Mathematics Commons^™

Modulation Of Airway Inflammation By Immunostimulatory Cpg Oligodeoxynucleotides In A Murine Model Of Allergic Aspergillosis, Banani Banerjee, Kevin J. Kelly, Jordan N. Fink, James D. Henderson Jr., Naveen K. Bansal, Viswanath P. Kurup

Mathematics, Statistics and Computer Science Faculty Research and Publications

Allergic aspergillosis is a Th2 T-lymphocyte-mediated pulmonary complication in patients with atopic asthma and cystic fibrosis. Therefore, any therapeutic strategy that selectively inhibits Th2 T-cell activation may be useful in downregulating allergic lung inflammation in asthma. In the present study, we developed a CpG oligodeoxynucleotide (ODN)-based immune intervention of allergic inflammation in a mouse model of allergic aspergillosis. Four different groups of mice were used in a short-term immunization protocol. Three experimental groups of animals (groups 1 to 3) were sensitized with Aspergillus fumigatus antigens. Animals in group 1 were immunized with A. fumigatus antigen alone, while those in group …

Deadline Analysis Of Interrupt-Driven Software, Dennis Brylow, Jens Palsberg

Mathematics, Statistics and Computer Science Faculty Research and Publications

Real-time, reactive, and embedded systems are increasingly used throughout society (e.g., flight control, railway signaling, vehicle management, medical devices, and many others). For real-time, interrupt-driven software, timely interrupt handling is part of correctness. It is vital for software verification in such systems to check that all specified deadlines for interrupt handling are met. Such verification is a daunting task because of the large number of different possible interrupt arrival scenarios. For example, for a Z86-based microcontroller, there can be up to six interrupt sources and each interrupt can arrive during any clock cycle. Verification of such systems has traditionally relied …

Enhancements To Crisp Possibilistic Reconstructability Analysis, Anas Al-Rabadi, Martin Zwick

Complex Systems Faculty Publications and Presentations

Modified Reconstructibility Analysis (MRA), a novel decomposition within the framework of set-theoretic (crisp possibilistic) Reconstructibility Analysis, is presented. It is shown that in some cases while 3-variable NPN-classified Boolean functions are not decomposable using Conventional Reconstructibility Analysis (CRA), they are decomposable using Modified Reconstructibility Analysis (MRA). Also, it is shown that whenever a decomposition of 3-variable NPN-classified Boolean functions exists in both MRA and CRA, MRA yields simpler or equal complexity decompositions. A comparison of the corresponding complexities for Ashenhurst-Curtis decompositions, and Modified Reconstructibility Analysis (MRA) is also presented. While both AC and MRA decompose some but …

Large Prandtl Number Behavior Of The Boussinesq System Of Rayleigh-Bénard Convection, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We establish the validity of the infinite Prandtl number model as an approximation of the Boussinesq system at large Prandtl number on finite and infinite time interval, as well as in some statistical sense. © 2004 Elsevier Ltd. All rights reserved.

Oscillation Of Symplectic Dynamic Systems, Martin Bohner, Ondřej Došlý

Mathematics and Statistics Faculty Research & Creative Works

We investigate oscillatory properties of a perturbed symplectic dynamic system on a time scale that is unbounded above. the unperturbed system is supposed to be Non oscillatory, and we give conditions on the perturbation matrix, which guarantee that the perturbed system becomes oscillatory. Examples illustrating the general results are given as well. © Australian Mathematical Society 2004.

Sub-Supersolution Method For Quasilinear Parabolic Variational Inequalities, Siegfried Carl, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

This paper is about a systematic attempt to apply the sub-supersolution method to parabolic variational inequalities. We define appropriate concepts of sub-supersolutions and derive existence, comparison, and extremity results for such inequalities.

The Robustness Of Factor Analyses When The Data Does Not Conform To Standard Parametric Requirements, Haisong Peng

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Objective: To access the robustness of factor analyses when the data does not conform to standard parametric requirements.

Methods: Data were simulated in package R. Maximum likelihood was used to fit and assess the factor models. Chi-square statistics were obtained to test hypotheses about the correct number of factors in simulated settings where the true number of factors was known. The number of true factors varied between 1 and 3; the number of observed variables was either 6 (for 1 factor) or 3 per factor for 2 or more factors.

Results: With standard normal factor populations, and normal errors added …

Mathematical And Empirical Modeling Of Chemical Reactions In A Microreactor, Jing Hu

Doctoral Dissertations

This dissertation is concerned with mathematical and empirical modeling to simulate three important chemical reactions (cyclohexene hydrogenation and dehydrogenation, preferential oxidation of carbon monoxide, and the Fischer-Tropsch (F-T) synthesis in a microreaction system.

Empirical modeling and optimization techniques based on experimental design (Central Composite Design (CCD)) and response surface methodology were applied to these three chemical reactions. Regression models were built, and the operating conditions (such as temperature, the ratio of the reactants, and total flow rate) which maximize reactant conversion and product selectivity were determined for each reaction.

A probability model for predicting the probability that a certain species …

Multiple Solutions For Quasilinear Elliptic Neumann Problems In Orlicz-Sobolev Spaces, Nikolaos Halidias, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

We investigate the existence of multiple solutions to quasilinear elliptic problems containing Laplace like operators (ϕ-Laplacians). We are interested in Neumann boundary value problems and our main tool is Brézis-Nirenberg's local linking theorem.

Tid And See Testing Results Of Altera Cyclone Field Programmable Gate Array, Stephen L. Clark, K. Avery, R. Parker

Mathematics and Statistics Faculty Research & Creative Works

Total ionizing dose (TID) and single event effects testing was performed on Altera Cyclone FPGAs. The devices exhibit slight performance degradation to a TID of 1 Mrad (Si), but also exhibited single event latchup at a low LET.

Hereditarily Unicoherent Continua And Their Absolute Retracts, J. J. Charatonik, W. J. Charatonik, Janusz R. Prajs

Mathematics and Statistics Faculty Research & Creative Works

We investigate absolute retracts for classes of hereditarily unicoherent continua, tree-like continua, λ- dendroids, dendroids and some other related ones. The main results are: (1) the inverse limits of trees with confluent bonding mappings are absolute retracts of hereditarily unicoherent continua; (2) each tree-like continuum is embeddable in a special way in a tree-like absolute retract for the class of hereditarily unicoherent continua; (3) a dendroid is an absolute retract for hereditarily unicoherent continua if and only if it can be embedded as a retract into the Mohler-Nikiel universal smooth dendroid.

Existence And Comparison Results For Quasilinear Evolution Hemivariational Inequalities, Siegfried Carl, Vy Khoi Le, Dumitru Motreanu

Mathematics and Statistics Faculty Research & Creative Works

We generalize the sub-supersolution method known for weak solutions of single and multivalued nonlinear parabolic problems to quasilinear evolution hemivariational inequalities. To this end we first introduce our basic notion of sub- and supersolutions on the basis of which we then prove existence, comparison, compactness and extremality results for the hemivariational inequalities under considerations.

Oscillation Of Second Order Nonlinear Dynamic Equations On Time Scales, S. H. Saker, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

By means of Riccati transformation techniques, we establish some oscillation criteria for a second order nonlinear dynamic equation on time scales in terms of the coefficients. We give examples of dynamic equations to which previously known oscillation criteria are not applicable.

Oscillation Theory For Second Order Dynamic Equations [Book Review], Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Cr Approximation On A Nonrigid Hypersurface Graph In Cⁿ, Al Boggess, Roman Dwilewicz

Mathematics and Statistics Faculty Research & Creative Works

Let M be a hypersurface in Cⁿ that is the graph over a (2n - 1)-linear real space. the main result of the paper is that any CR function on M can be uniformly approximated on compact subsets by entire functions on Cⁿ.

The Independence Of Characters On Nonabelian Groups, David E. Grow, Kathryn E. Hare

Mathematics and Statistics Faculty Research & Creative Works

We show that there are characters of compact, connected, nonabelian groups that approximate random choices of signs. The work was motivated by Kronecker's theorem on the independence of exponential functions and has applications to thin sets.

Discrete-Time Approximations Of Stochastic Delay Equations: The Milstein Scheme, Yaozhong Hu, Salah-Eldin A. Mohammed, Feng Yan

Articles and Preprints

In this paper, we develop a strong Milstein approximation scheme for solving stochastic delay differential equations (SDDE's). The scheme has convergence order 1. In order to establish the scheme, we prove an infinite-dimensional Itô formula for "tame" functions acting on the segment process of the solution of an SDDE. It is interesting to note that the presence of the memory in the SDDE requires the use of the Malliavin calculus and the anticipating stochastic analysis of Nualart and Pardoux. Given the non-anticipating nature of the SDDE, the use of anticipating calculus methods appears to be novel.

Evaluation Of Multiple Models To Distinguish Closely Related Forms Of Disease Using Dna Microarray Data: An Application To Multiple Myeloma, Johanna S. Hardin, Michael Waddell, C. David Page, Fenghuang Zhan, Bart Barlogie, John Shaughnessy, John J. Crowley

Pomona Faculty Publications and Research

Motivation: Standard laboratory classification of the plasma cell dyscrasia monoclonal gammopathy of undetermined significance (MGUS) and the overt plasma cell neoplasm multiple myeloma (MM) is quite accurate, yet, for the most part, biologically uninformative. Most, if not all, cancers are caused by inherited or acquired genetic mutations that manifest themselves in altered gene expression patterns in the clonally related cancer cells. Microarray technology allows for qualitative and quantitative measurements of the expression levels of thousands of genes simultaneously, and it has now been used both to classify cancers that are morphologically indistinguishable and to predict response to therapy. It is …

Reliability Estimation Based On System Data With An Unknown Load Share Rule, Hyoungtae Kim, Paul H. Kvam

Department of Math & Statistics Faculty Publications

We consider a multicomponent load-sharing system in which the failure rate of a given component depends on the set of working components at any given time. Such systems can arise in software reliability models and in multivariate failure-time models in biostatistics, for example. A load-share rule dictates how stress or load is redistributed to the surviving components after a component fails within the system. In this paper, we assume the load share rule is unknown and derive methods for statistical inference on load-share parameters based on maximum likelihood. Components with (individual) constant failure rates are observed in two environments: (1) …

A Nonlinear Random Coefficients Model For Degradation Testing, Suk Joo Bae, Paul H. Kvam

Department of Math & Statistics Faculty Publications

As an alternative to traditional life testing, degradation tests can be effective in assessing product reliability when measurements of degradation leading to failure can be observed. This article presents a degradation model for highly reliable light displays, such as plasma display panels and vacuum fluorescent displays (VFDs). Standard degradation models fail to capture the burn-in characteristics of VFDs, when emitted light actually increases up to a certain point in time before it decreases (or degrades) continuously. Random coefficients are used to model this phenomenon in a nonlinear way, which allows for a nonmonotonic degradation path. In many situations, the relative …

Gamma-Set Domination Graphs. I: Complete Biorientations Of Q-Extended Stars And Wounded Spider Graphs, Kim A. S. Factor

Mathematics, Statistics and Computer Science Faculty Research and Publications

The domination number of a graph G, γ(G), and the domination graph of a digraph D, dom(D) are integrated in this paper. The γ-set domination graph of the complete biorientation of a graph G, dom_γ(G) is created. All γ-sets of specific trees T are found, and dom-_γ(T) is characterized for those classes.

Uniqueness Theorems In Bioluminescence Tomography, Ge Wang, Yi Li, Ming Jiang

Mathematics and Statistics Faculty Publications

Motivated by bioluminescent imaging needs for studies on gene therapy and other applications in the mouse models, a bioluminescence tomography (BLT) system is being developed in the University of Iowa. While the forward imaging model is described by the well-known diffusion equation, the inverse problem is to recover an internal bioluminescent source distribution subject to Cauchy data. Our primary goal in this paper is to establish the solution uniqueness for BLT under practical constraints despite the ill-posedness of the inverse problem in the general case. After a review on the inverse source literature, we demonstrate that in the general case …

The Dual Spectral Set Conjecture, Steen Pedersen

Mathematics and Statistics Faculty Publications

Suppose that Λ = (aZ + b) ∪ (cZ + d) where a, b, c, d are real numbers such that a ≠ 0 and c ≠ 0. The union is not assumed to be disjoint. It is shown that the translates Ω + λ, λ is an element of Λ, tile the real line for some bounded measurable set Ω if and only if the exponentials e_λ(x) = e^i2πλx, λ is an element of Λ, form an orthogonal basis for some bounded measurable set Ω'.

A Comparison Of Modified Reconstructability Analysis And Ashenhurst‐Curtis Decomposition Of Boolean Functions, Anas Al-Rabadi, Marek Perkowski, Martin Zwick

Complex Systems Faculty Publications and Presentations

Modified reconstructability analysis (MRA), a novel decomposition technique within the framework of set‐theoretic (crisp possibilistic) reconstructability analysis, is applied to three‐variable NPN‐classified Boolean functions. MRA is superior to conventional reconstructability analysis, i.e. it decomposes more NPN functions. MRA is compared to Ashenhurst‐Curtis (AC) decomposition using two different complexity measures: log‐functionality, a measure suitable for machine learning, and the count of the total number of two‐input gates, a measure suitable for circuit design. MRA is superior to AC using the first of these measures, and is comparable to, but different from AC, using the second.

Global Solutions To The Lake Equations With Isolated Vortex Regions, Chaocheng Huang

Mathematics and Statistics Faculty Publications

The vorticity formulation for the lake equations in R² is studied.

Results Of Soy-Based Meal Replacement Formula On Weight, Anthropometry, Serum Lipids & Blood Pressure During A 40-Week Clinical Weight Loss Trial, Kevin R. Fontaine, Dongyan Yang, Gary L. Gadbury, Stanley Heshka, Linda G. Schwartz, Radha Murugesan, Jennifer L. Kraker, Moonseong Heo, Steven B. Heymsfield, David B. Allison

Mathematics and Statistics Faculty Research & Creative Works

Background: to evaluate the intermediate-term health outcomes associated with a soy-Based meal replacement, and to compare the weight loss efficacy of two distinct patterns of caloric restriction. Methods: Ninety overweight/obese (28 < BMI ≤ 41 kg/m2) adults received a single session of dietary counseling and were randomized to either 12 weeks at 1200 kcal/day, 16 weeks at 1500 kcal/d and 12 weeks at 1800 kcal/d (i.e., the 12/15/18 diet group), or 28 weeks at 1500 kcal/d and 12 weeks at 1800 kcal/d (i.e., the 15/18 diet group). Weight, body fat, waist circumference, blood pressure and serum lipid concentrations were measured at 4-week intervals throughout the 40-week trial. Results: Subjects in both treatments showed statistically significant improvements in outcomes. a regression model for weight change suggests that subjects with larger baseline weights tended to lose more weight and subjects in the 12/15/18 group tended to experience, on average, an additional 0.9 kg of weight loss compared with subjects in the 15/18 group. Conclusion: Both treatments using the soy-Based meal replacement program were associated with significant and comparable weight loss and improvements on selected health variables.

Almost Periodic Sets And Subactions In Topological Dynamics, Ethan Akin, Joseph Auslander

Mathematics and Statistics Faculty Research & Creative Works

Let Γ be a group with subgroup λ. We show, under certain conditions, that an almost periodic point for the action of λ is also almost periodic for Γ. This is applied to obtain a theorem of Glasner.

Exact Multiplicity For Periodic Solutions Of Duffing Type, Hongbin Chen, Yi Li, Xiaojie Hou

Mathematics and Statistics Faculty Publications

In this paper, we study the following Duffing-type equation:

x″+cx′+g(t,x)=h(t),

where g(t,x) is a 2π-periodic continuous function in t and concave–convex in x, and h(t) is a small continuous 2π-periodic function. The exact multiplicity and stability of periodic solutions are obtained.

Randomization Tests For Small Samples: An Application For Genetic Expression Data, Gary L. Gadbury, Grier P. Page, Moonseong Heo, John D. Mountz, David B. Allison

Mathematics and Statistics Faculty Research & Creative Works

An advantage of randomization tests for small samples is that an exact P-value can be computed under an additive model. a disadvantage with very small sample sizes is that the resulting discrete distribution for P-values can make it mathematically impossible for a P-value to attain a particular degree of significance. We investigate a distribution of P-values that arises when several thousand randomization tests are conducted simultaneously using small samples, a situation that arises with microarray gene expression data. We show that the distribution yields valuable information regarding groups of genes that are differentially expressed between two groups: A treatment group …

Modern Statistical Methods For Handling Missing Repeated Measurements In Obesity Trial Data: Beyond Locf, Gary L. Gadbury, C. S. Coffey, D. B. Allison

Mathematics and Statistics Faculty Research & Creative Works

This paper brings together some modern statistical methods to address the problem of missing data in obesity trials with repeated measurements. Such missing data occur when subjects miss one or more follow-up visits or drop out early from an obesity trial. a common approach to dealing with missing data because of dropout is 'last observation carried forward' (LOCF). This method, although intuitively appealing, requires restrictive assumptions to produce valid statistical conclusions. We review the need for obesity trials, the assumptions that must be made regarding missing data in such trials, and some modern statistical methods for analyzing data containing missing …