Censoring, Factorizations, and Spectral Analysis for Transition Matrices with Block-Repeating Entries

In this paper, we use the Markov chain censoring technique to study infinite state Markov chains whose transition matrices possess block-repeating entries. We demonstrate that a number of important probabilistic measures are invariant under censoring. Informally speaking, these measures involve first passage times or expected numbers of visits to certain levels where other levels are taboo;they are closely related to the so-called fundamental matrix of the Markov chain which is also studied here. Factorization theorems for the characteristic equation of the blocks of the transition matrix are obtained. Necessary and sufficient conditions are derived for such a Markov chain to be positive recurrent, null recurrent, or transient based either on spectral analysis, or on a property of the fundamental matrix. Explicit expressions are obtained for key probabilistic measures, including the stationary probability vector and the fundamental matrix, which could be potentially used to develop various recursivealgorithms for computing these measures.block-Toeplitz transition matrices, factorization of characteristic functions, spectral analysis, fundamental matrix, conditions of recurrence and transience.

Comprehensive entropy weight observability-controllability risk analysis and its application to water resource decision-making

Decision making for water resource planning is often related to social, economic and environmental factors. There are various methods for making decisions about water resource planning alternatives and measures with various shortcomings. A comprehensive entropy weight observability-controllability risk analysis approach is presented in this study. Computing methods for entropy weight (EW) and subjective weight (SW) are put forward based on information entropy theory and experimental psychology principles, respectively. Comprehensive weight (CW) consisting of EW and SW is determined. The values of observability-controllability risk (Roc) and gain by comparison (Gbc) are obtained based on the CWs. The quantitative analysis of alternatives and measures is achieved based on Roc and Gbc. A case study on selection of water resource planning alternatives and measures in the Yellow River Basin, China, was performed. Results demonstrate that the approach presented in this study can achieve optimal decision-making results

Prenatal exposure to valproic acid induces a dose dependent impairment in sensorimotor gating in a mouse model of autism

Poster Sessionspublished_or_final_versionThe 27th World Congress of the International College of Neuro-Psychopahrmacology (CINP), Hong Kong, 6–10 June 2010. In International Journal of Neuropsychopharmacology, 2010, v. 13, suppl. S1, p. 68, abstract no. P-02.03

Study of B→K(∗)ℓ+ℓ−B\to K^{(*)} \ell^+\ell^- Decays in the Family Non-universal Z′Z' Models

In a combined investigation of the $B\to K^{(*)}\ell^+\ell^-$ decays, constraints on the related couplings in family non-universal $Z^{\prime}$ models are derived. We find that within the allowed parameter space, the recently observed forward-backward asymmetry in the $B\to K^*\ell^+\ell^-$ decay can be explained, by flipping the signs of the Wilson coefficients $C_9^{\rm eff}$ and $C_{10}$. With the obtained constraints, we also calculate the branching ratio of the $B_s\to\mu^+\mu^-$ decay. The upper bound of our prediction is near the upper bound given by CDF Collaboration recently.Comment: 19 pages, 4 figures, some errors corrected; Journal versio

Maximum Path Information and Fokker-Planck Equation

We present in this paper a rigorous method to derive the nonlinear Fokker-Planck (FP) equation of anomalous diffusion directly from a generalization of the principle of least action of Maupertuis proposed by Wang for smooth or quasi-smooth irregular dynamics evolving in Markovian process. The FP equation obtained may take two different but equivalent forms. It was also found that the diffusion constant may depend on both q (the index of Tsallis entropy) and the time t.Comment: 7 page

Geometric entanglement from matrix product state representations

An efficient scheme to compute the geometric entanglement per lattice site for quantum many-body systems on a periodic finite-size chain is proposed in the context of a tensor network algorithm based on the matrix product state representations. It is systematically tested for three prototypical critical quantum spin chains, which belong to the same Ising universality class. The simulation results lend strong support to the previous claim [Q.-Q. Shi, R. Or\'{u}s, J. O. Fj{\ae}restad, and H.-Q. Zhou, New J. Phys \textbf{12}, 025008 (2010); J.-M. St\'{e}phan, G. Misguich, and F. Alet, Phys. Rev. B \textbf{82}, 180406R (2010)] that the leading finite-size correction to the geometric entanglement per lattice site is universal, with its remarkable connection to the celebrated Affleck-Ludwig boundary entropy corresponding to a conformally invariant boundary condition.Comment: 4+ pages, 3 figure

Evaluation of methods for the determination of tortuosity of Li-ion battery separators

The porosities and tortuosities are commonly utilized to characterize the microstructure of a Li-ion battery's separator and are adopted as key input parameters in advanced battery models. Herein, a general classification of the tortuosity for a porous medium is introduced based on its bi-fold significance, i.e., the geometrical and physical tortuosities. Then, three different methods for the determination of separator's electrical tortuosity are introduced and compared, which include the empirical Bruggeman equation, the experimental method using Electrochemical Impedance Spectrum (EIS) testing a the numerical method using realistic 3D microstructure of the separator obtained from nanoscale X-ray Computed Tomography (XCT). In addition, the connection between the geometrical tortuosity and the electrical tortuosity of a separator is established by introducing the electrical phenomenological factor (\b{eta}_e), which can facilitate the understanding of the relationship between the microstructure characteristics and transport properties of the separators. Furthermore, to quantitively compare the values of the tortuosities determined by different methods, the corresponding effective transport coefficients ({\delta}) are compared, which was usually used as a correction for effective diffusivity and conductivity of electrolytes in porous media.Comment: 30 pages, 6 figures, submitted to journal of energy storag

Demonstration of dual gain mechanism in an InGaAs/InAlAs superlattice photodiode

A high‐gain photodiode in which the internal gain can result from either potential barrier lowering or mass filtering action, depending on device geometry and bias conditions, is proposed and demonstrated. The photodiode structure is similar to a modulated barrier diode and uses In0.53Ga0.47As and InGaAs/InAlAs superlattice absorption regions. The superlattice helps to reduce the dark current and aids in mass filtering. The devices reported here were made with multilayered InP‐based materials grown by molecular beam epitaxy and exhibit responsivity as high as 1000 A/W.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69816/2/APPLAB-50-17-1176-1.pd