Mathematics Commons^™

Security In Pervasive Computing: Current Status And Open Issues, Munirul Haque, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

Million of wireless device users are ever on the move, becoming more dependent on their PDAs, smart phones, and other handheld devices. With the advancement of pervasive computing, new and unique capabilities are available to aid mobile societies. The wireless nature of these devices has fostered a new era of mobility. Thousands of pervasive devices are able to arbitrarily join and leave a network, creating a nomadic environment known as a pervasive ad hoc network. However, mobile devices have vulnerabilities, and some are proving to be challenging. Security in pervasive computing is the most critical challenge. Security is needed to …

Chainability And Hemmingsen's Theorem, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

On the surface, the definitions of chainability and Lebesgue covering dimension ⩽1 are quite similar as covering properties. Using the ultracoproduct construction for compact Hausdorff spaces, we explore the assertion that the similarity is only skin deep. In the case of dimension, there is a theorem of E. Hemmingsen that gives us a first-order lattice-theoretic characterization. We show that no such characterization is possible for chainability, by proving that if κ is any infinite cardinal and AA is a lattice base for a nondegenerate continuum, then AA is elementarily equivalent to a lattice base for a continuum Y …

A Survey Of The Methods To Find Probability Density Functions, Nancy Picinic Ricca

Theses, Dissertations and Culminating Projects

Various methods are described in this thesis that will approximate probability density functions (PDF), also known as invariant measures for chaotic maps. When studying discrete dynamical systems, the measure of a map is important in describing its behavior because it captures the statistics of long term simulations. Being invariant means that this distribution remains the same, no matter when you observe it. The main goal is to understand how to obtain these PDFs for various one-dimensional maps using alternative methods to time series data.

The methods studied in this thesis include the Z-matrix and the Frobenius-Perron Operator, which are analytic …

Boundary Behavior Of Laplace Transforms, Timothy Ferguson

Honors Theses

In this thesis, we examine the boundary behavior of Laplace transforms (as analytic functions on the right and left half planes) of certain bounded functions. The types of bounded functions we consider are Fourier transforms of measures and almost periodic functions.

On Conway's Generalization Of The 3x + 1 Problem, Robin M. Givens

Honors Theses

This thesis considers a variation of the 3x+1, or Collatz, Problem involving a function we call the Conway function. The Conway function is defined by letting C3(n)=2k for n=3k and C3(n)=4k±1 for n=3k±1, where n is an integer. The iterates of this function generate a few 'short' cycles, but the s' tructural dynamics are otherwise unknown. We investigate properties of the Conway function and other related functions. We also discuss the possibility of using the Conway function to generate keys for cryptographic use based on a fast, efficient binary implemenation of the function. Questions related to the conjectured tree-like structure …

2nd Annual Undergraduate Research Conference Abstract Book, University Of Missouri--Rolla

Undergraduate Research Conference at Missouri S&T

No abstract provided.

Hessian Matrix-Free Lagrange-Newton-Krylov-Schur-Schwarz Methods For Elliptic Inverse Problems, Widodo Samyono

Mathematics & Statistics Theses & Dissertations

This study focuses on the solution of inverse problems for elliptic systems. The inverse problem is constructed as a PDE-constrained optimization, where the cost function is the L² norm of the difference between the measured data and the predicted state variable, and the constraint is an elliptic PDE. Particular examples of the system considered in this stud, are groundwater flow and radiation transport. The inverse problems are typically ill-posed due to error in measurements of the data. Regularization methods are employed to partially alleviate this problem. The PDE-constrained optimization is formulated as the minimization of a Lagrangian functional, formed …

An Implicit Level Set Model For Firespread, Pallop Huabsomboon

Mathematics & Statistics Theses & Dissertations

The level set method is a mathematical and computational, technique for tracking a moving interface over time. It can naturally handle topological changes such as merging or breaking interfaces. Intrinsic geometric properties of the interface, such as curvature and normal direction, are easily determined from the level set function &phis;. There are many applications of the level set method, including kinetic crystal growth, epitaxial growth of thin films, image restoration, vortex dominated flows, and so forth. Most applications described in the growing literature on the applications of level sets advance the level set equation with explicit time integration. Hence, small …

Analysis Of Mass Spectrometry Data Using Bayesian Wavelet-Based Functional Mixed Models, Jeffrey S. Morris, Philip J. Brown, Keith A. Baggerly, Kevin R. Coombes

Jeffrey S. Morris

In this chapter, we demonstrate how to analyze MALDI-TOF/SELDITOF mass spectrometry data using the wavelet-based functional mixed model introduced by Morris and Carroll (2006), which generalizes the linear mixed models to the case of functional data. This approach models each spectrum as a function, and is very general, accommodating a broad class of experimental designs and allowing one to model nonparametric functional effects for various factors, which can be conditions of interest (e.g. cancer/normal) or experimental factors (blocking factors). Inference on these functional effects allows us to identify protein peaks related to various outcomes of interest, including dichotomous outcomes, categorical …

Application Of Fuzzy State Aggregation And Policy Hill Climbing To Multi-Agent Systems In Stochastic Environments, Dean C. Wardell

Theses and Dissertations

Reinforcement learning is one of the more attractive machine learning technologies, due to its unsupervised learning structure and ability to continually even as the operating environment changes. Applying this learning to multiple cooperative software agents (a multi-agent system) not only allows each individual agent to learn from its own experience, but also opens up the opportunity for the individual agents to learn from the other agents in the system, thus accelerating the rate of learning. This research presents the novel use of fuzzy state aggregation, as the means of function approximation, combined with the policy hill climbing methods of Win …

Spanning Eulerian Subgraphs In Claw-Free Graphs, Zhi-Hong Chen, Hong-Jian Lai, Weiqi Luo, Yehomg Shao

Scholarship and Professional Work - LAS

A graph is claw-free if it has no induced K 1,3, subgraph. A graph is essential 4-edge-connected if removing at most three edges, the resulting graph has at most one component having edges. In this note, we show that every essential 4-edge-connected claw free graph has a spanning Eulerian subgraph with maximum degree at most 4.

Atomic Hardy Space Theory For Unbounded Singular Integrals, Ryan Berndt

Mathematics Faculty Scholarship

No abstract provided.

Place-Valued Logics Around Cybernetic Ontology, The Bcl And Afosr, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

From Ruby To Rudy, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

The Chinese Challenge. Hallucinations For Other Futures, Rudolf Kaehr

Rudolf Kaehr

The main question is: What can we learn from China that China is not teaching us? It is proposed that a study of polycontextural logic and morphogrammatics could be helpful to discover this new kind of rationality.

Use Of Pen-Based Technology In Calculus Courses, John R. Hubbard

Department of Math & Statistics Faculty Publications

The author and his students used Tablet computers in Calculus I and Calculus II classes, providing students with dynamic digital transcripts that they could replay at their convenience. He and his students agreed that these graphic replays provide an effective alternative to the static explanations found in textbooks and in traditional course notes. Two specific examples are given in this paper.

The Formal Laplace-Borel Transform Of Fliess Operators And The Composition Product, Yaqin Li, W. Steven Gray

Electrical & Computer Engineering Faculty Publications

The formal Laplace-Borel transform of an analytic integral operator, known as a Fliess operator, is defined and developed. Then, in conjunction with the composition product over formal power series, the formal Laplace-Borel transform is shown to provide an isomorphism between the semigroup of all Fliess operators under operator composition and the semigroup of all locally convergent formal power series under the composition product. Finally, the formal Laplace-Borel transform is applied in a systems theory setting to explicitly derive the relationship between the formal Laplace transform of the input and output functions of a Fliess operator. This gives a compact interpretation …

Coalgebras And Their Logics, Alexander Kurz

Engineering Faculty Articles and Research

"Transition systems pervade much of computer science. This article outlines the beginnings of a general theory of specification languages for transition systems. More specifically, transition systems are generalised to coalgebras. Specification languages together with their proof systems, in the following called (logical or modal) calculi, are presented by the associated classes of algebras (e.g., classical propositional logic by Boolean algebras). Stone duality will be used to relate the logics and their coalgebraic semantics."

Interdependency Of Pharmacokinetic Parameters: A Chicken-And-Egg Problem? Not!, Reza Mehvar

Pharmacy Faculty Articles and Research

Pharmacokinetic (PK) software packages are widely used by scientists in different disciplines to estimate PK parameters. However, their use without a clear understanding of physiological parameters affecting the PK parameters and how different PK parameters are related to each other may result in erroneous interpretation of data. Often, mathematical relationships used for the estimation of PK parameters obscure the true physiological relationships among these parameters, prompting a discussion of which parameter came first and giving the appearance of the-chicken-and-the-egg dilemma. In this article, the author attempts to show how different PK parameters are related to physiological parameters and each other …

The Chang-Los-Suszko Theorem In A Topological Setting, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

The Chang-Łoś-Suszko theorem of first-order model theory characterizes universal-existential classes of models as just those elementary classes that are closed under unions of chains. This theorem can then be used to equate two model-theoretic closure conditions for elementary classes; namely unions of chains and existential substructures. In the present paper we prove a topological analogue and indicate some applications.

Specific Antibodies To Recombinant Allergens Of Aspergillus Fumigatus In Cystic Fibrosis Patients With Abpa, Viswanath P. Kurup, Alan P. Knutsen, Richard B. Moss, Naveen K. Bansal

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background

Aspergillus fumigatus, a widely distributed fungus, has been implicated in causing life threatening infections as well as severe asthma and allergic diseases in man. Allergic affliction like allergic bronchopulmonary aspergillosis (ABPA) is a disabling lung disease frequently seen in patients with asthma and cystic fibrosis. Immunodiagnosis of the former is comparatively easier due to the availability of purified antigens and sensitive methods. However, this is not true with cystic fibrosis patients where the prevalence of ABPA is fairly high and the morbidity and mortality are significant.

Methods

In the present study, we have evaluated purified recombinant allergens from …

Spanning Trails Containing Given Edges, Weiqi Luo, Zhi-Hong Chen, Wei-Guo Chen

Scholarship and Professional Work - LAS

A graph G is Eulerian-connected if for any u and v in V ( G ) , G has a spanning ( u , v ) -trail. A graph G is edge-Eulerian-connected if for any e ′ and e ″ in E ( G ) , G has a spanning ( e ′ , e ″ ) -trail. For an integer r ⩾ 0 , a graph is called r -Eulerian-connected if for any X ⊆ E ( G ) with | X | ⩽ r , and for any u , v ∈ V ( G ) , G …

The Tablet Pc For Faculty: A Pilot Project, Rob Weitz, Bert Wachsmuth, Danielle Mirliss

Bert Wachsmuth

This paper describes a pilot project with the purpose of evaluating the usefulness of tablet PCs for university professors. The focus is on the value of tablets primarily with respect to teaching and learning (and not for research or administrative work). Sixty-four professors, distributed across the various schools of a university, were provided with tablet PCs and were trained in their use.