Mean square stabilization of discrete-time switching Markov jump linear systems

This paper consider a special class of hybrid system called switching Markov jump linear system. The system transition is governed by two rules. One is Markov chain and the other is a deterministic rule. Furthermore, the transition probability of the Markov chain is not only piecewise but also orchestrated by a deterministic switching rule. In this paper the mean square stability of the systems is studied when the deterministic switching is subject to two different dwell time conditions: having a lower bound and having both lower and high bounds. The main contributions of this paper are two relevant stability theorems for the systems under study. A numerical example is provided to demonstrate the theoretical results

Symmetric multiparty-controlled teleportation of an arbitrary two-particle entanglement

We present a way for symmetric multiparty-controlled teleportation of an arbitrary two-particle entangled state based on Bell-basis measurements by using two Greenberger-Horne-Zeilinger states, i.e., a sender transmits an arbitrary two-particle entangled state to a distant receiver, an arbitrary one of the $n+1$ agents via the control of the others in a network. It will be shown that the outcomes in the cases that $n$ is odd or it is even are different in principle as the receiver has to perform a controlled-not operation on his particles for reconstructing the original arbitrary entangled state in addition to some local unitary operations in the former. Also we discuss the applications of this controlled teleporation for quantum secret sharing of classical and quantum information. As all the instances can be used to carry useful information, its efficiency for qubits approaches the maximal value.Comment: 9 pages, 3 figures; the revised version published in Physical Review A 72, 022338 (2005). The detail for setting up a GHZ-state quantum channel is adde

High-order BDF convolution quadrature for stochastic fractional evolution equations driven by integrated additive noise

The numerical analysis of stochastic time fractional evolution equations presents considerable challenges due to the limited regularity of the model caused by the nonlocal operator and the presence of noise. The existing time-stepping methods exhibit a significantly low order convergence rate. In this work, we introduce a smoothing technique and develop the novel high-order schemes for solving the linear stochastic fractional evolution equations driven by integrated additive noise. Our approach involves regularizing the additive noise through an $m$-fold integral-differential calculus, and discretizing the equation using the $k$-step BDF convolution quadrature. This novel method, which we refer to as the ID$m$-BDF$k$ method, is able to achieve higher-order convergence in solving the stochastic models. Our theoretical analysis reveals that the convergence rate of the ID$2$-BDF2 method is $O(\tau^{\alpha + \gamma -1/2})$ for $1< \alpha + \gamma \leq 5/2$, and $O(\tau^{2})$ for $5/2< \alpha + \gamma <3$, where $\alpha \in (1, 2)$ and $\gamma \in (0, 1)$ denote the time fractional order and the order of the integrated noise, respectively. Furthermore, this convergence rate could be improved to $O(\tau^{\alpha + \gamma -1/2})$ for any $\alpha \in (1, 2)$ and $\gamma \in (0, 1)$, if we employ the ID$3$-BDF3 method. The argument could be easily extended to the subdiffusion model with $\alpha \in (0, 1)$. Numerical examples are provided to support and complement the theoretical findings.Comment: 22page

(Z)-1-(2,4-Difluoro­phen­yl)-3-(4-fluoro­phen­yl)-2-(1H-1,2,4-triazol-1-yl)prop-2-en-1-one

In the title mol­ecule, C17H10F3N3O, the C=C bond connecting the triazole ring and 4-fluoro­phenyl groups adopts a Z conformation. The triazole ring forms dihedral angles of 15.3 (1) and 63.5 (1)°, with the 2,4-difluoro-substituted and 4-fluoro-substituted benzene rings, respectively. The dihedral angle between the two benzene rings is 51.8 (1)°

Sparse multivariate factor analysis regression models and its applications to integrative genomics analysis

The multivariate regression model is a useful tool to explore complex associations between two kinds of molecular markers, which enables the understanding of the biological pathways underlying disease etiology. For a set of correlated response variables, accounting for such dependency can increase statistical power. Motivated by integrative genomic data analyses, we propose a new methodologyâ sparse multivariate factor analysis regression model (smFARM), in which correlations of response variables are assumed to follow a factor analysis model with latent factors. This proposed method not only allows us to address the challenge that the number of association parameters is larger than the sample size, but also to adjust for unobserved genetic and/or nongenetic factors that potentially conceal the underlying responseâ predictor associations. The proposed smFARM is implemented by the EM algorithm and the blockwise coordinate descent algorithm. The proposed methodology is evaluated and compared to the existing methods through extensive simulation studies. Our results show that accounting for latent factors through the proposed smFARM can improve sensitivity of signal detection and accuracy of sparse association map estimation. We illustrate smFARM by two integrative genomics analysis examples, a breast cancer dataset, and an ovarian cancer dataset, to assess the relationship between DNA copy numbers and gene expression arrays to understand genetic regulatory patterns relevant to the disease. We identify two transâ hub regions: one in cytoband 17q12 whose amplification influences the RNA expression levels of important breast cancer genes, and the other in cytoband 9q21.32â 33, which is associated with chemoresistance in ovarian cancer.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135396/1/gepi22018.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/135396/2/gepi22018_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/135396/3/gepi22018-sup-0001-SuppMat.pd