A new similarity measure for collaborative filtering to alleviate the new user cold-starting problem

Collaborative filtering is one of the most successful and widely used methods of automated product recommendation in online stores. The most critical component of the method is the mechanism of finding similarities among users using product ratings data so that products can be recommended based on the similarities. The calculation of similarities has relied on traditional distance and vector similarity measures such as Pearson’s correlation and cosine which, however, have been seldom questioned in terms of their effectiveness in the recommendation problem domain. This paper presents a new heuristic similarity measure that focuses on improving recommendation performance under cold-start conditions where only a small number of ratings are available for similarity calculation for each user. Experiments using three different datasets show the superiority of the measure in new user cold-start conditions.     

Bounds for the solution of the Lyapunov matrix equation — A unified approach

In recent years, several bounds have been reported for the solution of the continuous and the discrete Lyapunov equations. Using the unified Lyapunov equation, we give in this paper bounds for the solution of this equation. In the limiting cases, the bounds reduce to existing bounds for both the continuous and discrete Lyapunov equations.     

A new solution for the Byzantine agreement problem

Reliability is an important research topic in distributed computing systems consisting of a large number of processors. To achieve reliability, the fault-tolerance scheme of the distributed computing system must be revised. This kind of problem is known as a Byzantine agreement (BA) problem. It requires all fault-free processors to agree on a common value, even if some components are corrupt. Consequently, there have been significant studies of this agreement problem in distributed systems. However, the traditional BA protocols focus on running ⌊(n−1)/3⌋+1 rounds of message exchange continuously to make each fault-free processor reach an agreement. In other words, since having a large number of messages results in a large protocol overhead, those protocols are inefficient and unreasonable, especially for some network environments which have large number of processors. In this study, we propose a novel and efficient protocol to reduce the number of messages. Our protocol can collect, compare and replace the received values to find the reliable processors and replace the values sent by the unreliable processors. Subsequently, each processor can agree on a common value through three rounds of message exchange. Furthermore, the proposed protocol can use the minimum number of messages to tolerate the maximum number of faulty components in a distributed system.     

The solution of a nonclassic problem for one-dimensional hyperbolic equation using the decomposition procedure

In this article, we propose a new approach for solving an initial–boundary value problem with a non-classic condition for the one-dimensional wave equation. Our approach depends mainly on Adomian's technique. We will deal here with new type of nonlocal boundary value problems that are the solution of hyperbolic partial differential equations with a non-standard boundary specification. The decomposition method of G. Adomian can be an effective scheme to obtain the analytical and approximate solutions. This new approach provides immediate and visible symbolic terms of analytic solution as well as numerical approximate solution to both linear and nonlinear problems without linearization. The Adomian's method establishes symbolic and approximate solutions by using the decomposition procedure. This technique is useful for obtaining both analytical and numerical approximations of linear and nonlinear differential equations and it is also quite straightforward to write computer code. In comparison to traditional procedures, the series-based technique of the Adomian decomposition technique is shown to evaluate solutions accurately and efficiently. The method is very reliable and effective that provides the solution in terms of rapid convergent series. Several examples are tested to support our study.     

A new technique for the solution of the Saha equation

A new computational technique for solving the Saha equation, which calculates the ionization states of gases, is presented. The algorithm is safe, converges quickly and is simple to implement. Pseudocode of the program is given to assist such implementation. Accuracy checks are described. Limitations of the technique at high ionization are discussed.     

A new modeling and solution approach for the set-partitioning problem

The set-partitioning problem (SPP) is widely known for both its application potential and its computational challenge. This NP-hard problem is known to pose considerable difficulty for classical solution methods such as those based on LP technologies. In recent years, the unconstrained binary quadratic program has proven to perform well as a unified modeling and solution framework for a variety of IP problems. In this paper we illustrate how this unified framework can be applied to SPP. Computational experience is presented, illustrating the attractiveness of the approach.     

一种新的项目调度解表示方法

基于解集合的准启发式方法是解决资源约束下项目调度问题的有效方法,解的表示形式一直是这种方法的一个重要研究问题。只有充分利用解的形式和目标函数之间的联系,才可能达到在少数枚举下得到尽可能好的解。详细分析了解空间性质,提出了用额外关系表示一个可行解的方法,给出了这种表示方法的理论依据。并介绍了用该方法产生邻域的方法。     

A new explicit method for the solution of

An explicit finite difference approximation procedure which is unconditionally stable for the solution of the general multidimensional, non-homogeneous diffusion equation is presented. This method possesses the advantages of the implicit methods, i.e., no severe limitation on the size of the time increment. Also it has the simplicity of the explicit methods and employs the same “marching” type technique of solution. Results obtained by this method for several different problems were compared with the exact solution and agreed closely with those obtained by other finite-difference methods. For the examples solved the numerical results obtained by the present method are in satisfactory agreement with the exact solution.     

A model with a solution algorithm for the cash transportation vehicle routing and scheduling problem

Cash transportation vehicle routing and scheduling are essential for security carriers to minimize their operating costs and ensure safe cash conveyance. In real operations, to increase cash conveyance safety, there must be significant variation in daily cash transportation vehicle routes and schedules, making such vehicle routes and schedules difficult to formulate. However, for convenient planning purposes, security carriers normally plan such routes and schedules based on personal experience, without considering variations in routes and schedules from a system perspective. As a result, the obtained routes and schedules are neither safe nor efficient for transporting cash. In this study, a model is developed where the time–space network technique is utilized to formulate the potential movements of cash transportation vehicles among all demand points in the dimensions of time and space. This model incorporates a new concept of similarity of time and space for routing and scheduling, which is expected to help security carriers formulate more flexible routing and scheduling strategies. This is helpful to reduce the risk of robbery. Mathematically, the model is formulated as an integer multiple-commodity network flow problem. A solution algorithm, based on a problem decomposition/collapsing technique, coupled with the use of a mathematical programming software, is developed to efficiently solve the problem. The case study results show that our model and solution algorithm could be useful references for security carriers in actual practice.     

Well posedness and numerical solution for a non-local pseudohyperbolic initial boundary value problem

ABSTRACT

In this paper, we study a non-local initial boundary value problem for a one-dimensional pseudohyperbolic equation. We first establish the existence and uniqueness of strong solution, then a numerical solutions for the system will be derived by using the finite-difference method.     

A new effective algorithm for the resonant state of a Schrödinger equation

In this paper we present a new effective algorithm for the Schrödinger equation. This new method differs from the original Numerov method only in one simple coefficient, by which we can extend the interval of periodicity from 6 to infinity and obtain an embedded correct factor to improve the accuracy. We compare the new method with the original Numerov method by the well-known problem of Woods-Saxon potential. The numerical results show that the new method has great advantage in accuracy over the original. Particularly for the resonant state, the accuracy is improved with four orders overall, and even six to seven orders for the highest oscillatory solution. Surely, this method will replace the original Numerov method and be widely used in various area.     

矩形正交各向异性薄板弯曲受迫振动问题的分析解

通过恰当的辛内积定义,首先将矩形正交各向异性薄板弯曲受迫振动问题导入到辛对偶体系,并应用分离变量和辛本征展开的有效数学物理方法给出其受迫振动稳态解的一个解析求解方法.然后,具体讨论了对边简支和对边固支两种典型边界条件的正交各向异性薄板弯曲受迫振动问题的辛本征问题,并给出了对应的辛本征值超越方程和辛本征向量的解析表达式.最后,应用本文的方法分析求解了两个具体算例,并将受均布谐载作用的四边简支矩形板受迫振动稳态解的分析解与传统的Navier法进行了精度和收敛性的对比,结果表明本文的方法比传统的分析求解方法具有更好的精度和收敛性,尤其是对内力.     

A new filtering method for the Cauchy problem of the Laplace equation

In the present paper, we consider a Cauchy problem for the Laplace equation in a rectangle domain. A new filtering method is presented for approximating the solution of this problem, and the Hölder-type error estimates are obtained by the different parameter choice rules. Numerical illustration shows that the proposed method works effectively.     

A new axiomatic methodology for the image similarity

In this paper, a new theoretical framework is introduced which explores the notion of image similarity in two axiomatic conditions. The first one resembles to the concept of frequency in matching image patches. The second one formalizes the high-level strategy for computing the image similarity. A realization of this theoretical framework is a new image similarity measure based on approximate matching of patches shared between the images. The approximate match is defined in terms of normalized 2D Hamming distance, and verified within a given neighbourhood from the position of the patches in the images. The similarity measure is computed as the average area of these shared patches. The proposed approach is tested on well-known benchmark datasets. The obtained results show that the proposed method overcomes, in terms of retrieval precision and computational complexity, other competing measures adopted in image retrieval.     

CIM—still the solution for manufacturing industry

In today's economic environment, enterprises that solely rely on traditional technologies cannot meet dynamic customer demands. Hence, proactive enterprises seek the application of intelligent and integrated manufacturing systems in order to meet the customer's demands and be the winners in the competitive market. Although, with available technologies and systems in Computer Integrated Manufacturing (CIM) and its related technologies, the application of CIM in manufacturing enterprises is a reality and can meet the need of the enterprises; today mangers in many enterprises are confused with varying technologies and new terminologies that prevail in the public domain. To make adoption and implementation issues complicated, there are many researchers pursing similar concepts but in different names to solve part of the issues that are or can be addressed by a CIM system. Therefore, this paper summarises the evolution of manufacturing technologies that are associated with developments towards a CIM system, and reviewed some of the new terminologies and technologies, which were proposed during the last four decades. This review is aimed at overcoming the confusion with the new terminologies that have been generated in the past four decades. Further, this paper articulates that all these new proposals are in deed the sub-system or sub-solutions of CIM. Finally, this article focuses on latest research developments in CIM and provides a stepwise justification methodology towards a CIM system for a small or a medium enterprise.     

A probabilistic solution discovery algorithm for solving 0-1 knapsack problem

Abstract

In this paper, a probabilistic solution discovery algorithm is developed to solve the NP-hard 0-1 knapsack problem. The proposed method consists of three steps: strategy development, strategy analysis, and solution discovery. In the first step, Monte Carlo simulation is used to generate the strategies based on a vector defining the probability that each item is included in the knapsack. In the second step, we analyse the capacity imposed by each strategy previously generated and penalise the objective value for those strategies exceeding the capacity of the knapsack. At the last step, a subset of ordered strategies is used to update the vector that defines the probability of choosing each item. Two numerical examples are used to demonstrate the efficiency and the performance of the proposed method.     

A new static output feedback approach to the suboptimal mixed H2/H∞ problem

In this paper we propose a new approach to solve the static output feedback suboptimal mixed H₂/H_∞ control problem using a state fixed‐structure feedback design. We formulate the static output feedback problem as a constrained static state feedback problem and obtain three coupled design equations: one Riccati equation, one Lyapunov equation, and a gain equation. We will prove the equivalence of the proposed solution to the existing solution. A very simple iterative algorithm is then presented to solve the design equations for the stabilizing output feedback gain that minimizes an upper bound of H₂ norm while satisfying the H_∞ disturbance attenuation requirement. A unique feature of the new approach is that it admits the Kalman gain as an initial stabilizing gain to start the above iterative solution procedure, which is computationally attractive and advantageous compared to the direct approach, as the latter has to deal with the difficult algorithm initialization problem. Some illustrative numerical examples are given to demonstrate the effectiveness of the approach. Copyright © 2004 John Wiley & Sons, Ltd.     

二端面弹性转轴非线性动力学方程拓扑反变解

在非相对性原理下建立的二端面弹性转轴的非线性动力学方程,在工程应用中具有时变、强耦合和高度非线性等动力学特征.基于拓扑反变算法,建立二端面弹性转轴的原始系统空间、目标系统空间以及两空间的拓扑反变映射,得到其简单的解耦的目标系统空间及相应方程的拓扑反变解.