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.
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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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.
A high accurate Rayleigh–Ritz method is developed for solving fractional variational problems (FVPs). The Jacobi poly-fractonomials proposed by Zayernouri and Karniadakis (2013, “Fractional Sturm–Liouville Eigen-Pr...
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A high accurate Rayleigh–Ritz method is developed for solving fractional variational problems (FVPs). The Jacobi poly-fractonomials proposed by Zayernouri and Karniadakis (2013, “Fractional Sturm–Liouville Eigen-Problems: Theory and Numerical Approximation,” J. Comput. Phys.,252(1), pp. 495–517.) are chosen as basis functions to approximate the true solutions, and the Rayleigh–Ritz technique is used to reduce FVPs to a system of algebraic equations. This method leads to exponential decay of the errors, which is superior to the existing methods in the literature. The fractional variational errors are discussed. Numerical examples are given to illustrate the exponential convergence of the method.
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://121.199.20.25/. 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.
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.
Gold nanoparticles （Au NPs） can serve as visualized colorimetric probes for various targets and modification-free sensing strategies are preferred. The donor-acceptor interaction between the electron-rich melamine ...
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Gold nanoparticles （Au NPs） can serve as visualized colorimetric probes for various targets and modification-free sensing strategies are preferred. The donor-acceptor interaction between the electron-rich melamine （MA） and the electron-deficient trinitrotoluene （TNT） allows formation of a supramolecule in aqueous solution. Melamine alone makes the initially individual reddish Au NPs aggregate into gray/blue Au NP assemblies due to melamine forming multiple ligand sites toward the Au NPs. Interestingly, the preformed supramolecule of MA-TNT disenables aggregation of the Au NPs. Therefore the unmodified Au NPs provide facile colorimetric probes for TNT detection in aqueous solution. Rapid identification of TNT is established by naked eye inspection. By using spectrophotometer tools, quantification of TNT is accomplished with a linear range of 80μmol L-1 to 1.2 mmol/L-1 and a limit of detection （LOD） of 27μmol/L^-1. In contrast to previous strategy with surface-modified Au NPs, here a modification-free sensing strategy for TNT assay has been developed with greater convenience, rapidity, and cost-effectiveness.
Silver nanoplates as novel optical sensors for Cu^2＋ detection have been *** nanoplates are synthesized via previous H_2O_2-NaBH_4 cyclic oxidation-reduction *** introduction of ascorbate as mild reductants,Cu^2＋ io...
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Silver nanoplates as novel optical sensors for Cu^2＋ detection have been *** nanoplates are synthesized via previous H_2O_2-NaBH_4 cyclic oxidation-reduction *** introduction of ascorbate as mild reductants,Cu^2＋ ions are reduced into Cu~＋ and the Cu^＋ is further reduced to Cu,which is deposited on the surface of the silver *** deposition of the Cu on the surface of the silver nanoplates allows a significant red-shift of their plasmon ***,trace Cu^2＋ can be *** shift of the plasmon absorption wavelength of silver nanoplates is proportional to the Cu^2＋concentration over a range of 40-340 μmol L^（-1） with a limit of detection of 9.0 μmol L^（-1）.Moreover,such silver nanoplate-based optical sensors provide good selectivity for Cu^2＋ detection,and most other metal ions do not disturb its ***,the practicality of the proposed sensor was *** Cu^2＋assay is advantageous in its simplicity,selectivity,and cost-effectiveness.
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