t) in the risky asset increases as the expected return increases but decreases as the spot rate increases; (2) y*(t) decreases as the holding period shortens; and (3) y*(t) decreases as the risk aversion parameter-γ is larger.     

A generic stochastic model for supply-and-return network design

This paper presents a generic stochastic model for the design of networks comprising both supply and return channels, organized in a closed loop system. Such situations are typical for manufacturing/re-manufacturing type of systems in reverse logistics. The model accounts for a number of alternative scenarios, which may be constructed based on critical levels of design parameters such as demand or returns. We describe a decomposition approach to this model, based on the branch-and-cut procedure known as the integer L-shaped method. Computational results in an illustrative numerical setting show a consistent performance efficiency of the method. Moreover, the stochastic solution features a significant improvement in terms of average performance over the individual scenario solutions. A modeling and solution methodology as presented here can contribute to the efficient solution of network design models under uncertainty for reverse logistics.     

满足匹配律的策略参数搜索决策模型

匹配律是决策理论的基本定律之一,它建立了对备选目标的偏好与所获奖励之间的对应关系.通过构建获得匹配律的策略模型,研究了该定律成立的可能机制.基于再励学习理论,提出了通过调整策略参数以满足决策目标的策略搜索模型.在该策略模型的基础上,通过设定简单的假设条件推导出满足匹配律的策略算法.理论分析和数值仿真结果均验证了算法的正确性.另一方面利用该算法模拟了经典的心理学与神经生理学的匹配行为实验.研究结果不仅对匹配行为给出了合理的解释,也为建立基于奖励的决策模型提供了一种有效的理论建模方法.     

Determination of the structure of multivariable stochastic linear systems

The problem of determination of the structure of a multivariable linear system from given input/output data is considered, for both deterministic and stochastic cases. A new canonical input/output form is proposed for this study. A systematic procedure, normalized residual technique, for the estimation of the canonical form is presented. A comparison of our result with others is discussed.     

Real-time management of berth allocation with stochastic arrival and handling times

In this research we study the berth allocation problem (BAP) in real time as disruptions occur. In practice, the actual arrival times and handling times of the vessels deviate from their expected or estimated values, which can disrupt the original berthing plan and possibly make it infeasible. We consider a given baseline berthing schedule, and solve the BAP on a rolling planning horizon with the objective to minimize the total realized cost of the updated berthing schedule, as the actual arrival and handling time data is revealed in real time. The uncertainty in the data is modeled by making appropriate assumptions about the probability distributions of the uncertain parameters based on past data. We present an optimization-based recovery algorithm based on set partitioning and a smart greedy algorithm to reassign vessels in the event of disruption. Our research problem derives from the real-world issues faced by the Saqr port, Ras Al Khaimah, UAE, where the berthing plans are regularly disrupted owing to a high degree of uncertainty in information. A simulation study is carried out to assess the solution performance and efficiency of the proposed algorithms, in which the baseline schedule is the solution of the deterministic BAP without accounting for any uncertainty. Results indicate that the proposed reactive approaches can significantly reduce the total realized cost of berthing the vessels as compared to the ongoing practice at the port.