Statistics and Probability Commons^™

Cybersecurity: Probabilistic Behavior Of Vulnerability And Life Cycle, Sasith Maduranga Rajasooriya

USF Tampa Graduate Theses and Dissertations

Analysis on Vulnerabilities and Vulnerability Life Cycle is at the core of Cybersecurity related studies. Vulnerability Life Cycle discussed by S. Frei and studies by several other scholars have noted the importance of this approach. Application of Statistical Methodologies in Cybersecurity related studies call for a greater deal of new information. Using currently available data from National Vulnerability Database this study develops and presents a set of useful Statistical tools to be applied in Cybersecurity related decision making processes.

In the present study, the concept of Vulnerability Space is defined as a probability space. Relevant theoretical analyses are conducted and …

Comparing Grounded Theory And Topic Modeling: Extreme Divergence Or Unlikely Convergence?, Eric P.S. Baumer, David Mimno, Shion Guha, Emily Quan, Geri K. Gay

Mathematics, Statistics and Computer Science Faculty Research and Publications

Researchers in information science and related areas have developed various methods for analyzing textual data, such as survey responses. This article describes the application of analysis methods from two distinct fields, one method from interpretive social science and one method from statistical machine learning, to the same survey data. The results show that the two analyses produce some similar and some complementary insights about the phenomenon of interest, in this case, nonuse of social media. We compare both the processes of conducting these analyses and the results they produce to derive insights about each method's unique advantages and drawbacks, as …

Symptom Levels In Care-Seeking Bangladeshi And Nepalese Adults With Advanced Cancer, Richard Love, Tahmina Ferdousy, Bishnu D. Paudel, Shamsun Nahar, Rumana Dowla, Mohammad Adibuzzaman, Golam Mushih Tanimul Ahsan, Miftah Uddin, Reza Selim, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

Purpose

Three-fourths of patients with advanced cancer are reported to suffer from pain. A primary barrier to provision of adequate symptom treatment is failure to appreciate the intensity of the symptoms patients are experiencing. Because data on Bangladeshi and Nepalese patients’ perceptions of their symptomatic status are limited, we sought such information using a cell phone questionnaire.

Methods

At tertiary care centers in Dhaka and Kathmandu, we recruited 640 and 383 adult patients, respectively, with incurable malignancy presenting for outpatient visits and instructed them for that single visit on one-time completion of a cell phone platform 15-item survey of questions …

A Direct D-Bar Method For Partial Boundary Data Electrical Impedance Tomography With A Priori Information, Melody Alsaker, Sarah J. Hamilton, Andreas Hauptmann

Mathematics, Statistics and Computer Science Faculty Research and Publications

Electrical Impedance Tomography (EIT) is a non-invasive imaging modality that uses surface electrical measurements to determine the internal conductivity of a body. The mathematical formulation of the EIT problem is a nonlinear and severely ill-posed inverse problem for which direct D-bar methods have proved useful in providing noise-robust conductivity reconstructions. Recent advances in D-bar methods allow for conductivity reconstructions using EIT measurement data from only part of the domain (e.g., a patient lying on their back could be imaged using only data gathered on the accessible part of the body). However, D-bar reconstructions suffer from a loss of sharp edges …

On The Analysis Of The Sir Epidemic Model For Small Networks: An Application In Hospital Settings, Martin Lopez-Garcia

Biology and Medicine Through Mathematics Conference

No abstract provided.

Physiological Health Parameters Among College Students To Promote Chronic Disease Prevention And Health Promotion, David R. Black, Daniel C. Coster, Samantha R. Paige

Mathematics and Statistics Faculty Publications

This study aimed to provide physiologic health risk parameters by gender and age among college students enrolled in a U.S. Midwestern University to promote chronic disease prevention and ameliorate health. A total of 2615 college students between 18 and 25 years old were recruited annually using a series of cross-sectional designs during the spring semester over an 8-year period. Physiologic parameters measured included body mass index (BMI), percentage body fat (%BF), blood serum cholesterol (BSC), and systolic (SBP) and diastolic (DBP) blood pressure. These measures were compared to data from NHANES to identify differences in physiologic parameters among 18-25 year …

Cox Processes For Visual Object Counting, Yongming Ma

Student Research Symposium

We present a model that utilizes Cox processes and CNN classifiers in order to count the number of instances of an object in an image. Poisson processes are well suited to events that occur randomly in space, like the location of objects in an image, as well as to the task of counting. Mixed Poisson processes also offer increased flexibility, however they do not easily scale with image size: they typically require O(n3) computation time and O(n2) storage, where n is the number of pixels. To mitigate this problem, we employ Kronecker algebra which takes advantage of the direct product …

Oscillation Criteria For Third-Order Nonlinear Functional Difference Equations With Damping, Martin Bohner, C. Dharuman, R. Srinivasan, Ethiraju Thandapani

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we obtain some new criteria for the oscillation of certain third-order difference equations using comparison principles with a suitable couple of first-order difference equations. The presented results improve and extend the earlier ones. Examples are provided to illustrate the main results.

Weighted Distributions: A Brief Review, Perspective And Characterizations, Aamir Saghir, Gholamhossein G. Hamedani, Sadaf Tazeem, Aneeqa Khadim

Mathematics, Statistics and Computer Science Faculty Research and Publications

The weighted distributions are widely used in many fields such as medicine, ecology and reliability, to name a few, for the development of proper statistical models. Weighted distributions are milestone for efficient modeling of statistical data and prediction when the standard distributions are not appropriate. A good deal of studies related to the weight distributions have been published in the literature. In this article, a brief review of these distributions is carried out. Implications of the differing weight models for future research as well as some possible strategies are discussed. Finally, characterizations of these distributions based on a simple relationship …

Joint Modelling Of Longitudinal Measurements And Time-To-Event Data : Application To Hiv Study, Mirna Walid Halawani

Theses, Dissertations and Culminating Projects

Longitudinal and survival data are frequently collected in biomedical studies. The research questions of interest in these studies often require separate analysis of the outcomes. But in many occasions interest also lies in studying their association structures, such as in biomarker research, where the clinical studies are designed to identify biomarkers with strong prognostic capabilities for event time outcomes. In the separate analyses, a linear mixed-effects model is used for modeling the longitudinal data to study the changing trend of the response overtime when controlling some covariates and a survival model is used to model the time-to-event data. A common …

Eit Imaging Of Admittivities With A D-Bar Method And Spatial Prior: Experimental Results For Absolute And Difference Imaging, Sarah J. Hamilton

Mathematics, Statistics and Computer Science Faculty Research and Publications

Electrical impedance tomography (EIT) is an emerging imaging modality that uses harmless electrical measurements taken on electrodes at a body's surface to recover information about the internal electrical conductivity and or permittivity. The image reconstruction task of EIT is a highly nonlinear inverse problem that is sensitive to noise and modeling errors making the image reconstruction task challenging. D-bar methods solve the nonlinear problem directly, bypassing the need for detailed and time-intensive forward models, to provide absolute (static) as well as time-difference EIT images. Coupling the D-bar methodology with the inclusion of high confidence a priori data results in a …

Peptide Identification: Refining A Bayesian Stochastic Model, Theophilus Barnabas Kobina Acquah

Electronic Theses and Dissertations

Notwithstanding the challenges associated with different methods of peptide identification, other methods have been explored over the years. The complexity, size and computational challenges of peptide-based data sets calls for more intrusion into this sphere. By relying on the prior information about the average relative abundances of bond cleavages and the prior probability of any specific amino acid sequence, we refine an already developed Bayesian approach in identifying peptides. The likelihood function is improved by adding additional ions to the model and its size is driven by two overall goodness of fit measures. In the face of the complexities associated …

Irrational Eigenvalues Of The Discrete Laplacian: A Study Of Simplical Complexes, Brian Bollen

Psychology

We study the behavior of eigenvalues of the discrete Laplacian of an abstract simplicial complex K when subdividing a single face of K . We show that if K is a simplex, performing this kind of restricted subdivision twice on a single face produces irrational eigenvalues for the discrete Laplacian.

Combinatorial Games On Graphs, Trevor K. Williams

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Combinatorial Games are intriguing and have a tendency to engross students and lead them into a serious study of mathematics. The engaging nature of games is the basis for this thesis. Two combinatorial games and some educational tools are presented which were developed by the author in the pursuit of the solution of these games.

Optimal Experimental Design To Characterize A Wave Source Using Dosimeter Measurements, Renee L. Gooding

Mathematics & Statistics ETDs

When modeling physical phenomena we want to solve the inverse problem by estimating the parameters that characterize the source model that we are interested in. In this thesis, we focus on the optimal placement of a finite number of individual sensors, called dosimeters, in two and three dimensions with a time dependent Gaussian wave source. Using a computational model along with experimental data, we design an iterative process to determine the optimal placement of an additional sensor such that the noise in the measurements has a minimal effect on the parameter estimation. First, we estimate the parameters that characterize the …

Deterministic And Probabilistic Methods For Seismic Source Inversion, Juan Pablo Madrigal Cianci

Mathematics & Statistics ETDs

The national Earthquake Information Center (NEIC) reports an occurrence of about 13,000 earthquakes every year, spanning different values on the Richter scale from very mild (2) to "giant earthquakes'' (8 and above). Being able to study these earthquakes provides useful information for a wide range of applications in geophysics. In the present work we study the characteristics of an earthquake by performing seismic source inversion; a mathematical problem that, given some recorded data, produces a set of parameters that when used as input in a mathematical model for the earthquake generates synthetic data that closely resembles the measured data. There …

Cancer Modeling: From Optimal Cell Renewal To Immunotherapy, Cesar L. Alvarado

Mathematics & Statistics ETDs

Cancer is a disease caused by mutations in normal cells. According to the National Cancer Institute, in 2016, an estimated 1.6 million people were diagnosed and approximately 0.5 million people died from the disease in the United States. There are many factors that shape cancer at the cellular and organismal level, including genetic, immunological, and environmental components. In this thesis, we show how mathematical modeling can be used to provide insight into some of the key mechanisms underlying cancer dynamics. First, we use mathematical modeling to investigate optimal homeostatic cell renewal in tissues such as the small intestine with an …

Modeling Trait Evolutionary Processes With More Than One Gene, Huan Jiang

Mathematics & Statistics ETDs

Phylogenetic comparative methods have been used to test evolutionary signals through trait evolutionary processes. Traditionally, biologists use one phylogenetic tree as a tool to handle dependent data for the traits of interest and hence utilize one gene only. However, it is more informative if the evolutionary processes of a trait are presented by phylogenetic trees reconstructed by the DNA alignments from more than one gene. In this work, we explain and develop two methods involving modeling the trait evolutionary processes: (a) two gene trees via the Brownian motion (BM) model; and (b) two gene trees via the Ornstein-Uhlenbeck (OU) model. …

The Value Of A Win: Analysis Of Playoff Structures, Matthew Orsi

Honors Projects in Mathematics

The purpose of this Senior Capstone project is to analyze the distinctions between existing playoff systems. In particular, we are looking to analyze the differences between the standard single-elimination tournament (which the NCAA has used since the inception of the tournament) and other potential options: double-elimination and multiple game series. Popular sports such as Major League Baseball and the National Basketball Association all use multiple game series for their playoffs. This project will use probability theory and simulation to determine the likelihood of different seeds winning a championship as well as the expected number of victories by seed in each …

Stationary Acceleration Of Frenet Curves, Nemat Abazari, Martin Bohner, Ilgin Sager, Yusuf Yayli

Mathematics and Statistics Faculty Research & Creative Works

In this paper, the stationary acceleration of the spherical general helix in a 3-dimensional Lie group is studied by using a bi-invariant metric. The relationship between the Frenet elements of the stationary acceleration curve in 4-dimensional Euclidean space and the intrinsic Frenet elements of the Lie group is outlined. As a consequence, the corresponding curvature and torsion of these curves are computed. In Minkowski space, for the curves on a timelike surface to have a stationary acceleration, a necessary and sufficient condition is refined.

Deriving A Provisional Tolerable Intake For Intravenous Exposure To Silver Nanoparticles Released From Medical Devices, Laura C. Savery, Rene Vinas, Amber M. Nagy, Prachi Pradeep, Stephen Merrill, Subhas G. Malghan, Peter L. Goering, Ronald P. Brown

Mathematics, Statistics and Computer Science Faculty Research and Publications

Silver nanoparticles (AgNP) are incorporated into medical devices for their anti-microbial characteristics. The potential exposure and toxicity of AgNPs is unknown due to varying physicochemical particle properties and lack of toxicological data. The aim of this safety assessment is to derive a provisional tolerable intake (pTI) value for AgNPs released from blood-contacting medical devices. A literature review of in vivo studies investigating critical health effects induced from intravenous (i. v.) exposure to AgNPs was evaluated by the Annapolis Accords principles and Toxicological Data Reliability Assessment Tool (ToxRTool). The point of departure (POD) was based on an i. v. 28-day …

Regime Switching In Cointegrated Time Series, Bradley David Zynda Ii

Undergraduate Honors Capstone Projects

Volatile commodities and markets can often be difficult to model and forecast given significant breaks in trends through time. To account such breaks, regime switching methods allow for models to accommodate abrupt changes in behavior of the data. However, the difficulty often arises in beginning the process of choosing a model and its associated parameters with which to represent the data and the objects of interest. To improve model selection for these volatile markets, this research examines time series with regime switching components and argues that a synthesis of vector error correction models with regime switching models with ameliorate financial …

Predoctoral Dental Students’ Perceptions Of Dental Implant Training: Effect Of Preclinical Simulation And Clinical Experience, Soni Prasad, Naveen K. Bansal

School of Dentistry Faculty Research and Publications

The aims of this study were to assess 1) differences in perceptions of dental implant training between dental students who received didactic training alone (control group) and those who received didactic plus simulation training (test group); 2) differences in response between students with and without clinical experience in implant dentistry; and 3) the interaction effect of simulation training and clinical experience on students’ satisfaction. A survey was distributed to the control group in 2014 and to the test group in 2015; both groups were at the same U.S. dental school. Data were collected on confidence levels with various implant restorative …

Modeling In Finance And Insurance With Levy-It'o Driven Dynamic Processes Under Semi Markov-Type Switching Regimes And Time Domains, Patrick Armand Assonken Tonfack

USF Tampa Graduate Theses and Dissertations

Mathematical and statistical modeling have been at the forefront of many significant advances in many disciplines in both the academic and industry sectors. From behavioral sciences to hard core quantum mechanics in physics, mathematical modeling has made a compelling argument for its usefulness and its necessity in advancing the current state of knowledge in the 21rst century. In Finance and Insurance in particular, stochastic modeling has proven to be an effective approach in accomplishing a vast array of tasks: risk management, leveraging of investments, prediction, hedging, pricing, insurance, and so on. However, the magnitude of the damage incurred in recent …

Lies, Statistics, Mathematics And The Truth, Nathan L. Tintle

Faculty Work Comprehensive List

"Recognizing a key distinction between mathematics and statistics is helpful in understanding how we know if a statement is true."

Posting about deductive and inductive reasoning­­­­­­­­ from In All Things - an online hub committed to the claim that the life, death, and resurrection of Jesus Christ has implications for the entire world.

http://inallthings.org/lies-statistics-mathematics-and-the-truth/

Mass Action In Two-Sex Population Models: Encounters, Mating Encounters And The Associated Numerical Correction, Katherine Snyder, Brynja R. Kohler, Luis F. Gordillo

Mathematics and Statistics Faculty Publications

Ideal gas models are a paradigm used in Biology for the phenomenological modelling of encounters between individuals of different types. These models have been used to approximate encounter rates given densities, velocities and distance within which an encounter certainly occurs. When using mass action in two-sex populations, however, it is necessary to recognize the difference between encounters and mating encounters. While the former refers in general to the (possibly simultaneous) collisions between particles, the latter represents pair formation that will produce offspring. The classical formulation of the law of mass action does not account this difference. In this short paper, …

Application Of Inverse Problems In Imaging, Xiaoyue Luo

Post-Grant Reports

In this project, we studied how to enhance image quality by denoising and deblurring a given image mathematically. We compared some existing state-of-the-art methods for image denoising and deblurring. We implemented the algorithms numerically using Matlab.

We studied the possibility of combining statistical analysis with the traditional image restoration methods including using wavelets and framelets and we derived some encouraging preliminary results.

My research student Alleta Maier gave a sequence of talks on the project including the Pacific Northwest Mathematical Association of America conference at Oregon State University in April, 2016; Linfield College Taylor Series in March, 2016, and Linfield …

Sexual Dimorphism In Digit Ratios Derived From Dorsal Digit Length Among Adults And Children, Sanjay Kumar, Martin Voracek, Maharaj Singh

Mathematics, Statistics and Computer Science Faculty Research and Publications

Sexual dimorphism in ventrally measured digit ratios (2D:4D and other) has been related to prenatal sex-hormone levels. In the present series of three studies, we measured all digit lengths (excluding the thumb) on the dorsal, rather than the ventral, side of left and right hands and investigated the sexual dimorphism in digit ratios in three independent samples, two of them comprising adults (Study I, N = 104; Study II, N = 154), and one further, comprising kindergarten children (Study III, N = 64). Results show that men have lower digit-ratio values compared to women in digit ratios that include digit …

An Online Educational Program Improves Pediatric Oncology Nurses’ Knowledge, Attitudes, And Spiritual Care Competence, Cheryl L. Petersen, Margaret Callahan, Donna O. Mccarthy, Ronda G. Hughes, Rosemary White-Traut, Naveen K. Bansal

Mathematics, Statistics and Computer Science Faculty Research and Publications

This study evaluated the potential impact of an online spiritual care educational program on pediatric nurses’ attitudes toward and knowledge of spiritual care and their competence to provide spiritual care to children with cancer at the end of life. It was hypothesized that the intervention would increase nurses’ positive attitudes toward and knowledge of spiritual care and increase nurses’ level of perceived spiritual care competence. A positive correlation was expected between change in nurses’ perceived attitudes toward and knowledge of spiritual care and change in nurses’ perceived spiritual care competence. A prospective, longitudinal design was employed, and analyses included one-way …

Genome Resources For Climate‐Resilient Cowpea, An Essential Crop For Food Security, Maria Munoz-Amatriain, Hamid Mirebrahim, Pei Xu, Steve Wanamaker, Ming-Cheng Luo, Hind Alhakami, Matthew Alpert, Ibrahim Atokple, Benoit J. Batieno, Ousmane Boukar, Serdar Bozdag, Ndiaga Cisse, Issa Drabo, Jeffrey D. Ehlers, Andrew Farmer, Christian Fatokun, Yong Q. Gu, Yi-Ning Guo, Bao-Lam Huynh, Scott A. Jackson, Francis Kusi, Cynthia T. Lawley, Mitchell R. Lucas, Yaqin Ma, Michael P. Timko, Jiajie Wu, Frank You, Noelle A. Barkley, Philip A. Roberts, Stefano Lonardi, Timothy J. Close

Mathematics, Statistics and Computer Science Faculty Research and Publications

Cowpea (Vigna unguiculata L. Walp.) is a legume crop that is resilient to hot and drought‐prone climates, and a primary source of protein in sub‐Saharan Africa and other parts of the developing world. However, genome resources for cowpea have lagged behind most other major crops. Here we describe foundational genome resources and their application to the analysis of germplasm currently in use in West African breeding programs. Resources developed from the African cultivar IT97K‐499‐35 include a whole‐genome shotgun (WGS) assembly, a bacterial artificial chromosome (BAC) physical map, and assembled sequences from 4355 BACs. These resources and WGS sequences of …