Computing availability for redundant flow systems

There are many papers in the literature about computing reliability for binary redundant systems. However in the real world there are many systems, whose economics depend on average availability of flow throughout the life span of the system rather than reliability on one particular threshold level only. Such systems exist in oil and gas redundant flow networks. To best of this author’s knowledge no attempt has been made yet to compute availability of such systems. Computing availability of flow is of utmost importance for the economical planning and design of any industrial flow networks. In this paper an approach is proposed to compute availability of flow in redundant flow systems. The proposed approach is compared with the approach used in the weighted $k$ -out-of- $n$ systems for computing reliability. The results show the better performance of the proposed approach in terms of computational time if the system bears heavier weights. Furthermore proposed scheme has additional advantage of being capable of handling fractional weights.     

Numerically Computing Real Points on Algebraic Sets

Given a polynomial system f, a fundamental question is to determine if f has real roots. Many algorithms involving the use of infinitesimal deformations have been proposed to answer this question. In this article, we transform an approach of Rouillier, Roy, and Safey El Din, which is based on a classical optimization approach of Seidenberg, to develop a homotopy based approach for computing at least one point on each connected component of a real algebraic set. Examples are presented demonstrating the effectiveness of this parallelizable homotopy based approach.     

A Cluster Reduction for Computing the Subtree Distance Between Phylogenies

Calculating the rooted subtree prune and regraft (rSPR) distance between two rooted binary phylogenetic trees is a frequently applied process in various areas of molecular evolution. However, computing this distance is an NP-hard problem and practical algorithms for computing it exactly are rare. In this paper, a divide-and-conquer approach to calculating the rSPR distance is established. This approach breaks the problem instance into a number of smaller and more tractable subproblems. Two reduction rules which were previously used to show that computing the rSPR distance is fixed-parameter tractable can easily be used to complement this new theoretical result, and so a significant positive impact on the running time of calculating this distance in practice is likely.     

Computing the resolvent of the sum of operators with application to best approximation problems

Optimization Letters - We propose a flexible approach for computing the resolvent of the sum of weakly monotone operators in real Hilbert spaces. This relies on splitting methods where strong...     

Fuzzy optimization for distribution of frozen food with imprecise times

Problems concerning the distribution routes for frozen products need to incorporate constraints that avoid breaks in the cold chain. The decision making process under uncertain environments is a common one in real logistics problems. The purpose of this study is to apply a fuzzy approach which will provide an optimal solution to the distribution of frozen food with uncertainty in its time values. A soft computing approach is used where fuzzy constraints are included in the modeling and the solution of the problem.     

Stochastic Approximation in Real Time: A Pipe Line Approach

1.IntroductionTheobjectiveofthisworkistostudystochasticapproximationinrea1time.Apipelineapproachissuggested.Asymptoticpropertiesoftheprocedurearedeve1oped,andcomparisonsofrateofconvergencewiththeclassicalalgorithmsaremade.LetxeE',andf(.):EL-FL-Thetraditio…     

Computing complex and real tropical curves using monodromy

Tropical varieties capture combinatorial information about how coordinates of points in a classical variety approach zero or infinity. We present algorithms for computing the rays of a complex and real tropical curve defined by polynomials with constant coefficients. These algorithms rely on homotopy continuation, monodromy loops, and Cauchy integrals. Several examples are presented which are computed using an implementation that builds on the numerical algebraic geometry software Bertini.     

Bessel,sine and cosine functions and extrapolation methods for computing molecular multi-center integrals

In this work, we present an extremely efficient approach for a fast numerical evaluation of highly oscillatory spherical Bessel integrals occurring in the analytic expressions of the so-called molecular multi-center integrals over exponential type functions. The approach is based on the Slevinsky-Safouhi formulae for higher derivatives applied to spherical Bessel functions and on extrapolation methods combined with practical properties of sine and cosine functions. Recurrence relations are used for computing the approximations of the spherical Bessel integrals, allowing for a control of accuracy and the stability of the algorithm. The computer algebra system Maple was used in our development, mainly to prove the applicability of the extrapolation methods. Among molecular multi-center integrals, the three-center nuclear attraction and four-center two-electron Coulomb and exchange integrals are undoubtedly the most difficult ones to evaluate rapidly to a high pre-determined accuracy. These integrals are required for both density functional and ab initio calculations. Already for small molecules, many millions of them have to be computed. As the molecular system gets larger, the computation of these integrals becomes one of the most laborious and time consuming steps in molecular electronic structure calculation. Improvement of the computational methods of molecular integrals would be indispensable to a further development in computational studies of large molecular systems. Convergence properties are analyzed to show that the approach presented in this work is a valuable contribution to the existing literature on molecular integral calculations as well as on spherical Bessel integral calculations.     

Model-based clustering of high-dimensional data streams with online mixture of probabilistic PCA

Model-based clustering is a popular tool which is renowned for its probabilistic foundations and its flexibility. However, model-based clustering techniques usually perform poorly when dealing with high-dimensional data streams, which are nowadays a frequent data type. To overcome this limitation of model-based clustering, we propose an online inference algorithm for the mixture of probabilistic PCA model. The proposed algorithm relies on an EM-based procedure and on a probabilistic and incremental version of PCA. Model selection is also considered in the online setting through parallel computing. Numerical experiments on simulated and real data demonstrate the effectiveness of our approach and compare it to state-of-the-art online EM-based algorithms.     

Bounds on total economic capital: the DNB case study

Most banks use the top-down approach to aggregate their risk types when computing total economic capital. Following this approach, marginal distributions for each risk type are first independently estimated and then merged into a joint model using a copula function. Due to lack of reliable data, banks tend to manually select the copula as well as its parameters. In this paper we assess the model risk related to the choice of a specific copula function. The aim is to compute upper and lower bounds on the total economic capital for the aggregate loss distribution of DNB, the largest Norwegian bank, and the key tool for computing these bounds is the Rearrangement Algorithm introduced in Embrechts et al. (J. Bank. Financ. 37(8):2750–2764 2013). The application of this algorithm to a real situation poses a series of numerical challenges and raises a number of warnings which we illustrate and discuss.     

Application of neural-network methods for prediction of the job execution characteristics in multiprocessor computing systems

In recent years, the architecture of multiprocessor computing systems has become more and more complex and needs in large amounts of computations rapidly increase, together with the number of users of multiprocessor systems. Because of a large number of factors acting on the user job inside such a system, analytical approaches to solution of the job scheduling problem are very complex and expensive. This paper considers a neural-network approach to scheduling the computations in multiprocessor systems (which uses a method that predicts certain characteristics of the job execution procedure) and estimates the applicability of this approach in real conditions. Ways for increasing the accuracy of prediction are proposed.     

带赔偿的云计算服务拍卖机制研究

云计算提供了按需获取、按使用付费的IT资源获取模式,由于存在大量的云计算服务提供商,以市场化的形式来组织云计算资源的分配与获取是一种合理的方式.以面向市场的云计算服务架构为基础,研究了云计算用户和服务提供商之间的匹配问题.采用拍卖方式实现具体的匹配过程,并将服务失败时的赔偿问题纳入考虑,结合服务提供商的违约率提出了两种带赔偿的云计算服务拍卖机制一在逆向一级密封拍卖上增加赔偿因子,分析了其二人博弈和多人博弈的均衡;同时,研究了服务权再分配对该机制的影响.     

Practical statistical models of environmental pollution

The paper summarises recent theoretical work on turbulent diffusion that is based on a simple extension of exact results for the ideal case when there is no molecular diffusion. The results are consistent with data and appear to provide a new and promising approach for practical models that can be used in real time.     

Finding Eigenvalues of Holomorphic Fredholm Operator Pencils Using Boundary Value Problems and Contour Integrals

Investigating the stability of nonlinear waves often leads to linear or nonlinear eigenvalue problems for differential operators on unbounded domains. In this paper we propose to detect and approximate the point spectra of such operators (and the associated eigenfunctions) via contour integrals of solutions to resolvent equations. The approach is based on Keldysh’ theorem and extends a recent method for matrices depending analytically on the eigenvalue parameter. We show that errors are well-controlled under very general assumptions when the resolvent equations are solved via boundary value problems on finite domains. Two applications are presented: an analytical study of Schrödinger operators on the real line as well as on bounded intervals and a numerical study of the FitzHugh–Nagumo system. We also relate the contour method to the well-known Evans function and show that our approach provides an alternative to evaluating and computing its zeros.     

On the Topology of Real Algebraic Plane Curves

We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular and critical points, is also relevant. A challenge is to compute efficiently this information for the given coordinate system even if the curve is not in generic position. Previous methods based on the cylindrical algebraic decomposition use sub-resultant sequences and computations with polynomials with algebraic coefficients. A novelty of our approach is to replace these tools by Gröbner basis computations and isolation with rational univariate representations. This has the advantage of avoiding computations with polynomials with algebraic coefficients, even in non-generic positions. Our algorithm isolates critical points in boxes and computes a decomposition of the plane by rectangular boxes. This decomposition also induces a new approach for computing an arrangement of polylines isotopic to the input curve. We also present an analysis of the complexity of our algorithm. An implementation of our algorithm demonstrates its efficiency, in particular on high-degree non-generic curves.     

Energy-aware software: Challenges,opportunities and strategies

Energy consumption of computing systems has become a major concern. Constrained by cost, environmental concerns and policy, minimising the energy foot-print of computing systems is one of the primary goals of many initiatives.As we move towards exascale computing, energy constraints become very real and are a major driver in design decisions. The issue is also apparent at the scale of desk top machines, where many core and accelerator chips are common and offer a spectrum of opportunities for balancing energy and performance.Conventionally, approaches for reducing energy consumption have been either at the operational level (such as powering down all or part of systems) or at the hardware design level (such as utilising specialised low-energy components). In this paper, we are interested in a different approach; energy-aware software. By measuring the energy consumption of a computer application and understanding where the energy usage lies, may allow a change of the software to provide opportunities for energy savings.In order to understand the complexities of this approach, we specifically look at multithreaded algorithms and applications. By an evaluation of a benchmark suite on multiple architectures and multiple environments, we show how basic parameters, such as threading options, compilers and frequencies, can impact energy consumption. As such, we provide an overview of the challenges that face software developers in this regard. We then offer a view of the directions that need to be taken and possible strategies needed for building energy-aware software.     

An analysis of the effect of rounding errors on the flow of control in numerical processes

Rounding errors may change the flow of control in numerical computing processes by leading to changes in some branching decisions of the process. In this paper some general topological and measure theoretical results associated with this effect of rounding errors are derived. The approach is based on a model of numerical computation related to program schemes. Each computing process specified by the model computes a partial functionR ⁿ R ^m using rational operations and simple tests on real numbers. The topological structure of input point sets inR ⁿ on which the computation follows the same execution path is studied. We also investigate input points, called sensitive, on which rounding errors may change the execution path followed. Conditions concerning computing processes are given which guarantee that the Lebesgue measure of sensitive points approaches zero (i.e. the probability of a branching error gets arbitrarily small) as the precision of the arithmetic increases. Most numerical processes used in practice are easily seen to satisfy these conditions.     

Mathematical programming and the sensitivity of multi-criteria decisions

We report on the current state of a project whose aim is to implement a framework for sensitivity analysis in Multi-Criteria Decision Making (MCDM). The framework is largely based on mathematical programming. Due to the potentially large number and nature of the mathematical programmes, it is far from trivial to provide solutions to all of them in acceptable computing times. The challenge is even greater when we recognize that much decision analysis is performed in the context of decision conferences where any sensitivity analysis needs to be conducted in near real time (preferably) on a PC. We present a parallel processing approach to this challenge and point to some of the difficulties still to be resolved. Preliminary results obtained on a network of transputers are discussed.