Computer Sciences Commons^™

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.

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 …

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 …

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 …

Atomic Hardy Space Theory For Unbounded Singular Integrals, Ryan Berndt

Mathematics Faculty Scholarship

No abstract provided.

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 …

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.

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 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 …

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.

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 …

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.

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."

The Stochastic Dance Of Early Hiv Infection, Stephen J. Merrill

Mathematics, Statistics and Computer Science Faculty Research and Publications

The stochastic nature of early HIV infection is described in a series of models, each of which captures aspects of the dance of HIV during the early stages of infection. It is to this highly variable target that the immune response must respond. The adaptability of the various components of the immune response is an important aspect of the system's operation, as the nature of the pathogens that the response will be required to respond to and the order in which those responses must be made cannot be known beforehand. As HIV infection has direct influence over cells responsible for …

Self-Adaptive Scheduler Parameterization, Barry Lawson, Evgenia Smirni

Department of Math & Statistics Technical Report Series

High-end parallel systems present a tremendous research challenge on how to best allocate their resources to match dynamic workload characteristics and user habits that are often unique to each system. Although thoroughly investigated, job scheduling for production systems remains an inexact science, requiring significant experience and intuition from system administrators to properly configure batch schedulers. State-of-the-art schedulers provide many parameters for their configuration, but tuning these to optimize performance and to appropriately respond to the continuously varying characteristics of the workloads can be very difficult — the effects of different parameters and their interactions are often unintuitive.

In this paper, …

Application Of Information-Theoretic Data Mining Techniques In A National Ambulatory Practice Outcomes Research Network, Adam Wright, Thomas N. Ricciardi, Martin Zwick

Complex Systems Faculty Publications and Presentations

The Medical Quality Improvement Consortium data warehouse contains de-identified data on more than 3.6 million patients including their problem lists, test results, procedures and medication lists. This study uses reconstructability analysis, an information-theoretic data mining technique, on the MQIC data warehouse to empirically identify risk factors for various complications of diabetes including myocardial infarction and microalbuminuria. The risk factors identified match those risk factors identified in the literature, demonstrating the utility of the MQIC data warehouse for outcomes research, and RA as a technique for mining clinical data warehouses.

A Survey On Intrusion Detection Approaches, A Murali M. Rao

International Conference on Information and Communication Technologies

Intrusion detection plays one of the key roles in computer security techniques and is one of the prime areas of research. Usages of computer network services are tremendously increasing day by day and at the same time intruders are also playing a major role to deny network services, compromising the crucial services for Email, FTP and Web. Realizing the importance of the problem due to intrusions, many researchers have taken up research in this area and have proposed several solutions. It has come to a stage to take a stock of the research results and project a comprehensive view so …

Specific Ige Response To Purified And Recombinant Allergens In Latex Allergy, Viswanath P. Kurup, Gordon L. Sussman, Hoong Y. Yeang, Nancy Elms, Heimo Breiteneder, Siti Am Arif, Kevin J. Kelly, Naveen K. Bansal, Jordan N. Fink

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background

In recent years, allergy to natural rubber latex has emerged as a major allergy among certain occupational groups and patients with underlying diseases. The sensitization and development of latex allergy has been attributed to exposure to products containing residual latex proteins. Although improved manufacturing procedures resulted in a considerable reduction of new cases, the potential risk for some patient groups is still great. In addition the prevalent cross-reactivity of latex proteins with other food allergens poses a major concern. A number of purified allergens and a few commercial kits are currently available, but no concerted effort was undertaken to …

Object Information Repository In A Christian Theory Of Technology, Longy O. Anyanwu

ACMS Conference Proceedings 2005

It has not been easy to formulate a stable Christian theory of technology. Nonetheless, some ideas and Christian theories of technology have been fielded by a handful of distinguished Christian scientists and technology experts. Although some of these ideas and theories are substantively at variance, others have sizeable common base. Important, though, is the seeming agreement on the visualization of technology as an object with embedded values and information. With object information repository as the primary focus, this study, therefore, attempts to provoke the consideration of a possible synthesis and agreement on the foundational essence of Christian theory of technology …

The Five Orders Of Ignorance: Knowledge, Ignorance, And The Nature Of Software, Phillip Armour

ACMS Conference Proceedings 2005

Software is not a product, it is a medium in which we store knowledge. As simple as this idea seems, the consequences of it are quite significant. If software is not a product, then software development is not a product of production activity, despite the common practice of managing it as such. Most organizations believe that job of software developers is to build a system that we then ship to a customer. It is not. The system we build and ship to the customer is actually the by-product of the real activity which is learning. Software development is the activity …

Mathematics As Poesis: A Preliminary Project Report, Sam Stueckle, Jeremy Case, Ken Constantine, Troy Riggs

ACMS Conference Proceedings 2005

This paper talks about the various viewpoints of mathematics, beginning with classical perspectives and ending with the idea of poesis, or the theology of math as the art of making.

Integrating Catholic And Marianist Historical Perspectives In A Mathematics Coruse For Elementary Education Majors, Mary Wagner-Krankel

ACMS Conference Proceedings 2005

St. Mary's University in San Antonio recently reaffirmed their distinctive nature as a Catholic university promoting the Marianist tradition. This new affirmation is in response to the smaller number of Marianists serving in teaching and administrative positions on campus. Faculty have been encouraged to explore new ways to integrate Catholic and Marianist values and historical perspectives in their teaching and research. I will discuss some major Catholic mathematicians and some classroom activities that I developed for the course MT3304- Mathematics for the Elementary Teacher.

Does The Success Of Mathematics Defeat Naturalism?, Russell W. Howell

ACMS Conference Proceedings 2005

This paper discusses the arguments for and against Intelligent Design from the perspectives of mathematics.

The Artificial Gravity Pitch, Andrew Simoson

ACMS Conference Proceedings 2005

Toss a ball into the air; we analyze and contrast the resultant trajectories when standing both on the Little Prince’s Asteroid B-612 of 1943 and in Arthur C. Clark’s rotating space ship Discovery of 2001.

Explicit Null Space Of Discrete Laplacian, Hanna Vanderzee

ACMS Conference Proceedings 2005

For a given partial differential equation, such as Poisson’s equation in two dimensions, stipulating the null-space component of the solution is sometimes a useful alternative to specifying boundary conditions in order to determine a unique solution. To implement this approach computationally, we need a sparse and well-conditioned representation of the null space of the relevant differential operator. We discuss how the null-space method works and present an explicit formula for generating a sparse null basis for a uniform, finite-difference discretization of Laplacian operator on the unit square. The formula makes use of a triangular array which has the large Schroeder …

Artificial Intelligence: Can We Create Machines In Our Own Image?, Derek C. Shuurman

ACMS Conference Proceedings 2005

The field of Artificial Intelligence (AI) leads to many questions about what it means to be human. Some researchers claim that inevitably computers will reach a certain threshold of complexity that will enable them to “think” and artificial consciousness will emerge. This speculation, taken a step further, leads some to believe that computer technology will eventually set humans free from the frailty of their bodies and enable them to achieve immortality. Underlying these claims is a reductionistic philosophy about what it means to be human and how one approaches the mind-body problem. Ever since the fall people have wanted to …

Integration Of Faith, Learning, And Christian Vocation With First-Year Mathematics Majors, Doug Phillippy, Angela Hare

ACMS Conference Proceedings 2005

The mission of Messiah College is "to educate men and women toward maturity of intellect, character, and Christian faith, in preparation for lives of service, leadership and reconciliation in church and society". Therefore, as faculty in the Mathematical Sciences Department at this college, how we build maturity in our students, not only a mature mathematical intellect, but also maturity of character and Christian faith, reflects our commitment to the mission of the College. Further, our departmental mission statement includes the objective "to challenge students to live out their faith in their vocation as they become servant leaders in society, church, …

Writing Math Lessons That Integrate Christian Beliefs: The Kuyers Institute Grant Project, Dave Klanderman, Gary Talsma

ACMS Conference Proceedings 2005

In this paper, we describe multiple math lessons designed to incorporate a Christian perspective. A total of nine lessons, some with materials for multiple class sessions, will soon be published by the Kuyers Institute. These lessons are appropriate for use at the middle school and high school level.

A Christian Constructivist? The Impact Of Worldview On Learning Theories And The Mathematics Education Research Community, Jeffrey Barrett, Dave Klanderman

ACMS Conference Proceedings 2005

This paper analyzes the role of worldview and its impact on learning theories within the mathematics education research community. The authors propose a scholarly agenda for engaging this issue in future research projects.