Physical Sciences and Mathematics Commons^™

Post-Quantum Hermite-Jensen-Mercer Inequalities, Martin Bohner, Hüseyin Budak, Hasan Kara

Mathematics and Statistics Faculty Research & Creative Works

The Jensen-Mercer inequality, which is well known in the literature, has an important place in mathematics and related disciplines. In this work, we obtain the Hermite-Jensen-Mercer inequality for post-quantum integrals by utilizing Jensen-Mercer inequalities. Then we investigate the connections between our results and those in earlier works. Moreover, we give some examples to illustrate our main results. This is the first paper about Hermite-Jensen-Mercer inequalities for post-quantum integrals.

Forecasting Remission Time Of A Treatment Method For Leukemia As An Application To Statistical Inference Approach, Mahmoud Mansour, Rashad El-Sagheer, Ahmed Galal Attia, Beha S. El-Desouky Prof.

Basic Science Engineering

In this paper, Weibull-Linear Exponential distribution (WLED) has been investigated whether being it is a well-fit distribution to a clinical real data. These data represent the duration of remission achieved by a certain drug used in the treatment of leukemia for a group of patients. The statistical inference approach is used to estimate the parameters of the WLED through the set of the fitted data. The estimated parameters are utilized to evaluate the survival and hazard functions and hence assessing the treatment method through forecasting the duration of remission times of patients. A two-sample prediction approach has been applied to …

Modeling And Fitting Two-Way Tables Containing Outliers, David L. Farnsworth

Articles

A model is proposed for two-way tables of measurement data containing outliers. The two independent variables are categorical and error free. Neither missing values nor replication are present. The model consists of the sum of a customary additive part that can be fit using least squares and a part that is composed of outliers. Recommendations are made for methods for identifying cells containing outliers and for fitting the model. A graph of the observations is used to determine the outliers’ locations. For all cells containing an outlier, replacement values are determined simultaneously using a classical missing-data tool. The result is …

Psychometric Properties Of A Combined Go/No-Go And Continuous Performance Task Across Childhood, Caron A.C. Clark, Kaitlyn Cook, Rui Wang, Michael Rueschman, Jerilynn Radcliffe, Susan Redline, H. Gerry Taylor

Statistical and Data Sciences: Faculty Publications

Despite the critical importance of attention for children’s self-regulation and mental health, there are few task-based measures of this construct appropriate for use across a wide childhood age range including very young children. Three versions of a combined go/no-go and continuous performance task (GNG/CPT) were created with varying length and timing parameters to maximize their appropriateness for age groups spanning early to middle childhood. As part of the baseline assessment of a clinical trial, 452 children aged 3–12 years (50% male, 50% female; 52% White, non-Hispanic, 27% Black, 16% Hispanic/Latinx; 6% other ethnicity/race) completed the task. Confirmatory factor analysis indicated …

Supplementary Files For "Adaptive Mapping Of Design Ground Snow Loads In The Conterminous United States", Jadon Wagstaff, Jesse Wheeler, Brennan Bean, Marc Maguire, Yan Sun

Browse all Datasets

Recent amendments to design ground snow load requirements in ASCE 7-22 have reduced the size of case study regions by 91% from what they were in ASCE 7-16, primarily in western states. This reduction is made possible through the development of highly accurate regional generalized additive regression models (RGAMs), stitched together with a novel smoothing scheme implemented in the R software package remap, to produce the continental- scale maps of reliability-targeted design ground snow loads available in ASCE 7-22. This approach allows for better characterizations of the changing relationship between temperature, elevation, and ground snow loads across the Conterminous United …

Three Solutions For Discrete Anisotropic Kirchhoff-Type Problems, Martin Bohner, Giuseppe Caristi, Ahmad Ghobadi, Shapour Heidarkhani

Mathematics and Statistics Faculty Research & Creative Works

In this article, using critical point theory and variational methods, we investigate the existence of at least three solutions for a class of double eigenvalue discrete anisotropic Kirchhoff-type problems. An example is presented to demonstrate the applicability of our main theoretical findings.

Inequalities For Interval-Valued Riemann Diamond-Alpha Integrals, Martin Bohner, Linh Nguyen, Baruch Schneider, Tri Truong

Mathematics and Statistics Faculty Research & Creative Works

We propose the concept of Riemann diamond-alpha integrals for time scales interval-valued functions. We first give the definition and some properties of the interval Riemann diamond-alpha integral that are naturally investigated as an extension of interval Riemann nabla and delta integrals. With the help of the interval Riemann diamond-alpha integral, we present interval variants of Jensen inequalities for convex and concave interval-valued functions on an arbitrary time scale. Moreover, diamond alpha Hölder's and Minkowski's interval inequalities are proved. Also, several numerical examples are provided in order to illustrate our main results.

Oscillation Of Second-Order Half-Linear Neutral Noncanonical Dynamic Equations, Martin Bohner, Hassan El-Morshedy, Said Grace, Irena Jadlovská

Mathematics and Statistics Faculty Research & Creative Works

In This Paper, We Shall Establish Some New Criteria for the Oscillation of Certain Second-Order Noncanonical Dynamic Equations with a Sublinear Neutral Term. This Task is Accomplished by Reducing the Involved Nonlinear Dynamic Equation to a Second-Order Linear Dynamic Inequality. We Also Establish Some New Oscillation Theorems Involving Certain Integral Conditions. Three Examples, Illustrating Our Results, Are Presented. Our Results Generalize Results for Corresponding Differential and Difference Equations.

Tennessee Brewconomy: Navigating The Wholesale Beer Tax Landscape, Lauren E. Dansbury

Science University Research Symposium (SURS)

In 2013, Tennessee transitioned from a price-based wholesale tax model to a per barrelage assessment. This research delves into the repercussions of this tax reform, assessing its impact on the brewing and wholesale distribution sectors. Despite the shift, Tennessee maintains the nation's highest wholesale beer tax for 16 consecutive years. The study examines the opportunity costs associated with this elevated tax, exploring alternative uses for the funds. Utilizing data on annual revenue collected by wholesalers from 2019 to 2022, segmented by city and county, the research provides actionable insights advocating for a reduction in the wholesale tax. The argument posits …

Trilinear Immersed-Finite-Element Method For Three-Dimensional Anisotropic Interface Problems In Plasma Thrusters, Yajie Han, Guangqing Xia, Chang Lu, Xiaoming He

Mathematics and Statistics Faculty Research & Creative Works

Accurately solving the anisotropic interface problem is one of the difficulties in aerospace plasma applications. Based on cubic Cartesian meshes, this paper develops a trilinear nonhomogeneous immersed finite element (IFE) method for solving the complex anisotropic 3D elliptic interface model with nonhomogeneous flux jump. Compared with the existing 3D linear IFE spaces based on tetrahedron meshes, the newly designed trilinear IFE space for the target model simplifies the mesh generation, significantly reduces the number of mesh elements and interface elements, provides much more convenient and efficient ways for finding the intersections between interfaces and mesh edges, and decreases the errors. …

Statistical Modeling: Regression, Survival Analysis, And Time Series Analysis, Lawrence Leemis

Open Education Resources (OER)

Statistical Modeling provides an introduction to regression, survival analysis, and time series analysis for students who have completed calculus-based courses in probability and mathematical statistics. The book uses the R language to fit statistical models, conduct Monte Carlo simulation experiments and generate graphics. Over 300 exercises at the end of the chapters makes this an appropriate text for a class in statistical modeling.

Part 1: Regression
Chapter 1: Simple Linear Regression
Chapter 2: Inference in Simple Linear Regression
Chapter 3: Topics in Regression

Part II: Survival Analysis
Chapter 4: Probability Models in Survival Analysis
Chapter 5: Statistical Methods in Survival …

Vibrio Cholerae In Rural And Urban Bangladesh, Findings From Hospital-Based Surveillance, 2000–2021, Rina Das, Sabiha Nasrin, Parag Palit, Rukaeya Amin Sobi, Al-Afroza Sultana, Soroar Hossain Khan, Md. Ahshanul Haque, Sharika Nuzhat, Tahmeed Ahmed, A. S. G. Faruque, Mohammod Jobayer Chisti

Biostatistics and Epidemiology Faculty Publications Series

With more than 100,000 cases estimated each year, Bangladesh is one of the countries with the highest number of people at risk for cholera. Moreover, Bangladesh is formulating a countrywide cholera-control plan to satisfy the GTFCC (The Global Task Force on Cholera Control) Roadmap's goals. With a particular focus on cholera trends, variance in baseline and clinical characteristics of cholera cases, and trends in antibiotic susceptibility among clinical isolates of Vibrio cholerae, we used data from facility-based surveillance systems from icddr,b’s Dhaka, and Matlab Hospitals from years 2000 to 2021. Female patients comprised 3,553 (43%) in urban and 1,099 (51.6%) …

Wright State University Fact Sheet, 2022-2023, Office Of Institutional Research & Effectiveness, Wright State University

Wright State University Fact Sheets

The Wright State University Fact Sheet showcasing numbers and statistics for Wright State University including demographics, funding, programs, and employment for the 2022-2023 academic year.

Variable-Dependent Partial Dimension Reduction, Lu Li, Kai Tan, Xuerong Meggie Wen, Zhou Yu

Mathematics and Statistics Faculty Research & Creative Works

Sufficient dimension reduction reduces the dimension of a regression model without loss of information by replacing the original predictor with its lower-dimensional linear combinations. Partial (sufficient) dimension reduction arises when the predictors naturally fall into two sets X and W, and pursues a partial dimension reduction of X. Though partial dimension reduction is a very general problem, only very few research results are available when W is continuous. To the best of our knowledge, none can deal with the situation where the reduced lower-dimensional subspace of X varies with W. To address such issue, we in this paper propose a …

Variable-Dependent Partial Dimension Reduction, Lu Li, Kai Tan, Xuerong Meggie Wen, Zhou Yu

Mathematics and Statistics Faculty Research & Creative Works

Sufficient dimension reduction reduces the dimension of a regression model without loss of information by replacing the original predictor with its lower-dimensional linear combinations. Partial (sufficient) dimension reduction arises when the predictors naturally fall into two sets X and W, and pursues a partial dimension reduction of X. Though partial dimension reduction is a very general problem, only very few research results are available when W is continuous. To the best of our knowledge, none can deal with the situation where the reduced lower-dimensional subspace of X varies with W. To address such issue, we in this paper propose a …

The Generalized Lyapunov Function As Ao’S Potential Function: Existence In Dimensions 1 And 2, Haoyu Wang, Wenqing Hu, Xiaoliang Gan, Ping Ao

Mathematics and Statistics Faculty Research & Creative Works

By using Ao's decomposition for stochastic dynamical systems, a new notion of potential function has been introduced by Ao and his collabora-tors recently. We show that this potential function agrees with the generalized Lyapunov function of the deterministic part of the stochastic dynamical sys-tem. We further prove the existence of Ao's potential function in dimensions 1 and 2 via the solution theory of first-order partial differential equations. Our framework reveals the equivalence between Ao's potential function and Lyapunov function, the latter being one of the most significant central notions in dynamical systems. Using this equivalence, our existence proof can also …

Second Order, Unconditionally Stable, Linear Ensemble Algorithms For The Magnetohydrodynamics Equations, John Carter, Daozhi Han, Nan Jiang

Mathematics and Statistics Faculty Research & Creative Works

We Propose Two Unconditionally Stable, Linear Ensemble Algorithms with Pre-Computable Shared Coefficient Matrices Across Different Realizations for the Magnetohydrodynamics Equations. the Viscous Terms Are Treated by a Standard Perturbative Discretization. the Nonlinear Terms Are Discretized Fully Explicitly within the Framework of the Generalized Positive Auxiliary Variable Approach (GPAV). Artificial Viscosity Stabilization that Modifies the Kinetic Energy is Introduced to Improve Accuracy of the GPAV Ensemble Methods. Numerical Results Are Presented to Demonstrate the Accuracy and Robustness of the Ensemble Algorithms.

Graphs Without A 2c3-Minor And Bicircular Matroids Without A U3,6-Minor, Daniel Slilaty

Mathematics and Statistics Faculty Publications

In this note we characterize all graphs without a 2C3-minor. A consequence of this result is a characterization of the bicircular matroids with no U3,6-minor.

Odd Solutions To Systems Of Inequalities Coming From Regular Chain Groups, Daniel Slilaty

Mathematics and Statistics Faculty Publications

Hoffman’s theorem on feasible circulations and Ghouila-Houry’s theorem on feasible tensions are classical results of graph theory. Camion generalized these results to systems of inequalities over regular chain groups. An analogue of Camion’s result is proved in which solutions can be forced to be odd valued. The obtained result also generalizes the results of Pretzel and Youngs as well as Slilaty. It is also shown how Ghouila-Houry’s result can be used to give a new proof of the graph- coloring theorem of Minty and Vitaver.

Classification Of Adult Income Using Decision Tree, Roland Fiagbe

Data Science and Data Mining

Decision tree is a commonly used data mining methodology for performing classification tasks. It is a tree-based supervised machine learning algorithm that is used to classify or make predictions in a path of how previous questions are answered. Generally, the decision tree algorithm categorizes data into branch-like segments that develop into a tree that contains a root, nodes, and leaves. This project seeks to explore the decision tree methodology and apply it to the Adult Income dataset from the UCI Machine Learning Repository, to determine whether a person makes over 50K per year and determine the necessary factors that improve …

Probability Distribution Of Sars-Cov-2 (Covid) Infectivity Following Onset Of Symptoms: Analysis From First Principles, Mark P. Silverman

Faculty Scholarship

The phasing out of protective measures by governments and public health agencies, despite continued seriousness of the coronavirus pandemic, leaves individuals who are concerned for their health with two basic options over which they have control: 1) minimize risk of infection by being vaccinated and by wearing a face mask when appropriate, and 2) minimize risk of transmission upon infection by self-isolating. For the latter to be effective, it is essential to have an accurate sense of the probability of infectivity as a function of time following the onset of symptoms. Epidemiological considerations suggest that the period of infectivity follows …

Invasion Dynamics Of The European Collared-Dove In North America Are Explained By Combined Effects Of Habitat And Climate, Yiran Shao, Danielle Ethier, Simon Bonner

Statistical and Actuarial Sciences Publications

Global biodiversity is increasingly threatened by the spread of invasive species. Understanding the mechanisms influencing the initial colonization and persistence of invaders is therefore needed if conservation actions are to prevent new invasions or strive to slow their spread. The Eurasian Collared-Dove (Streptopelia decaocto, EUCO) is one of the most successful avian invasive species in North America; however, to our knowledge, no study has simultaneously examined the role that climate-matching, human activity, directional propagation, and local density have in this invasion process. Our research expands upon a cellular-automata-based hierarchical model developed to assess directional invasion dynamics to further quantify the …

A Method For Quantifying Individual Decision Thresholds Of Latent Print Examiners, Amanda Luby

Mathematics & Statistics Faculty Works

In recent years, ‘black box’ studies in forensic science have emerged as the preferred way to provide information about the overall validity of forensic disciplines in practice. These studies provide aggregated error rates over many examiners and comparisons, but errors are not equally likely on all comparisons. Furthermore, inconclusive responses are common and vary across examiners and comparisons, but do not fit neatly into the error rate framework. This work introduces Item Response Theory (IRT) and variants for the forensic setting to account for these two issues. In the IRT framework, participant proficiency and item difficulty are estimated directly from …

Early Detection Of Covid-19 In Female Athletes Using Wearable Technology, Liliana I. Rentería, Casey E. Greenwalt, Sarah Johnson, Shiloah Shiloah Kviatkovsky, Marine Dupuit, Elisa Angeles, Sachin Narayanan, Tucker Zeleny, Michael J. Ormsbee

Department of Statistics: Faculty Publications

Background: Heart rate variability (HRV), respiratory rate (RR), and resting heart rate (RHR) are common variables measured by wrist-worn activity trackers to monitor health, fitness, and recovery in athletes. Variations in RR are observed in lower-respiratory infections, and preliminary data suggest changes in HRV and RR are linked to early detection of COVID-19 infection in nonathletes.

Hypothesis: Wearable technology measuring HRV, RR, RHR, and recovery will be successful for early detection of COVID-19 in NCAA Division I female athletes.

Study Design: Cohort study.

Level of Evidence: Level 2.

Methods: Female athletes wore WHOOP, Inc. bands …

Forecasting Remission Time Of A Treatment Method For Leukemia As An Application To Statistical Inference Approach, Ahmed Galal Atia, Mahmoud Mansour, Rashad Mohamed El-Sagheer, B. S. El-Desouky

Basic Science Engineering

In this paper, Weibull-Linear Exponential distribution (WLED) has been investigated whether being it is a well-fit distribution to a clinical real data. These data represent the duration of remission achieved by a certain drug used in the treatment of leukemia for a group of patients. The statistical inference approach is used to estimate the parameters of the WLED through the set of the fitted data. The estimated parameters are utilized to evaluate the survival and hazard functions and hence assessing the treatment method through forecasting the duration of remission times of patients. A two-sample prediction approach has been applied to …

Utilizing Markov Chains To Estimate Allele Progression Through Generations, Ronit Gandhi

Honors Theses

All populations display patterns in allele frequencies over time. Some alleles cease to exist, while some grow to become the norm. These frequencies can shift or stay constant based on the conditions the population lives in. If in Hardy-Weinberg equilibrium, the allele frequencies stay constant. Most populations, however, have bias from environmental factors, sexual preferences, other organisms, etc. We propose a stochastic Markov chain model to study allele progression across generations. In such a model, the allele frequencies in the next generation depend only on the frequencies in the current one.

We use this model to track a recessive allele …

Assessing Spurious Correlations In Big Search Data, Jesse T. Richman, Ryan J. Roberts

Political Science & Geography Faculty Publications

Big search data offers the opportunity to identify new and potentially real-time measures and predictors of important political, geographic, social, cultural, economic, and epidemiological phenomena, measures that might serve an important role as leading indicators in forecasts and nowcasts. However, it also presents vast new risks that scientists or the public will identify meaningless and totally spurious ‘relationships’ between variables. This study is the first to quantify that risk in the context of search data. We find that spurious correlations arise at exceptionally high frequencies among probability distributions examined for random variables based upon gamma (1, 1) and Gaussian random …

An Exploration Of Parameter Duality In Statistical Inference, Suzanne Thornton, M. Xie

Mathematics & Statistics Faculty Works

Well-known debates among statistical inferential paradigms emerge from conflicting views on the notion of probability. One dominant view understands probability as a representation of sampling variability; another prominent view understands probability as a measure of belief. The former generally describes model parameters as fixed values, in contrast to the latter. We propose that there are actually two versions of a parameter within both paradigms: a fixed unknown value that generated the data and a random version to describe the uncertainty in estimating the unknown value. An inferential approach based on CDs deciphers seemingly conflicting perspectives on parameters and probabilities.

Fitting Time Series Models To Fisheries Data To Ascertain Age, Kathleen S. Kirch, Norou Diawara, Cynthia M. Jones

OES Faculty Publications

The ability of government agencies to assign accurate ages of fish is important to fisheries management. Accurate ageing allows for most reliable age-based models to be used to support sustainability and maximize economic benefit. Assigning age relies on validating putative annual marks by evaluating accretional material laid down in patterns in fish ear bones, typically by marginal increment analysis. These patterns often take the shape of a sawtooth wave with an abrupt drop in accretion yearly to form an annual band and are typically validated qualitatively. Researchers have shown key interest in modeling marginal increments to verify the marks do, …

Evaluation Of Edison's Data Science Competency Framework Through A Comparative Literature Analysis, Karl R. B. Schmitt, Linda Clark, Katherine M. Kinnaird, Ruth E. H. Wertz, Björn Sandstede

Statistical and Data Sciences: Faculty Publications

During the emergence of Data Science as a distinct discipline, discussions of what exactly constitutes Data Science have been a source of contention, with no clear resolution. These disagreements have been exacerbated by the lack of a clear single disciplinary 'parent.' Many early efforts at defining curricula and courses exist, with the EDISON Project's Data Science Framework (EDISON-DSF) from the European Union being the most complete. The EDISON-DSF includes both a Data Science Body of Knowledge (DS-BoK) and Competency Framework (CF-DS). This paper takes a critical look at how EDISON's CF-DS compares to recent work and other published curricular or …