Statistics and Probability Commons^™

Sex-Specific Differences In Lung Mitochondrial Function And Injury In Rats Exposed To Hyperoxia, Taheri Pardis, Abraham G. Taye, Devanshi D. Dave, Elizabeth R. Jacobs, Guru Prasad Sharma, Anne V. Clough, Ranjan K. Dash, Said H. Audi

Mathematical and Statistical Science Faculty Research and Publications

Hyperoxia is both an essential therapy and a contributor to lung injury in acute respiratory distress syndrome. We hypothesized that adult female rats are relatively protected from hyperoxia-induced acute lung injury (HALI) compared with males and that this protection is associated with sex-dependent differences in lung mitochondrial bioenergetics and H₂O₂ production. Adult rats were exposed to room air (normoxia) or hyperoxia (>95% O₂) for up to 60 h. Lung injury was assessed by pleural effusion, lung wet weight, pulmonary vascular filtration coefficient (K_f), histologic injury scores, and cleaved caspase-3 (CC3) staining. …

Molecular Lung Imaging Following Exposure To Radiation Predicts Long-Term Survival In Rats, Anne V. Clough, Kathrina Mpala, Taheri Pardis, Laura Norwood Toro, Andreas M. Beyer, Tracy Gasperetti, Ming Zhao, Sarah Kerns, Heather A. Himburg, Said H. Audi

Mathematical and Statistical Science Faculty Research and Publications

Delayed effects of acute radiation exposure (DEARE), including radiation pneumonitis (lung-DEARE), develop weeks to months after radiation exposure. Pathway-targeted biomarkers that capture early oxidative stress and cell death could improve risk stratification and provide objective measures of mitigator efficacy. The objective was to test whether molecular lung imaging predicts long-term survival and mitigator response after irradiation. Rats received 13.5 Gy leg-out partial-body irradiation with a subset treated with the radiation-injury mitigator lisinopril. Rats underwent lung imaging at weeks 2 and 4 post-irradiation with ^99mTc-duramycin (cell death) and ^99mTc-HMPAO (oxidative stress). Plasma mitochondrial damage-associated molecular patterns (mtDAMPs) were also …

Likelihood-Based Inference For Random Networks With Changepoints, Daniel Cirkovic, Tiandong Wang, Xianyang Zhang

Mathematical and Statistical Science Faculty Research and Publications

Generative, temporal network models play an important role in analyzing the dependence structure and evolution patterns of complex networks. Due to the complicated nature of real network data, it is often naive to assume that the underlying data-generative mechanism itself is invariant with time. Such observation leads to the study of changepoints or sudden shifts in the distributional structure of the evolving network. In this paper, we propose a likelihood-based methodology to detect changepoints in undirected, affine preferential attachment networks where, upon introduction, a new node selects one old to attach to with probability proportional to its degree. In particular, …

Graph Convolutional Networks Enable Fast Hemorrhagic Stroke Monitoring With Electrical Impedance Tomography, J. Toivanen, V. Kolehmainen, A. Paldanius, A. Hänninen, A. Hauptmann, Sarah J. Hamilton

Mathematical and Statistical Science Faculty Research and Publications

Objective: To develop a fast image reconstruction method for stroke monitoring with electrical impedance tomography with image quality comparable to computationally expensive nonlinear model-based methods. Methods: A post-processing approach with graph convolutional networks is employed. Utilizing the flexibility of the graph setting, a graph U-net is trained on linear difference reconstructions from 2D simulated stroke data and applied to fully 3D images from realistic simulated and experimental data. An additional network, trained on 3D vs. 2D images, is also considered for comparison. Results: Post-processing the linear difference reconstructions through the graph U-net significantly improved the image quality, resulting in images …

Radiation-Induced Cardiotoxicity In Hypertensive Salt-Sensitive Rats: A Feasibility Study, Dayeong An, Alison Kriegel, Suresh N. Kumar, Heather A. Himburg, Brian Fish, S. Klawikowski, Daniel B. Rowe, Marek Lenarczyk, John Baker, El Sayed H. Ibrahim

Mathematical and Statistical Science Faculty Research and Publications

Radiation therapy (RT) plays a vital role in managing thoracic cancers, though it can lead to adverse effects, including significant cardiotoxicity. Understanding the risk factors like hypertension in RT is important for patient prognosis and management. A Dahl salt-sensitive (SS) female rat model was used to study hypertension effect on RT-induced cardiotoxicity. Rats were fed a high-salt diet to induce hypertension and then divided into RT and sham groups. The RT group received 24 Gy of whole-heart irradiation. Cardiac function was evaluated using MRI and blood pressure measurements at baseline, 8 weeks and 12 weeks post-RT. Histological examination was performed …

A Bayesian Approach To Grappa Parallel Fmri Image Reconstruction Increases Snr And Power Of Task Detection, Chase J. Sakitis, Daniel B. Rowe

Mathematical and Statistical Science Faculty Research and Publications

In fMRI, capturing brain activation during a task is dependent on how quickly k-space arrays are obtained. Acquiring full k-space arrays, which are reconstructed into images using the inverse Fourier transform (IFT), that make up volume images can take a considerable amount of scan time. Undersampling k-space reduces the acquisition time but results in aliased, or “folded,” images. GeneRalized Autocalibrating Partial Parallel Acquisition (GRAPPA) is a parallel imaging technique that yields full images from subsampled arrays of k-space. GRAPPA uses localized interpolation weights, which are estimated prescan and fixed over time, to fill in the missing …

Efficient Fully Bayesian Approach To Brain Activity Mapping With Complex-Valued Fmri Data, Zhengxin Wang, Daniel B. Rowe, Xinyi Li, D. Andrew Brown

Mathematical and Statistical Science Faculty Research and Publications

Functional magnetic resonance imaging (fMRI) enables indirect detection of brain activity changes via the blood-oxygen-level-dependent (BOLD) signal. Conventional analysis methods mainly rely on the real-valued magnitude of these signals. In contrast, research suggests that analyzing both real and imaginary components of the complex-valued fMRI (cv-fMRI) signal provides a more holistic approach that can increase power to detect neuronal activation. We propose a fully Bayesian model for brain activity mapping with cv-fMRI data. Our model accommodates temporal and spatial dynamics. Additionally, we propose a computationally efficient sampling algorithm, which enhances processing speed through image partitioning. Our approach is shown to be …

Exploring The Potential Of Strongly Coupled Lagrangian Data Assimilation In An Ocean–Atmosphere System, Luyu Sun, Amit Apte, Laura Slivinski, Elaine T. Spiller

Mathematical and Statistical Science Faculty Research and Publications

Precise measurements of ocean surface flow velocities are essential for refining forecasts in a coupled ocean–atmosphere system. While oceanic data are generally sparse, surface drifters present an opportunity by providing detailed and frequently observed sea surface currents, which are a critical component in the dynamics at air–sea interface. Such observations could potentially address the usual data gaps in a coupled ocean–atmosphere assimilation system. In this study, we investigate the implications of assimilating drifter data within a coupled system with intermediate complexity based on a quasigeostrophic model—Modular Arbitrary-Order Ocean–Atmosphere Model (MAOOAM)—using observing system simulation experiments (OSSEs). Two main strategies for assimilating …

Generation Of Patient Specific Cardiac Chamber Models Using Generative Neural Networks Under A Bayesian Framework For Electroanatomical Mapping, Sunil Mathew, Jasbir Sra, Daniel B. Rowe

Mathematical and Statistical Science Faculty Research and Publications

Electroanatomical mapping is a technique used in cardiology to create a detailed 3D map of the electrical activity in the heart. It is useful for diagnosis, treatment planning and real time guidance in cardiac ablation procedures to treat arrhythmias like atrial fibrillation. A probabilistic machine learning model trained on a library of CT/MRI scans of the heart can be used during electroanatomical mapping to generate a patient-specific 3D model of the chamber being mapped. The use of probabilistic machine learning models under a Bayesian framework provides a way to quantify uncertainty in results and provide a natural framework of interpretability …

Bayesian Merged Utilization Of Grappa And Sense (Bmugs) For In-Plane Accelerated Reconstruction Increases Fmri Detection Power, Chase J. Sakitis, Daniel B. Rowe

Mathematical and Statistical Science Faculty Research and Publications

In fMRI, capturing brain activity during a task is dependent on how quickly the k-space arrays for each volume image are obtained. Acquiring the full k-space arrays can take a considerable amount of time. Under-sampling k-space reduces the acquisition time, but results in aliased, or “folded,” images after applying the inverse Fourier transform (IFT). GeneRalized Autocalibrating Partial Parallel Acquisition (GRAPPA) and SENSitivity Encoding (SENSE) are parallel imaging techniques that yield reconstructed images from subsampled arrays of k-space. With GRAPPA operating in the spatial frequency domain and SENSE in image space, these techniques have been separate but can …

A Bayesian Complex-Valued Latent Variable Model Applied To Functional Magnetic Resonance Imaging, Chase J. Sakitis, D. Andrew Brown, Daniel B. Rowe

Mathematical and Statistical Science Faculty Research and Publications

In linear regression, the coefficients are simple to estimate using the least squares method with a known design matrix for the observed measurements. However, real-world applications may encounter complications such as an unknown design matrix and complex-valued parameters. The design matrix can be estimated from prior information but can potentially cause an inverse problem when multiplying by the transpose as it is generally ill-conditioned. This can be combat by adding regularizers to the model but does not always mitigate the issues. Here, we propose our Bayesian approach to a complex-valued latent variable linear model with an application to functional magnetic …

A New G Family: Properties, Characterizations, Different Estimation Methods And Port-Var Analysis For U.K. Insurance Claims And U.S. House Prices Data Sets, Ahmad M. Aboalkhair, Gholamhossein Hamedani, Nazar Ali Ahmed, Mohamed Ibrahim, Mohammad A. Zayed, Haitham M. Yousof

Mathematical and Statistical Science Faculty Research and Publications

This paper introduces a new class of probability distributions, termed the generated log exponentiated polynomial (GLEP) family, designed to enhance flexibility in modeling complex real financial data. The proposed family is constructed through a novel cumulative distribution function that combines logarithmic and exponentiated polynomial structures, allowing for rich distributional shapes and tail behaviors. We present comprehensive mathematical properties, including useful series expansions for the density, cumulative, and quantile functions, which facilitate the derivation of moments, generating functions, and order statistics. Characterization results based on the reverse hazard function and conditional expectations are established. The model parameters are estimated using various …

Coarctation Duration And Severity Predict Risk Of Hypertension Precursors In A Preclinical Model And Hypertensive Status Among Patients, Arash Ghorbannia, Hilda Jurkiewicz, Lith Nasif, Abdillahi Ahmed, Jennifer Co-Vu, Mehdi Maadooliat, Ronald K. Woods, John F. Ladisa Jr.

Mathematical and Statistical Science Faculty Research and Publications

BACKGROUND:

Coarctation of the aorta (CoA) often leads to hypertension posttreatment. Evidence is lacking for the current >20 mm Hg peak-to-peak blood pressure (BP) gradient (BPGpp) guideline, which can cause aortic thickening, stiffening, and dysfunction. This study sought to find the BPGpp severity and duration that avoid persistent dysfunction in a preclinical model and test if predictors translate to hypertension status in patients with CoA.

METHODS:

Rabbits (n=75; 5–12/group) were exposed to mild, intermediate, or severe CoA (≤12, 13–19, ≥20 mm Hg BPGpp) for ≈1, 3, or 22 weeks using dissolvable and permanent sutures with thickening, stiffening, contraction, and endothelial …

Extremal Graphs For Widom–Rowlinson Colorings In K-Chromatic Graphs, John Engbers, Aysel Erey

Mathematical and Statistical Science Faculty Research and Publications

The Widom–Rowlinson graph, H_WR , is the fully looped path on three vertices. Let hom(G,H_WR) be the number of graph homomorphisms from G to H_WR or, equivalently, the number of H_WR-colorings of G. We investigate extremal graphs for hom(G,H_WR) for G in the family of k-chromatic graphs subject to various connectivity requirements. In particular, we determine the graphs G maximizing hom(G,H_WR) in the families of n-vertex k-chromatic graphs, n-vertex connected k-chromatic graphs, n-vertex k-chromatic graphs with c components, n …

Gwid: An R Package And Shiny Application For Genome-Wide Analysis Of Ibd Data, Soroush Mahmoudiandehkordi, Mehdi Maadooliat, Steven J. Schrodi

Mathematical and Statistical Science Faculty Research and Publications

Summary

Genome-wide identity by descent (gwid) is an R package developed for the analysis of identity-by-descent (IBD) data pertaining to dichotomous traits. This package offers a set of tools to assess differential IBD levels for the two states of a binary trait, yielding informative and meaningful results. Furthermore, it provides convenient functions to visualize the outcomes of these analyses, enhancing the interpretability and accessibility of the results. To assess the performance of the package, we conducted an evaluation using real genotype data derived from the SNPs to investigate rheumatoid arthritis susceptibility from the Marshfield Clinic Personalized Medicine Research Project.

Availability …

A Journey From Univariate To Multivariate Functional Time Series: A Comprehensive Review, Hossein Haghbin, Mehdi Maadooliat

Mathematical and Statistical Science Faculty Research and Publications

Functional time series (FTS) analysis has emerged as a potent framework for modeling and forecasting time-dependent data with functional attributes. In this comprehensive review, we navigate through the intricate landscape of FTS methodologies, meticulously surveying the core principles of univariate FTS and delving into the nuances of multivariate FTS. The journey commences with an exploration of the foundational aspects of univariate FTS analysis. We delve into representation, estimation, and modeling, spotlighting the effectiveness of various parametric and nonparametric models at our disposal. The stage then transitions to multivariate FTS analysis, where we confront the intricacies posed by high-dimensional data. We …

Maximizing The Number Of H-Colorings Of Graphs With A Fixed Minimum Degree, John Engbers

Mathematical and Statistical Science Faculty Research and Publications

For graphs G and H, an H-coloring of G is an adjacency-preserving map from the vertex set of G to the vertex set of H.

Optimizing Model Observer Performance In Learning-Based Ct Reconstruction, Gregory Ongie, Emil Y. Sidky, Ingrid S. Reiser, Xiaochuan Pan

Mathematical and Statistical Science Faculty Research and Publications

Deep neural networks used for reconstructing sparse-view CT data are typically trained by minimizing a pixel- wise mean-squared error or similar loss function over a set of training images. However, networks trained with such losses are prone to wipe out small, low-contrast features that are critical for screening and diagnosis. To remedy this issue, we introduce a novel training loss inspired by the model observer framework to enhance the detectability of weak signals in the reconstructions. We evaluate our approach on the reconstruction of synthetic sparse-view breast CT data, and demonstrate an improvement in signal detectability with the proposed loss.

The Unit Generalized Log Burr Xii Distribution: Properties And Application, Fiaz Ahmad Bhatti, Azeem Ali, Gholamhossein Hamedani, Mustafa Ç. Korkmaz, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a three-parameter bounded unit distribution with a flexible hazard rate called the unit generalized log Burr XII (UGLBXII) distribution is derived. To show the importance of the proposed distribution, we establish some of its mathematical properties such as random number generator, ordinary moments, generalized TL moments, conditional moments, reliability and uncertainty measures. We characterize the UGLBXII distribution via innovative techniques. We also present the bivariate‐ and multivariate‐type distributions via Morgenstern (Mor) family and via Clayton family. Six estimation methods such as the maximum likelihood, maximum product spacings, least squares, weighted least squares, Cramer-von Mises and Anderson-Darling methods …

Predicting Daily Confirmed Cases In Midwestern Central States In U.S. By Using Aima And Lstm, Yi Zheng

Master's Theses (2009 -)

Covid-19 is an epidemic disease caused by SARS-Cov-2 virus, which is a type of coronavirus. This virus is highly contiguous, and the confirmed cases of this disease have increased rapidly in a short period. After one month of the first reported case, the World Health Organization (WHO) claims that the Covid-19 will become an international public health emergency. The main purpose of this thesis is to predict the daily confirmed cases of Covid-19 in the midwestern central states in the U.S, by using Autoregression Integrated Moving Average (ARIMA) model and Long Short-Term Memory network (LSTM), which is a type of …

Statistical Modeling Of Daily Confirmed Covid-19 Cases And Deaths In Europe And United States, Zerui Zhang

Master's Theses (2009 -)

A novel coronavirus disease was first discovered in Wuhan, China, in December 2019. This new coronavirus named COVID-19 has rapidly spread and become a global threat affecting almost all the countries in the world. Therefore, it is important to know the trend of coronavirus disease to mitigate its effects. A good prediction model is crucial for the health care system to understand the trend of the COVID-19. This study aims to construct a good prediction model. Firstly, we detect change points of the time series data of daily confirmed cases and deaths of COVID-19 in the United States and Europe, …

On Burr Iii-Inverse Weibull Distribution With Covid-19 Applications, Fiaz Ahmad Bhatti, Sedigheh Mirzaei Salehabadi, Gholamhossein G. Hamedani

Mathematical and Statistical Science Faculty Research and Publications

We introduce a flexible lifetime distribution called Burr III-Inverse Weibull (BIII-IW). The new proposed distribution has well-known sub-models. The BIII-IW density function includes exponential, left-skewed, right-skewed and symmetrical shapes. The BIII-IW model’s failure rate can be monotone and non-monotone depending on the parameter values. To show the importance of the BIII-IW distribution, we establish various mathematical properties such as random number generator, ordinary moments, conditional moments, residual life functions, reliability measures and characterizations. We address the maximum likelihood estimates (MLE) for the BIII-IW parameters and estimate the precision of the maximum likelihood estimators via a simulation study. We consider applications …

On The Burr Xii-Power Cauchy Distribution: Properties And Applications, Fiaz Ahmad Bhatti, Gholamhossein Hamedani, Mashail M. Al Sobhi, Mustafa Ç. Korkmaz

Mathematical and Statistical Science Faculty Research and Publications

We propose a new four-parameter lifetime model with flexible hazard rate called the Burr XII Power Cauchy (BXII-PC) distribution. We derive the BXII-PC distribution via (i) the T-X family technique and (ii) nexus between the exponential and gamma variables. The new proposed distribution is flexible as it has famous sub-models such as Burr XII-half Cauchy, Lomax-power Cauchy, Lomax-half Cauchy, Log-logistic-power Cauchy, log-logistic-half Cauchy. The failure rate function for the BXII-PC distribution is flexible as it can accommodate various shapes such as the modified bathtub, inverted bathtub, increasing, decreasing; increasing-decreasing and decreasing-increasing-decreasing. Its density function can take shapes such as exponential, …

On The Burr Xii-Moment Exponential Distribution, Fiaz Ahmad Bhatti, Gholamhossein Hamedani, Mustafa Ç. Korkmaz, Menhui Sheng, Azeem Ali

Mathematical and Statistical Science Faculty Research and Publications

In this study, a new flexible lifetime model called Burr XII moment exponential (BXII-ME) distribution is introduced. We derive some of its mathematical properties including the ordinary moments, conditional moments, reliability measures and characterizations. We employ different estimation methods such as the maximum likelihood, maximum product spacings, least squares, weighted least squares, Cramer-von Mises and Anderson-Darling methods for estimating the model parameters. We perform simulation studies on the basis of the graphical results to see the performance of the above estimators of the BXII-ME distribution. We verify the potentiality of the BXII-ME model via monthly actual taxes revenue and fatigue …

A New Generalized Modified Weibull Distribution, Morad Alizadeh, Muhammad Nauman Khan, Mahdi Rasekhi, Gholamhossein Hamedani

Mathematical and Statistical Science Faculty Research and Publications

We introduce a new distribution, so called A new generalized modified Weibull (NGMW) distribution. Various structural properties of the distribution are obtained in terms of Meijer’s G–function, such as moments, moment generating function, conditional moments, mean deviations, order statistics and maximum likelihood estimators. The distribution exhibits a wide range of shapes with varying skewness and assumes all possible forms of hazard rate function. The NGMW distribution along with other distributions are fitted to two sets of data, arising in hydrology and in reliability. It is shown that the proposed distribution has a superior performance among the compared distributions as …

Maintaining Rich Dialogic Interactions In The Transition To Synchronous Online Learning, Hyunyi Jung, Corey Brady

Mathematical and Statistical Science Faculty Research and Publications

A central premise across a variety of educational research and policy documents is that students learn with greater understanding in classrooms where they engage in exploring, reasoning, and communicating about their thinking (Hiebert and Wearne, 1993; National Council of Teachers of English, 2016; National Council of Teachers of Mathematics, 2000). With the recent emergency transition to remote online instruction in higher education, opportunities for rich synchronous learning have been diminished in many courses. Most instructors have had to adapt rapidly from in-person classroom settings to online environments without sufficient time and training. Accordingly, college students have shared concerns about the …

The Weighted Exponentiated Family Of Distributions: Properties, Applications And Characterizations, Zubair Ahmad, Gholamhossein G. Hamedani, Mohammed Elgarhy

Mathematical and Statistical Science Faculty Research and Publications

In this paper a new method of introducing an additional parameter to a continuous distribution is proposed, which leads to a new class of distributions, called the weighted exponentiated family. A special sub-model is discussed. General expressions for some of the mathematical properties of this class such as the moments, quantile function, generating function and order statistics are derived; and certain characterizations are also discussed. To estimate the model parameters, the method of maximum likelihood is applied. A simulation study is carried out to assess the finite sample behavior of the maximum likelihood estimators. Finally, the usefulness of the proposed …

The Weibull Topp-Leone Generated Family Of Distributions: Statistical Properties And Applications, Hamid Karamikabir, Mahmoud Afshari, Haitham M. Yousof, Morad Alizadeh, Gholamhossein G. Hamedani

Mathematical and Statistical Science Faculty Research and Publications

Statistical distributions are very useful in describing and predicting real world phenomena. Consequently, the choice of the most suitable statistical distribution for modeling given data is very important. In this paper, we propose a new class of lifetime distributions called the Weibull Topp-Leone Generated (WTLG) family. The proposed family is constructed via compounding the Weibull and the Topp-Leone distributions. It can provide better fits and is very flexible in comparison with the various known lifetime distributions. Several general statistical properties of the WTLG family are studied in details including density and hazard shapes, limit behavior, mixture representation, skewness and kurtosis, …

Alarm Forecasting In Natural Gas Pipelines, Colin Quinn

Master's Theses (2009 -)

This thesis examines alarm forecasting methods for a natural gas production pipeline to assure the efficient transportation of high-quality natural gas. Natural gas production companies use pipelines to transport natural gas from the extraction well to a distribution point. Forecasting natural gas pipeline pressure alarms helps control room operators maintain a functioning pipeline and avoid costly down time. As gas enters the pipeline and travels to the distribution point, it is expected that the gas meets certain specifications set in place by either state law or the customer receiving the gas. If the gas meets these standards and is accepted …

Using Zero-Inflated Poisson Model And Zero-Inflated Negative Binomial Model On Dental Services Of Wisconsin, 2014 Data, Ke Xu

Master's Theses (2009 -)

Professional dental care to ensure optimum oral health of public plays an important role in the public health system. Facing the truth that there has been decline in dental care utilization for decade in 20th century, more and more attention has been paid to the oral health of children from this century. Children from age 0 to 21 years old experience rapid physical and oral development. Investigating the utilization of dental service for these children will provide useful information for the future study of the insurance system. In this thesis, two regression methods will be studied, the Zero-Inflated Poisson model …