Physical Sciences and Mathematics Commons^™

Using A Digital Library Of Images For Communication: Comparison Of A Card-Based System To Pda Software, Trudi Miller '08, Gondy Leroy, John Huang '05, Serena Chuang '05

CGU Faculty Publications and Research

Autism spectrum disorder has become one of the most prevalent developmental disorders and one of the main impairments is difficulty with communication. One method of augmentative and alternative communication is the use of the Picture Exchange Communication System (PECS) to create messages using a series of images printed on cards and organized in binders. We are developing a digital alternative based on an image library that is displayed on a personal digital assistant (PDA). We conducted an initial user acceptance study that compared the effectiveness and usability of both systems. The study showed that the PDA system was able to …

Reporting On-Campus Crime Online: User Intention To Use, Gondy A. Leroy, Alicia Iriberri '06, Nathan Garrett

CGU Faculty Publications and Research

National surveys demonstrate that millions of crimes go unreported in the United States. Several reasons may contribute to this lack of reporting and we are investigating these potential reasons and how they may be addressed. We are developing an online system that provides an anonymous and secure mechanism for both victims and witnesses to report crimes to police. The system is being implemented and tested on a university campus. Potential users (i.e., students, staff) were surveyed to determine their intent to use the system. Respondents claimed to report crimes already, which is in contrast with the findings from the national …

Dynamic Generation Of A Table Of Contents With Consumer-Friendly Labels, Trudi Miller '08, Gondy Leroy, Elizabeth Wood

CGU Faculty Publications and Research

Consumers increasingly look to the Internet for health information, but available resources are too difficult for the majority to understand. Interactive tables of contents (TOC) can help consumers access health information by providing an easy to understand structure. Using natural language processing and the Unified Medical Language System (UMLS), we have automatically generated TOCs for consumer health information. The TOC are categorized according to consumer-friendly labels for the UMLS semantic types and semantic groups. Categorizing phrases by semantic types is significantly more correct and relevant. Greater correctness and relevance was achieved with documents that are difficult to read than with …

Health Information Text Characteristics, Gondy Leroy, Evren Eryilmaz '11, Benjamin T. Laroya

CGU Faculty Publications and Research

Millions of people search online for medical text, but these texts are often too complicated to understand. Readability evaluations are mostly based on surface metrics such as character or words counts and sentence syntax, but content is ignored. We compared four types of documents, easy and difficult WebMD documents, patient blogs, and patient educational material, for surface and content-based metrics. The documents differed significantly in reading grade levels and vocabulary used. WebMD pages with high readability also used terminology that was more consumer-friendly. Moreover, difficult documents are harder to understand due to their grammar and word choice and because they …

Complex Symmetric Operators And Applications, Stephan Ramon Garcia, Mihai Putinar

Pomona Faculty Publications and Research

We study a few classes of Hilbert space operators whose matrix representations are complex symmetric with respect to a preferred orthonormal basis. The existence of this additional symmetry has notable implications and, in particular, it explains from a unifying point of view some classical results. We explore applications of this symmetry to Jordan canonical models, self-adjoint extensions of symmetric operators, rank-one unitary perturbations of the compressed shift, Darlington synthesis and matrix-valued inner functions, and free bounded analytic interpolation in the disk.

Review: Stability Of Bases And Frames Of Reproducing Kernels In Model Spaces, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Analyzing Dna Microarrays With Undergraduate Statisticians, Johanna S. Hardin, Laura Hoopes, Ryan Murphy '06

Pomona Faculty Publications and Research

With advances in technology, biologists have been saddled with high dimensional data that need modern statistical methodology for analysis. DNA microarrays are able to simultaneously measure thousands of genes (and the activity of those genes) in a single sample. Biologists use microarrays to trace connections between pathways or to identify all genes that respond to a signal. The statistical tools we usually teach our undergraduates are inadequate for analyzing thousands of measurements on tens of samples. The project materials include readings on microarrays as well as computer lab activities. The topics covered include image analysis, filtering and normalization techniques, and …

Conjugation And Clark Operators, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Yeast Through The Ages: A Statistical Analysis Of Genetic Changes In Aging Yeast, Alison Wise '05, Johanna S. Hardin, Laura Hoopes

Pomona Faculty Publications and Research

Microarray technology allows for the expression levels of thousands of genes in a cell to be measured simultaneously. The technology provides great potential in the fields of biology and medicine, as the analysis of data obtained from microarray experiments gives insight into the roles of specific genes and the associated changes across experimental conditions (e.g., aging, mutation, radiation therapy, drug dosage). The application of statistical tools to microarray data can help make sense of the experiment and thereby advance genetic, biological, and medical research. Likewise, microarrays provide an exciting means through which to explore statistical techniques.

Intrinsic Linking And Knotting Of Graphs In Arbitrary 3–Manifolds, Erica Flapan, Hugh Howards, Don Lawrence, Blake Mellor

Pomona Faculty Publications and Research

We prove that a graph is intrinsically linked in an arbitrary 3–manifold M if and only if it is intrinsically linked in S³. Also, assuming the Poincaré Conjecture, we prove that a graph is intrinsically knotted in M if and only if it is intrinsically knotted in S³.

Super Solutions Of The Dynamical Yang-Baxter Equation, Gizem Karaali

Pomona Faculty Publications and Research

Solutions of the classical dynamical Yang-Baxter equation on a Lie superalgebra are called super dynamical r−matrices. A super dynamical r−matrix r satisfies the zero weight condition if

[h ⊗ 1 + 1 ⊗ h, r(λ)] = 0 for all h ∈ ɧ, λ ∈ ɧ ∗ .

In this paper we classify super dynamical r−matrices with zero weight.

What I Learned At The Maa Digital Library Workshop, Gizem Karaali

Pomona Faculty Publications and Research

Toward the end of July 2006, an item appeared briefly on the MAA website. This was the call for participants for the MAA Digital Library Workshop. Curious surfers like me clicked on it to find the description of this workshop, which was to be held over the course of a weekend in October 2006 in Washington, DC. The announcement included a cryptic sentence of the form “The primary aims of the workshop are to provide an overview of the two MAA digital libraries and of the National Science Digital Library, and to prepare participants to offer a short workshop on …

Sustainability Reporting At Higher Education Institutions, Robert Heilmayr

CMC Senior Theses

Multiple declarations, governmental and non-profit organizations and universities have issued a call for proper reporting of social and environmental impacts and initiatives within academia. Such reporting can increase awareness of environmental and social impacts, encourage development of sustainable policy and build a campus culture more committed to sustainability. Sustainability reporting at Higher Education Institutions (HEIs) has the added benefit of being a powerful teaching aid. This paper follows multiple lines of inquiry in order to determine whether HEIs are taking advantage of the opportunities afforded by sustainability reporting. The analysis evaluates the history of sustainability reporting at HEIs and compares …

Growing A Better Food System: An Analysis Of The Impact Of California School Gardens On The Sustainable Food And Food Security Movements, Michael Press

Pomona Senior Theses

In recent decades, environmental problems associated with conventional agriculture, children’s nutrition, and concern over the adequacy of the current food supply have led to the emergence of the sustainable food and food security movements. These issues have also inspired the state of California to pass legislation to place a garden in every school in the state. This thesis analyzes the accuracy of this policy’s implementation and its effects on the sustainable food and food security movements. Research found that the loss of state funding for this policy and the administrative, logistical, and informational barriers to establishing garden education programs has …

Looking Beyond The Curriculum In Jamaica, Jon T. Jacobsen, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

In August 2004, we had the opportunity to travel to Jamaica to lead a pilot workshop for Jamaican high school math teachers. The workshop focused on the importance of mathematical context in the teaching of mathematics. It was sponsored by the Gibraltar Institute, a Jamaica-based nongovernmental organization led by Trevor Campbell (Pomona College) and Reginald Nugent (Cal State Pomona), Jamaica’s College of Agriculture, Science and Education, and Harvey Mudd College.

Pythagorean Primes And Palindromic Continued Fractions, Arthur T. Benjamin, Doron Zeilberger

All HMC Faculty Publications and Research

In this note, we prove that every prime of the form 4m + 1 is the sum of the squares of two positive integers in a unique way. Our proof is based on elementary combinatorial properties of continued fractions. It uses an idea by Henry J. S. Smith ([3], [5], and [6]) most recently described in [4] (which provides a new proof of uniqueness and reprints Smith's paper in the original Latin). Smith's proof makes heavy use of nontrivial properties of determinants. Our purely combinatorial proof is self-contained and elementary.

Recounting The Odds Of An Even Derangement, Arthur T. Benjamin, Curtis D. Bennet, Florence Newberger

All HMC Faculty Publications and Research

No abstract provided in this article.

Fibonacci Determinants — A Combinatorial Approach, Arthur T. Benjamin, Naiomi T. Cameron, Jennifer J. Quinn

All HMC Faculty Publications and Research

In this paper, we provide combinatorial interpretations for some determinantal identities involving Fibonacci numbers. We use the method due to Lindström-Gessel-Viennot in which we count nonintersecting n-routes in carefully chosen digraphs in order to gain insight into the nature of some well-known determinantal identities while allowing room to generalize and discover new ones.

Grid-Enabling A Vibroacoustic Analysis Application, Brian Bentow, Jon Dodge, Aaron Homer, Christopher D. Moore, Robert M. Keller, Matthew T. Presley, Robert Davis, Jorge Seidel, Craig Lee, Joseph Betser

All HMC Faculty Publications and Research

This paper describes the process of grid-enabling a vibroacoustic analysis application using the Globus Toolkit 3.2.1. This is the first step in a project intended to grid-enable a suite of tools being developed as a service-oriented architecture for spacecraft telemetry analysis. Many of the applications in the suite are compute intensive and would benefit from significantly improved performance. In this paper we show the advantage of using Globus to grid-enable a single tool in a vibroacoustic analysis flow, with the result that using as few as eleven nodes, that tool’s runtime improved by a factor of eight. While communication overhead …

Using Ultrasonic Atomization To Produce An Aerosol Of Micron-Scale Particles, Thomas D. Donnelly, J. Hogan '03, A. Mugler '04, M. Schubmehl '02, N. Schommer '04, Andrew J. Bernoff, S. Dasnurkar, T. Ditmire

All HMC Faculty Publications and Research

A device that uses ultrasonic atomization of a liquid to produce an aerosol of micron-scale droplets is described. This device represents a new approach to producing targets relevant to laser-driven fusion studies, and to rare studies of nonlinear optics in which wavelength-scale targets are irradiated. The device has also made possible tests of fluid dynamics models in a novel phase space. The distribution of droplet sizes produced by the device and the threshold power required for droplet production are shown to follow scaling laws predicted by fluid dynamics.

Proof Without Words: Alternating Sums Of Odd Numbers, Arthur T. Benjamin

All HMC Faculty Publications and Research

Proof for alternating sums of odd numbers in two figures.

Q.954 And A.954, Quickie Problem And Solution, Arthur T. Benjamin, Michel Bataille

All HMC Faculty Publications and Research

Problem and proof proposed by authors.

Another proof, using lattice paths, can be found in Robert A. Sulanke's article, Objects Counted by the Central Delannoy Numbers, The Journal of Integer Sequences, Vol 6, 2003. A proof by polynomials is in Michel Bataille's paper Some Identities about an Old Combinatorial Sum, The Mathematical Gazette, March 2003, pp. 144-8. A slight change in the above proof leads to m ≥ n, a generalization proved by Li Zhou using lattice paths in The Mathematical Gazette.

A Constructive Proof Of Ky Fan's Generalization Of Tucker's Lemma, Timothy Prescott '02, Francis E. Su

All HMC Faculty Publications and Research

We present a proof of Ky Fan's combinatorial lemma on labellings of triangulated spheres that differs from earlier proofs in that it is constructive. We slightly generalize the hypotheses of Fan's lemma to allow for triangulations of Sⁿ that contain a flag of hemispheres. As a consequence, we can obtain a constructive proof of Tucker's lemma that holds for a more general class of triangulations than the usual version.

Upper Estimates For The Energy Of Solutions Of Nonhomogeneous Boundary Value Problems, Alfonso Castro, Mónica Clapp

All HMC Faculty Publications and Research

We establish upper bounds for the energy of critical levels of the functional associated to a perturbed superlinear elliptic boundary value problem. We show that the perturbed problem satisfies the estimates obtained by Bahri and Lions (1988) for the symmetric problem. We use these estimates to prove the existence of nonradial solutions to a radial elliptic boundary value problem. Our results fill a gap in an earlier paper by Aduén and Castro.

Effects Of Information And Machine Learning Algorithms On Word Sense Disambiguation With Small Datasets, Gondy Leroy, Thomas C. Rindflesch

CGU Faculty Publications and Research

Current approaches to word sense disambiguation use (and often combine) various machine learning techniques. Most refer to characteristics of the ambiguity and its surrounding words and are based on thousands of examples. Unfortunately, developing large training sets is burdensome, and in response to this challenge, we investigate the use of symbolic knowledge for small datasets. A naïve Bayes classifier was trained for 15 words with 100 examples for each. Unified Medical Language System (UMLS) semantic types assigned to concepts found in the sentence and relationships between these semantic types form the knowledge base. The most frequent sense of a word …

Two-Dimensional Self-Assembly In Diblock Copolymers, Anette E. Hosoi, Dmitriy Kogan '03, Caitlin E. Devereaux '02, Andrew J. Bernoff, Shenda M. Baker

All HMC Faculty Publications and Research

Diblock copolymers confined to a two-dimensional surface may produce uniform features of macromolecular dimensions (∼10–100  nm). We present a mathematical model for nanoscale pattern formation in such polymers that captures the dynamic evolution of a solution of poly(styrene)-b-poly(ethylene oxide), PS-b-PEO, in solvent at an air-water interface. The model has no fitting parameters and incorporates the effects of surface tension gradients, entanglement or vitrification, and diffusion. The resultant morphologies are quantitatively compared with experimental data.

Harmonic Generation In Thin Films And Multilayers, William S. Kolthammer '04, Dustin Barnard '03, Nicole Carson, Aaron D. Edens '00, Nathan A. Miller '01, Peter N. Saeta

All HMC Faculty Publications and Research

A general method for computing harmonic generation in reflection and transmission from planar nonmagnetic multilayer structures is described. The method assumes plane waves and treats harmonic generation in the parametric approximation. The method is applied in studying the second- and third-harmonic generation properties of thin crystal silicon layers surrounded by thermal oxide. Most independent components of the nonlinear susceptibility tensor have unique signatures with silicon layer thickness d, allowing their strength to be determined in principle by measuring harmonic generation as a function of d. Surface and bulk contributions to third-harmonic generation are cleanly distinguished, with the bulk signal dominating. …

Some Effective Diophantine Results Over Q-Bar, Lenny Fukshansky

CMC Faculty Publications and Research

In his 1999 paper D. W. Masser talks about effective search bounds for polynomial equations over integers and rationals. This discussion can also be extended over number fields. Unfortunately, as illustrated by Matiasevich's negative answer to Hilbert's 10-th problem, search bounds in general probably do not exist. Some special cases are understood, but in general very little is known. I will talk about effective search bounds for solutions of polynomial equations over Q-bar with some additional arithmetic conditions. This discussion also naturaly ties into the realm of "absolute" diophantine results, like Siegel's lemma of Roy and Thunder. I will try …

Book Review: Across The Board: The Mathematics Of Chessboard Problems By John J. Watkins, Arthur T. Benjamin

All HMC Faculty Publications and Research

I think I became a mathematician because I loved to play games as a child. I learned about probability and expectation by playing games like backgammon, bridge, and Risk. But I experienced the greater thrill of careful deductive reasoning through games like Mastermind and chess. In fact, for many years I took the game of chess quite seriously and played in many tournaments. But I gave up the game when I started college and turned my attention to more serious pursuits, like learning real mathematics.

Counting On Determinants, Arthur T. Benjamin, Naiomi T. Cameron

All HMC Faculty Publications and Research

No abstract provided in this article.