A Legendre-collocation method is proposed to solve the nonlinear Volterra integral equations of the second *** provide a rigorous error analysis for the proposed method,which indicate that the numerical errors in L2-n...
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A Legendre-collocation method is proposed to solve the nonlinear Volterra integral equations of the second *** provide a rigorous error analysis for the proposed method,which indicate that the numerical errors in L2-norm and L¥-norm will decay exponentially provided that the kernel function is sufficiently *** results are presented,which confirm the theoretical prediction of the exponential rate of convergence.
In this work,we investigate wave propagation through a zero index meta-material(ZIM)waveguide embedded with triangular dielectric *** provide a theoretical guidance on how to achieve total reflection and total transmis...
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In this work,we investigate wave propagation through a zero index meta-material(ZIM)waveguide embedded with triangular dielectric *** provide a theoretical guidance on how to achieve total reflection and total transmission(i.e.,cloaking)by adjusting the defect sizes and/or permittivities of the *** work provides a systematical way in manipulating wave propagation through ZIM in addi-tion to the widely studied dielectric defects with cylindrical and rectangular geome-tries.
Protein folding, prediction of protein structure and functions are most important problems in bioinformatics. The protein fold process mainly reflects in the kinetic order of folding. Predicting the structural classes...
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UNLABELLED:Traditional methods for sequence comparison and phylogeny reconstruction rely on pair wise and multiple sequence alignments. But alignment could not be directly applied to whole genome/proteome comparison a...
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UNLABELLED:Traditional methods for sequence comparison and phylogeny reconstruction rely on pair wise and multiple sequence alignments. But alignment could not be directly applied to whole genome/proteome comparison and phylogenomic studies due to their high computational complexity. Hence alignment-free methods became popular in recent years. Here we propose a fast alignment-free method for whole genome/proteome comparison and phylogeny reconstruction using higher order Markov model and chaos game representation. In the present method, we use the transition matrices of higher order Markov models to characterize amino acid or DNA sequences for their comparison. The order of the Markov model is uniquely identified by maximizing the average Shannon entropy of conditional probability distributions. Using one-dimensional chaos game representation and linked list, this method can reduce large memory and time consumption which is due to the large-scale conditional probability distributions. To illustrate the effectiveness of our method, we employ it for fast phylogeny reconstruction based on genome/proteome sequences of two species data sets used in previous published papers. Our results demonstrate that the present method is useful and efficient.
AVAILABILITY AND IMPLEMENTATION:The source codes for our algorithm to get the distance matrix and genome/proteome sequences can be downloaded from ftp://1.1.1.9.20.25/. The software Phylip and EvolView we used to construct phylogenetic trees can be referred from their websites.
The difference method for the space fractional coupled nonlinear Schrödinger equations (CNLS) is studied. The fractional centered difference is used to approximate the space fractional Laplacian. This scheme cons...
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The difference method for the space fractional coupled nonlinear Schrödinger equations (CNLS) is studied. The fractional centered difference is used to approximate the space fractional Laplacian. This scheme conserves the discrete mass and energy. Due to the nonlocal nature of fractional Laplacian, in the classic Sobolev space, it is hard to obtain the error estimation in l ∞ . To overcome this difficulty, the fractional Sobolev space H α / 2 and a fractional norm equivalence in H α / 2 are introduced. Then the convergence of order O ( h 2 + τ 2 ) in l ∞ is proved by fractional Sobolev inequality, where h is the mesh size and τ is the time step. Numerical examples are given to illustrate the theoretical results at last.
A new first-order optimality condition for the basis pursuit denoise （BPDN） problem is derived. This condition provides a new approach to choose the penalty param- eters adaptively for a fixed point iteration algori...
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A new first-order optimality condition for the basis pursuit denoise （BPDN） problem is derived. This condition provides a new approach to choose the penalty param- eters adaptively for a fixed point iteration algorithm. Meanwhile, the result is extended to matrix completion which is a new field on the heel of the compressed sensing. The numerical experiments of sparse vector recovery and low-rank matrix completion show validity of the theoretic results.
A kind of equal-task multiple traveling salesman problem (ET-mTSP) was proposed based on the mTSP and its corresponding mathematical model was constructed;Then, a series of discrete operations for firefly algorithm (F...
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In this paper, applying majorization inequalities, new upper and lower bounds for summation of eigenvalues (including the trace) of the solution of the continuous algebraic Riccati equation are presented. Correspondin...
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There has been a growing interest in alignment-free methods for whole genome comparison and phylogenomic studies. In this study, we propose an alignment-free method for phylogenetic tree construction using whole-prote...
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There has been a growing interest in alignment-free methods for whole genome comparison and phylogenomic studies. In this study, we propose an alignment-free method for phylogenetic tree construction using whole-proteome sequences. Based on the inter-amino-acid distances, we first convert the whole-proteome sequences into inter-amino-acid distance vectors, which are called observed inter-amino-acid distance profiles. Then, we propose to use conditional geometric distribution profiles (the distributions of sequences where the amino acids are placed randomly and independently) as the reference distribution profiles. Last the relative deviation between the observed and reference distribution profiles is used to define a simple metric that reflects the phylogenetic relationships between whole-proteome sequences of different organisms. We name our method inter-amino-acid distances and conditional geometric distribution profiles (IAGDP). We evaluate our method on two data sets: the benchmark dataset including 29 genomes used in previous published papers, and another one including 67 mammal genomes. Our results demonstrate that the new method is useful and efficient.
The method of recovering a low-rank matrix with an unknown fraction whose entries are arbitrarily corrupted is known as the robust principal component analysis （RPCA）. This RPCA problem, under some conditions, can b...
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The method of recovering a low-rank matrix with an unknown fraction whose entries are arbitrarily corrupted is known as the robust principal component analysis （RPCA）. This RPCA problem, under some conditions, can be exactly solved via convex optimization by minimizing a combination of the nuclear norm and the 1. norm. In this paper, an algorithm based on the Douglas-Rachford splitting method is proposed for solving the RPCA problem. First, the convex optimization problem is solved by canceling the constraint of the variables, and ~hen the proximity operators of the objective function are computed alternately. The new algorithm can exactly recover the low-rank and sparse components simultaneously, and it is proved to be convergent. Numerical simulations demonstrate the practical utility of the proposed algorithm.
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