Mathematics 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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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.

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 …

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 …

Generation Of Cardiac Chamber Models Using Interpretable Generative Neural Networks For Electrophysiology Studies, Sunil Mathew

Dissertations (1934 -)

An Electrophysiology study is conducted to diagnose and treat heart rhythm disorders, such as arrhythmias (abnormal heartbeat) like atrial fibrillation. A catheter is inserted into the chamber of interest to acquire 3D location and electrical information to create an electroanatomical map. This dissertation explores the design of a mapping system based on interpretable generative neural networks for generating patient specific cardiac models. Chapter 1 provides an introduction to electroanatomical mapping, the need for interpretability in neural networks and other relevant topics that are discussed in detail in the chapters that follow. Neural networks are often very large models with millions …

Enots Wolley Variations And Related Sequences, Nathan Myles Nichols

Master's Theses (2009 -)

The Enots Wolley sequence is a lexicographically earliest sequence (LES) that is closely related to the Yellowstone sequence. It is an open conjecture by N. J. Sloane that every number with at least two distinct prime factors appears as a term of the Enots Wolley sequence. In this thesis, this conjecture is proved for a variation of the Enots Wolley sequence that operates on the binary representation of a positive integer rather than the prime factorization. The methods used are then applied to prove some new properties of the prime factorization Enots Wolley sequence.

Graph Neural Networks For Inverse Problems With Flexible Meshes, William Herzberg

Dissertations (1934 -)

This thesis addresses the electrical impedance tomography (EIT) image reconstruction problem where samples may have irregular discretizations and presents two, new, learned reconstruction algorithms which leverage a graph framework. These new frameworks consider the irregular, non-uniform data as a graph thus allowing graph neural networks to be applied directly to the data defined over irregular meshes. Currently in imaging, convolutional neural networks are used most frequently in learned methods because they are spatially invariant and have the ability to leverage localized information. In addition, many images are represented by rows and columns of uniformly sized pixels which can easily be …

Transcriptional Profile Of Cohesin Complex Mutations In The Background Of Npm1 And Runx1-Runx1t1 Aml, Jacob Tiegs

Master's Theses (2009 -)

Acute Myeloid Leukemia is a cancer of the blood, characterized by a heterogenous mixture of disease causing mutations. Mutations of the cohesin complex is a group of such mutations and occur alongside several other driving mutations in the development of Acute Myeloid Leukemia. This thesis specifically focuses on cohesin complex mutations in the context of concurrence with NPM1 mutation and the Core Binding Factor (CBF) mutation RUNX1-RUNX1T1 in three distinct components. The first two components involved Differential Expression Analysis (DEA) to identify significantly differentiated genes in each model, followed by Gene Set Enrichment Analysis (GSEA) to identify Gene Ontology (GO) …

Disjoint And Simultaneously Hypercyclic Pseudo-Shifts, Nurhan Çolakoğlu, Özgür Martin, Rebecca Sanders

Mathematical and Statistical Science Faculty Research and Publications

We characterize disjoint and simultaneously hypercyclic tuples of unilateral pseudo-shift operators on ℓ^p(ℕ) . As a consequence, complementing the results of Bernal and Jung, we give a characterization for simultaneously hypercyclic tuples of unilateral weighted shifts. We also give characterizations for unilateral pseudo-shifts that satisfy the Disjoint and Simultaneous Hypercyclicity Criterions. Contrary to the disjoint hypercyclicity case, tuples of weighted shifts turn out to be simultaneously hypercyclic if and only if they satisfy the Simultaneous Hypercyclicity Criterion.

The Role Of Self-Tutorial In Introductory Physics Student Performance On Test Of Understanding Of Vectors, Katherine Finegan

Master's Theses (2009 -)

A single-interaction self-guided lesson was designed to teach basic vector concepts to introductory physics students. The self-guided lesson was tested for efficacy by comparing pre-test and post-test subscores on a Test of Understanding of Vectors (TUV) and comparing subscore differences to students in the same physics courses who had not taken the self-guided lesson. Analysis showed no significant differences in subscore differences between students taking the self-guided lesson and those in comparable control groups, indicating that more robust interventions are needed and/or further work must be done on the self-guided lesson to improve student vector understanding.

Temporal Sentiment Mapping System For Time-Synchronized Data, Jiachen Ma

Dissertations (1934 -)

Temporal sentiment labels are used in various multimedia studies. They are useful for numerous classification and detection tasks such as video tagging, segmentation, and labeling. However, generating a large-scale sentiment dataset through manual labeling is usually expensive and challenging. Some recent studies explored the possibility of using online Time-Sync Comments (TSCs) as the primary source of their sentiment maps. Although the approach has positive results, existing TSCs datasets are limited in scale and content categories. Guidelines for generating such data within a constrained budget are yet to be developed and discussed. This dissertation tries to address the above issues by …

All Pairs Routing Path Enumeration Using Latin Multiplication And Julia, Haochen Sun

Dissertations (1934 -)

Enumerating all routing paths among Autonomous Systems (ASes) at an Internet-scale is an intractable problem. The Border Gateway Protocol (BGP) is the standard exterior gateway protocol through which ASes exchange reachability information. Building an efficient path enumeration tool for a given network is an essential step toward estimating the resiliency of the network to cyber security attacks, such as routing origin and path hijacking. In our work, we use the matrix Latin multiplication method to compute all possible paths among all pairs of nodes. We parallelize this computation through the domain decomposition for matrix multiplication and implement our solution in …

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.

A Computationally Efficient Framework For Vector Representation Of Persistence Diagrams, Kit C. Chan, Umar Islambekov, Alexey Luchinsky, Rebecca Sanders

Mathematical and Statistical Science Faculty Research and Publications

In Topological Data Analysis, a common way of quantifying the shape of data is to use a persistence diagram (PD). PDs are multisets of points in R² computed using tools of algebraic topology. However, this multi-set structure limits the utility of PDs in applications. Therefore, in recent years efforts have been directed towards extracting informative and efficient summaries from PDs to broaden the scope of their use for machine learning tasks. We propose a computationally efficient framework to convert a PD into a vector in Rⁿ, called a vectorized persistence block (VPB). We show that our representation …

Functional Singular Spectrum Analysis, Hossein Haghbin, Seyed Morteza Najibi, Rahim Mahmoudvand, Jordan Trinka, Mehdi Maadooliat

Mathematical and Statistical Science Faculty Research and Publications

In this paper, we develop a new extension of the singular spectrum analysis (SSA) called functional SSA to analyze functional time series. The new methodology is constructed by integrating ideas from functional data analysis and univariate SSA. Specifically, we introduce a trajectory operator in the functional world, which is equivalent to the trajectory matrix in the regular SSA. In the regular SSA, one needs to obtain the singular value decomposition (SVD) of the trajectory matrix to decompose a given time series. Since there is no procedure to extract the functional SVD (fSVD) of the trajectory operator, we introduce a computationally …

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 …

Characterizations And Reliability Measures Of The Generalized Log Burr Xii Distribution, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Azeem Ali, Sedigheh Mirzaei Salehabadi, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, we derive the generalized log Burr XII (GLBXII) distribution [2] from the generalized Burr-Hatke differential equation. We characterize the GLBXII distribution via innovative techniques. We derive various reliability measures (series and parallel). We also authenticate the potentiality of the GLBXII model via economics applications. The applications of characterizations and reliability measures of the GLBXII distribution in different disciplines of science will be profitable for scientists.