New Exact Traveling Wave Solutions of (2 + 1)-Dimensional Time-Fractional Zoomeron Equation

In this paper, the new mapping approach and the new extended auxiliary equation approach were used to investigate the exact traveling wave solutions of (2 + 1)-dimensional time-fractional Zoomeron equation with the conformable fractional derivative. As a result, the singular soliton solutions, kink and anti-kink soliton solutions, periodic function soliton solutions, Jacobi elliptic function solutions and hyperbolic function solutions of (2 + 1)-dimensional time-fractional Zoomeron equation were obtained. Finally, the 3D and 2D graphs of some solutions were drawn by setting the suitable values of parameters with Maple, and analyze the dynamic behaviors of the solutions.

The No-Ellipsoidal Bound of Reachable Sets for Neutral Markovian Jump Systems with Disturbances

This paper is concerned with the reachable set estimation problem for neutral Markovian jump systems with bounded peak disturbances, which was rarely proposed for neutral Markovian jump systems. The main consideration is to find a proper method to obtain the no-ellipsoidal bound of the reachable set for neutral Markovian jump system as small as possible. By applying Lyapunov functional method, some derived conditions are obtained in the form of matrix inequalities. Finally, numerical examples are presented to demonstrate the effectiveness of the theoretical results.

Traveling Wave Solution of the Modified Benjamin-Bona-Mahony Equation

In this paper, the ansatze method is implemented to study the exact solutions for the modified Benjamin-Bona-Mahony equation (mBBM). The singular-shaped traveling wave solution, the Bell-shape is traveling wave solution, the kink-shaped traveling wave solution and the periodic traveling wave solution is obtained. With the assist of computational software MATLAB, the graphical exemplifications of solutions are illustrated of the two-dimension (2D) and three-dimension (3D) plots.

A distributed stochastic optimization algorithm with gradient-tracking and distributed heavy-ball acceleration

Distributed optimization has been well developed in recent years due to its wide applications in machine learning and signal processing.In this paper,we focus on investigating distributed optimization to minimize a global objective.The objective is a sum of smooth and strongly convex local cost functions which are distributed over an undirected network of n nodes.In contrast to existing works,we apply a distributed heavy-ball term to improve the convergence performance of the proposed algorithm.To accelerate the convergence of existing distributed stochastic first-order gradient methods,a momentum term is combined with a gradient-tracking technique.It is shown that the proposed algorithm has better acceleration ability than GT-SAGA without increasing the complexity.Extensive experiments on real-world datasets verify the effectiveness and correctness of the proposed algorithm.

APFD:an effective approach to taxi route recommendation with mobile trajectory big data

With the rapid development of data-driven intelligent transportation systems,an efficient route recommendation method for taxis has become a hot topic in smart cities.We present an effective taxi route recommendation approach(called APFD)based on the artificial potential field(APF)method and Dijkstra method with mobile trajectory big data.Specifically,to improve the efficiency of route recommendation,we propose a region extraction method that searches for a region including the optimal route through the origin and destination coordinates.Then,based on the APF method,we put forward an effective approach for removing redundant nodes.Finally,we employ the Dijkstra method to determine the optimal route recommendation.In particular,the APFD approach is applied to a simulation map and the real-world road network on the Fourth Ring Road in Beijing.On the map,we randomly select 20 pairs of origin and destination coordinates and use APFD with the ant colony(AC)algorithm,greedy algorithm(A*),APF,rapid-exploration random tree(RRT),non-dominated sorting genetic algorithm-II(NSGA-II),particle swarm optimization(PSO),and Dijkstra for the shortest route recommendation.Compared with AC,A*,APF,RRT,NSGA-II,and PSO,concerning shortest route planning,APFD improves route planning capability by 1.45%–39.56%,4.64%–54.75%,8.59%–37.25%,5.06%–45.34%,0.94%–20.40%,and 2.43%–38.31%,respectively.Compared with Dijkstra,the performance of APFD is improved by 1.03–27.75 times in terms of the execution efficiency.In addition,in the real-world road network,on the Fourth Ring Road in Beijing,the ability of APFD to recommend the shortest route is better than those of AC,A*,APF,RRT,NSGA-II,and PSO,and the execution efficiency of APFD is higher than that of the Dijkstra method.

A distributed EEMDN-SABiGRU model on Spark for passenger hotspot prediction

To address the imbalance problem between supply and demand for taxis and passengers,this paper proposes a distributed ensemble empirical mode decomposition with normalization of spatial attention mechanism based bi-directional gated recurrent unit(EEMDN-SABiGRU)model on Spark for accurate passenger hotspot prediction.It focuses on reducing blind cruising costs,improving carrying efficiency,and maximizing incomes.Specifically,the EEMDN method is put forward to process the passenger hotspot data in the grid to solve the problems of non-smooth sequences and the degradation of prediction accuracy caused by excessive numerical differences,while dealing with the eigenmodal EMD.Next,a spatial attention mechanism is constructed to capture the characteristics of passenger hotspots in each grid,taking passenger boarding and alighting hotspots as weights and emphasizing the spatial regularity of passengers in the grid.Furthermore,the bi-directional GRU algorithm is merged to deal with the problem that GRU can obtain only the forward information but ignores the backward information,to improve the accuracy of feature extraction.Finally,the accurate prediction of passenger hotspots is achieved based on the EEMDN-SABiGRU model using real-world taxi GPS trajectory data in the Spark parallel computing framework.The experimental results demonstrate that based on the four datasets in the 00-grid,compared with LSTM,EMDLSTM,EEMD-LSTM,GRU,EMD-GRU,EEMD-GRU,EMDN-GRU,CNN,and BP,the mean absolute percentage error,mean absolute error,root mean square error,and maximum error values of EEMDN-SABiGRU decrease by at least 43.18%,44.91%,55.04%,and 39.33%,respectively.

A Geometric Strategy Algorithm for Orthogonal Pro jection onto a Parametric Surface

In this paper, we investigate how to compute the minimum distance between a point and a parametric surface, and then to return the nearest point (foot point) on the surface as well as its corresponding parameter, which is also called the point projection problem of a parametric surface. The geometric strategy algorithm (hereafter GSA) presented consists of two parts as follows. The normal curvature to a given parametric surface is used to find the corresponding foot point firstly, and then the Taylor's expansion of the parametric surface is employed to compute parameter increments and to get the iteration formula to calculate the orthogonal projection point of test point to the parametric surface. Our geometric strategy algorithm is essentially dependent on the geometric property of the normal curvature, and performs better than existing methods in two ways. Firstly, GSA converges faster than existing methods, such as the method to turn the problem into a root-finding of nonlinear system, subdividing methods, clipping methods, geometric methods (tangent vector and geometric curvature) and hybrid second-order method, etc. Specially, it converges faster than the classical Newton's iterative method. Secondly, GSA is independent of the initial iterative value, which we prove in Theorem 1. Many numerical examples confirm GSA's robustness and efficiency.