Mathematics Commons^™

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 Classical Dirichlet Space, William T. Ross

Department of Math & Statistics Faculty Publications

In this survey paper, we will present a selection of results concerning the class of analytic functions f on the open unit disk D := {z ϵ C : │z│ < 1} which have finite Dirichlet integral.

Temporal Processing In The Exponential Integrate-And-Fire Model Is Nonlinear, Joanna R. Wares, Todd W. Troyer

Department of Math & Statistics Faculty Publications

The exponential integrate-and-fire (EIF) model was introduced by Fourcaud-Trocme et al. (2003) as an extension of the standard leaky integrate-and-fire model (LIF). Here, the nonlinearity in the EIF model’s temporal response to square-wave inputs is investigated. Comparing the time course of onset and offset responses revealed that offset responses have a steeper initial slope, but a slower approach to equilibrium. A linear systems analysis performed for these square-wave inputs indicates that at frequencies above ~40 Hz, gain was slightly smaller for square-wave inputs, but phase did not change significantly relative to simulations in which the corresponding sinusoids were presented in …

[Introduction To] The Cauchy Transform, William T. Ross, Joseph A. Cima, Alec L. Matheson

Bookshelf

The Cauchy transform of a measure on the circle is a subject of both classical and current interest with a sizable literature. This book is a thorough, well-documented, and readable survey of this literature and includes full proofs of the main results of the subject. This book also covers more recent perturbation theory as covered by Clark, Poltoratski, and Aleksandrov and contains an in-depth treatment of Clark measures.

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, …

Improving Pro Forma Analysis Through Better Terminal Value Estimates, Tom Arnold, David S. North, Roy A. Wiggins

Finance Faculty Publications

Basic pro forma analysis often estimates the terminal value input using a simple growing perpetuity assumption. While this assumption is easy to implement, it potentially creates an upward bias in some inputs leading to lower firm or project value outputs. The purpose of this paper is to demonstrate a more accurate way to estimate the terminal value input. Further, by allowing for multiple sales growth rates and by not restricting other input variables to necessarily grow at these same rates, a more accurate, flexible, compact, and thorough analysis is possible.

Relative Difference Sets In 2-Groups : A Group Cohomological Viewpoint, Brian Wyman

Honors Theses

No abstract provided.

Ecological Niching In An Interactive Simulation, Ryan T. Webb

Honors Theses

Our goal is to create a simulation platform for the study of ecological niching that can be extended to suit the needs of biological research. Ecological niching and the accompanying evolutionary process of speciation are difficult to observe in situ, which makes them prime candidates for study via the methods of computer simulation. To this end, we have created an interactive, real-time ecosystem simulation based on the standard predator/prey interaction model, in which interacting populations of organisms exhibit swarming behavior. We hope to provide the basic simulation components necessary to bring about niching and speciation, that may be extended for …

An Excel Application For Valuing European Options With Monte Carlo Analysis, Tom Arnold, Stephen C. Henry

Finance Faculty Publications

By developing the basic intuition of how Monte Carlo simulation works within an Excel spreadsheet framework, this paper allows the undergraduate student to use Monte Carlo simulation techniques to price European style options without additional sophisticated software. Further, the skills and intuition developed provide the basis for much more complex simulation techniques.

The Backward Shift On HP, William T. Ross

Department of Math & Statistics Faculty Publications

In this semi-expository paper, we examine the backward shift operator

Bf := (f-f(0)/z

on the classical Hardy space H^p. Through there are many aspects of this operator worthy of study [20], we will focus on the description of its invariant subspaces by which we mean the closed linear manifolds Ɛ ⊂ H^p for which BƐ ⊂ Ɛ. When 1 < p < ∞, a seminal paper of Douglas, Shapiro, and Shields [8] describes these invariant subspaces by using the important concept of a pseudocontinuation developed earlier by Shapiro [26]. When p = 1, the description is the same [1] except that in the proof, one must be mindful of some technical considerations involving the functions of bounded mean oscillation.

Estimating Load-Sharing Properties In A Dynamic Reliability System, Paul H. Kvam, Edsel A. Peña

Department of Math & Statistics Faculty Publications

An estimator for the load-share parameters in an equal load-share model is derived based on observing k-component parallel systems of identical components that have a continuous distribution function F (˙) and failure rate r (˙). In an equal load-share model, after the first of k components fails, failure rates for the remaining components change from r (t) to γ1r (t), then to γ2r (t) after the next failure, and so on. On the basis of observations on n independent and identical systems, a semiparametric estimator of the component baseline …

Factorization Of Polynomials And Real Analytic Function, Radoslaw L. Stefanski

Honors Theses

In this project, we address the question: When can a polynomial p(x, y) of two variables be factored as p(x, y) = f(x)g(y), where f and g are polynomials of one variable. We answer this question, using linear algebra, and create a Mathematica program which carries out this factorization. For example,

3+3x-5x^3+y+xy-5/3x^3y+y^2+xy^2-5/3x^3y^2 = (1+x-5/3x^3)(3+y+y^2)

We then generalize this concept and ask: When can p(x,y) can be written as

p(x,y) = f1(x)g2(y)+f2(x)g2(y)+...+fr(x)gr(y)

where fj,gj are polynomials. This can certainly be done (for large enough r). Which is the minimum such r? Again, we have a Mathematica program which carries out this …

Discovering The Potential For Advancements In Intrusion Detection Systems, Kenneth J. Buonforte

Honors Theses

An intrusion detection system (IDS) is a collection of monitors strategically placed on a network or individual host in order to detect anomalous behavior. Since James Anderson introduced one of the first frameworks for an intrusion detection system in [1]. researchers have extended the capabilities of these systems. IDSs take many forms, from systems as basic as command line audit logs to those that emulate the defense mechanisms of the human immune system. However, as intrusion detection has evolved, scientists and administrators alike are beginning to question the need for this technology due to its lack of quantifiable performance and …

Securing Distributed Computations : In Search Of Reliable Large-Scale Compute Power And Refreshed Redundancy, Edward P. Kenney

Honors Theses

The Internet may be the single largest technological advance or significant societal change in the last century. Not only does it allow access to more information than any human could ever hope to digest, but it produces the potential of having millions of computers combining their computational forces for the betterment of a single cause .. Tl is is the fundamental goal of distributed computing. A distributed system is defined to be a network of machines with some degree of centralized direction. In a distributed computational system each machine will accept computational tasks from a supervisor in a master-slave relationship. …

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 …

Zeros Of Functions With Finite Dirichlet Integral, William T. Ross, Stefan Richter, Carl Sundberg

Department of Math & Statistics Faculty Publications

In this paper, we refine a result of Nagel, Rudin, and Shapiro (1982) concerning the zeros of holomorphic functions on the unit disk with finite Dirichlet integral.

Tree-Like Continua And 2-To-1 Maps, Jo Heath, Van C. Nall

Department of Math & Statistics Faculty Publications

It is not known if there is a 2-to-1 map from a continuum onto a tree-like continuum. In fact, it is not known if there is a 2-to-1 map onto a hereditarily decomposable tree-like continuum. We show that the domain of such a map would have to contain an indecomposable continuum.

Prolongations And Cyclic Vectors, William T. Ross, Harold S. Shapiro

Department of Math & Statistics Faculty Publications

For functions belonging to invariant subspaces of the backward shift operator Bf = (f − f(0))/z on spaces of analytic functions on the unit disk D, we explore, in a systematic way, the continuation properties of these functions.

The Backward Shift On The Space Of Chauchy Transforms, William T. Ross, Joseph A. Cima, Alec L. Matheson

Department of Math & Statistics Faculty Publications

This note examines the subspaces of the space of Cauchy transforms of measures on the unit circle that are invariant under the backward shift operator f --> z^-1 (f—f (0)). We examine this question when the space of Cauchy transforms is endowed with both the norm and weak* topologies.

Common Cyclic Vectors For Normal Operators, William T. Ross, Warren R. Wogen

Department of Math & Statistics Faculty Publications

If μis a finite compactly supported measure on C, then the set S_μ of multiplication operators Mᵩ : L² (μ) --> L² (μ), Mᵩ f = ᵩ f, where ᵩ ϵ L ∞ (μ) is injective on a set of full μ measure, is the complete set of cyclic multiplication operators on L² (μ) In this paper, we explore the question as to whether or not S_μ has a common cyclic vector

[Introduction To] Schaum's Outline Of Programming With Java, John R. Hubbard

Bookshelf

Tough Test Questions? Missed Lectures? Not Enough Time?

Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

This Schaum's Outline gives you

• Practice problems with full explanations that reinforce knowledge
• Coverage of the most up-to-date developments in your course field
• In-depth review of practices …

[Introduction To] Data Structures With Java, John R. Hubbard, Anita Huray

Bookshelf

For a freshman/sophomore-level course in Data Structures in Computer Science. This text teaches the use of direct source code implementations and the use of the Java libraries; it helps students prepare for later work on larger Java software solutions by adhering to software engineering principles and techniques such as the UML and the Java Collections Framework (JCF). Using the spiral approach to cover such topics as linked structures, recursion, and algorithm analysis, this text also provides revealing illustrations, summaries, review questions, and specialized reference sections.

Determining Error Bars In Measurements Of Ultrashort Laser Pulses, Ziyang Wang, Erik Zeek, Rick Trebino, Paul Kvam

Department of Math & Statistics Faculty Publications

We present a simple and automatic method for determining the uncertainty in the retrieved intensity and phase versus time (and frequency) due to noise in a frequency-resolved optical-gating trace, independent of noise source. It uses the ‘‘bootstrap’’ statistical method and also yields an automated method for phase blanking (omitting the phase when the intensity is too low to determine it).

A Contrast-Based Neural Control System For Ant Navigation, Joanna R. Wares, Predrag-Peter Ilich, Daniel P. Dougherty

Department of Math & Statistics Faculty Publications

A mathematical model for a neural control system of ant locomotion was developed. Contrast-based detectors using excitation and inhibition were tuned to specific contrast orientations. A control system using multiple orientation contrast detectors was then developed and optimized for a model ant, which could move via a biased random walk. The system allowed sufficient control to guide the ant through various mazes.

Advanced Portfolio Theory: Why Understanding The Math Matters, Tom Arnold

Finance Faculty Publications

The goal of this paper is to motivate the use of efficient set mathematics for portfolio analysis [as seen in Roll, 1977] in the classroom. Many treatments stop at the two asset portfolio case (avoiding the use of matrix algebra) and an alarming number of treatments rely on illustration and templates to provide a heuristic sense of the material without really teaching how efficient portfolios are generated. This is problematic considering that the benefits of understanding efficient set mathematics go beyond portfolio analysis and into such topics as regression analysis (as demonstrated here).

Self-Similarity In Network Traffic, Francisco Chinchilla

Honors Theses

It is critical to properly understand the nature of network traffic in order to effectively design models describing network behavior. These models are usually used to simulate network traffic, which in turn are used to construct congestion control techniques, perform capacity planning studies, and/or evaluate the behavior of new protocols. Using the wrong models could lead to potentially serious problems such as delayed packet transmissions or an increase in packet drop rates.

Traditionally, packet arrivals were assumed to follow a Poisson arrival process. Although Poisson processes have several properties that make them easy to work with, they do not accurately …

Nonparametric Estimation Of A Distribution Subject To A Stochastic Precedence Constraint, Miguel A. Arcones, Paul H. Kvam, Francisco J. Samaniego

Department of Math & Statistics Faculty Publications

For any two random variables X and Y with distributions F and G defined on [0,∞), X is said to stochastically precede Y if P(X≤Y) ≥ 1/2. For independent X and Y, stochastic precedence (denoted by X≤_spY) is equivalent to E[G(X–)] ≤ 1/2. The applicability of stochastic precedence in various statistical contexts, including reliability modeling, tests for distributional equality versus various alternatives, and the relative performance of comparable tolerance bounds, is discussed. The problem of estimating the underlying distribution(s) of experimental data under the assumption that they obey a …

Common Cause Failure Prediction Using Data Mapping, Paul H. Kvam, J. Glenn Miller

Department of Math & Statistics Faculty Publications

To estimate power plant reliability, a probabilistic safety assessment might combine failure data from various sites. Because dependent failures are a critical concern in the nuclear industry, combining failure data from component groups of different sizes is a challenging problem. One procedure, called data mapping, translates failure data across component group sizes. This includes common cause failures, which are simultaneous failure events of two or more components in a group. In this paper, we present methods for predicting future plant reliability using mapped common cause failure data. The prediction technique is motivated by discrete failure data from emergency diesel generators …

[Introduction To] Generalized Analytic Continuation, William T. Ross, Harold S. Shapiro

Bookshelf

The theory of generalized analytic continuation studies continuations of meromorphic functions in situations where traditional theory says there is a natural boundary. This broader theory touches on a remarkable array of topics in classical analysis, as described in the book. This book addresses the following questions: (1) When can we say, in some reasonable way, that component functions of a meromorphic function on a disconnected domain, are "continuations" of each other? (2) What role do such "continuations" play in certain aspects of approximation theory and operator theory? The authors use the strong analogy with the summability of divergent series …