Mathematics Commons^™

99mtc-Hexamethylpropyleneamine Oxime Imaging For Early Detection Of Acute Lung Injury In Rats Exposed To Hyperoxia Or Lipopolysaccharide Treatment, Said H. Audi, Anne V. Clough, Steven T. Haworth, Meetha Medhora, Mahsa Ranji, John C. Densmore, Elizabeth R. Jacobs

Biomedical Engineering Faculty Research and Publications

^99mTc-Hexamethylpropyleneamine oxime (HMPAO) is a clinical single-photon emission computed tomography biomarker of tissue oxidoreductive state. Our objective was to investigate whether HMPAO lung uptake can serve as a preclinical marker of lung injury in two well-established rat models of human acute lung injury (ALI).

Rats were exposed to >95% O₂ (hyperoxia) or treated with intratracheal lipopolysaccharide (LPS), with first endpoints obtained 24 h later. HMPAO was administered intravenously before and after treatment with the glutathione-depleting agent diethyl maleate (DEM), scintigraphy images were acquired, and HMPAO lung uptake was quantified from the images. We also measured breathing rates, heart …

Genome Resources For Climate-Resilient Cowpea, An Essential Crop For Food Security, María Muñoz-Amatriaín, Hamid Mirebrahim, Pei Xu, Steve Wanamaker, Mingcheng 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 …

Maximizing H-Colorings Of Connected Graphs With Fixed Minimum Degree, John Engbers

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

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

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce and study general mathematical properties of a new generator of continuous distributions with two extra parameters called the Another generalized transmuted family of distributions. We present some special models. We investigate the asymptotes and shapes. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. We obtain explicit expressions for the ordinary and incomplete moments and generating functions, Bonferroni and Lorenz curves, asymptotic distribution of the extreme values, Shannon and Renyi entropies and order statistics, which hold for any baseline model, certain characterisations are presented. Further, we …

Ultracoproduct Continua And Their Regular Subcontinua, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

We continue our study of ultracoproduct continua, focusing on the role played by the regular subcontinua—those subcontinua which are themselves ultracoproducts. Regular subcontinua help us in the analysis of intervals, composants, and noncut points of ultracoproduct continua. Also, by identifying two points when they are contained in the same regular subcontinua, we naturally generalize the partition of a standard subcontinuum of ℍ * into its layers.

Accuracy And Precision Of Occlusal Contacts Of Stereolithographic Casts Mounted By Digital Interocclusal Registrations, Jason T. Krahenbuhl, Seok-Hwan Cho, Jon Patrick Irelan, Naveen K. Bansal

Mathematics, Statistics and Computer Science Faculty Research and Publications

Statement of problem

Little peer-reviewed information is available regarding the accuracy and precision of the occlusal contact reproduction of digitally mounted stereolithographic casts.

Purpose

The purpose of this in vitro study was to evaluate the accuracy and precision of occlusal contacts among stereolithographic casts mounted by digital occlusal registrations.

Material and methods

Four complete anatomic dentoforms were arbitrarily mounted on a semi-adjustable articulator in maximal intercuspal position and served as the 4 different simulated patients (SP). A total of 60 digital impressions and digital interocclusal registrations were made with a digital intraoral scanner to fabricate 15 sets of mounted stereolithographic …

Biomarkers For Radiation Pneumonitis Using Noninvasive Molecular Imaging, Meetha Medhora, Steven Haworth, Yu Liu, Jayashree Narayanan, Feng Gao, Ming Zhao, Said H. Audi, Elizabeth R. Jacobs, Brian L. Fish, Anne V. Clough

Mathematics, Statistics and Computer Science Faculty Research and Publications

Our goal is to develop minimally invasive biomarkers for predicting radiation-induced lung injury before symptoms develop. Currently, there are no biomarkers that can predict radiation pneumonitis. Radiation damage to the whole lung is a serious risk in nuclear accidents or in radiologic terrorism. Our previous studies have shown that a single dose of 15 Gy of x-rays to the thorax causes severe pneumonitis in rats by 6–8 wk. We have also developed a mitigator for radiation pneumonitis and fibrosis that can be started as late as 5 wk after radiation. Methods: We used 2 functional SPECT probes in vivo in …

Characterizations Of Pareto, Weibull And Power Function Distributions Based On Generalized Order Statistics, M. Ahsanullah, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterization of Pareto and Weibull distributions based on the conditional expectation of generalized order statistics extending the characterization results reported by Jin and Lee (2014). We also present a characterization of the power function distribution based on the conditional expectation of lower generalized order statistics.

Complex-Valued Time-Series Correlation Increases Sensitivity In Fmri Analysis, Mary C. Kociuba, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Purpose

To develop a linear matrix representation of correlation between complex-valued (CV) time-series in the temporal Fourier frequency domain, and demonstrate its increased sensitivity over correlation between magnitude-only (MO) time-series in functional MRI (fMRI) analysis.

Materials and Methods

The standard in fMRI is to discard the phase before the statistical analysis of the data, despite evidence of task related change in the phase time-series. With a real-valued isomorphism representation of Fourier reconstruction, correlation is computed in the temporal frequency domain with CV time-series data, rather than with the standard of MO data. A MATLAB simulation compares the Fisher-z transform …

Testing Multiple Hypotheses With Skewed Alternatives, Naveen K. Bansal, Gholamhossein G. Hamedani, Mehdi Maadooliat

Mathematics, Statistics and Computer Science Faculty Research and Publications

In many practical cases of multiple hypothesis problems, it can be expected that the alternatives are not symmetrically distributed. If it is known a priori that the distributions of the alternatives are skewed, we show that this information yields high power procedures as compared to the procedures based on symmetric alternatives when testing multiple hypotheses. We propose a Bayesian decision theoretic rule for multiple directional hypothesis testing, when the alternatives are distributed as skewed, under a constraint on a mixed directional false discovery rate. We compare the proposed rule with a frequentist's rule of Benjamini and Yekutieli (2005) using simulations. …

Treatment With Actriib-Mfc Produces Myofiber Growth And Improves Lifespan In The Acta1 H40y Murine Model Of Nemaline Myopathy, Jennifer E. Tinklenberg, Hui W. Meng, Lin J. Yang, Fujun Liu, Raymond G. Hoffmann, Mahua Dasgupta, Kenneth P. Allen, Alan H. Beggs, Edna C. Hardeman, R. Scott Pearsall, Robert H. Fitts, Michael W. Lawlor

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Kings And Heirs: A Characterization Of The (2,2)-Domination Graphs Of Tournaments, Kim A. S. Factor, Larry J. Langley

Mathematics, Statistics and Computer Science Faculty Research and Publications

In 1980, Maurer coined the phrase king when describing any vertex of a tournament that could reach every other vertex in two or fewer steps. A (2,2)-domination graph of a digraph D, dom_2,2(D), has vertex set V(D), the vertices of D, and edge uv whenever u and v each reach all other vertices of D in two or fewer steps. In this special case of the (i,j)-domination graph, we see that Maurer’s theorem plays an important role in establishing which vertices form the kings that create some of the edges in dom_2,2(D). But of even more …

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

Mathematics, Statistics and Computer Science Faculty Research and Publications

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

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

Mathematics, Statistics and Computer Science Faculty Research and Publications

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

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

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

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

Mathematics, Statistics and Computer Science Faculty Research and Publications

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

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

Mathematics, Statistics and Computer Science Faculty Research and Publications

Purpose

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

Materials and Methods

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

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

Mathematics, Statistics and Computer Science Faculty Research and Publications

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

Out-Tournament Adjacency Matrices With Equal Ranks, Zachary Buelow

Dissertations (1934 -)

Much work has been done in analyzing various classes of tournaments, giving a partial characterization of tournaments with adjacency matrices having equal and full real, nonnegative integer, Boolean, and term ranks. Relatively little is known about the corresponding adjacency matrix ranks of local out-tournaments, a larger family of digraphs containing the class of tournaments. Based on each of several structural theorems from Bang-Jensen, Huang, and Prisner, we will identify several classes of out-tournaments which have the desired adjacency matrix rank properties. First we will consider matrix ranks of out-tournament matrices from the perspective of the structural composition of the strong …

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

Mathematics, Statistics and Computer Science Faculty Research and Publications

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

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

Mathematics, Statistics and Computer Science Faculty Research and Publications

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

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

Mathematics, Statistics and Computer Science Faculty Research and Publications

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

Certain Characterizations Of Recently Introduced Distributions, Gholamhossein G. Hamedani, Seyed Morteza Najibi

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of twenty two recently introduced distributions are presented. These characterizations are based on: (I) ration of two truncated moments; (ii) the hazard function and (iii) conditional expectations.

A New Weibull-G Family Of Distributions, M. H. Tahir, Muhammad Zubair, M. Mansoor, Gauss M. Cordeiro, Morad Alizadeh, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Statistical analysis of lifetime data is an important topic in reliability engineering, biomedical and social sciences and others. We introduce a new generator based on the Weibull random variable called the new Weibull-G family. We study some of its mathematical properties. Its density function can be symmetrical, left-skewed, right-skewed, bathtub and reversed-J shaped, and has increasing, decreasing, bathtub, upside-down bathtub, J, reversed-J and S shaped hazard rates. Some special models are presented. We obtain explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Renyi entropy, order statistics and reliability. Three useful characterizations based on truncated moments are …

Worldwide Cutaneous Malignant Melanoma Incidences Analyzed By Sex, Age, And Skin Type Over Time (1955–2007): Is Hpv Infection Of Androgenic Hair Follicular Melanocytes A Risk Factor For Developing Melanoma Exclusively In People Of European-Ancestry?, Stephen Merrill, Madhan Subramanian, Dianne E. Godar

Mathematics, Statistics and Computer Science Faculty Research and Publications

The cutaneous malignant melanoma (CMM) incidence has been increasing in an exponential manner in certain populations around the world for over 7 decades. To help illuminate the etiology, we performed worldwide temporal (1955–2007) CMM incidence analysis by sex, age (0–14, 15–29, 30–49, 50–69, 70–85+), and skin type on 6 continents using data from the International Agency for Research on Cancer. We observe an exponential increase in the CMM incidence over time and an increase of about 2 orders of magnitude between age groups 0–14 and 15–29 exclusively in European-ancestry populations around the world independent of skin type (I–III or III–IV). …

An Ensemble Model Of Qsar Tools For Regulatory Risk Assessment, Prachi Pradeep, Richard J. Povinelli, Shannon White, Stephen Merrill

Mathematics, Statistics and Computer Science Faculty Research and Publications

Quantitative structure activity relationships (QSARs) are theoretical models that relate a quantitative measure of chemical structure to a physical property or a biological effect. QSAR predictions can be used for chemical risk assessment for protection of human and environmental health, which makes them interesting to regulators, especially in the absence of experimental data. For compatibility with regulatory use, QSAR models should be transparent, reproducible and optimized to minimize the number of false negatives. In silico QSAR tools are gaining wide acceptance as a faster alternative to otherwise time-consuming clinical and animal testing methods. However, different QSAR tools often make conflicting …

Solving Set Cover With Pairs Problem Using Quantum Annealing, Yudong Cao, Shuxian Jiang, Debbie Perouli, Sabre Kais

Mathematics, Statistics and Computer Science Faculty Research and Publications

Here we consider using quantum annealing to solve Set Cover with Pairs (SCP), an NP-hard combinatorial optimization problem that plays an important role in networking, computational biology, and biochemistry. We show an explicit construction of Ising Hamiltonians whose ground states encode the solution of SCP instances. We numerically simulate the time-dependent Schrödinger equation in order to test the performance of quantum annealing for random instances and compare with that of simulated annealing. We also discuss explicit embedding strategies for realizing our Hamiltonian construction on the D-wave type restricted Ising Hamiltonian based on Chimera graphs. Our embedding on the Chimera graph …

A Generalized Gamma-Weibull Distribution: Model, Properties And Applications, R. S. Meshkat, H. Torabi, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We prepare a new method to generate family of distributions. Then, a family of univariate distributions generated by the Gamma random variable is defined. The generalized gamma-Weibull (GGW) distribution is studied as a special case of this family. Certain mathematical properties of moments are provided. To estimate the model parameters, the maximum likelihood estimators and the asymptotic distribution of the estimators are discussed. Certain characterizations of GGW distribution are presented. Finally, the usefulness of the new distribution, as well as its effectiveness in comparison with other distributions, are shown via an application of a real data set.

Collective Estimation Of Multiple Bivariate Density Functions With Application To Angular-Sampling-Based Protein Loop Modeling, Mehdi Maadooliat, Lan Zhou, Seyed Morteza Najibi, Xin Gao, Jianhua Z. Huang

Mathematics, Statistics and Computer Science Faculty Research and Publications

This article develops a method for simultaneous estimation of density functions for a collection of populations of protein backbone angle pairs using a data-driven, shared basis that is constructed by bivariate spline functions defined on a triangulation of the bivariate domain. The circular nature of angular data is taken into account by imposing appropriate smoothness constraints across boundaries of the triangles. Maximum penalized likelihood is used to fit the model and an alternating blockwise Newton-type algorithm is developed for computation. A simulation study shows that the collective estimation approach is statistically more efficient than estimating the densities individually. The proposed …

A Hybrid Segmentation And D-Bar Method For Electrical Impedance Tomography, Sarah J. Hamilton, J. M. Reyes, Samuli Siltanen, X. Zhang

Mathematics, Statistics and Computer Science Faculty Research and Publications

The regularized D-bar method for electrical impedance tomography (EIT) provides a rigorous mathematical approach for solving the full nonlinear inverse problem directly, i.e., without iterations. It is based on a low-pass filtering in the (nonlinear) frequency domain. However, the resulting D-bar reconstructions are inherently smoothed, leading to a loss of edge distinction. In this paper, a novel method that combines a D-bar approach with the edge-preserving nature of total variation (TV) regularization is presented. The method also includes a data-driven contrast adjustment technique guided by the key functions (CGO solutions) of the D-bar method. The new TV-enhanced D-bar …

Pain Level Detection From Facial Image Captured By Smartphone, Md Kamrul Hasan, Golam Mushih Tanimul Ahsan, Sheikh Iqbal Ahamed, Rechard Love, Reza Salim

Mathematics, Statistics and Computer Science Faculty Research and Publications

Accurate symptom of cancer patient in regular basis is highly concern to the medical service provider for clinical decision making such as adjustment of medication. Since patients have limitations to provide self-reported symptoms, we have investigated how mobile phone application can play the vital role to help the patients in this case. We have used facial images captured by smart phone to detect pain level accurately. In this pain detection process, existing algorithms and infrastructure are used for cancer patients to make cost low and user-friendly. The pain management solution is the first mobile-based study as far as we found …