Singularity of classical and quantum correlations at critical points of the Lipkin-Meshkov-Glick model in bipartition and tripartition of spins

We study the classical correlation (CC) and quantum discord (QD) between two spin subgroups of the Lipkin-Meshkov-Glick (LMG) model in both binary and trinary decompositions of spins. In the case of bipartition, we find that the classical correlations and all the quantum correlations including the QD, the entanglement of formation (EoF) and the logarithmic negativity (LN) are divergent in the same singular behavior at the critical point of the LMG model. In the case of tripartition, however, the classical correlation is still divergent but all the quantum correlation measures remain finite at the critical point. The present result shows that the classical correlation is very robust but the quantum correlation is much frangible to the environment disturbance. The present result may also lead to the conjecture that the classical correlation is responsible for the singularity behavior of physics quantities at critical points of a many-body quantum system.Comment: 4 figure

Binary Nonlinearization of AKNS Spectral Problem under Higher-Order Symmetry Constraints

Binary nonlinearization of AKNS spectral problem is extended to the cases of higher-order symmetry constraints. The Hamiltonian structures, Lax representations, $r$-matrices and integrals of motion in involution are explicitly proposed for the resulting constrained systems in the cases of the first four orders. The obtained integrals of motion are proved to be functionally independent and thus the constrained systems are completely integrable in the Liouville sense.Comment: 16 pages, latex, to appear in Chaos, Solitons and Fractal

Maximum-frequency gene tree: a simplified genome-scale approach to overcoming incongruence in molecular phylogenies

Genomes and genes diversify during evolution; however, it is unclear to what extent genes still retain the relationship among species. Model species for molecular phylogenetic studies include yeasts and viruses whose genomes were sequenced as well as plants that have the fossil-supported true phylogenetic trees available. In this study, we generated single gene trees of seven yeast species as well as single gene trees of nine baculovirus species using all the orthologous genes among the species compared. Homologous genes among seven known plants were used for validation of the fi nding. Four algorithms: maximum parsimony, minimum evolution, maximum likelihood, and neighbor-joining, were used. Trees were reconstructed before and after weighting the DNA and protein sequence lengths among genes. Rarely a gene can always generate the "true tree" by all the four algorithms. However, the most frequent gene tree, termed "maximum gene-support tree" (MGS tree, or WMGS tree for the weighted one), in yeasts, baculoviruses, or plants was consistently found to be the "true tree" among the species. The results provide insights into the overall degree of divergence of orthologous genes of the genomes analyzed and suggest the following: 1) The true tree relationship among the species studied is still maintained by the largest group of orthologous genes; 2) There are usually more orthologous genes with higher similarities between genetically closer species than between genetically more distant ones; and 3) The maximum gene-support tree refl ects the phylogenetic relationship among species in comparison. Keywords: genome, gene evolution, molecular phylogeny, true treeComment: 10 pages, 5 figures, Evolution 2006, July 23-27 Stony Brook University, NY, US

GeneSupport Maximum Gene-Support Tree Approach to Species Phylogeny Inference

Summary: GeneSupport implements a genome-scale algorithm: Maximum Gene-Support Tree to estimate species tree from gene trees based on multilocus sequences. It provides a new option for multiple genes to infer species tree. It is incorporated into popular phylogentic program: PHYLIP package with the same usage and user interface. It is suitable for phylogenetic methods such as maximum parsimony, maximum likelihood, Baysian and neighbour-joining, which is used to reconstruct single gene trees firstly with a variety of phylogenetic inference programs.Comment: Application not

Virasoro Symmetry Algebra of Dirac Soliton Hierarchy

A hierarchy of first-degree time-dependent symmetries is proposed for Dirac soliton hierarchy and their commutator relations with time-dependent symmetries are exhibited. Meantime, a hereditary structure of Dirac soliton hierarchy is elucidated and a Lax operator algebra associated with Virasoro symmetry algebra is given.Comment: 8 pages, latex, to appear in Inverse Problem

Lipschitz equivalence of a class of self-similar sets

We consider a class of homogeneous self-similar sets with complete overlaps and give a sufficient condition for the Lipschitz equivalence between members in this class.Comment: A remark was added. To appear in Ann. Acad. Sci. Fenn. Mat

Estimating the Hausdorff dimensions of univoque sets for self-similar sets

An approach is given for estimating the Hausdorff dimension of the univoque set of a self-similar set. This sometimes allows us to get the exact Hausdorff dimensions of the univoque sets.Comment: 11 page

When Bifidelity Meets CoKriging: An Efficient Physics-Informed Multifidelity Method

In this work, we propose a framework that combines the approximation-theory-based multifidelity method and Gaussian-process-regression-based multifidelity method to achieve data-model convergence when stochastic simulation models and sparse accurate observation data are available. Specifically, the two types of multifidelity methods we use are the bifidelity and CoKriging methods. The new approach uses the bifidelity method to efficiently estimate the empirical mean and covariance of the stochastic simulation outputs, then it uses these statistics to construct a Gaussian process (GP) representing low-fidelity in CoKriging. We also combine the bifidelity method with Kriging, where the approximated empirical statistics are used to construct the GP as well. We prove that the resulting posterior mean by the new physics-informed approach preserves linear physical constraints up to an error bound. By using this method, we can obtain an accurate construction of a state of interest based on a partially correct physical model and a few accurate observations. We present numerical examples to demonstrate performance of the method

Sliced-Inverse-Regression-Aided Rotated Compressive Sensing Method for Uncertainty Quantification

Compressive-sensing-based uncertainty quantification methods have become a pow- erful tool for problems with limited data. In this work, we use the sliced inverse regression (SIR) method to provide an initial guess for the alternating direction method, which is used to en- hance sparsity of the Hermite polynomial expansion of stochastic quantity of interest. The sparsity improvement increases both the efficiency and accuracy of the compressive-sensing- based uncertainty quantification method. We demonstrate that the initial guess from SIR is more suitable for cases when the available data are limited (Algorithm 4). We also propose another algorithm (Algorithm 5) that performs dimension reduction first with SIR. Then it constructs a Hermite polynomial expansion of the reduced model. This method affords the ability to approximate the statistics accurately with even less available data. Both methods are non-intrusive and require no a priori information of the sparsity of the system. The effec- tiveness of these two methods (Algorithms 4 and 5) are demonstrated using problems with up to 500 random dimensions.Comment: In section 4, numerical examples 3-5, replaced the mean of the error with the quantiles and mean of the error. Added section 4.6 to compare different method

Relativistic baryon-baryon interactions in chiral perturbation theory

We report on the recent studies of leading order baryon-baryon interactions in covariant baryon chiral perturbation theory. In the strangeness $S=0$ sector, one can achieve a rather good description of the Nijmegen $np$ phase shifts with angular momenta $J\leq 1$, particularly the $^1S_0$ and $^3P_0$ partial waves, comparable with the next-to-leading order (NLO) heavy baryon approach. In the strangeness $S=-1$ hyperon-nucleon sector, the best fit of the 36 scattering data is similar to the sophisticated phenomenological models and the NLO heavy baryon approach.Comment: 5 pages, 3 figures; presented by Li-Sheng Geng at the 11th APCTP - BLTP JINR - PNPI NRC KI - SPbU Joint Workshop, July 23-28, Saint-Petersbur