Enhancing Cybersecurity through Cloud Computing Solutions in the United States

This study investigates how cybersecurity can be enhanced through cloud computing solutions in the United States. The motive for this study is due to the rampant loss of data, breaches, and unauthorized access of internet criminals in the United States. The study adopted a survey research design, collecting data from 890 cloud professionals with relevant knowledge of cybersecurity and cloud computing. A machine learning approach was adopted, specifically a random forest classifier, an ensemble, and a decision tree model. Out of the features in the data, ten important features were selected using random forest feature importance, which helps to achieve the objective of the study. The study’s purpose is to enable organizations to develop suitable techniques to prevent cybercrime using random forest predictions as they relate to cloud services in the United States. The effectiveness of the models used is evaluated by utilizing validation matrices that include recall values, accuracy, and precision, in addition to F1 scores and confusion matrices. Based on evaluation scores (accuracy, precision, recall, and F1 scores) of 81.9%, 82.6%, and 82.1%, the results demonstrated the effectiveness of the random forest model. It showed the importance of machine learning algorithms in preventing cybercrime and boosting security in the cloud environment. It recommends that other machine learning models be adopted to see how to improve cybersecurity through cloud computing.

An improving energy efficiency cooperation algorithm based on Nash bargaining solution in selfish user cooperative networks

A bandwidth-exchange cooperation algorithm based on the Nash bargaining solution （NBS） is proposed to encourage the selfish users to participate with more cooperation so as to improve the users＇ energy efficiency. As a result, two key problems, i.e. , when to cooperate and how to cooperate, are solved. For the first problem, a proposed cooperation condition that can decide when to cooperate and guarantee users＇ energy efficiency achieved through cooperation is not lower than that achieved without cooperation. For the second problem, the cooperation bandwidth allocations （CBAs） based on the NBS solve the problem how to cooperate when cooperation takes place. Simulation results show that, as the modulation order of quadrature amplitude modulation （QAM） increases, the cooperation between both users only occurs with a large signal-to-noise ratio （SNR）. Meanwhile, the energy efficiency decreases as the modulation order increases. Despite all this, the proposed algorithm can obviously improve the energy efficiency measured in bits-per-Joule compared with non-cooperation.

An Algorithm for Solutions of Nonlinear Difference-differential Equations

In this paper,an algorithm is developed for using the G' /G-expansion method to obtain exact solutions for discrete nonlinear systems.Applying this method,some kinds of travelling wave solutions for AL system and Toda lattice system are derived.These solutions are expressed by hyperbolic function,trigonometric function and rational function with parameters.When the parameters are taken as special values,some known solutions including kink-type solitary wave solution and singular travelling wave solution are recovered. It is shown that the developed algorithm is effective and direct.It also can be used for many other nonlinear differential-difference equations in mathematical physics.

Two Structure-Preserving-Doubling Like Algorithms to Solve the Positive Definite Solution of the Equation X-A^(H)X^(-1)A=Q

In this paper,we study the nonlinear matrix equation X-A^(H)X^(-1)A=Q,where A,Q∈C^(n×n),Q is a Hermitian positive definite matrix and X∈C^(n×n)is an unknown matrix.We prove that the equation always has a unique Hermitian positive definite solution.We present two structure-preserving-doubling like algorithms to find the Hermitian positive definite solution of the equation,and the convergence theories are established.Finally,we show the effectiveness of the algorithms by numerical experiments.

Optimized quantum random-walk search algorithm for multi-solution search

This study investigates the multi-solution search of the optimized quantum random-walk search algorithm on the hypercube. Through generalizing the abstract search algorithm which is a general tool for analyzing the search on the graph to the multi-solution case, it can be applied to analyze the multi-solution case of quantum random-walk search on the graph directly. Thus, the computational complexity of the optimized quantum random-walk search algorithm for the multi-solution search is obtained. Through numerical simulations and analysis, we obtain a critical value of the proportion of solutions q. For a given q, we derive the relationship between the success rate of the algorithm and the number of iterations when q is no longer than the critical value.

PCR ALGORITHM FOR PARALLEL COMPUTING MINIMUM-NORM LEAST-SQUARES SOLUTION OF INCONSISTENT LINEAR EQUATIONS

This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obtained in T = n(log2m + log2(n - r + 1) + 5) + log2m + 1 steps with P=mn processors when m × 2(n - 1) and with P = 2n(n - 1) processors otherwise.

TWO TYPES OF NEW ALGORITHMS FOR FINDING EXPLICIT ANALYTICAL SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS

The idea of AC = BD was applied to solve the nonlinear differential equations. Suppose that Au = 0 is a given equation to he solved and Dv = 0 is an equation to be easily solved. If the transformation u = Cv is obtained so that v satisfies Dv = 0, then the solutions for Au = 0 can be found. In order to illustrate this approach, several examples about the transformation C are given.

Generating Epsilon-Efficient Solutions in Multiobjective Optimization by Genetic Algorithm

We develop a new evolutionary method of generating epsilon-efficient solutions of a continuous multiobjective programming problem. This is achieved by discretizing the problem and then using a genetic algorithm with some derived probabilistic stopping criteria to obtain all minimal solutions for the discretized problem. We prove that these minimal solutions are the epsilon-optimal solutions to the original problem. We also present some computational examples illustrating the efficiency of our method.

Sniffer Technique for Numerical Solution of Korteweg-de Vries Equation Using Genetic Algorithm

A novel heuristic technique has been developed for solving Ordinary Differential Equation (ODE) numerically under the framework of Genetic Algorithm (GA). The method incorporates a sniffer procedure that helps carry out a memetic search within the solution domain in the vicinity of the currently found best chromosome. The technique has been successfully applied to the Korteweg- de Vries (KdV) equation, a well-known nonlinear Partial Differential Equation (PDE). In the present study we consider its solution in the regime of solitary waves, or solitons that is first used to convert the PDE into an ODE. It is then shown that using the sniffer technique assisted GA procedure, numerical solution has successfully been generated quite efficiently for the one-dimensional ODE version of the KdV equation in space variable (x). The technique is quite promising for its applications to systems involving ODE equations where analytical solutions are not directly available.

Algebraic or Algorithmic: Searching for Optimal Solutions in Multi-Stage Supply Chain Models

In this paper we proposed an AMH Supply Chain model to obtain optimal solutions for Two-, Three- and Four-Stage for deterministic models. Besides deriving its algebraic solutions, a simple searching method is successfully applied in obtaining optimal total costs and its integer multipliers. Our model has shown promising results in comparison to Equal Cycle Time and other existing ones. The tests focused on obtaining optimal total annual costs and other related details of Two-, Three- and Four-Stage for deterministic models. The results are run under Visual Basic Programming platform using Intel? CoreTM2 Duo T6500 Processor.

Multi-Objective Genetic Algorithm to Design Manufacturing Process Line Including Feasible and Infeasible Solutions in Neighborhood

This paper treats multi-objective problem for manufacturing process design. A purpose of the process design is to decide combinations of work elements assigned to different work centers. Multiple work elements are ordinarily assigned to each center. Here, infeasible solutions are easily generated by precedence relationship of work elements in process design. The number of infeasible solutions generated is ordinarily larger than that of feasible solutions generated in the process. Therefore, feasible and infeasible solutions are located in any neighborhood in solution space. It is difficult to seek high quality Pareto solutions in this problem by using conventional multi-objective evolutional algorithms. We consider that the problem includes difficulty to seek high quality solutions by the following characteristics： （1） Since infeasible solutions are resemble to good feasible solutions, many infeasible solutions which have good values of objective functions are easily sought in the search process, （2） Infeasible solutions are useful to select new variable conditions generating good feasible solutions in search process. In this study, a multi-objective genetic algorithm including local search is proposed using these characteristics. Maximum value of average operation times and maximum value of dispersion of operation time in all work centers are used as objective functions to promote productivity. The optimal weighted coefficient is introduced to control the ratio of feasible solutions to all solutions selected in crossover and selection process in the algorithm. This paper shows the effectiveness of the proposed algorithm on simple model.

Dykstra’s Algorithm for the Optimal Approximate Symmetric Positive Semidefinite Solution of a Class of Matrix Equations

Dykstra’s alternating projection algorithm was proposed to treat the problem of finding the projection of a given point onto the intersection of some closed convex sets. In this paper, we first apply Dykstra’s alternating projection algorithm to compute the optimal approximate symmetric positive semidefinite solution of the matrix equations AXB = E, CXD = F. If we choose the initial iterative matrix X0 = 0, the least Frobenius norm symmetric positive semidefinite solution of these matrix equations is obtained. A numerical example shows that the new algorithm is feasible and effective.

Solution to Polynomial Equations, a New Approach

A new approach for solving polynomial equations is presented in this study. Two techniques for solving quartic equations are described that are based on a new method which was recently developed for solving cubic equations. Higher order polynomial equations are solved by using a new and efficient algorithmic technique. The proposed methods rely on initially identifying the vicinities of the roots and do not require the use of complicated formulas, roots of complex numbers, or application of graphs. It is proposed that under the stated conditions, the methods presented provide efficient techniques to find the roots of polynomial equations.

New Exact Travelling Wave Solutions to Kundu Equation

Based on a first-order nonlinear ordinary differential equation with six-degree nonlinear term, we first present a new auxiliary equation expansion method and its algorithm. Being concise and straightforward, the method is applied to the Kundu equation. As a result, some new exact travelling wave solutions are obtained, which include bright and dark solitary wave solutions, triangular periodic wave solutions, and singular solutions. This algorithm can also be applied to other nonlinear evolution equations in mathematical physics.

Improving Wilson-θ and Newmark-β Methods for Quasi-Periodic Solutions of Nonlinear Dynamical Systems

Quasi-periodic responses can appear in a wide variety of nonlinear dynamical systems. To the best of our knowledge, it has been a tough job for years to solve quasi-periodic solutions, even by numerical algorithms. Here in this paper, we will present effective and accurate algorithms for quasi-periodic solutions by improving Wilson-θ and Newmark-β methods, respectively. In both the two methods, routinely, the considered equations are rearranged in the form of incremental equilibrium equations with the coefficient matrixes being updated in each time step. In this study, the two methods are improved via a predictor-corrector algorithm without updating the coefficient matrixes, in which the predicted solution at one time point can be corrected to the true one at the next. Numerical examples show that, both the improved Wilson-θ and Newmark-β methods can provide much more accurate quasi-periodic solutions with a smaller amount of computational resources. With a simple way to adjust the convergence of the iterations, the improved methods can even solve some quasi-periodic systems effectively, for which the original methods cease to be valid.

Sparse Solutions of Mixed Complementarity Problems

In this paper, we consider an extragradient thresholding algorithm for finding the sparse solution of mixed complementarity problems (MCPs). We establish a relaxation l1 regularized projection minimization model for the original problem and design an extragradient thresholding algorithm (ETA) to solve the regularized model. Furthermore, we prove that any cluster point of the sequence generated by ETA is a solution of MCP. Finally, numerical experiments show that the ETA algorithm can effectively solve the l1 regularized projection minimization model and obtain the sparse solution of the mixed complementarity problem.

Separating iterative solution model of generalized nonlinear dynamic least squares for data processing in building of digital earth

Data coming from different sources have different types and temporal states. Relations between one type of data and another ones, or between data and unknown parameters are almost nonlinear. It is not accurate and reliable to process the data in building the digital earth with the classical least squares method or the method of the common nonlinear least squares. So a generalized nonlinear dynamic least squares method was put forward to process data in building the digital earth. A separating solution model and the iterative calculation method were used to solve the generalized nonlinear dynamic least squares problem. In fact, a complex problem can be separated and then solved by converting to two sub problems, each of which has a single variable. Therefore the dimension of unknown parameters can be reduced to its half, which simplifies the original high dimensional equations.

ON NUMERICAL SOLUTIONS OF PERIODICALLY PERTURBED CONSERVATIVE SYSTEMS

A nonlinear perturbed conservative system is discussed. BY means of Hadamard's theorem. the existence and uniqueness of the solution of the continuous problem arc proved. When the equation is discreted on the uniform meshes, it is proved that the corresponding discrete problem has a unique solution, Finally, the accuracy of the numerical solution is considered and a simple algorithm is provided for solving the nonlinear difference equation.

An explicit solution to the matrix equation AV+BW=EVJ

In this note, the matrix equation AV ＋ BW = EVJ is considered, where E, A and B are given matrices of appropriate dimensions, J is an arbitrarily given Jordan matrix, V and W are the matrices to be determined. Firstly, a right factorization of （sE - A）^-1 B is given based on the Leverriver algorithm for descriptor systems. Then based on this factorization and a proposed parametric solution, an alternative parametric solution to this matrix equation is established in terms of the R-controllability matrix of （E, A, B）, the generalized symmetric operator and the observability matrix associated with the Jordan matrix d and a free parameter matrix. The proposed results provide great convenience for many analysis and design problems. Moreover, some equivalent forms are proposed. A numerical example is employed to illustrate the effect of the proposed approach.

Numerical Solution of Differential Equations by Direct Taylor Expansion

A variation of the direct Taylor expansion algorithm is suggested and applied to several linear and nonlinear differential equations of interest in physics and engineering, and the results are compared with those obtained from other algorithms. It is shown that the suggested algorithm competes strongly with other existing algorithms, both in accuracy and ease of application, while demanding a shorter computation time.