Statistics and Probability Commons^™

Uniform Stability In Nonlinear Infinite Delay Volterra Integro-Differential Equations Using Lyapunov Functionals, Youssef Raffoul, Habib Rai

Mathematics Faculty Publications

In [10] the first author used Lyapunov functionals and studied the exponential stability of the zero solution of nite delay Volterra Integro-dierential equation. In this paper, we use modified version of the Lyapunov functional that were used in [10] to obtain criterion for the stability of the zero solution of the infinite delay nonlinear Volterra integro-dierential equation

x′(t) = Px(t) + ^t∫ _−∞ C(t, s)g(x(s))ds.

Data Driven Sample Generator Model With Application To Classification, Alvaro Emilio Ulloa Cerna

Mathematics & Statistics ETDs

Despite the rapidly growing interest, progress in the study of relations between physiological abnormalities and mental disorders is hampered by complexity of the human brain and high costs of data collection. The complexity can be captured by machine learning approaches, but they still may require significant amounts of data. In this thesis, we seek to mitigate the latter challenge by developing a data driven sample generator model for the generation of synthetic realistic training data. Our method greatly improves generalization in classification of schizophrenia patients and healthy controls from their structural magnetic resonance images. A feed forward neural network trained …

The Eyes Have It: Eye Tracking Data Visualizations Of Viewing Patterns Of Statistical Graphics, Trent Fawcett

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

As statistical graphics continue to expand to manage an ever growing amount of diverse data, a need to evaluate the effectiveness of graphics, both basic and complex, has arisen. Technological advancements have given a means to evaluate the effectiveness of graphs and graphical components through eye tracking systems. Eye tracking systems are likewise in need of software that will enable easy evaluation and exploration of data. The focus of this Master's Report is to evaluate the dual solution. An exploration of an eye tracker setup is made, with extensive consideration of testing statistical graphics providing a basis for continued research …

New Flexible Regression Models Generated By Gamma Random Variables With Censored Data, Elizabeth M. Hashimoto, Gauss M. Cordeiro, Edwin M. M. Ortega, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We propose and study a new log-gamma Weibull regression model. We obtain explicit expressions for the raw and incomplete moments, quantile and generating functions and mean deviations of the log-gamma Weibull distribution. We demonstrate that the new regression model can be applied to censored data since it represents a parametric family of models which includes as sub-models several widely-known regression models and therefore can be used more effectively in the analysis of survival data. We obtain the maximum likelihood estimates of the model parameters by considering censored data and evaluate local influence on the estimates of the parameters by taking …

Self-Monitoring Practices, Attitudes, And Needs Of Individuals With Bipolar Disorder: Implications For The Design Of Technologies To Manage Mental Health, Elizabeth L. Murnane, Dan Cosley, Pamara Chang, Shion Guha, Ellen Frank, Geri K. Gay, Mark Matthews

Mathematics, Statistics and Computer Science Faculty Research and Publications

Objective To understand self-monitoring strategies used independently of clinical treatment by individuals with bipolar disorder (BD), in order to recommend technology design principles to support mental health management.

Materials and Methods Participants with BD (N = 552) were recruited through the Depression and Bipolar Support Alliance, the International Bipolar Foundation, and WeSearchTogether.org to complete a survey of closed- and open-ended questions. In this study, we focus on descriptive results and qualitative analyses.

Results Individuals reported primarily self-monitoring items related to their bipolar disorder (mood, sleep, finances, exercise, and social interactions), with an increasing trend towards the use of digital …

Bases For Mckay Centralizer Algebras, Lucas Gagnon

Mathematics, Statistics, and Computer Science Honors Projects

The finite subgroups of the special unitary group SU2 have been classified to be isomorphic to one of the following groups: cyclic, binary dihedral, binary tetrahedral, binary octahedral, and binary icosahedral, of order n, 4n, 24, 48, and 120, respectively. Associated to each group is a representation graph, which by the McKay correspondence is a Dynkin diagram of type Aˆ n−1, Dˆ n+2, Eˆ 6, Eˆ 7, or Eˆ 8. The centralizer algebra Zk(G) = EndG(V ⊗k ) is the algebra of transformations that commute with G acting on the k-fold tensor product of the defining representation V = C …

Building Voters: Exploring Interdependent Preferences In Binary Contexts, Ian Calaway

Mathematics, Statistics, and Computer Science Honors Projects

In this thesis we develop a new method for constructing binary preference orders for given interdependent structures, called characters. We introduce the preference space, which is a vector space of preference vectors. The preference vectors correspond to binary preference orders. We show that the hyperoctahedral group, Z2 o Sn, describes the symmetries of binary preferences orders and then define an action of Z2 o Sn on our preference vectors. We find a natural basis for a preference space. These basis vectors are indexed by subsets of proposals. We show that when completely separable binary preference vectors are decomposed using this …

Takens Theorem With Singular Spectrum Analysis Applied To Noisy Time Series, Thomas K. Torku

Electronic Theses and Dissertations

The evolution of big data has led to financial time series becoming increasingly complex, noisy, non-stationary and nonlinear. Takens theorem can be used to analyze and forecast nonlinear time series, but even small amounts of noise can hopelessly corrupt a Takens approach. In contrast, Singular Spectrum Analysis is an excellent tool for both forecasting and noise reduction. Fortunately, it is possible to combine the Takens approach with Singular Spectrum analysis (SSA), and in fact, estimation of key parameters in Takens theorem is performed with Singular Spectrum Analysis. In this thesis, we combine the denoising abilities of SSA with the Takens …

To Dot Product Graphs And Beyond, Sean Bailey

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We will introduce three new vector representations of graphs. These representations are based on relationships between the vectors that are used. Specifically, we will examine scenarios where we ignore specific relationships, where we consider if information is missing, and where we look for when the information in common is not of a specified amount.

Bayesian Models For Repeated Measures Data Using Markov Chain Monte Carlo Methods, Yuanzhi Li

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Bayesian models for repeated measures data are fitted to three different data an analysis projects. Markov Chain Monte Carlo (MCMC) methodology is applied to each case with Gibbs sampling and/or an adaptive Metropolis-Hastings (MH) algorithm used to simulate the posterior distribution of parameters. We implement a Bayesian model with different variance-covariance structures to an audit fee data set. Block structures and linear models for variances are used to examine the linear trend and different behaviors before and after regulatory change during year 2004-2005. We proposed a Bayesian hierarchical model with latent teacher effects, to determine whether teacher professional development (PD) …

Blossom: A Language Built To Grow, Jeffrey Lyman

Mathematics, Statistics, and Computer Science Honors Projects

No abstract provided.

Pooling Strength Amongst Limited Datasets Using Hierarchical Bayesian Analysis, With Application To Pyroclastic Density Current Mobility Metrics, Sarah E. Ogburn, James Berger, Eliza S. Calder, Danilo Lopes, Abani K. Patra, E. Bruce Pitman, Regis Rutarindwa, Elaine Spiller, Robert L. Wolpert

Mathematics, Statistics and Computer Science Faculty Research and Publications

In volcanology, the sparsity of datasets for individual volcanoes is an important problem, which, in many cases, compromises our ability to make robust judgments about future volcanic hazards. In this contribution we develop a method for using hierarchical Bayesian analysis of global datasets to combine information across different volcanoes and to thereby improve our knowledge at individual volcanoes. The method is applied to the assessment of mobility metrics for pyroclastic density currents in order to better constrain input parameters and their related uncertainties for forward modeling. Mitigation of risk associated with such flows depends upon accurate forecasting of possible inundation …

A Statistical Analysis Of Hurricanes In The Atlantic Basin And Sinkholes In Florida, Joy Marie D'Andrea

USF Tampa Graduate Theses and Dissertations

Beaches can provide a natural barrier between the ocean and inland communities, ecosystems, and resources. These environments can move and change in response to winds, waves, and currents. When a hurricane occurs, these changes can be rather large and possibly catastrophic. The high waves and storm surge act together to erode beaches and inundate low-lying lands, putting inland communities at risk. There are thousands of buoys in the Atlantic Basin that record and update data to help predict climate conditions in the state of Florida. The data that was compiled and used into a larger data set came from two …

Does Academic Performance Predict Workplace Productivity?, Jodie-Gaye Hunter

Honors Projects in Economics

This research examines if college GPA affects productivity and compensation in the workplace. It uses data collected from a survey of approximately 23,000 Bryant University graduates in different stages of their career. About 10 percent of the alumni surveyed completed the survey. The econometric model used in this study allows estimating the effect of GPA on income after controlling for various demographic and socioeconomic variables, including education, major, occupation, gender, among others. The empirical work provides evidence that GPA has a positive and statistically significant impact on workplace productivity for females, but GPA seems to be a weaker predictor of …

Separation Of Parallel Encoded Complex-Valued Slices (Specs) From A Single Complex-Valued Aliased Coil Image, Daniel B. Rowe, Iain P. Bruce, Andrew S. Nencka, James S. Hyde, Mary C. Kociuba

Mathematics, Statistics and Computer Science Faculty Research and Publications

Purpose

Achieving a reduction in scan time with minimal inter-slice signal leakage is one of the significant obstacles in parallel MR imaging. In fMRI, multiband-imaging techniques accelerate data acquisition by simultaneously magnetizing the spatial frequency spectrum of multiple slices. The SPECS model eliminates the consequential inter-slice signal leakage from the slice unaliasing, while maintaining an optimal reduction in scan time and activation statistics in fMRI studies.

Materials and Methods

When the combined k-space array is inverse Fourier reconstructed, the resulting aliased image is separated into the un-aliased slices through a least squares estimator. Without the additional spatial information from …

Roles Of A Teacher And Researcher During In Situ Professional Development Around The Implementation Of Mathematical Modeling Tasks, Hyunyi Jung, Corey Brady

Mathematics, Statistics and Computer Science Faculty Research and Publications

Partnership with teachers for professional development has been considered beneficial because of the potential of collaborative work in the teacher’s own classroom to be relevant to practice. From this perspective, both teachers and researchers can draw on their own expertise and work as authentic partners. In this study, we address the need for such collaboration and focus on how a teacher and a researcher performed their roles when collaboratively implementing mathematical modeling tasks within a context of in situ professional development. Using multi-tier design-based research, as a framework, a researcher worked in a teacher’s classroom to implement a series of …

Asymptotically Periodic Solutions Of Volterra Integral Equations, Muhammad Islam

Mathematics Faculty Publications

We study the existence of asymptotically periodic solutions of a nonlinear Volterra integral equation. In the process, we obtain the existence of periodic solutions of an associated nonlinear integral equation with infinite delay. Schauder's fixed point theorem is used in the analysis.

Smallest Eigenvalues For A Right Focal Boundary Value Problem, Paul W. Eloe, Jeffrey T. Neugebauer

Mathematics Faculty Publications

We establish the existence of smallest eigenvalues for the fractional linear boundary value problems D^α₀₊u+λ₁p(t)u = 0 and D^α₀₊u+λ₂q(t)u = 0, 0

On The Dynamics Of Boolean Gene Regulatory Networks With Stochasticity, Yuezhe Li

Theses and Dissertations

Genes are responsible for producing proteins that are essential to the construction of complex biological systems. The mechanisms by which this production is regulated have long been the center of wide spread research efforts. Deterministic Boolean gene regulatory models have been a particularly effective avenue of research in this field. However these models fall short of accounting for variations in the gene functionality due to the uncertain internal or external environmental conditions. One of the recent attempts to overcome this weakness is by (Murrugarra, 2012), in which a probabilistic component is introduced as the fixed activation/degradation propensities at the cellular …

Counter Machines And Crystallographic Structures, Natasha Jonoska, Mile Krajcevski, Gregory Mccolm

Mathematics and Statistics Faculty Publications

One way to depict a crystallographic structure is by a periodic (di)graph, i.e., a graph whose group of automorphisms has a translational subgroup of finite index acting freely on the structure. We establish a relationship between periodic graphs representing crystallographic structures and an infinite hierarchy of intersection languages DCL_d,d=0,1,2,…, within the intersection classes of deterministic context-free languages. We introduce a class of counter machines that accept these languages, where the machines with d counters recognize the class DCL_d. An intersection of d languages in DCL₁ defines DCL_d. We prove that there is …

Skewed Factor Models Using Selection Mechanisms, Hyoung-Moon Kim, Mehdi Maadooliat, Reinaldo B. Arellano-Valle, Marc G. Genton

Mathematics, Statistics and Computer Science Faculty Research and Publications

Traditional factor models explicitly or implicitly assume that the factors follow a multivariate normal distribution; that is, only moments up to order two are involved. However, it may happen in real data problems that the first two moments cannot explain the factors. Based on this motivation, here we devise three new skewed factor models, the skew-normal, the skew-t, and the generalized skew-normal factor models depending on a selection mechanism on the factors. The ECME algorithms are adopted to estimate related parameters for statistical inference. Monte Carlo simulations validate our new models and we demonstrate the need for skewed factor models …

A Feature Selection Algorithm To Compute Gene Centric Methylation From Probe Level Methylation Data, Brittany Baur, Serdar Bozdag

Mathematics, Statistics and Computer Science Faculty Research and Publications

DNA methylation is an important epigenetic event that effects gene expression during development and various diseases such as cancer. Understanding the mechanism of action of DNA methylation is important for downstream analysis. In the Illumina Infinium HumanMethylation 450K array, there are tens of probes associated with each gene. Given methylation intensities of all these probes, it is necessary to compute which of these probes are most representative of the gene centric methylation level. In this study, we developed a feature selection algorithm based on sequential forward selection that utilized different classification methods to compute gene centric DNA methylation using probe …

A Transformation Class For Spatio-Temporal Survival Data With A Cure Fraction, Sandra M. Hurtado Rua, Dipak K. Dey

Mathematics and Statistics Faculty Publications

We propose a hierarchical Bayesian methodology to model spatially or spatio-temporal clustered survival data with possibility of cure. A flexible continuous transformation class of survival curves indexed by a single parameter is used. This transformation model is a larger class of models containing two special cases of the well-known existing models: the proportional hazard and the proportional odds models. The survival curve is modeled as a function of a baseline cumulative distribution function, cure rates, and spatio-temporal frailties. The cure rates are modeled through a covariate link specification and the spatial frailties are specified using a conditionally autoregressive model with …

Pension Building, Washington Dc, E Laura Golberg

Journal of Humanistic Mathematics

No abstract provided.

A Meeting Of Minds: An Alternate Humor For Teaching Mathematics To Non-Stem Majors, Paul H. Grawe

Journal of Humanistic Mathematics

John Allen Paulos argued essentially for three forms of humor dear to mathematics: Incongruity, Gotcha, and Word Play. Unfortunately, these three are often combative forms and easily drive non-STEM majors out of mathematics and statistics.

William Dunham in The Mathematical Universe shows how a fine mathematician can use humor to draw non-specialists in. Central to Dunham’s success is his use of Sympathetic Pain humor, which creates softer synthetic Reconciler, Consoler, or Bridgebuilder humor styles.

Sexual Assault And The Doctrine Of Chances In The Courtroom, Ryan Wallentine

Research on Capitol Hill

Sexual assault can have devastating and long-lasting effects on victims, but many assailants get away with their crime without being prosecuted.

The doctrine of chances is a rule of evidence allowing evidences of past crimes, wrongs, or acts to show it is unlikely a defendant would be repeatedly and innocently involved in similar, suspicious circumstances.

Given that about 63.3% of assailants are repeat offenders, the doctrine of chances could effectively be used in sexual assault cases.

The main objective is to determine a precise probabilistic threshold for allowing the use of the doctrine of chances in sexual assault cases such …

Generalized Transmuted Family Of Distributions: Properties And Applications, Morad Alizadeh, Faton Merovci, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce and study general mathematical properties of a new generator of continuous distributions with two extra parameters called the Generalized Transmuted Family of Distributions. We investigate the shapes and present some special models. The new density function can be expressed as a linear combination of exponentiated densities in terms of the same baseline distribution. We obtain explicit expressions for the ordinary and incomplete moments and generating function, Bonferroni and Lorenz curves, asymptotic distribution of the extreme values, Shannon and R´enyi entropies and order statistics, which hold for any baseline model. Further, we introduce a bivariate extension of the new …

Asymptotic Behavior Of Certain Integrodifferential Equations, Said R. Grace, Elvan Akin

Mathematics and Statistics Faculty Research & Creative Works

This paper deals with asymptotic behavior of nonoscillatory solutions of certain forced integrodifferential equations of the form: (a(t)x'(t))' = e (t) + ∫ ^t_c (t - s)^{α - 1}k(t,s)ƒ(s,x(s))ds, c > 1, 0 < α < 1. From the obtained results, we derive a technique which can be applied to some related integrodifferential as well as integral equations.

Nonoscillation Criteria For Two-Dimensional Time-Scale Systems, Ozkan Ozturk, Elvan Akin

Mathematics and Statistics Faculty Research & Creative Works

We study the existence and nonexistence of nonoscillatory solutions of a two-dimensional system of first-order dynamic equations on time scales. Our approach is based on the Knaster and Schauder fixed point theorems and some certain integral conditions. Examples are given to illustrate some of our main results.

Qualitative Analysis On Differential, Fractional Differential, And Dynamic Equations And Related Topics, Said R. Grace, Taher S. Hassan, Shurong Sun, Elvan Akin

Mathematics and Statistics Faculty Research & Creative Works

This issue on qualitative analysis on differential, fractional differential, and dynamic equations and related topics aims at an all-around research and the state-of-the-art theoretical, numerical, and practical achievements that contribute to this field.