Controlling predator-prey discrete dynamics utilizing a threshold policy with hysteresis

This paper introduces a threshold policy with hysteresis (TPH) for the control of the logistic one-species model, the Lotka-Volterra and Rosenzweig-MacArthur two species density-dependent predator-prey models. A nonstandard scheme is used for the discretization of the models since it results in preservation of the qualitative characteristics of the continuous-time models. Two theorems that establish the global stability of the discrete logistic model subject to the threshold policy (TP) and the TPH are proved. The proposed policy (TPH) is more realistic than a pure threshold policy (TP) proposed earlier in the literature and changes the dynamics of the system in such a way that a low amplitude bounded oscillation, far from the extinction region, is achieved. Furthermore, it can be designed by a suitable choice of so called virtual equilibrium points in a simple and intuitive manner.     

Markov Control Processes with the Expected Total Cost Criterion: Optimality, Stability, and Transient Models

This paper studies the expected total cost (ETC) criterion for discrete-time Markov control processes on Borel spaces, and possibly unbounded cost-per-stage functions. It presents optimality results which include conditions for a control policy to be ETC-optimal and for the ETC-value function to be a solution of the dynamic programming equation. Conditions are also given for the ETC-value function to be the limit of the -discounted cost value function as 1, and for the Markov control process to be `stable" in the sense of Lagrange and almost surely. In addition, transient control models are fully analized. The paper thus provides a fairly complete, up-dated, survey-like presentation of the ETC criterion for Markov control processes on Borel spaces.     

Optimal control of terrorism and global reputation: A case study with novel threshold behavior

A control model is presented which studies optimal spending for the fight against terrorism. Under the assumptions that economic damages are larger the greater the number of terrorists and that the success of counter terror operations depends on public opinion, it is demonstrated that a so-called DNSS threshold may exist, separating the basin of attraction of optimal paths.     

时滞离散网络模型的动力学分析与同步

复杂网络广泛存在于日常生活,首先,给出几类标准的网络模型;然后,利用稳定性控制方法设计并实现了具有时滞与非时滞耦合的复杂网络模型快速控制;最后,通过构造优化Lyapunov函数,讨论其模型的射影同步问题,得到了系统全局稳定的条件和有效的控制器,以实例数值验证其方法的可行性。     

Analyzing the effect of the inventory policy on order and inventory variability with linear control theory

In this paper we apply linear control theory to study the effect of various inventory policies on order and inventory variability, which are key drivers of supply chain performance. In particular, we study a two-echelon supply chain with a stationary demand pattern under the influence of three inventory policies: an inventory-on-hand policy that bases orders on the visible inventory at an installation, an installation-stock policy that bases orders on the inventory position (on-hand plus on-order inventory) at an installation, and an echelon-stock policy that bases orders on the inventory position at that installation and all downstream installations. We prove analytically that the inventory-on-hand policy is unstable in practical settings, confirming analytically what has been observed in experimental settings and in practice. We also prove that the installation-stock and echelon-stock policies are stable and analyze their effect on order and inventory fluctuation. Specifically, we show the general superiority of the echelon-stock in our setting and demonstrate analytically the effect of forecasting parameters on order and inventory fluctuations, confirming the results in other research.     

Peeling Layers of an Onion: Inventory Model with Multiple Delivery Modes and Forecast Updates

This paper is concerned with a periodic review inventory system with fast and slow delivery modes and regular demand forecast updates. At the beginning of each period, on-hand inventory and demand information are updated. At the same time, decisions on how much to order using fast and slow delivery modes are made. Fast and slow orders are delivered at the end of the current and the next periods, respectively. It is shown that there exists an optimal Markov policy and that it is a modified base-stock policy.     

在预报更新的环境下具有两种配送方式的供应链模型

本文研究在预报更新环境下具有快、慢两种配送方式和需求预报更新的库存系统，为了得到更多关于费用参数和预报改进对最优定货量以及最优的平均费用的影响，我们考虑两个周期的情形．以动态规划为工具我们得到了系统的最优策略．对于需求预报服从均匀分布情形，本文得到了最优定货量和最优的平均总费用的精确表达式．我们通过一些数值例子来说明库存费用、罚金、需求的预报改进和预报误差对最优定货量和最优的     

The European regional policy and the socio-economic diversity of European regions: A multivariate analysis

There are significant differences among the European Union regions, which have been heightened due to the most recent enlargement in 2004. This paper aims to analyse this diversity and to propose a classification of European regions that is adjusted to the different axes of socio-economic development and, simultaneously, is useful for European regional policy purposes. Multivariate statistical techniques allow the identification of clusters of socio-economic similarity, which are contrasted with the classes considered in the financial proposal of the European Commission (EC) for the period 2007–2013.     

Determination of the optimal ordering policy for the retailer with limited capitals when a supplier offers 2 levels of trade credit

In this article, we consider and investigate the cases when the retailer's capitals are restricted and when the supplier offers another kind of 2‐level trade credit. This means that the supplier offers 2‐level trade credit for the retailer to settle the account and the retailer's capitals are restricted, so the retailer decides to pay off the unpaid balance as follows: Firstly, the retailer decides to pay off the unpaid balance at the end of the first credit period if the retailer can pay off all accounts and, in addition, the retailer can use the sales revenue to earn interest throughout the replenishment cycle time. Secondly, the retailer decides to pay off all accounts either after the end of the first credit period, but before the second credit period, or after the second credit period if the retailer cannot pay off the unpaid balance at the end of the first credit period. Additionally, the delay will incur interest charges on the unpaid and overdue balance due to the difference between the interest earned and the interest charged. Consequently, the main purpose of this article is to characterize the optimal solution processes and (in accordance with the functional behavior of the cost function) to search for the optimal replenishment cycle time. Finally, numerical examples are given to illustrate the theoretical results which are proven in this article by means of mathematical solution procedures.     

ParadisEO: A Framework for the Reusable Design of Parallel and Distributed Metaheuristics

In this paper, we present the ParadisEO white-box object-oriented framework dedicated to the reusable design of parallel and distributed metaheuristics (PDM). ParadisEO provides a broad range of features including evolutionary algorithms (EA), local searches (LS), the most common parallel and distributed models and hybridization mechanisms, etc. This high content and utility encourages its use at European level. ParadisEO is based on a clear conceptual separation of the solution methods from the problems they are intended to solve. This separation confers to the user a maximum code and design reuse. Furthermore, the fine-grained nature of the classes provided by the framework allow a higher flexibility compared to other frameworks. ParadisEO is of the rare frameworks that provide the most common parallel and distributed models. Their implementation is portable on distributed-memory machines as well as on shared-memory multiprocessors, as it uses standard libraries such as MPI, PVM and PThreads. The models can be exploited in a transparent way, one has just to instantiate their associated provided classes. Their experimentation on the radio network design real-world application demonstrate their efficiency.     

Analysis of Data with Censored Initiating and Terminating Times: A Missing-Data Approach

Survival data with censored initiating and terminating times have surfaced in some recent epidemiologic studies. Unlike standard survival analysis with known initiating times, analysis of data with both censored initiating and terminating times requires maximization of a complicated bivariate likelihood, which is often difficult to carry out. This article considers a missing-data formulation of the problem and focuses on the use of EM-type algorithms to simplify the computation of maximum likelihood estimates. This approach provides a feasible way of performing regression analysis with such bivariate survival data. Several illustrative examples are provided, including a real-data analysis application involving a cohort of HIV-infected hemophiliac patients.     

Propagation of nonlinear thermoelastic waves in porous media within the theory of heat conduction with memory: physical derivation and exact solutions

In this paper, we study a mathematical model of nonlinear thermoelastic wave propagation in fluid‐saturated porous media, considering memory effect in the heat propagation. In particular, we derive the governing equations in one dimension by using the Gurtin–Pipkin theory of heat flux history model and specializing the relaxation function in such a way to obtain a fractional Erdélyi–Kober integral. In this way, we obtain a nonlinear model in the framework of time‐fractional thermoelasticity, and we find an explicit analytical solution by means of the invariant subspace method. A second memory effect that can play a significant role in this class of models is parametrized by a generalized time‐fractional Darcy law. We study the equations obtained also in this case and find an explicit traveling wave type solution. Copyright © 2016 John Wiley & Sons, Ltd.     

A hybrid type of soliton equations with self-consistent sources: KP and Toda cases

Source generation procedure is applied to construct a hybrid type of soliton equations with self-consistent sources (SESCSs). The examples include the KP equation with self-consistent sources (KPESCS) and two-dimensional TodaESCS. One typical feature for this hybrid type of SESCSs is that soliton solutions of these new systems contain arbitrary functions of a linear combination of two independent variables, which is different from the normal SESCSs where soliton solutions only contain arbitrary functions of one independent variable. What's more, the obtained two hybrid SESCSs can be reduced to two different simpler SESCSs respectively.     

Development and application of Halanay-type theory: Evolutionary differential and difference equations with time lag

We consider extensions, developments and modifications of a result due to Halanay, and the application of “Halanay-type inequalities” in the analysis and numerics of retarded functional-differential equations, difference equations, and retarded functional-difference equations. Our emphasis is on the variety, structure and development, and future development, of Halanay-type results and their applications. We classify and present novel results of Halanay type (linear and non-linear, discrete, semi-discrete, and continuous) and establish their relevance to delay-differential equations, discretized analogues (we consider ?-methods), and difference equations. A rôle for such results in stability and contractivity analysis is made apparent.     

具有带临界和非临界故障的可修k/N:G冗余表决系统研究中出现的投影算子的表达式及其应用(英文)

当修复率为常数时通过研究具有带临界和非临界故障的可修k/N:G冗余表决系统研究中出现的投影算子的表达式得到该系统的时间依赖解指数收敛于该系统的稳态解.     

A class of one-dimensional geometric variational problems with energy involving the curvature and its derivatives: a geometric measure-theoretic approach

The notions of Legendrian and Gaussian towers are defined and investigated. Then applications in the context of one-dimensional geometric variational problems with the energy involving the curvature and its derivatives are provided. Particular attention is paid to the case when the functional is defined on smooth boundaries of plane sets.      

Perfect simulation of processes with long memory: A “coupling into and from the past” algorithm

We describe a new algorithm for the perfect simulation of variable length Markov chains and random systems with perfect connections. This algorithm, which generalizes Propp and Wilson's simulation scheme, is based on the idea of coupling into and from the past. It improves on existing algorithms by relaxing the conditions on the kernel and by accelerating convergence, even in the simple case of finite order Markov chains. Although chains of variable or infinite order have been widely investigated for decades, their use in applied probability, from information theory to bio‐informatics and linguistics, has recently led to considerable renewed interest. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 46, 300–319, 2015