Physical Sciences and Mathematics Commons^™

Turbulence And Overturning Gravity Wave Effects Deduced From Mesospheric Na Density Between 100-105 Km At Andes Lidar Observatory, Chile, Alan Z. Liu, Channing P. Philbrick, Gary R. Swenson, Fabio A. Vargas

Publications

Atmospheric turbulence activity in the mesosphere and lower thermosphere (MLT) region is determined from narrowband Na lidar measurements obtained over 27 nights between 85-105 km altitude at the Andes Lidar Observatory (ALO) in Cerro Pachón, Chile (30.3ºS, 70.7ºW). Photocount perturbations in the applicable spectral subrange are used as a tracer of turbulence activity. Mean altitude profiles reveal a log-scale linear increase in turbulence perturbation amplitude above 95 km. The observed trend is compared against global mean constituent transport profiles derived from SABER and SCIAMACHY satellite borne measurements.

Chemical Transport Of Neutral Atmospheric Constituents By Waves And Turbulence: Theory And Observations, Chester S. Gardner, Alan Liu

Publications

Vertical chemical transport occurs when the density fluctuations of a species, caused by perturbations of its chemistry, are strongly correlated with the vertical wind fluctuations. Chemical transport can exceed dynamical and eddy transport of chemically active species. Theoretical expressions are derived for the chemical fluxes and transport velocities and used to characterize the vertical transport of mesospheric O3 and meteoric Na and Fe between 85 and 100 km. Chemical transport is dependent on the intrinsic frequency spectrum of the temperature fluctuations and on the chemical cutoff periods of the species. For O3 only high-frequency fluctuations contribute to chemical transport because …

Southern Hemisphere Summer Mesopause Responses To El Niño–Southern Oscillation, Tao Li, Natalia Calvo, Jia Yue, James Russell Iii, Alan Liu

Publications

In the Southern Hemisphere (SH) polar region, satellite observations reveal a significant uppermesosphere cooling and a lower-thermosphere warming during warm ENSO events in December. An opposite pattern is observed in the tropical mesopause region. The observed upper-mesosphere cooling agrees with a climate model simulation. Analysis of the simulation suggests that enhanced planetary wave (PW) dissipation in the Northern Hemisphere (NH) high-latitude stratosphere during El Niño strengthens the Brewer–Dobson circulation and cools the equatorial stratosphere. This increases the magnitude of the SH stratosphere meridional temperature gradient and thus causes the anomalous stratospheric easterly zonal wind and early breakdown of the SH …

Evidence Of The Excitation Of A Ring-Like Gravity Wave In The Mesosphere Over The Andes Lidar Observatory, Fabio Vargas, Gary Swenson,, Alan Liu, Dominique Pautet

Publications

On 23 March 2012, our all-sky imager recorded a concentric, ring-like gravity wave pattern. The wave arose within the area covered by images of both OH and O(1S) nightglow emissions taken at the Andes Lidar Observatory (ALO), Chile (30.3°S, 70.7°W). We have estimated the observed and intrinsic parameters of the event and located the wave source within the lower mesosphere altitude range using a reverse ray tracing method. By the analysis of GOES and LIS satellite images, we have not found evidence of neither convective nor lightning activity nearby ALO, indicating that the source of the ring-like wave …

From Enrollment To Employment: A Dacum Approach To Information Systems And Information Security And Assurance Curriculum Design, Leila Halawi, Wendi M. Kappers, Aaron Glassman

Publications

Issues associated with information security are numerous and diverse. Since the majority of organizational actions rely greatly on information and communication technologies, Information Systems (IS) security is now a main concern for firms, governments, institutes, and society as a whole. As a result, a plethora of graduate programs have been created, covering nearly every aspect of IS security. The authors review the current state of the IS industry presented in the literature, and identify a panel of IS experts in which to explore current job skill needs using a “Developing a Curriculum,” DACUM, process to support curriculum design for two …

Plasma Density Analysis Of Cubesat Wakes In The Earth’S Ionosphere, Robert M. Albarran Ii, Aroh Barjatya

Publications

Spinning or tumbling CubeSats with Langmuir probes deployed on booms will render spin-modulated plasma densities as the probes move in and out of the spacecraft wake. It is traditionally assumed that the lower-density measurements from the spin cycle are made in the spacecraft wake, and the higher-density measurements are outside the wake. Although this assumption is valid for larger spacecraft in the Earth’s ionosphere, this paper scrutinizes its validity for CubeSats in similar conditions. Spacecraft–plasma interactions (surface charging, plasma sheaths, and wakes) are less understood for CubeSats, and the small CubeSat dimensions must be considered with respect to characteristic length …

Statistical Methods For Handling Intentional Inaccurate Responders, Kristen J. Mcquerry

Theses and Dissertations--Statistics

In self-report data, participants who provide incorrect responses are known as intentional inaccurate responders. This dissertation provides statistical analyses for address intentional inaccurate responses in the data.

Previous work with adolescent self-report, labeled survey participants who intentionally provide inaccurate answers as mischievous responders. This phenomenon also occurs in clinical research. For example, pregnant women who smoke may report that they are nonsmokers. Our advantage is that we do not solely have self-report answers and can verify responses with lab values. Currently, there is no clear method for handling these intentional inaccurate respondents when it comes to making statistical inferences.

We …

Continuous Time Multi-State Models For Interval Censored Data, Lijie Wan

Theses and Dissertations--Statistics

Continuous-time multi-state models are widely used in modeling longitudinal data of disease processes with multiple transient states, yet the analysis is complex when subjects are observed periodically, resulting in interval censored data. Recently, most studies focused on modeling the true disease progression as a discrete time stationary Markov chain, and only a few studies have been carried out regarding non-homogenous multi-state models in the presence of interval-censored data. In this dissertation, several likelihood-based methodologies were proposed to deal with interval censored data in multi-state models.

Firstly, a continuous time version of a homogenous Markov multi-state model with backward transitions was …

Statistical Methods For Environmental Exposure Data Subject To Detection Limits, Yuchen Yang

Theses and Dissertations--Statistics

In this dissertation, we develop unified and efficient nonparametric statistical methods for estimating and comparing environmental exposure distributions in presence of detection limits. In the first part, we propose a kernel-smoothed nonparametric estimator for the exposure distribution without imposing any independence assumption between the exposure level and detection limit. We show that the proposed estimator is consistent and asymptotically normal. Simulation studies demonstrate that the proposed estimator performs well in practical situations. A colon cancer study is provided for illustration. In the second part, we develop a class of test statistics to compare exposure distributions between two groups by using …

Aggregated Quantitative Multifactor Dimensionality Reduction, Rebecca E. Crouch

Theses and Dissertations--Statistics

We consider the problem of making predictions for quantitative phenotypes based on gene-to-gene interactions among selected Single Nucleotide Polymorphisms (SNPs). Previously, Quantitative Multifactor Dimensionality Reduction (QMDR) has been applied to detect gene-to-gene interactions associated with elevated quantitative phenotypes, by creating a dichotomous predictor from one interaction which has been deemed optimal. We propose an Aggregated Quantitative Multifactor Dimensionality Reduction (AQMDR), which exhaustively considers all k-way interactions among a set of SNPs and replaces the dichotomous predictor from QMDR with a continuous aggregated score. We evaluate this new AQMDR method in a series of simulations for two-way and three-way interactions, …

Improved Models For Differential Analysis For Genomic Data, Hong Wang

Theses and Dissertations--Statistics

This paper intend to develop novel statistical methods to improve genomic data analysis, especially for differential analysis. We considered two different data type: NanoString nCounter data and somatic mutation data. For NanoString nCounter data, we develop a novel differential expression detection method. The method considers a generalized linear model of the negative binomial family to characterize count data and allows for multi-factor design. Data normalization is incorporated in the model framework through data normalization parameters, which are estimated from control genes embedded in the nCounter system. For somatic mutation data, we develop beta-binomial model-based approaches to identify highly or lowly …

Understanding Electrical Conduction In Lithium Ion Batteries Through Multi-Scale Modeling, Jie Pan

Theses and Dissertations--Chemical and Materials Engineering

Silicon (Si) has been considered as a promising negative electrode material for lithium ion batteries (LIBs) because of its high theoretical capacity, low discharge voltage, and low cost. However, the utilization of Si electrode has been hampered by problems such as slow ionic transport, large stress/strain generation, and unstable solid electrolyte interphase (SEI). These problems severely influence the performance and cycle life of Si electrodes. In general, ionic conduction determines the rate performance of the electrode, while electron leakage through the SEI causes electrolyte decomposition and, thus, causes capacity loss. The goal of this thesis research is to design Si …

Visual Properties Of Generalized Kloosterman Sums, Paula Burkhardt '16, Alice Zhuo-Yu Chan '14, Gabriel Currier '16, Stephan Ramon Garcia, Florian Luca, Hong Suh '16

Pomona Faculty Publications and Research

For a positive integer m and a subgroup A of the unit group (Z/mZ)^x, the corresponding generalized Kloosterman sum is the function K(a, b, m, A) = Σ_uEA e(au+bu^-1/m). Unlike classical Kloosterman sums, which are real valued, generalized Kloosterman sums display a surprising array of visual features when their values are plotted in the complex plane. In a variety of instances, we identify the precise number-theoretic conditions that give rise to particular phenomena.

Lattices From Hermitian Function Fields, Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, Hiren Maharaj

Pomona Faculty Publications and Research

We consider the well-known Rosenbloom-Tsfasman function field lattices in the special case of Hermitian function fields. We show that in this case the resulting lattices are generated by their minimal vectors, provide an estimate on the total number of minimal vectors, and derive properties of the automorphism groups of these lattices. Our study continues previous investigations of lattices coming from elliptic curves and finite Abelian groups. The lattices we are faced with here are more subtle than those considered previously, and the proofs of the main results require the replacement of the existing linear algebra approaches by deep results of …

Empirical Likelihood And Differentiable Functionals, Zhiyuan Shen

Theses and Dissertations--Statistics

Empirical likelihood (EL) is a recently developed nonparametric method of statistical inference. It has been shown by Owen (1988,1990) and many others that empirical likelihood ratio (ELR) method can be used to produce nice confidence intervals or regions. Owen (1988) shows that -2logELR converges to a chi-square distribution with one degree of freedom subject to a linear statistical functional in terms of distribution functions. However, a generalization of Owen's result to the right censored data setting is difficult since no explicit maximization can be obtained under constraint in terms of distribution functions. Pan and Zhou (2002), instead, study the …

Topics In Logistic Regression Analysis, Zhiheng Xie

Theses and Dissertations--Statistics

Discrete-time Markov chains have been used to analyze the transition of subjects from intact cognition to dementia with mild cognitive impairment and global impairment as intervening transient states, and death as competing risk. A multinomial logistic regression model is used to estimate the probability distribution in each row of the one-step transition matrix that correspond to the transient states. We investigate some goodness of fit tests for a multinomial distribution with covariates to assess the fit of this model to the data. We propose a modified chi-square test statistic and a score test statistic for the multinomial assumption in each …

Developing An Alternative Way To Analyze Nanostring Data, Shu Shen

Theses and Dissertations--Statistics

Nanostring technology provides a new method to measure gene expressions. It's more sensitive than microarrays and able to do more gene measurements than RT-PCR with similar sensitivity. This system produces counts for each target gene and tabulates them. Counts can be normalized by using an Excel macro or nSolver before analysis. Both methods rely on data normalization prior to statistical analysis to identify differentially expressed genes. Alternatively, we propose to model gene expressions as a function of positive controls and reference gene measurements. Simulations and examples are used to compare this model with Nanostring normalization methods. The results show that …

Statistical Inference On Trimmed Means, Lorenz Curves, And Partial Area Under Roc Curves By Empirical Likelihood Method, Yumin Zhao

Theses and Dissertations--Statistics

Traditionally the inference on trimmed means, Lorenz Curves, and partial AUC (pAUC) under ROC curves have been done based on the asymptotic normality of the statistics. Based on the theory of empirical likelihood, in this dissertation we developed novel methods to do statistical inferences on trimmed means, Lorenz curves, and pAUC. A common characteristic among trimmed means, Lorenz curves, and pAUC is that their inferences are not based on the whole set of samples. Qin and Tsao (2002), Qin et al. (2013), and Qin et al. (2011) recently published their re- searches on the inferences of trimmed means, Lorenz curves, …

Neutron Stars: Compact Objects With Relativistic Gravity, Kazim Yavuz Ekşi̇

Turkish Journal of Physics

General properties of neutron stars are briefly reviewed with an emphasis on the indispensability of general relativity in our understanding of these fascinating objects. In Newtonian gravity the pressure within a star merely plays the role of opposing self-gravity. In general relativity all sources of energy and momentum contribute to the gravity. As a result, the pressure not only opposes gravity but also enhances it. The latter role of pressure becomes more pronounced with increasing compactness, $M/R$, where $M$ and $R$ are the mass and radius of the star, and sets a critical mass beyond which collapse is inevitable. This …

Factorizations Related To The Reciprocal Pascal Matrix, Helmut Prodinger

Turkish Journal of Mathematics

The reciprocal Pascal matrix has entries $\binom{i+j}{j}^{-1}$. Explicit formul$\ae{}$ for its LU-decomposition, the LU-decomposition of its inverse, and some related matrices are obtained. For all results, $q$-analogues are also presented.

Some Results Concerning The Summability Of Spliced Sequences, Tuğba Yurdakadi̇m, Mehmet Ünver

Turkish Journal of Mathematics

A spliced sequence is formed by combining all of the terms of two or more convergent sequences, in their original order, into a new spliced sequence. In this paper replacing convergent sequences by bounded sequences, we study the summability of spliced sequences and give some inequalities that provide us with approximation of the core of transformation of these sequences by a summability matrix. We also present some further results via the Lebesgue integral.

Colorings, Determinants And Alexander Polynomials For Spatial Graphs, Terry Kong, Alec Lewald, Blake Mellor, Vadim Pigrish

Mathematics, Statistics and Data Science Faculty Works

A {\em balanced} spatial graph has an integer weight on each edge, so that the directed sum of the weights at each vertex is zero. We describe the Alexander module and polynomial for balanced spatial graphs (originally due to Kinoshita \cite{ki}), and examine their behavior under some common operations on the graph. We use the Alexander module to define the determinant and p-colorings of a balanced spatial graph, and provide examples. We show that the determinant of a spatial graph determines for which p the graph is p-colorable, and that a p-coloring of a graph corresponds to a representation of …

Alexander And Writhe Polynomials For Virtual Knots, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

We give a new interpretation of the Alexander polynomial Δ₀ for virtual knots due to Sawollek and Silver and Williams, and use it to show that, for any virtual knot, Δ₀ determines the writhe polynomial of Cheng and Gao (equivalently, Kauffman's affine index polynomial). We also use it to define a second-order writhe polynomial, and give some applications.

Consistency Of Cheeger And Ratio Graph Cuts, Nicolas Garcia Trillos, Dejan Slepcev, James Von Brecht, Thomas Laurent, Xavier Bresson

Mathematics, Statistics and Data Science Faculty Works

This paper establishes the consistency of a family of graph-cut- based algorithms for clustering of data clouds. We consider point clouds obtained as samples of a ground-truth measure. We investigate approaches to clustering based on minimizing objective functionals defined on proximity graphs of the given sample. Our focus is on functionals based on graph cuts like the Cheeger and ratio cuts. We show that minimizers of these cuts converge as the sample size increases to a minimizer of a corresponding continuum cut (which partitions the ground truth measure). Moreover, we obtain sharp conditions on how the connectivity radius can be …

Links With Finite N-Quandles, Jim Hoste, Patrick D. Shanahan

Mathematics, Statistics and Data Science Faculty Works

We prove a conjecture of Przytycki which asserts that the n-quandle of a link L in the 3-sphere is finite if and only if the fundamental group of the n-fold cyclic branched cover of the 3-sphere, branched over L, is finite.

Involutory Quandles Of (2,2,R)-Montesinos Links, Jim Hoste, Patrick D. Shanahan

Mathematics, Statistics and Data Science Faculty Works

In this paper we show that Montesinos links of the form L(1/2, 1/2, p/q;e), which we call (2,2,r)-Montesinos links, have finite involutory quandles. This generalizes an observation of Winker regarding the (2, 2, q)-pretzel links. We also describe some properties of these quandles.

The Regularity Of The Boundary Of A Multidimensional Aggregation Patch, Andrea L. Bertozzi, John B. Garnett, Thomas Laurent, Joan Verdera

Mathematics, Statistics and Data Science Faculty Works

We consider solutions to the aggregation equation with Newtonian potential where the initial data are the characteristic function of a domain with boundary of class $C^{1+\gamma}$ ,$0<\gamma<1$. Such initial data are known to yield a solution that, going forward in time, retains a patch-like structure with a constant time-dependent density inside an evolving region, which collapses on itself in a finite time, and which, going backward in time, converges in an $L^1$ sense to a self-similar expanding ball solution. In this work, we prove $C^{1+\gamma}$ regularity of the domain's boundary on the time interval on which the solution exists as an $L^\infty$ patch, up to the collapse time going forward in time and for all finite times going backward in time.

The Segal–Shale–Weil Representation, The Indices Of Kashiwara And Maslov, And Quantum Mechanics, Michael C. Berg

Mathematics, Statistics and Data Science Faculty Works

We produce a connection between the Weil 2-cocycles defining the local and adèlic metaplectic groups defined over a global field, i.e. the double covers of the attendant local and adèlic symplectic groups, and local and adèlic Maslov indices of the type considered by Souriau and Leray. With the latter tied to phase integrals occurring in quantum mechanics, we provide a formulation of quadratic reciprocity for the underlying field, first in terms of an adèlic phase integral, and then in terms of generalized time evolution unitary operators.

Generalized Local And Nonlocal Master Equations For Some Stochastic Processes, Yanping Ma

Mathematics, Statistics and Data Science Faculty Works

In this paper, we present a study on generalized local and nonlocal equations for some stochastic processes. By considering the net flux change in a region determined by the transition probability, we derive the master equation to describe the evolution of the probability density function. Some examples, such as classical Fokker-Planck equations, models for Lévy process, and stochastic coagulation equations, are provided as illustrations. A particular application is a consistent derivation of coupled dynamical systems for spatially inhomogeneous stochastic coagulation processes.

Carbon Cycling In Santa Barbara Basin Sediments: A Modeling Study, David J. Burdige, Tomoko Komada, Cédric Magen, Jeffrey P. Chanton

OES Faculty Publications

The primary input of organic matter to almost all marine sediments comes from deposition at the sediment surface. However, in many continental margin settings, reduced carbon can also be added to sediments from below—for example, from “deep” geologic hydrocarbon reservoirs derived from ancient source rocks or from the decomposition of deeply buried gas hydrate deposits. To examine the impact of these two differing reduced carbon inputs on sediment biogeochemistry, a modified reaction-transport model for anoxic marine sediments is described here and applied to data from sediment cores in Santa Barbara Basin to a depth of 4.6 m. Excellent model fits …