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Item In-Sphere Property and Reverse Inequalities for Matrix Means(2019) Dinh, Trung-Hoa; Tam, Tin-Yau; Vo, Bich-Khue T.The in-sphere property for matrix means is studied. It is proved that the matrix power mean satisfies in-sphere property with respect to the Hilbert-Schmidt norm. A new characterization of the matrix arithmetic mean is provided. Some reverse AGM inequalities involving unitarily invariant norms and operator monotone functions are also obtained.Item Bayesian panel smooth transition model with spatial correlation(2019) Li, Kunming; Fang, Liting; Lu, TaoIn this paper, we propose a spatial lag panel smoothing transition regression (SLPSTR) model ty considering spatial correlation of dependent variable in panel smooth transition regression model. This model combines advantages of both smooth transition model and spatial econometric model and can be used to deal with panel data with wide range of heterogeneity and cross-section correlation simultaneously. We also propose a Bayesian estimation approach in which the Metropolis-Hastings algorithm and the method of Gibbs are used for sampling design for SLPSTR model. A simulation study and a real data study are conducted to investigate the performance of the proposed model and the Bayesian estimation approach in practice. The results indicate that our theoretical method is applicable to spatial data with a wide range of spatial structures under finite sample.Item A Single-Subject Method to Detect Pathways Enriched With Alternatively Spliced Genes(2019) Schissler, Alfred Grant; Aberasturi, Dillon; Kenost, Colleen; Lussier, Yves A.Participants in White et al.’s (1) study performed a semantic categorization task while viewing pairs of words presented simultaneously to the right and left of fixation. On each trial, participants viewed two briefly displayed words (nouns), one displayed to the left of fixation, and the other to the right of fixation, and categorized one of the words as either living or nonliving. In a “focal cue” condition, participants performed the task on either the left or the right word, according to a precue. In a “distributed cue” condition, participants paid attention to both words and subsequently reported the semantic category of one of the words, but without knowing which in advance. The authors, in a previous behavioral study (2), used a similar task to show that even highly skilled readers are able to recognize only one word at a time. In the current study, participants performed the task during fMRI scanning, which measures blood oxygen level-dependent (BOLD) signals with millimeter-level spatial resolution.Item A 3D Numerical Study of Interface Effects Influencing Viscous Gravity Currents in a Parabolic Fissure, with Implications for Modeling with 1D Nonlinear Diffusion Equations(2019) Furtak-Cole, Eden; Telyakovskiy, Aleksey S.Although one-dimensional non-linear diffusion equations are commonly used to model flow dynamics in aquifers and fissures, they disregard multiple effects of real-life flows. Similarity analysis may allow further analytical reduction of these equations, but it is often difficult to provide applicable initial and boundary conditions in practice, or know the magnitude of effects neglected by the 1D model. Furthermore, when multiple simplifying assumptions are made, the sources of discrepancy between modeled and observed data are difficult to identify. We derive one such model of viscous flow in a parabolic fissure from first principals. The parabolic fissure is formed by extruding an upward opening parabola in a horizontal direction. In this setting, permeability is a power law function of height, resulting in a generalized Boussinesq equation. To gauge the effects neglected by this model, 3D Navier-Stokes multiphase flow simulations are conducted for the same geometry. Parameter variations are performed to assess the nature of errors induced by applying the 1D model to a realistic scenario, where the initial and boundary conditions can not be matched exactly. Numerical simulations reveal an undercutting effect observed in laboratory experiments, but not modeled when the Dupuit-Forchheimer assumption is applied. By selectively controlling the effects placed on the free surface in 3D simulations, we are able to demonstrate that free surface slope is the primary driver of the undercutting effect. A consistent lag and overshoot flow regime is observed in the 3D simulations as compared to the 1D model, based on the choice of initial condition. This implies that the undercutting effect is partially induced by the initial condition. Additionally, the presented numerical evidence shows that some of the flow behavior unaccounted for in the 1D model scales with the 1D model parameters.Item Probability of ruin in discrete insurance risk model with dependent Pareto claims(2019) Constantinescu, Corina D.; Kozubowski, Tomasz J.; Qian, Haoyu H.We present basic properties and discuss potential insurance applications of a new class of probability distributions on positive integers with power law tails. The distributions in this class are zero-inflated discrete counterparts of the Pareto distribution. In particular, we obtain the probability of ruin in the compound binomial risk model where the claims are zero-inflated discrete Pareto distributed and correlated by mixture.