We consider a problem of trajectory planning for road-like path on the two-dimensional plane. As the basic tool for constructing trajectories, we employ smoothing splines using normalized uniform B-splines as the basi...
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We consider a problem of trajectory planning for road-like path on the two-dimensional plane. As the basic tool for constructing trajectories, we employ smoothing splines using normalized uniform B-splines as the basis functions. The pass is assumed to possess piecewise linear boundaries, specified by a series of pairs of right and left corner points. We allow two-fold corner points in order to allow flexible description of the path. On constructing smoothing splines, we impose the boundary constraints as a collection of inequality pairs by right and left boundary lines, yielding a set of linear inequality constraints on the so-called control point vector. Unlike standard smoothing spline settings, a piecewise linear centerline of the given path is provided as the data for the trajectory to follow, where the given entire time interval is divided into subintervals according to the centripetal distribution rule. Other constraints, typically as the initial and final conditions, can be imposed on the trajectory easily, and we see that the problem reduces to strictly convex QP (quadraticprogramming) problem. Efficient QP solvers are available for numerical solution, and the effectiveness of the proposed method is confirmed by three examples: two with piecewise linear boundaries including an example of obstacle avoidance problem, and the third with piecewise linear approximation of circular boundaries.
An exterior point algorithm for positive definite (PD) and positive semidefinite (PSD) linear complementarity problems (LCPs) is introduced. The algorithm exploits the ellipsoid method to find a starting point in the ...
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An exterior point algorithm for positive definite (PD) and positive semidefinite (PSD) linear complementarity problems (LCPs) is introduced. The algorithm exploits the ellipsoid method to find a starting point in the case of positive definite linear complementarity problems (PDLCPs) and to check for the problem feasibility in case of positive semidefinite linear complementarity problems (PSDLCPs). The algorithm starts from a point on the boundary on which the complementarity condition is satisfied and generates a sequence of points on that same boundary. These points converge to the solution. The algorithm is modified to speed up the convergence for some PDLCPs and PSDLCPs that arise in certain mechanical models. A numerical example and a practical example in robotics are solved to test the algorithm.
Alternative transcription units (ATUs) are dynamically encoded under different conditions and display overlapping patterns (sharing one or more genes) under a specific condition in bacterial genomes. Genome-scale iden...
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Alternative transcription units (ATUs) are dynamically encoded under different conditions and display overlapping patterns (sharing one or more genes) under a specific condition in bacterial genomes. Genome-scale identification of ATUs is essential for studying the emergence of human diseases caused by bacterial organisms. However, it is unrealistic to identify all ATUs using experimental techniques because of the complexity and dynamic nature of ATUs. Here, we present the first-of-its-kind computational framework, named SeqATU, for genome-scale ATU prediction based on next-generation RNA-Seq data. The framework utilizes a convex quadratic programming model to seek an optimum expression combination of all of the to-be-identified ATUs. The predicted ATUs in Escherichia coif reached a precision of 0.77/0.74 and a recall of 0.75/0.76 in the two RNA-Sequencing datasets compared with the benchmarked ATUs from third-generation RNA-Seq data. In addition, the proportion of 5'- or 3'-end genes of the predicted ATUs, having documented transcription factor binding sites and transcription termination sites, was three times greater than that of no 5'- or 3'-end genes. We further evaluated the predicted ATUs by Gene Ontology and Kyoto Encyclopedia of Genes and Genomes functional enrichment analyses. The results suggested that gene pairs frequently encoded in the same ATUs are more functionally related than those that can belong to two distinct ATUs. Overall, these results demonstrated the high reliability of predicted ATUs. We expect that the new insights derived by SeqATU will not only improve the understanding of the transcription mechanism of bacteria but also guide the reconstruction of a genome-scale transcriptional regulatory network.
This paper focuses on the applications of the support vector machine in solving the problem of blind recover in digital communication *** introduce the technique of support vector machine briefly,the development of bl...
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This paper focuses on the applications of the support vector machine in solving the problem of blind recover in digital communication *** introduce the technique of support vector machine briefly,the development of blind equalization and analyze the problems which need to be resolved of the blind *** the applicability of support vector machine in blind problem is highlighted and ***,merit and shortage of blind equalization using support vector machine which is already exist to be discussed and the direction of further research is indicated.
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