Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching

A more general class of stochastic nonlinear systems with irreducible homogenous Markovian switching are considered in this paper. As preliminaries, the stability criteria and the existence theorem of strong solutions are first presented by using the inequality of mathematic expectation of a Lyapunov function. The state-feedback controller is designed by regarding Markovian switching as constant such that the closed-loop system has a unique solution, and the equilibrium is asymptotically stable in probability in the large. The output-feedback controller is designed based on a quadratic-plus-quartic-form Lyapunov function such that the closed-loop system has a unique solution with the equilibrium being asymptotically stable in probability in the large in the unbiased case and has a unique bounded-in-probability solution in the biased case

Estimating Photometric Redshifts of Quasars via K-nearest Neighbor Approach Based on Large Survey Databases

We apply one of lazy learning methods named k-nearest neighbor algorithm (kNN) to estimate the photometric redshifts of quasars, based on various datasets from the Sloan Digital Sky Survey (SDSS), UKIRT Infrared Deep Sky Survey (UKIDSS) and Wide-field Infrared Survey Explorer (WISE) (the SDSS sample, the SDSS-UKIDSS sample, the SDSS-WISE sample and the SDSS-UKIDSS-WISE sample). The influence of the k value and different input patterns on the performance of kNN is discussed. kNN arrives at the best performance when k is different with a special input pattern for a special dataset. The best result belongs to the SDSS-UKIDSS-WISE sample. The experimental results show that generally the more information from more bands, the better performance of photometric redshift estimation with kNN. The results also demonstrate that kNN using multiband data can effectively solve the catastrophic failure of photometric redshift estimation, which is met by many machine learning methods. By comparing the performance of various methods for photometric redshift estimation of quasars, kNN based on KD-Tree shows its superiority with the best accuracy for our case.Comment: 28 pages, 4 figures, 3 tables, accepted for publication in A

PCA-based bootstrap confidence interval tests for gene-disease association involving multiple SNPs.

BACKGROUND: Genetic association study is currently the primary vehicle for identification and characterization of disease-predisposing variant(s) which usually involves multiple single-nucleotide polymorphisms (SNPs) available. However, SNP-wise association tests raise concerns over multiple testing. Haplotype-based methods have the advantage of being able to account for correlations between neighbouring SNPs, yet assuming Hardy-Weinberg equilibrium (HWE) and potentially large number degrees of freedom can harm its statistical power and robustness. Approaches based on principal component analysis (PCA) are preferable in this regard but their performance varies with methods of extracting principal components (PCs). RESULTS: PCA-based bootstrap confidence interval test (PCA-BCIT), which directly uses the PC scores to assess gene-disease association, was developed and evaluated for three ways of extracting PCs, i.e., cases only(CAES), controls only(COES) and cases and controls combined(CES). Extraction of PCs with COES is preferred to that with CAES and CES. Performance of the test was examined via simulations as well as analyses on data of rheumatoid arthritis and heroin addiction, which maintains nominal level under null hypothesis and showed comparable performance with permutation test. CONCLUSIONS: PCA-BCIT is a valid and powerful method for assessing gene-disease association involving multiple SNPs.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

Lifshitz Scaling Effects on Holographic Superconductors

Via numerical and analytical methods, the effects of the Lifshitz dynamical exponent $z$ on holographic superconductors are studied in some detail, including $s$ wave and $p$ wave models. Working in the probe limit, we find that the behaviors of holographic models indeed depend on concrete value of $z$. We obtain the condensation and conductivity in both Lifshitz black hole and soliton backgrounds with general $z$. For both $s$ wave and $p$ wave models in the black hole backgrounds, as $z$ increases, the phase transition becomes more difficult and the growth of conductivity is suppressed. For the Lifshitz soliton backgrounds, when $z$ increases ($z=1,~2,~3$), the critical chemical potential decreases in the $s$ wave cases but increases in the $p$ wave cases. For $p$ wave models in both Lifshitz black hole and soliton backgrounds, the anisotropy between the AC conductivity in different spatial directions is suppressed when $z$ increases. The analytical results uphold the numerical results.Comment: Typos corrected; Footnote added; References added; To be published in Nuclear Physics

catena-Poly[[(1,10-phenanthroline)cobalt(II)]-di-μ-azido]

In the crystal structure of the binuclear title complex, [Co(N3)2(C12H8N2)]n, each CoII cation is coordinated by two N atoms from one chelating 1,10-phenanthroline ligand and four azide ligands in a slightly distorted octa­hedral coordination. The two CoII cations of the binuclear complex are related by an inversion centre and are bridged by two symmetry-related azide ligands in both μ1,1 and μ1,3 modes. The μ1,3 bridging mode gives rise to an infinite one-dimensional chain along the a axis, whereas the μ1,1 bridging mode is responsible for the formation of the binuclear CoII complex