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.     

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.     

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 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.     

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.     

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.     

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.     

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 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 approach for numerical solution of integro-differential equations via Haar wavelets

A new method is proposed for numerical solution of Fredholm and Volterra integro-differential equations of second kind. The proposed method is based on Haar wavelets approximation. Special characteristics of Haar wavelets approximation has been used in the derivation of this method. The new method is the extension of the recent work [Aziz and Siraj-ul-Islam, New algorithms for numerical solution of nonlinear Fredholm and Volterra integral equations using Haar wavelets, J. Comput. Appl. Math. 239 (2013), pp. 333–345] from integral equations to integro-differential equations. The method is specifically derived for nonlinear problems. Two new algorithms are also proposed based on this new method, one each for numerical solution of Fredholm and Volterra integro-differential equations. The proposed algorithms are generic and are applicable to all types of both nonlinear Fredholm and Volterra integro-differential equations of second kind. The cost of the new algorithms is considerably reduced by using the Broyden's method instead of Newton's method for solution of system of nonlinear equations. Most of the numerical methods designed for solution of integro-differential equations rely on some other technique for numerical integration. The advantage of our method is that it does not use numerical integration. The integrand is approximated using Haar wavelets approximation and then exact integration is performed. The method is tested on number of problems and numerical results are compared with existing methods in the literature. The numerical results indicate that accuracy of the obtained solutions is reasonably high even when the number of collocation points is small.     

A branch and bound algorithm for the cyclic job-shop problem with transportation

The cyclic job-shop problem with transportation can be used to describe optimization problems in fully automated manufacturing systems or assembly lines. We study the problem where the machines have no buffers, which rapidly decreases the number of feasible solutions and, therefore, makes it a lot harder to find those feasible solutions. After formulating the problem, we will characterize feasible solutions based on the route of the robot and their properties. With the aim of minimizing the cycle time, we have developed a tree search method to construct feasible solutions and combined it with a bounding procedure. Computational results are reported and compared to those gained by solving the problem with an LP solver.     

A rigorous solution of the infinite time interval LQ problem with constant state tracking

A linear quadratic constant state tracking problem is considered over an infinite time horizon. It is shown that the solution cannot be obtained as a limit from a finite time horizon problem, as in general the limiting problem is ill-posed. To obtain a rigorous solution, the problem is split in two natural well-posed subproblems. One optimal control problem addresses the transient and the other optimal control problem concerns the steady state behavior. It is shown that the transient problem and the steady state problem are solved by the same control law.     

Constructive solution of a bilinear optimal control problem for a Schrödinger equation

Often considered in numerical simulations related to the control of quantum systems, the so-called monotonic schemes have not been so far much studied from the functional analysis point of view. Yet, these procedures provide an efficient constructive method for solving a certain class of optimal control problems. This paper aims both at extending the results already available about these algorithms in the finite-dimensional case (i.e., the time-discretized case) and at completing those of the continuous case. This paper starts with some results about the regularity of a functional related to a wide class of models in quantum chemistry. These enable us to extend an inequality due to Łojasiewicz to the infinite-dimensional case. Finally, some inequalities proving the Cauchy character of the monotonic sequence are obtained, followed by an estimation of the rate of convergence.     

An approximate solution for the static beam problem and nonlinear integro-differential equations

We consider a Kirchhoff type nonlinear static beam and an integro-differential convolution type problem, and investigate the effectiveness of the Optimal Homotopy Asymptotic Method (OHAM), in solving nonlinear integro-differential equations. We compare our solutions via the OHAM, with bench mark solutions obtained via a finite element method, to show the accuracy and effectiveness of the OHAM in each of these problems. We show that our solutions are accurate and the OHAM is a stable accurate method for the problems considered.