Physical Sciences and Mathematics Commons^™

A Qualitative Analysis Of Hybrid Control Systems, Anca Georgeta Williams

Dissertations and Theses

Hybrid Control Systems are increasingly investigated as models for control systems where the interaction between continuous and discrete processes is tightly integrated. As yet, there is no general agreement as to what constitutes a canonical hybrid system. Rather various subclasses of systems combining continuous evolution and discrete event characteristics are analyzed for each application. In this dissertation we first unify the presentation of hybrid systems with a rich model which encompasses most examples of interest. We classify the available results and show how they fit together within the different subcategories. In the main part of the dissertation we prove that …

Which Chessboards Have A Closed Knight's Tour Within The Cube?, Joseph Demaio

Faculty Articles

A closed knight's tour of a chessboard uses legal moves of the knight to visit every square exactly once and return to its starting position. When the chessboard is translated into graph theoretic terms the question is transformed into the existence of a Hamiltonian cycle. There are two common tours to consider on the cube. One is to tour the six exterior n x n boards that form the cube. The other is to tour within the n stacked copies of the n x n board that form the cube. This paper is concerned with the latter. In this paper …

Some Results Of Backward Itô Formula, Guiseppe Da Prato, Jose-Luis Menaldi, Luciano Tubaro

Mathematics Faculty Research Publications

We use the notion of backward integration, with respect to a general Lévy process, to treat, in a simpler and unifying way, various classical topics as: Girsanov theorem, rst order partial differential equations, the Liouville (or Lyapunov) equations and the stochastic characteristic method.

Preprocessing Of Sar Interferometric Data Using Anisotropic Diffusion Filter, Kenneth Sartor, Josef Vaughn De Allen, Emile Ganthier, Gnana Bhaskar Tenali

Mathematics and System Engineering Faculty Publications

The most commonly used smoothing algorithms for complex data processing are blurring functions (i.e., Hanning, Taylor weighting, Gaussian, etc.). Unfortunately, the filters so designed blur the edges in a Synthetic Aperture Radar (SAR) scene, reduce the accuracy of features, and blur the fringe lines in an interferogram. For the Digital Surface Map (DSM) extraction, the blurring of these fringe lines causes inaccuracies in the height of the unwrapped terrain surface. Our goal here is to perform spatially non-uniform smoothing to overcome the above mentioned disadvantages. This is achieved by using a Complex Anisotropic Non-Linear Diffuser (CANDI) filter that is a …

Alliance Partitions In Graphs., Jason Lachniet

Electronic Theses and Dissertations

For a graph G=(V,E), a nonempty subset S contained in V is called a defensive alliance if for each v in S, there are at least as many vertices from the closed neighborhood of v in S as in V-S. If there are strictly more vertices from the closed neighborhood of v in S as in V-S, then S is a strong defensive alliance. A (strong) defensive alliance is called global if it is also a dominating set of G. The alliance partition number (respectively, strong …

An Extension Of Ramsey's Theorem To Multipartite Graphs, Brian Michael Cook

Mathematics Theses

Ramsey Theorem, in the most simple form, states that if we are given a positive integer l, there exists a minimal integer r(l), called the Ramsey number, such any partition of the edges of K_r(l) into two sets, i.e. a 2-coloring, yields a copy of K_l contained entirely in one of the partitioned sets, i.e. a monochromatic copy of Kl. We prove an extension of Ramsey's Theorem, in the more general form, by replacing complete graphs by multipartite graphs in both senses, as the partitioned set and as the desired monochromatic graph. More formally, given integers l and k, there …

Empirical Likelihood Confidence Intervals For The Sensitivity Of A Continuous-Scale Diagnostic Test, Angela Elaine Davis

Mathematics Theses

Diagnostic testing is essential to distinguish non-diseased individuals from diseased individuals. More accurate tests lead to improved treatment and thus reduce medical mistakes. The sensitivity and specificity are two important measurements for the diagnostic accuracy of a diagnostic test. When the test results are continuous, it is of interest to construct a confidence interval for the sensitivity at a fixed level of specificity for the test. In this thesis, we propose three empirical likelihood intervals for the sensitivity. Simulation studies are conducted to compare the empirical likelihood based confidence intervals with the existing normal approximation based confidence interval. Our studies …

Bayesian Approach To Three-Arm Non Inferiority Trials, Marcus Chenier Britton

Mathematics Theses

In non-inferiority trials, the goal is to show how an experimental treatment is statistically and clinically not inferior to the active control. The three-arm clinical trial usually recommended for non-inferiority trials by the FDA. The three-arm trial consists of a placebo, reference, and an experimental treatment. The three-arm trial shows the superiority of the reference over the placebo and comparison of the reference to an experimental treatment. In this paper, I will assess a non-inferiority trial with Bayesian methods. By employing Bayesian analysis, the parameters are random and assign vague prior distributions. I will compare the models involving different prior …

Analyzing The Behavior Of Rats By Repeated Measurements, Kenita A. Hall

Mathematics Theses

Longitudinal data, which is also known as repeated measures, has grown increasingly within the past years because of its ability to monitor change both within and between subjects. Statisticians in many fields of study have chosen this way of collecting data because it is cost effective and it minimizes the number of subjects required to produce a meaningful outcome. This thesis will explore the world of longitudinal studies to gain a thorough understanding of why this type of collecting data has grown so rapidly. This study will also describe several methods to analyze repeated measures using data collected on the …

Omnibus Tests For Comparison Of Competing Risks With Covariate Effects Via Additive Risk Model, Duytrac Vu Nguyen

Mathematics Theses

It is of interest that researchers study competing risks in which subjects may fail from any one of K causes. Comparing any two competing risks with covariate effects is very important in medical studies. This thesis develops omnibus tests for comparing cause-specific hazard rates and cumulative incidence functions at specified covariate levels. In the thesis, the omnibus tests are derived under the additive risk model, that is an alternative to the proportional hazard model, with by a weighted difference of estimates of cumulative cause-specific hazard rates. Simultaneous confidence bands for the difference of two conditional cumulative incidence functions are also …

Spectrally Arbitrary And Inertially Arbitrary Sign Pattern Matrices, Nilay Sezin Demir

Mathematics Theses

A sign pattern(matrix) is a matrix whose entries are from the set {+,-,0}. An n x n sign pattern matrix is a spectrally arbitrary pattern(SAP) if for every monic real polynomial p(x) of degree n, there exists a real matrix B whose entries agree in sign with A such that the characteristic polynomial of B is p(x). An n x n pattern A is an inertialy arbitrary pattern(IAP) if (r,s,t) belongs to the inertia set of A for every nonnegative triple (r,s,t) with r+s+t=n. Some elementary results on these two classes of patterns are first exhibited. Tree sign patterns are …

A Study To Ascertain The Effects Of The Connected Mathematics Project On Student Achievement In The Buffalo Public Schools, Darryl A. King

Mathematics Education Theses

This study examines the impact of The Connected Mathematics Project (CMP) on student achievement in the Buffalo School District. Student scores were compared for the Grade 8 2005 and 2006 NY State Assessments and the Grade 7 2006 NY State Assessment. Students taught with NY State Math Standards were the control group. Students taught with CMP curriculum were the experimental group. This study found mixed results in favor of the standards group.

Statistical Pronouncements V, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

No abstract provided.

Existence Of Minimizers And Necessary Conditions In Set-Valued Optimization With Equilibrium Constraints, Truong Q. Bao, Boris S. Mordukhovich

Mathematics Research Reports

In this paper we study set-valued optimization problems with equilibrium constraints (SOPEOs) described by parametric generalized equations in the form 0 is an element of the set G(x) + Q(x) where both G and Q are set-valued mappings between infinite-dimensional spaces. Such models particularly arise from certain optimization-related problems governed by set-valued variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish general results on the existence of optimal solutions under appropriate assumptions of the PalaisSmale type and then derive necessary conditions for optimality in the models under consideration by using advanced tools of variational analysis and generalized differentiation.

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Sas Macro For Hierarchical Dependence In Meta Analysis, Matthew Wayne Maw

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

This project implemented a simple and useful SAS (Statistical Analysis Software) macro for meta-analysis. The macro was specifically designed for hierarchically dependent meta-analysis but may also be used for independent meta-analysis. Two data files are necessary for this macro. One data file contains the study names, control and treatment group sizes with corresponding means and standard errors, covariates to be tested, an indicator variable noting hierarchically dependent study groups, and a variable providing the degrees of freedom for interdependent studies. The second file contains a variance/covariance matrix for the studies. The macro returns useful information such as study estimates and …

Black-Scholes And Extended Black-Scholes Models: A Comparative Statistical Analysis, Bradley Thomas Bush

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

Much research has been done on options pricing. Black and Scholes [12] set the benchmark in 1973 with their model for arbitrage-free, risk-neutral options valuation. Arbitrage-free refers to a market environment where prices are such that trading opportunities with no risk do not exist and risk-neutral commodities earn a risk free interest rate. Since then the literature has seen a multitude of models improving the fit of the traditional Black -Scholes (BS) model. A brief overview of options and these models is given. A derivation and discussion of BS is followed by a derivation and discussion of the Extended Black-Scholes …

Decomposing Vector Space Representations Of The Lie Algebras S[2c And S[2r, Brian W. Gleason

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

It is known that any finite-dimensional representation of a semi-simple Lie algebra is decomposable into a direct sum of irreducible representations. Here we prove some theoretical results that allow us to construct an efficient algorithm for computing such a decomposition for representations of s[2C and s[2R. We then implement this algorithm in a procedure for the computer algebra system Maple that will quickly and easily perform the decomposition. We also give several examples of this decomposition performed by the procedure in order to illustrate its advantages over calculations done ‘by hand'.

A Method For Finding Standard Error Estimates For Rma Expression Levels Using Bootstrap, Gabriel Nicholas

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

Oligonucleotide arrays are used in many applications. Affymetrix GeneChip arrays are widely used. Before researchers can use the information from these arrays, the raw data must be transformed and summarized into a more meaningful and usable form. One of the more popular methods for doing so is RMA (Robust Multi-array Analysis).

A problem with RMA is that the end result (estimated gene expression levels) is based on a fairly complicated process that is unusual. Specifically, there is no closed-form estimate of standard errors for the estimated gene expression levels. The current recommendation is to use a naive estimate for the …

On Distribution Of Integral Well-Rounded Lattices In Dimension Two, Lenny Fukshansky

CMC Faculty Publications and Research

Lecture given at the Illinois Number Theory Fest, May 2007.

Clinical Experience And Examination Performance: Is There A Correlation?, Gary L. Beck, Mihaela Teodora Matache, Carrie Riha, Katherine Kerber, Frederick A. Mccurdy

Mathematics Faculty Publications

Context  The Liaison Committee on Medical Education (LCME) requires there to be: ‘…comparable educational experiences and equivalent methods of evaluation across all alternative instructional sites within a given discipline’. It is an LCME accreditation requirement that students encounter similar numbers of patients with similar diagnoses. However, previous empirical studies have not shown a correlation between the numbers of patients seen by students and performance on multiple-choice examinations.

Objective  This study examined whether student exposure to patients with specific diagnoses predicts performance on multiple-choice examination questions pertaining to those diagnoses.

Methods  The Department of Pediatrics at the University of Nebraska Medical …

Products Of Characters With Few Irreducible Constituents, Edith Adan-Bante

Faculty Publications

We study the solvable groups G that have an irreducible character χ ∈ Irr(G) such that χ^--χ has at most two nonprincipal irreducible constituents.

A Classification Of Real Indecomposable Solvable Lie Algebras Of Small Dimension With Codimension One Nilradicals, Alan R. Parry

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This thesis was concerned with classifying the real indecomposable solvable Lie algebras with codimension one nilradicals of dimensions two through seven. This thesis was organized into three chapters.

In the first, we described the necessary concepts and definitions about Lie algebras as well as a few helpful theorems that are necessary to understand the project. We also reviewed many concepts from linear algebra that are essential to the research.

The second chapter was occupied with a description of how we went about classifying the Lie algebras. In particular, it outlined the basic premise of the classification: that we can use …

Local Effective Potential Theory: Nonuniqueness Of Potential And Wave Function, Viraht Sahni, Marlina Slamet, Xiao-Yin Pan

Physics Faculty Publications

In local effective potential energy theories such as the Hohenberg-Kohn-Sham density functional theory (HKS-DFT) and quantal density functional theory (Q-DFT) electronic systems in their ground or excited states are mapped to model systems of noninteracting fermions with equivalent density. From these models, the equivalent total energy and ionization potential are also obtained. This paper concerns the nonuniqueness of the local effective potential energy function of the model system in the mapping from a nondegenerate ground state, the nonuniqueness of the local effective potential energy function in the mapping from a nondegenerate excited state, and in the mapping to a model …

Use Of Logic Game To Improve High School Students' Logical Reasoning Skills : Results Of A Teaching Experiment, Frank Forte

Theses, Dissertations and Culminating Projects

High school students often struggle with the concept of logical reasoning. A study conducted with 37 ninth grade geometry students involved a teaching experiment. This study documented whether instruction on a logic game called the Color of the Board Game helped students’ logical reasoning skills, and if those skills could be reflected in a “‘pencil and paper” test. Each student in a control and treatment group received a pre-test with 25 multiple-choice logic questions and an open-ended question. Multiple-choice questions were based on geometry and contextual logic. The treatment group received the Color of the Board Instructional Unit between the …

The Effects Of Using The Geometer’S Sketchpad On Student Learning Of Transformations In The Coordinate Plane, Leeann Elizabeth Gennett

Theses, Dissertations and Culminating Projects

The primary purpose of this study was to investigate how grade nine honors geometry students and grade ten regular geometry students learn and retain information about three basic rigid geometric transformations with the support of the software package The Geometer’s Sketchpad in comparison to the traditional, non-software supported method of instruction.

The study was conducted in a high school with two tenth grade regular geometry classes and two ninth grade honors geometry classes. The researcher and another teacher each conducted a one-week instructional unit on the three basic, isometric transformations. Thirty-four students agreed to participate in the study. Nineteen students …

Bounds On K-Regular Ramanujan Graphs And Separator Theorems, James Skees

Masters Theses & Specialist Projects

Expander graphs are a family of graphs that are highly connected. Finding explicit examples of expander graphs which are also sparse is a difficult problem. The best type of expander graph in a. certain sense is a Ramanujan graph. Families of graphs that have separator theorems fail to be Ramanujan if the vertex set gets sufficiently large. Using separator theorems to get an estimate on the expanding constant of graphs, we get bounds 011 the number of vertices for such fc-regular graphs in order for them to be Ramanujan.

Loop Edge Estimation In 4-Regular Hamiltonian Graphs, Yale Madden

Masters Theses & Specialist Projects

In knot theory, a knot is defined as a closed, non-self-intersecting curve embedded in three-dimensional space that cannot be untangled to produce a simple planar loop. A mathematical knot is essentially a conventional knot tied with rope where the ends of the rope have been glued together. One way to sample large knots is based on choosing a 4-regular Hamiltonian planar graph. A method for generating rooted 4-regular Hamiltonian planar graphs with n vertices is discussed in this thesis. In the generation process of these graphs, some vertices are introduced that can be easily eliminated from the resulting knot diagram. …

Ets (Efficient, Transparent, And Secured) Self-Healing Service For Pervasive Computing Applications, Shameem Ahmed, Moushumi Sharmin, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

To ensure smooth functioning of numerous handheld devices anywhere anytime, the importance of self-healing mechanism cannot be overlooked. Incorporation of efficient fault detection and recovery in device itself is the quest for long but there is no existing self-healing scheme for devices running in pervasive computing environments that can be claimed as the ultimate solution. Moreover, the highest degree of transparency, security and privacy attainability should also be maintained. ETS Self-healing service, an integral part of our developing middleware named MARKS (Middleware Adaptability for Resource discovery, Knowledge usability, and Self-healing), holds promise for offering all of those functionalities.

Dynamics Of Spatial Pattern Formation: Cases Of Spikes And Droplets, Yuya Sasaki

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This thesis studies the gradient system that forms spatial patterns such that the minimum distances of pairs among various points are maximized in the end. As this problem innately involves singularity issues, an extended system of the gradient system is proposed. Motivated by the spatial pattern suggested by a numerical example, this extended system is applied to a three-point problem and then to a two-point problem in a quotient space of ℝ² modulo a lattice.