Smoothed Analysis of the Condition Numbers and Growth Factors of Matrices

Let \orig{A} be any matrix and let $A$ be a slight random perturbation of \orig{A}. We prove that it is unlikely that $A$ has large condition number. Using this result, we prove it is unlikely that $A$ has large growth factor under Gaussian elimination without pivoting. By combining these results, we bound the smoothed precision needed by Gaussian elimination without pivoting. Our results improve the average-case analysis of Gaussian elimination without pivoting performed by Yeung and Chan (SIAM J. Matrix Anal. Appl., 1997).Comment: corrected some minor mistake

Color-octet scalars at the LHC

Color-octet scalars, if present at the TeV scale, will be produced in abundance at the LHC. We discuss in some detail the phenomenology of scalars in the (8,2)_{1/2} representation, recently identified by Manohar and Wise as an addition to the standard-model Higgs sector consistent with the principle of minimal flavor violation. Couplings of this multiplet to the Higgs lift the mass degeneracy among its states, possibly allowing for two-body decays of a heavier colored scalar to a lighter one and a gauge boson. We perform a renormalization group analysis of these couplings and find that limits from Tevatron searches leave little room for these decays. This fact, and the assumption of minimal flavor violation, lead us to study the case where the octets decay to the heaviest kinematically accessible fermion pairs. Focusing on pair-production events leading to (t t-bar t t-bar), (b b-bar b b-bar), and (b b-bar t t-bar) final states, we find that discovery at the LHC should be possible up to masses exceeding 1 TeV.Comment: 15 pages, 6 figues; corrected typos and added discussion of decays to b b-ba

A Study of Religious Attitudes and Problems as Perceived by Current and Former Seventh-day Adventist Students at Seventh-day Adventist Mission Secondary Schools in Hong Kong

Problem. In spite of the combined efforts of both the local churches and the schools, the church attendance of Seventh-day Adventist adolescents has been low. This present study was to identify the religious attitudes of current Adventist students and Adventist alumni of all Adventist mission secondary schools in Hong Kong and to determine the relationship of these attitudes to other selected variables such as Bible classes, spiritual assemblies, church services and activities, doctrinal beliefs, relationships with parents, teachers, and pastors, their own self-concepts, and peer and media influences. This study sought to relate also the attitudes with 14 background variables such as gender, grade level at baptism, level of education, years spent in Adventist schools, religious background of parents, parents\u27 marital status, church attendance, and residential status, whether dormitory or community students. Method. The subjects of this study were 165 current students from Form/Middle One to Five and 199 alumni who had left the Adventist secondary schools, not more than 5 years previously. The survey instrument utilized was the Youth Perceptual Inventory developed by Dudley (1977), modified by Laurent (1986), then further modified and translated into the Chinese language, and validated. Results. An investigation of the alienation scores indicated that 7% of the Adventist population might be considered to have negative attitudes toward religion. The variables that elicited the most negative attitudes concerned uninteresting sermons, unhappiness while attending an Adventist school or church, restrictive church standards, not feeling accepted at church, and unenjoyable church youth activities. Eight of the 13 highest correlations dealt with church influences; school-influence variables ranked second. The influence of media and peers ranked 12th and 15th, respectively. Home-influence variables ranked no higher than 17th. The best predictors for alienation in descending order were: lack of church involvement, lack of personal interest of teachers, authoritarianism in pastors, unbelief in Adventist doctrines, lack of personal interest of pastors, negative media influence, lack of religious sincerity of teachers, and family disharmony. Conclusion. It is important that parents, teachers, and religious leaders endeavor to manifest and communicate qualities associated with positive religious attitudes

Electrical Flows, Laplacian Systems, and Faster Approximation of Maximum Flow in Undirected Graphs

We introduce a new approach to computing an approximately maximum s-t flow in a capacitated, undirected graph. This flow is computed by solving a sequence of electrical flow problems. Each electrical flow is given by the solution of a system of linear equations in a Laplacian matrix, and thus may be approximately computed in nearly-linear time. Using this approach, we develop the fastest known algorithm for computing approximately maximum s-t flows. For a graph having n vertices and m edges, our algorithm computes a (1-\epsilon)-approximately maximum s-t flow in time \tilde{O}(mn^{1/3} \epsilon^{-11/3}). A dual version of our approach computes a (1+\epsilon)-approximately minimum s-t cut in time \tilde{O}(m+n^{4/3}\eps^{-8/3}), which is the fastest known algorithm for this problem as well. Previously, the best dependence on m and n was achieved by the algorithm of Goldberg and Rao (J. ACM 1998), which can be used to compute approximately maximum s-t flows in time \tilde{O}(m\sqrt{n}\epsilon^{-1}), and approximately minimum s-t cuts in time \tilde{O}(m+n^{3/2}\epsilon^{-3})

Vanadium Pentoxide (V2O5) Electrode for Aqueous Energy Storage: Understand Ionic Transport using Electrochemical, XRay, and Computational Tools

In this book chapter, we have discussed the recent results on vanadium oxide-based materials for energy storage applications. Primarily, we present the new results from our own research group on V2O5-layered nanostructures that are made from a facile wet chemistry synthesis. By fine control of the synthetic condition, the morphology, crystallinity, and layer-to-layer distance of V2O5 nanostructures can be tuned. Particularly, highly disordered V2O5 nanolayers which have an interplanar distance up to 1.1 nm, offering a fast transport of K-ion between layers in an aqueous electrolyte and hence the high-energy storage capacity and power density. Uniqueness of our results includes materials characterization and measurements using multiple spectroscopic tools, including synchrotron X-ray pair distribution function (PDF) analyses and in situ X-ray diffraction (XRD). Combined with half-cell and button-cell electrochemical measurements, the complementary results provide insight on the ionic transport of ions between the layers of V2O5 nanostructure