Sensitivity of sample values not generated by inversion

The perturbation generation rule of Suri (Ref. 1) is extended to cases where random variables are not generated by inversion. Conditions are given for the use of other methods. Infinitesimal perturbation analysis is shown to be compatible with common random number techniques in cases where finite-difference approximations are not.This work was supported by the National Science Foundation, Grants Nos. ECS-82-13680 and CDR-85-001-08.     

Integral estimation and adaptive stabilization of non-holonomic controlled systems

A method for the programmed stabilization of non-holonomic dynamic systems is proposed. The original problem is reduced to a constrained adaptive control problem with unknown perturbations, which are represented by the reactions of linear (not necessarily ideal) non-holonomic constraints. Effective control and parameter estimation algorithms are constructed for the exponential stabilization of the system. The method can be extended to non-holonomic systems whose parameters are not known in advance or undergo an unknown bounded drift with time.     

On balking from an empty queue

The intuition while observing the economy of queueing systems, is that one’s motivation to join the system, decreases with its level of congestion. Here we present a queueing model where sometimes the opposite is the case. The point of departure is the standard first-come first-served single server queue with Poisson arrivals. Customers commence service immediately if upon their arrival the server is idle. Otherwise, they are informed if the queue is empty or not. Then, they have to decide whether to join or not. We assume that the customers are homogeneous and when they consider whether to join or not, they assess their queueing costs against their reward due to service completion. As the whereabouts of customers interact, we look for the (possibly mixed) join/do not join Nash equilibrium strategy, a strategy that if adopted by all, then under the resulting steady-state conditions, no one has any incentive not to follow it oneself. We show that when the queue is empty then depending on the service distribution, both ‘avoid the crowd’ (ATC) and ‘follow the crowd’ (FTC) scenarios (as well as none-of-the-above) are possible. When the queue is not empty, the situation is always that of ATC. Also, we show that under Nash equilibrium it is possible (depending on the service distribution) that the joining probability when the queue is empty is smaller than it is when the queue is not empty. This research was supported by The Israel Science Foundation Grant No. 237/02.     

Über Die Stabilitätsdefinition Für Differenzengleichungen Die Partielle Differentialgleichungen Approximieren

For difference equations with constant coefficients necessary and sufficient algebraic stability conditions are given for the stability definitions used by G. Forsythe and W. Wasow (A) and P. D. Lax and R. D. Richtmyer (B). The application of these conditions for difference equations with variable coefficients is considered and it is shown that the stability condition of definitionA is not sufficient for stability. The same is true with respect to the definitionB if the difference equations are not parabolic and do not approximate first order systems. Therefore another stability definition is proposed and a number of properties are discussed.     

Relaxing mixed integer optimal control problems using a time transformation

Mixed integer control systems are used to model dynamical behavior that can change instantly, for example a driving car with different gears. Changing a gear corresponds to an instant change of the differential equation what is achieved in the model by changing the value of the integer control function. The optimal control of a mixed integer control system by a discretize-then-optimize approach leads to a mixed integer optimization problem that is not differentiable with respect to the integer variables, such that gradient based optimization methods can not be applied. In this work, differentiability with respect to all optimization variables is achieved by reformulating the mixed integer optimal control problem (MIOCP). A fixed integer control function and a time transformation are introduced. The combination of both allows to change the sequence of active differential equations by partially deactivating the fixed integer control function. In contrast to other works, here different fixed integer control functions are taken into account. Advantages of so called control consistent (CC) fixed integer control functions are discussed and confirmed on a numerical example. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A service flow model for the liner shipping network design problem

Global liner shipping is a competitive industry, requiring liner carriers to carefully deploy their vessels efficiently to construct a cost competitive network. This paper presents a novel compact formulation of the liner shipping network design problem (LSNDP) based on service flows. The formulation alleviates issues faced by arc flow formulations with regards to handling multiple calls to the same port. A problem which has not been fully dealt with earlier by LSNDP formulations. Multiple calls are handled by introducing service nodes, together with port nodes in a graph representation of the problem, and by introducing numbered arcs between a port and a novel service node. An arc from a port node to a service node indicate whether a service is calling the port or not. This representation allows recurrent calls of a service to a port, which previously could not be handled by LSNDP models. The model ensures strictly weekly frequencies of services, ensures that port-vessel draft capabilities are not violated, respects vessel capacities and the number of vessels available. The profit of the generated network is maximized, i.e. the revenue of flowed cargo subtracted operational costs of the network and a penalty for not flowed cargo. The model can be used to design liner shipping networks to utilize a container carrier’s assets efficiently and to investigate possible scenarios of changed market conditions. The model is solved as a Mixed Integer Program. Results are presented for the two smallest instances of the benchmark suite LINER-LIB-2012 presented in Brouer, Alvarez, Plum, Pisinger, and Sigurd (2013).     

A heuristic method for the open vehicle routing problem

The open vehicle routing problem (OVRP) differs from the classic vehicle routing problem (VRP) because the vehicles either are not required to return to the depot, or they have to return by revisiting the customers assigned to them in the reverse order. Therefore, the vehicle routes are not closed paths but open ones. A heuristic method for solving this new problem, based on a minimum spanning tree with penalties procedure, is presented. Computational results are provided.     

Belief updating in multiply sectioned Bayesian networks without repeated local propagations

Multiply sectioned Bayesian networks (MSBNs) provide a coherent and flexible formalism for representing uncertain knowledge in large domains. Global consistency among subnets in an MSBN is achieved by communication. When a subnet updates its belief with respect to an adjacent subnet, existing inference operations require repeated belief propagations (proportional to the number of linkages between the two subnets) within the receiving subnet, making communication less efficient. We redefine these operations such that two such propagations are sufficient. We prove that the new operations, while improving the efficiency, do not compromise the coherence. An MSBN must be initialized before inference can take place. The initialization involves dedicated operations not shared by inference operations according to existing methods. We show that the new inference operations presented here unify inference and initialization. Hence the new operations are not only more efficient but also simpler. The new results are presented such that their connection with the common inference methods for single Bayesian networks is highlighted.     

A non-symmetric singular cauchy problem

In this paper we replace uniformly convex (or reflexive and normal structure) as required by Browder and Kirk, by uniformly normal structure to obtain a fixed point theorem for non-expansive self mappings. Examples are given to show that spaces with uniformly normal structure are not all uniformly convex and spaces with normal structure do not all have uniformly normal structure.

AMS (MOS) subject classification (1970) Primary 47410.     

Ranking of countries in sporting events using two-stage data envelopment analysis models: a case of Summer Olympic Games 2016

After important sport events as the Summer Olympic Games (SOG) are, the participating countries are ranked according to the number of gold, silver and bronze medals. A lexicographic ranking is usually applied in official reports which leads to higher ranking of countries with one gold and no other medals comparing to countries without any gold but with several silver or bronze medals. Moreover, this ranking does not take into account the specific conditions of the countries (population, economic strength measured by gross domestic product and tradition in sports). The aim of the paper is not only to evaluate the absolute achievements of the countries but evaluate their performance with respect to the resources they can spent. A two-stage data envelopment analysis model is formulated and solved by an original slack-based measure procedure. The first stage evaluates the performance of the countries in training of athletes and the second stage evaluates the achievements of the nominated athletes. The models with variable returns to scale and weight restrictions are applied. The models and their results are illustrated on the case of Olympic Games 2016 and compared with results given by traditional approaches.     

Capacity of mismatched Gaussian channels with and without feedback

Summary Continuous time communication channels with additive noise are considered under an average power constraint. The noises are assumed to be Gaussian processes equivalent (or mutually absolutely continuous) to a Brownian motion. We study the problem whether the capacity of the channel is increased by feedback or not. It is given a sufficient condition under which the capacity is not increased by feedback. It is also given an example of a channel whose capacity is doubled by feedback.Research partially supported by ONR contract N00014-84-0212     

INACCESSIBLE CONTINUOUSLY STABLE STRATEGIES

ABSTRACT. The evolutionary stability concepts continuously stable strategies (CSS) and evolutionarily stable neighborhood invader strategies (ESNIS) share two properties in common. First, they are both evolutionarily stable strategies (ESS). Secondly, given any strategy in the close neighborhood of the CSS or ESNIS, there are some strategies that are closer to the CSS or ESNIS that can invade it. An ESNIS is a CSS but the converse is not true in general. We examine evolutionary adaptive dynamics in the neighborhood of a CSS that is not an ESNIS. We show that if an evolutionary game possesses a CSS which is not an ESNIS, the succession of strategies mediated by natural selection become arbitrarily close to the CSS but the precise value of the CSS cannot be attained unless the CSS is the first strategy to invade into the environment and is henceforth never perturbed. Thus if evolution does not start with the CSS that is not an ESNIS, we will have a phenomenon of bounded evolutionary succession that does not come to an end. The analysis is applied to a class of monomorphic population evolutionary game models in which species ecological interaction is modeled by the Lotka‐Volterra equations.     

Ranking decision-making units using common weights in DEA

Data envelopment analysis (DEA) is a linear programming technique that is used to measure the relative efficiency of decision-making units (DMUs). Liu et al. (2008) [13] used common weights analysis (CWA) methodology to generate a CSW using linear programming. They classified the DMUs as CWA-efficient and CWA-inefficient DMUs and ranked the DMUs using CWA-ranking rules. The aim of this study is to show that the criteria used by Liu et al. are not theoretically strong enough to discriminate among the CWA-efficient DMUs with equal efficiency. Moreover, there is no guarantee that their proposed model can select one optimal solution from the alternative components. The optimal solution is considered to be the only unique optimal solution. This study shows that the proposal by Liu et al. is not generally correct. The claims made by the authors against the theorem proposed by Liu et al. are fully supported using two counter examples.     

Dissolution point and isolation robustness: Robustness criteria for general cluster analysis methods

Two robustness criteria are presented that are applicable to general clustering methods. Robustness and stability in cluster analysis are not only data dependent, but even cluster dependent. Robustness is in the present paper defined as a property of not only the clustering method, but also of every individual cluster in a data set. The main principles are: (a) dissimilarity measurement of an original cluster with the most similar cluster in the induced clustering obtained by adding data points, (b) the dissolution point, which is an adaptation of the breakdown point concept to single clusters, (c) isolation robustness: given a clustering method, is it possible to join, by addition of g points, arbitrarily well separated clusters?Results are derived for k-means, k-medoids (k estimated by average silhouette width), trimmed k-means, mixture models (with and without noise component, with and without estimation of the number of clusters by BIC), single and complete linkage.     

Enumeration of Pareto optimal multi-criteria spanning trees – a proof of the incorrectness of Zhou and Gen's proposed algorithm

The minimum spanning tree (MST) problem is a well-known optimization problem of major significance in operational research. In the multi-criteria MST (mc-MST) problem, the scalar edge weights of the MST problem are replaced by vectors, and the aim is to find the complete set of Pareto optimal minimum-weight spanning trees. This problem is NP-hard and so approximate methods must be used if one is to tackle it efficiently. In an article previously published in this journal, a genetic algorithm (GA) was put forward for the mc-MST. To evaluate the GA, the solution sets generated by it were compared with solution sets from a proposed (exponential time) algorithm for enumerating all Pareto optimal spanning trees. However, the proposed enumeration algorithm that was used is not correct for two reasons: (1) It does not guarantee that all Pareto optimal minimum-weight spanning trees are returned. (2) It does not guarantee that those trees that are returned are Pareto optimal. In this short paper we prove these two theorems.     

Optimal control of vibrationally excited locomotion systems

Optimal controls are constructed for two types of mobile systems propelling themselves due to relative oscillatory motions of their parts. The system of the first type is modelled by a rigid body (main body) to which two links are attached by revolute joints. All three bodies interact with the environment with the forces depending on the velocity of motion of these bodies relative to the environment. The system is controlled by high-frequency periodic angular oscillations of the links relative to the main body. The system of the other type consists of two bodies, one of which (the main body) interacts with the environment and with the other body (internal body), which interacts with the main body but does not interact with the environment. The system is controlled by periodic oscillations of the internal body relative to the main body. For both systems, the motions with the main body moving along a horizontal straight line are considered. Optimal control laws that maximize the average velocity of the main body are found.     

带有止步和中途退出的成批到达的M~x/M/R/N同步休假排队系统的性能分析

研究了带有止步和中途退出的Mx/M/R/N同步休假排队系统.顾客成批到达.到达的顾客如果看到服务员正在休假或者全忙,他或者以概率b决定进入队列等待服务,或者以概率1-b止步(不进入系统).系统根据一定的原则以概率nk在未止步的k个顾客中选择n个进入系统.在系统中排队等待服务的顾客可能因为等待的不耐烦而在没有接受服务的情况下离开系统(中途退出).系统中一旦没有顾客,R个服务员立即进行同步多重休假.首先,利用马尔科夫过程理论建立了系统稳态概率满足的方程组.其次,在证明了相关矩阵可逆性的基础上,利用矩阵解法求出了系统稳态概率的明显表达式,并得到了系统的平均队长、平均等待队长及顾客的平均损失率等性能指标.     

平面Laplace问题的等价间接变量边界积分方程

利用变分法证明平面调和函数的外问题的确切形式；在此基础上，建立外问题的具有间接变量的等价边界积分方程；传统的外问题及边界积分方程不具有普遍适用性，本文对此进行了详细的讨论．     

一类超线性收敛的广义拟Newton算法

１引言考虑无约束最优化问题其中目标函数ｆ（ｘ）二阶连续可微,记ｆｋ＝ｆ（ｘ）,当充分小时,有如下近似关系：它们对二次函数皆严格成立．考虑选代其中Ｂ（Ｇ的近似）已知,为某种线搜索确定的步长．对Ｂ修正产生Ｂ,即Ｕ为待定ｎ阶矩阵．若要求Ｂ＋满足关系即Ｂ满足拟Ｎｅｗｔｏｎ方程,由它可导出许多著名的拟Ｎｅｗｔｏｎ算法［１－［４］）．若要求Ｂ满足关系则可导出伪Ｎｅｗｔｏｎ－δ族校正公式,它不再是Ｈｕａｎｇ族成员［６］．从信息资源的利用看,（１．６）仅利用了与信息,（１．７）仅利用了与信息．一般而言,较多的信…     

Ground-state electronic properties of LiH calculated from the “Bounce” version of quantum Monte Carlo

We calculate several ground-state electronic properties of LiH at its equilibrium geometry using the so-called “Bounce” version of quantum Monte Carlo. The importance sampling is performed with a single-determinant large (QZ4P) STO basis set. The computer codes were written to exploit the efficiencies engineered into modern, high-performance computing software.Our objective is to test the accuracy of the Bounce algorithm when applied to calculate electronic properties represented by operators that do not commute with the Hamiltonian. Our approach is to implement the algorithm for short, medium and long length reptiles. The highest quality Bounce-calculated energy and electric properties are found by using longest length reptiles. Nevertheless, these results are not competitive with those calculated using reptation quantum Monte Carlo for the same long-length reptiles.