In recent years, researchers have proposed several methods to transform time series (such as those of fractional Brownian motion) into complex networks. In this paper, we construct horizontal visibility networks (HVNs...
In recent years, researchers have proposed several methods to transform time series (such as those of fractional Brownian motion) into complex networks. In this paper, we construct horizontal visibility networks (HVNs) based on the -stable Lévy motion. We aim to study the relations of multifractal and Laplacian spectrum of transformed networks on the parameters and of the -stable Lévy motion. First, we employ the sandbox algorithm to compute the mass exponents and multifractal spectrum to investigate the multifractality of these HVNs. Then we perform least squares fits to find possible relations of the average fractal dimension , the average information dimension and the average correlation dimension against using several methods of model selection. We also investigate possible dependence relations of eigenvalues and energy on , calculated from the Laplacian and normalized Laplacian operators of the constructed HVNs. All of these constructions and estimates will help us to evaluate the validity and usefulness of the mappings between time series and networks, especially between time series of -stable Lévy motions and HVNs.
The atomic structure of recently synthesized thiolate-protected Au cluster is theoretically predicted via a simple structural rule summarized from the crystal structures of thiolate-protected Au（SR）, Au（SR） and Au...
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The atomic structure of recently synthesized thiolate-protected Au cluster is theoretically predicted via a simple structural rule summarized from the crystal structures of thiolate-protected Au（SR）, Au（SR） and Au（SR） clusters. We find that the Au（SR）（N = 7） and recently reported Au（SR）（N = 4）, Au（SR）（N = 3）, Au（SR）（N = 2） and Au（SR）（N = 1） belong to a family of homologous Au（SR） cluster whose Au-cores follow one-dimensional polytetrahedral growth pathway. The Au（SR） cluster is predicted to contain an anisotropic face-centered cubic（FCC） Au-core, which can be viewed as combination of two helical tetrahedra-Au4 chains and is remarkably different from the well-known spherical Au-core in ligand protected gold clusters in the size region of 1-2 nm. The intense near infrared（NIR） absorption of Au（SR） is attributed to the synergistic effect of anisotropic Au-core structure and ligand protections. A plausible cluster-to-cluster transformation mechanism is further suggested.
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://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 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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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.
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.
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