With the rapid development of internet economy, transparent logistics is stepping into a prosperity period with massive transportation data generated and collected every day. In this paper, we focus on the segmentation of GPS trajectory data generated in logistics transportation to analyze the vehicle behaviors and extract business affair information according to the vehicle behavior characteristics, which is challenging due to the complexity of trajectory data and unavailability of road information. We extract the stopping points from the trajectory data sequence based on the duration of nonmovement, and construct business time window and electronic fence by analyzing the driving habits of vehicles. Furthermore, we propose a probabilistic logic based data segmentation method (PLDSM) which not only helps finding all the business points but also assists in inferring the business affair categories. An efficient

In this paper, we design and analyze third order positivity-preserving discontinuous Galerkin (DG) schemes for solving the time-dependent system of Poisson–Nernst–Planck (PNP) equations, which have found much use in diverse applications. Our DG method with Euler forward time discretization is shown to preserve the positivity of cell averages at all time steps. The positivity of numerical solutions is then restored by a scaling limiter in reference to positive weighted cell averages. The method is also shown to preserve steady states. Numerical examples are presented to demonstrate the third order accuracy and illustrate the positivity-preserving property in both one and two dimensions.

The matrix completion problem is to recover a low-rank matrix from a subset of its entries. The main solution strategy for this problem has been based on nuclear-norm minimization which requires computing singular value decompositionsa task that is increasingly costly as matrix sizes and ranks increase. To improve the capacity of solving large-scale problems, we propose a low-rank factorization model and construct a nonlinear successive over-relaxation (SOR) algorithm that only requires solving a linear least squares problem per iteration. Extensive numerical experiments show that the algorithm can reliably solve a wide range of problems at a speed at least several times faster than many nuclear-norm minimization algorithms. In addition, convergence of this nonlinear SOR algorithm to a stationary point is analyzed.

In this paper, we propose and analyze a novel stabilized finite element method (FEM) for the system of generalized Stokes equations arising from the time-discretization of transient Stokes problem. The system involves a small viscosity, which is proportional to the inverse of large Reynolds number, and a large reaction coefficient, which is the inverse of small time step. The proposed stabilized FEM employs the $C^0$ piecewise linear elements for both velocity field and pressure on the same mesh and uses the residuals of the momentum equation and the divergence-free equation to define the stabilization terms. The stabilization parameters are fixed and element-independent, without a comparison of the viscosity, the reaction coefficient and the mesh size. Using the finite element solution of an auxiliary boundary value problem as the interpolating function for velocity and the $H^1$-seminorm projection for pressure, instead of the usual nodal interpolants, we derive error estimates for the stabilized finite element approximations to velocity and pressure in the $L^2$ and $H^1$ norms and most importantly, we explicitly establish the dependence of error bounds on the viscosity, the reaction coefficient and the mesh size. Our analysis reveals that this stabilized FEM is particularly suitable for the generalized Stokes system with a small viscosity and a large reaction coefficient, which has never been achieved before in the error analysis of other stabilization methods in the literature. We then numerically confirm the effectiveness of the proposed stabilized FEM. Comparisons made with other existing stabilization methods show that the newly proposed method can attain better accuracy and stability.

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