Mathematics and Statistics
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The Department of Mathematics and Statistics in the College of Science offers courses leading to the degrees of Bachelor of Science or Bachelor of Arts with a major in mathematics, Master of Science with a major in mathematics and Master of Arts for the teaching of mathematics. The department offers a complete complement of courses in a broad range of areas within mathematics including: applied mathematics, C*Algebras, discrete mathematics/operations research, game theory, geometry, topology, and statistics.
Mathematics is a language used in conveying the understanding of the physical world. It forms a crucial component in physics and engineering applications, business, economics, life sciences, social sciences and any other area where there is a need for quantification in analysis of phenomena.
Theses and Dissertations for Mathematics and Statistics
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Bayesian panel smooth transition model with spatial correlation
(2019)In 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 ... 
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InSphere Property and Reverse Inequalities for Matrix Means
(2019)The insphere property for matrix means is studied. It is proved that the matrix power mean satisfies insphere property with respect to the HilbertSchmidt norm. A new characterization of the matrix arithmetic mean is ... 
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A SingleSubject Method to Detect Pathways Enriched With Alternatively Spliced Genes
(2019)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 ... 
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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)Although onedimensional nonlinear diffusion equations are commonly used to model flow dynamics in aquifers and fissures, they disregard multiple effects of reallife flows. Similarity analysis may allow further analytical ... 
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Probability of ruin in discrete insurance risk model with dependent Pareto claims
(2019)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 zeroinflated discrete ... 
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A note on transportation cost inequalities for diffusions with reflections
(2019)We prove that reflected Brownian motion with normal reflections in a convex domain satisfies a dimension free Talagrand type transportation costinformation inequality. The result is generalized to other reflected diffusion ... 
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Delta channel networks: 2. Metrics of topologic and dynamic complexity for delta comparison, physical inference, and vulnerability assessment
(Water Resources Research, 2015)Deltas are landforms that deliver water, sediment and nutrient fluxes from upstream rivers to the deltaic surface and eventually to oceans or inland water bodies via multiple pathways. Despite their importance, quantitative ... 
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Delta channel networks: 1. A graphtheoretic approach for studying connectivity and steady state transport on deltaic surfaces
(Water Resources Research, 2015)River deltas are intricate landscapes with complex channel networks that selforganize to deliver water, sediment, and nutrients from the apex to the delta top and eventually to the coastal zone. The natural balance of ... 
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Quantifying the signature of sediment composition on the topologic and dynamic complexity of river delta channel networks and inferences toward delta classification
(Geophysical Research Letters, 2016)Deltas contain complex selforganizing channel networks that nourish the surface with sediment and nutrients. Developing a quantitative understanding of how controlling physical mechanisms of delta formation relate to the ... 
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Genomewide association analysis identifies common variants influencing infant brain volumes
(2017)Genomewide association studies (GWAS) of adolescents and adults are transforming our understanding of how genetic variants impact brain structure and psychiatric risk, but cannot address the reality that psychiatric ... 
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Entropy and optimality in river deltas
(2017)The form and function of river deltas is intricately linked to the evolving structure of their channel networks, which controls how effectively deltas are nourished with sediments and nutrients.Understanding the coevolution ... 
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Balancing an Academic Career in Mathematics with Motherhood and Life's Other Passions
(2018)I became a mother while a postdoctoral fellow, and solved my twobody problem shortly thereafter, becoming a tenuretrack professor in mathematics and statistics. My plan to have a second child came with an unexpected ... 
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Modeling Financial System with Interbank Flows, Borrowing, and Investing
(2018)In our model, private actors with interbank cash flows similar to, but more general than that by Carmona et al. (2013) borrow from the nonbanking financial sector at a certain interest rate, controlled by the central bank, ... 
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Scaledependent erosional patterns in steadystate and transientstate landscapes
(2017)Landscape topography is the expression of the dynamic equilibrium between external forcings (for example, climate and tectonics) and the underlying lithology. The magnitude and spatial arrangement of erosional and depositional ... 
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Network robustness assessed within a dual connectivity framework: joint dynamics of the Active and Idle Networks
(2017)Network robustness against attacks has been widely studied in fields as diverse as the Internet, power grids and human societies. But current definition of robustness is only accounting for half of the story: the connectivity ... 
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Aligning evidence: concerns regarding multiple sequence alignments in estimating the phylogeny of the Nudibranchia suborder Doridina
(2017)Molecular estimates of phylogenetic relationships rely heavily on multiple sequence alignment construction. There has been little consensus, however, on how to properly address issues pertaining to the alignment of variable ... 
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Stochastic shielding and edge importance for Markov chains with timescale separation
(2018)Nerve cells produce electrical impulses ("spikes") through the coordinated opening and closing of ion channels. Markov processes with voltagedependent transition rates capture the stochasticity of spike generation at the ... 
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Stochastic shielding and edge importance for Markov chains with timescale separation
(2018)Nerve cells produce electrical impulses ("spikes") through the coordinated opening and closing of ion channels. Markov processes with voltagedependent transition rates capture the stochasticity of spike generation at the ... 
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Sleep Apnea and Hypoventilation in Patients with Down Syndrome: Analysis of 144 Polysomnogram Studies
(2017)Patients with Down syndrome (DS) are at risk for both obstructive sleep apnea (OSA) and central sleep apnea (CSA) 
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Certain bivariate distributions and random processes connected with maxima and minima
(2018)The minimum and the maximum of t independent, identically distributed random variables have (F) over bar (t) and Ft for their survival (minimum) and the distribution (maximum) functions, where (F) over bar = 1  F and F ...