The Pohozaev-Schoen identity on asymptotically Euclidean manifolds: Conservation laws and their applications

The aim of this paper is to present a version of the generalized Pohozaev-Schoen identity in the context of asymptotically Euclidean manifolds. Since these kind of geometric identities have proven to be a very powerful tool when analysing different geometric problems for compact manifolds, we will present a variety of applications within this new context. Among these applications, we will show some rigidity results for asymptotically Euclidean Ricci-solitons and Codazzi-solitons. Also, we will present an almost-Schur type inequality valid in this non-compact setting which does not need restrictions on the Ricci curvature. Finally, we will show how some rigidity results related with static potentials also follow from these type of conservation principles.     

New challenges in dynamic load balancing

Data partitioning and load balancing are important components of parallel computations. Many different partitioning strategies have been developed, with great effectiveness in parallel applications. But the load-balancing problem is not yet solved completely; new applications and architectures require new partitioning features. Existing algorithms must be enhanced to support more complex applications. New models are needed for non-square, non-symmetric, and highly connected systems arising from applications in biology, circuits, and materials simulations. Increased use of heterogeneous computing architectures requires partitioners that account for non-uniform computing, network, and memory resources. And, for greatest impact, these new capabilities must be delivered in toolkits that are robust, easy-to-use, and applicable to a wide range of applications. In this paper, we discuss our approaches to addressing these issues within the Zoltan Parallel Data Services toolkit.     

具有非连续性系数的两相不可压缩可混溶问题的有限元法

Two phase ,miscible,incompressible flow in porous media is governed by a system of nonlinear partial differential equations. Many numerical methods have been given by didierent authors to this system,hut these methods need very high regularity conditions. Actualty,in most practical applications these regularity conditions couldn‘t be satisfied. In this paper,the problem of discontinuous coefficients with lower regularity conditions is considered and the error estimates are demonstrated.     

Some Extensions of Nonconvex Economic Modeling: Invexity,Quasimax, and New Stability Conditions

There are many applications in economics of nonlinear programming, usually under convexity assumptions. Some nonconvex models have also been discussed extensively in order to relax the restrictive assumption of convexity. The applicability can be extended considerably by further generalization to invexity and of maximum to quasimax. Some qualitatively different effects may occur with nonconvex models, such as nonunique optima at different objective levels and jumps in the consumption function, which have economic significance. This paper describes these effects and relates them to mathematical concepts.Thanks are due to Professor F. Giannessi for correcting a number of details of thepresentation     

Test case generators and computational results for the maximum clique problem

In the last years many algorithms have been proposed for solving the maximum clique problem. Most of these algorithms have been tested on randomly generated graphs. In this paper we present different test problem generators that arise from a variety of practical applications, as well as graphs with known maximum cliques. In addition, we provide computational experience with two exact algorithms using the generated test problems.     

On imposing connectivity constraints in integer programs

We study an extension of the classical graph cut problem, wherein we replace the modular (sum of edge weights) cost function by a submodular set function defined over graph edges. Special cases of this problem have appeared in different applications in signal processing, machine learning, and computer vision. In this paper, we connect these applications via the generic formulation of “cooperative graph cuts”, for which we study complexity, algorithms, and connections to polymatroidal network flows. Finally, we compare the proposed algorithms empirically.     

Computational complexity of edge modification problems in different classes of graphs

Edge modification problems in graphs have a lot of applications in different areas. Polynomial time algorithms and NP-completeness results appear in several works in the literature. In this paper, we prove new complexity results of these problems in some graph classes, such as, interval, circular-arc, permutation, circle, bridge and weakly chordal graphs.     

Recent progress of local search in handling the time window constraints of the vehicle routing problem

Vehicle routing and scheduling problems have a wide range of applications and have been intensively studied in the past half century. The condition that enforces each vehicle to start service at each customer in the period specified by the customer is called the time window constraint. This paper reviews recent results on how to handle hard and soft time window constraints, putting emphasis on its different definitions and algorithms. With these diverse time windows, the problem becomes applicable to a wide range of real-world problems.     

An algorithm for fitting circular arcs to data using the <Emphasis Type="Italic">l</Emphasis><Subscript><Emphasis Type="Italic">1</Emphasis></Subscript> norm

There are many applications of fitting circular arcs to data. We have for example, system control, using a computer controlled cutting machine, approximating hulls of boats, drawing and image techniques. Out of these applications comes the least squares norm to be the most commonly used criterion. This paper examines how the l ₁ norm is used which seems to be more appropriate than the use of least squares in the context of wild points in the data. An algorithm and different methods to determine the starting points are developed. However, numerical examples are given to help illustrate these methods.      

Recent progress of local search in handling the time window constraints of the vehicle routing problem

Vehicle routing and scheduling problems have a wide range of applications and have been intensively studied in the past half century. The condition that enforces each vehicle to start service at each customer in the period specified by the customer is called the time window constraint. This paper reviews recent results on how to handle hard and soft time window constraints, putting emphasis on its different definitions and algorithms. With these diverse time windows, the problem becomes applicable to a wide range of real-world problems.     

Correlation Wavelet and its Applications

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Some Simple Applications of the Travelling Salesman Problem

The travelling salesman problem arises in many different contexts. In this paper we report on typical applications in computer wiring, vehicle routing, clustering and job-shop scheduling. The formulation as a travelling salesman problem is essentially the simplest way to solve these problems. Most applications originated from real world problems and thus seem to be of particular interest. Illustrated examples are provided with each application.     

Bank-office Process Management in the Financial Services: a Simulation Approach Using a Model Generator

For the last ten years or so, developments in simulation software and methodology have been focused in two areas: (1) automating the model-building process; and (2) interfacing with other techniques and systems. That both academic and commercial research continues to be carried out in these areas is evidence of the continued popularity of the simulation technique. The most popular application areas where simulation modelling is used include manufacturing (engineering and process), warehousing and communications; not surprisingly, research and developments have therefore been concentrated in these areas. This paper describes the development of a simulation model generator for a different application area, that of clerical office processing of paper and documents for financial service companies. It outlines the reasons why there is a need for such a model generator and discusses the initial design requirements. The paper goes on to detail the developments and re-defined criteria required as the model generator brief changes as a result of practical applications.     

Real-time cardiovascular simulation using two microcomputers

Cardiovascular simulations have been developed for a number of different classes of applications: systems identification, benchmarks, physiologic research and teaching. The model presented in this paper is similar in structure to the PHYSBE benchmark model. Our purpose, however, is to teach medical students about the complex interactions of the cardiovascular system. Commonly, cardiovascular simulations have been implemented on poweful research computers using high-level languages. This paper reports on the use of a microprocessor, programmed in assembler, as the simulation engine. This more limited machine was chosen to minimize the cost of developing multiple student workstations while still providing real physiologic time analog outputs. A number of different models have been developed for teaching cardiovascular physiology using mainframe, mini, micro and analog computers. Of these, only the analog simulations and the present work are capable of real-physiologic time computation and pulsatile display. The digital computer system presented here achieves this result with a more flexible student interface.     

Clifford Fuzzy Support Vector Machines for Classification

A Clifford support vector machine (CSVM) learns the decision surface from multi distinct classes of the multiple input points using the Clifford geometric algebra. In many applications, each multiple input point may not be fully assigned to one of these multi-classes. In this paper, we apply a fuzzy membership to each multiple input point and reformulate the CSVM for multiclass classification to make different input points have their own different contributions to the learning of decision surface. We call the proposed method Clifford fuzzy SVM.     

Computer science and decision theory

This paper reviews applications in computer science that decision theorists have addressed for years, discusses the requirements posed by these applications that place great strain on decision theory/social science methods, and explores applications in the social and decision sciences of newer decision-theoretic methods developed with computer science applications in mind. The paper deals with the relation between computer science and decision-theoretic methods of consensus, with the relation between computer science and game theory and decisions, and with “algorithmic decision theory.”     

Granular computing applied to ontologies

Granular Computing is an emerging conceptual and computing paradigm of information-processing. A central notion is an information-processing pyramid with different levels of clarifications. Each level is usually represented by ‘chunks’ of data or granules, also known as information granules. Rough Set Theory is one of the most widely used methodologies for handling or defining granules.Ontologies are used to represent the knowledge of a domain for specific applications. A challenge is to define semantic knowledge at different levels of human-depending detail.In this paper we propose four operations in order to have several granular perspectives for a specific ontological commitment. Then these operations are used to have various views of an ontology built with a rough-set approach. In particular, a rough methodology is introduced to construct a specific granular view of an ontology.     

On Searching for Large Objects with Small Probes: A Search Model for Exploration

We propose a model for optimal allocation of effort when searching for large objects with small probes. Because of the size of the objects, search activities at different locations can be physically and statistically dependent, and consequently classical search models are inappropriate. The difficulties resulting from such statistical dependence can be overcome by using original data or Monte-Carlo derived scenarios in an integer linear programming model. The proposed optimization model should be of moderate size in typical applications, and by exploiting its special structure it can be solved optimally by standard methods. When this is uneconomical it may be solved approximately by efficient heuristics. Applications of these ideas have already been made to the detection of glaucoma. This paper focuses on possible applications in exploratory drilling for petroleum.     

Rank deficiency and superstability of hybrid systems

The objectives of this paper are to study the rank properties of flows of hybrid systems, show that they are fundamentally different from those of smooth dynamical systems, and to consider applications that emphasize the importance of these differences. It is well known that the flow of a smooth dynamical system has rank equal to the space on which it evolves. We prove that, in contrast, the rank of a solution to a hybrid system, a hybrid execution, is always less than the dimension of the space on which it evolves and in fact falls within possibly distinct upper and lower bounds that can be computed explicitly. The main contribution of this work is the derivation of conditions for when an execution fails to have maximal rank, i.e., when it is rank deficient. Given the importance of periodic behavior in many hybrid systems applications, for example in bipedal robots, these conditions are applied to the special case of periodic hybrid executions. Finally, we use the rank deficiency conditions to derive superstability conditions describing when periodic executions have rank equal to 0, that is, we determine when the execution is completely insensitive to perturbations in initial conditions. The results of this paper are illustrated on three separate applications, two of which are models of bipedal walking robots: the classical single-domain planar compass biped and the two-domain planar kneed biped.     

A Comparison of Discriminant Analysis versus Artificial Neural Networks

Artificial Neural Network (ANN) techniques have recently been applied to many different fields and have demonstrated their capabilities in solving complex problems. In a business environment, the techniques have been applied to predict bond ratings and stock price performance. In these applications, ANN techniques outperformed widely-used multivariate statistical techniques. The purpose of this paper is to compare the ANN method with the Discriminant Analysis (DA) method in order to understand the merits of ANN that are responsible for the higher level of performance. The paper provides an overview of the basic concepts of ANN techniques in order to enhance the understanding of this emerging technique. The similarities and differences between ANN and DA techniques in representing their models are described. This study also proposes a method to overcome the limitations of the ANN approach, Finally, a case study using a data set in a business environment demonstrates the superiority of ANN over DA as a method of classification of observations.