Physical Sciences and Mathematics Commons^™

Mobile Communication And Data Gathering Software For Autistic Children And Their Caregivers, Gondy Leroy, Gianluca De Leo

CGU Faculty Publications and Research

Positive design leads to positive change in our society. In most cases, discussions focus on those who receive the design. However, positive design may also have a positive, but often over-looked, effect on the designers themselves. Learning about difficulties others face and developing solutions is a benefit that can contribute to individual designers’ education and general sense of well-being. Having a broader understanding of alternative views and lifestyles makes one a better person. In addition, positive design may benefit the entire field of information science by improving its ability to renew itself and attract new, young talent.

The 99th Fibonacci Identity, Arthur T. Benjamin, Alex K. Eustis '06, Sean S. Plott '08

All HMC Faculty Publications and Research

We provide elementary combinatorial proofs of several Fibonacci and Lucas number identities left open in the book Proofs That Really Count [1], and generalize these to Gibonacci sequences G_n that satisfy the Fibonacci recurrence, but with arbitrary real initial conditions. We offer several new identities as well.

[1] A. T. Benjamin and J. J. Quinn, Proofs That Really Count: The Art of Combinatorial Proof, The Dolciani Mathematical Expositions, 27, Mathematical Association of America, Washington, DC, 2003

Designs And Optical Tests Of Thermal Links For An Optical Refrigerator, John Parker, David Mar, Steven Von Der Porten, John Hankinson, Kevin Byram, Chris Lee, Kai Mayeda, Richard C. Haskell, Qimin Yang, Scott R. Greenfield, Richard I. Epstein

All HMC Faculty Publications and Research

Dielectric mirror leakage at large angles of incidence limits the effectiveness of solid state optical refrigerators due to reheating caused by photon absorption in an attached load. In this paper, we present several thermally conductive link solutions to greatly reduce the net photon absorption. The Los Alamos Solid State Optical Refrigerator (LASSOR) has demonstrated cooling of a Yb/sup 3+/ doped ZBLANP glass to 208 K. We have designed optically isolating thermal link geometries capable of extending cooling to a typical heat load with minimal absorptive reheating, and we have tested the optical performance of these designs. A surrogate source operating …

Computer Modeling And Analysis Of Thermal Link Performance For An Optical Refrigerator, Kevin Byram, David Mar, John Parker, Steven Von Der Porten, John Hankinson, Chris Lee, Kai Mayeda, Richard C. Haskell, Qimin Yang, Scott R. Greenfield, Richard I. Epstein

All HMC Faculty Publications and Research

We have used the thermal modeling tool in COMSOL Multiphysics to investigate factors that affect the thermal performance of the optical refrigerator. Assuming an ideal cooling element and a non-absorptive dielectric trapping mirror, the three dominant heating factors are blackbody radiation from the surrounding environment, conductive heat transfer through mechanical supports, and the absorption of fluorescent photons transmitted through the thermal link. Laboratory experimentation coupled with computer modeling using Code V optical software have resulted in link designs capable of reducing the transmission to 0.04% of the fluoresced photons emitted toward the thermal link. The ideal thermal link will have …

Paint It Black -- A Combinatorial Yawp, Arthur T. Benjamin, Jennifer J. Quinn, James A. Sellers, Mark A. Shattuck

All HMC Faculty Publications and Research

No abstract provided in this paper.

A Combinatorial Approach To Fibonomial Coefficients, Arthur T. Benjamin, Sean S. Plott '08

All HMC Faculty Publications and Research

A combinatorial argument is used to explain the integrality of Fibonomial coefficients and their generalizations. The numerator of the Fibonomial coeffcient counts tilings of staggered lengths, which can be decomposed into a sum of integers, such that each integer is a multiple of the denominator of the Fibonomial coeffcient. By colorizing this argument, we can extend this result from Fibonacci numbers to arbitrary Lucas sequences.

Frobenius Number, Covering Radius, And Well-Rounded Lattices, Lenny Fukshansky, Sinai Robins

CMC Faculty Publications and Research

Lecture given at the Joint Mathematics Meeting in San Diego, January 2008.

Review: Lie Structure In Semiprime Superalgebras With Superinvolution, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Mathematics Of Voting, Darryl H. Yong

All HMC Faculty Publications and Research

Voting theory is a fascinating area of research involving mathematics, political scientists, and economists. The American Mathematical Society, the American Statistical Association, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics chose mathematics and voting as the theme for Mathematics Awareness Month 2008. There is more information on mathematics and voting at www.mathaware.org/mam/08/. It is a mathematical topic that is rich yet accessible to students, pertinent to their lives, especially during this election year, and has the potential to draw students who may not have a strong affinity for mathematics to become interested in mathematics.

The Art Of Teaching Mathematics, Garikai Campbell, Jon T. Jacobsen, Aimee S A Johnson, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

On June 10–12, 2007, Harvey Mudd College hosted A Conference on the Art of Teaching Mathematics. The conference brought together approximately thirty mathematicians from the Claremont Colleges, Denison, DePauw, Furman, Middlebury, Penn State, Swarthmore, and Vassar to explore the topic of teaching as an art. Assuming there is an element of artistic creativity in teaching mathematics, in what ways does it surface and what should we be doing to develop this creativity?

New Mechanism For Nonlocality From String Theory: Uv-Ir Quantum Entanglement And Its Imprints On The Cmb, Gregory Minton '08, Vatche Sahakian

All HMC Faculty Publications and Research

Puff field theories (PFT) arise as the decoupling limits of D3 branes in a Melvin universe and exhibit spatially nonlocal dynamics. Unlike other realizations of nonlocality in string theory, PFTs have full SO(3) rotational symmetry. In this work, we analyze the strongly coupled regime of a PFT through gravitational holography. We find a novel mechanism at the heart of the phenomenon of nonlocality: a quantum entanglement of UV and IR dynamics. In the holographic bulk, this translates to an apparent horizon splitting the space into two regions—with the UV completion of the PFT sitting at the horizon. We unravel this …

Distribution Of The Number Of Encryptions In Revocation Schemes For Stateless Receivers, Christopher Eagle, Zhicheng Gao, Mohamed Omar, Daniel Panario, Bruce Richmond

All HMC Faculty Publications and Research

We study the number of encryptions necessary to revoke a set of users in the complete subtree scheme (CST) and the subset-difference scheme (SD). These are well-known tree based broadcast encryption schemes. Park and Blake in: Journal of Discrete Algorithms, vol. 4, 2006, pp. 215--238, give the mean number of encryptions for these schemes. We continue their analysis and show that the limiting distribution of the number of encryptions for these schemes is normal. This implies that the mean numbers of Park and Blake are good estimates for the number of necessary encryptions used by these schemes.

A Model For Rolling Swarms Of Locusts, Chad M. Topaz, Andrew J. Bernoff, Sheldon Logan '06, Wyatt Toolson '07

All HMC Faculty Publications and Research

We construct an individual-based kinematic model of rolling migratory locust swarms. The model incorporates social interactions, gravity, wind, and the effect of the impenetrable boundary formed by the ground. We study the model using numerical simulations and tools from statistical mechanics, namely the notion of H-stability. For a free-space swarm (no wind and gravity), as the number of locusts increases, the group approaches a crystalline lattice of fixed density if it is H-stable, and in contrast becomes ever denser if it is catastrophic. Numerical simulations suggest that whether or not a swarm rolls depends on the statistical mechanical properties of …

Small Zeros Of Quadratic Forms Over The Algebraic Closure Of Q, Lenny Fukshansky

CMC Faculty Publications and Research

Let N >= 2 be an integer, F a quadratic form in N variables over (Q) over bar, and Z subset of (Q) over bar (N) an L-dimensional subspace, 1 <= L <= N. We prove the existence of a small-height maximal totally isotropic subspace of the bilinear space (Z, F). This provides an analogue over (Q) over bar of a well-known theorem of Vaaler proved over number fields. We use our result to prove an effective version of Witt decomposition for a bilinear space over (Q) over bar. We also include some related effective results on orthogonal decomposition and structure of isometries for a bilinear space over (Q) over bar. This extends previous results of the author over number fields. All bounds on height are explicit.

Enabling Synergy Between Psychology And Natural Language Processing For E-Government: Crime Reporting And Investigative Interview System, Alicia Iriberri '06, Chih Hao Ku '12, Gondy Leroy

CGU Faculty Publications and Research

We are developing an automated crime reporting and investigative interview system. The system incorporates cognitive interview techniques to maximize witness memory recall, and information extraction technology to extract and annotate crime entities from witness narratives and interview responses. Evaluations of the IE components of the system show that it captures 70 to 77% of information from witness narratives with 93 to 100% precision. Our development goal is for the system to approximate progressively the performance effectiveness of a human investigative interviewer and to generate graphical visualizations of crime report information.

Crime Information Extraction From Police And Witness Narrative Reports, Chih Hao Ku '12, Alicia Iriberri '06, Gondy A. Leroy

CGU Faculty Publications and Research

To solve crimes, investigators often rely on interviews with witnesses, victims, or criminals themselves. The interviews are transcribed and the pertinent data is contained in narrative form. To solve one crime, investigators may need to interview multiple people and then analyze the narrative reports. There are several difficulties with this process: interviewing people is time consuming, the interviews - sometimes conducted by multiple officers - need to be combined, and the resulting information may still be incomplete. For example, victims or witnesses are often too scared or embarrassed to report or prefer to remain anonymous. We are developing an online …

Women And Technology: Reversing The Trends Of Attrition And Obtaining A Balance, Gondy Leroy, Kristin M. Tolle, Linda Perkins

CGU Faculty Publications and Research

Many reports and technical news bulletins presented by organizations such as the National Science Foundation (NSF), the Institute of Electrical and Electronics Engineers (IEEE), the Association for Computing Machinery (ACM), and the National Center for Women & Information Technology (NCWIT) highlight that few female and minority college students are choosing science, technology, engineering, and math (STEM) fields of study or careers. For those who choose STEM fields, attrition both during education and in the workplace is pervasive. NSF reports in its 2006 Science Indicators that women account for only 27% of the bachelor’s degrees in computer sciences. And although the …

The Impact Of Directionality In Predications On Text Mining, Gondy Leroy, Marcelo Fiszman, Thomas C. Rindflesch

CGU Faculty Publications and Research

The number of publications in biomedicine is increasing enormously each year. To help researchers digest the information in these documents, text mining tools are being developed that present co-occurrence relations between concepts. Statistical measures are used to mine interesting subsets of relations. We demonstrate how directionality of these relations affects interestingness. Support and confidence, simple data mining statistics, are used as proxies for interestingness metrics. We first built a test bed of 126,404 directional relations extracted from biomedical abstracts, which we represent as graphs containing a central starting concept and 2 rings of associated relations. We manipulated directionality in four …

An Online Community For Teachers Of Children With Autism To Support, Observe, And Evaluate Communication Enabled With Smartphones, Gianluca De Leo, Gondy Leroy

CGU Faculty Publications and Research

We are developing an online community for teachers of children diagnosed with autism spectrum disorder that will provide tools to share, analyze, and evaluate assisted communication. The data will be collected from software on smartphones that allows children to communicate with teachers using images. Since this is the first approach towards systematic data collection for children with ASD, we expect a significant impact on current teaching methods.

Making Primarily Professional Terms More Comprehensible To The Lay Audience, Sergey Goryachev, Qing Zeng-Treitler, Catherine Arnott Smith, Allen C. Browne, Guy Divita, Alla Keselman, Gondy Leroy, Rosa Figueroa

CGU Faculty Publications and Research

Certain texts, such as clinical reports and clinical trial records, are written by professionals for professionals while being increasingly accessed by lay people. To improve the comprehensibility of such documents to the lay audience, we conducted a pilot study to analyze terms used primarily by health professionals, and explore ways to make them more comprehensible to lay people.

Natural Language Processing And E-Government: Crime Information Extraction From Heterogeneous Data Sources, Chih Hao Ku '12, Alicia Iriberri '06, Gondy Leroy

CGU Faculty Publications and Research

Much information that could help solve and prevent crimes is never gathered because the reporting methods available to citizens and law enforcement personnel are not optimal. Detectives do not have sufficient time to interview crime victims and witnesses. Moreover, many victims and witnesses are too scared or embarrassed to report incidents. We are developing an interviewing system that will help collect such information. We report here on one component, the crime information extraction module, which uses natural language processing to extract crime information from police reports, newspaper articles, and victims’ and witnesses’ crime narratives. We tested our approach with two …

Approximate Antilinear Eigenvalue Problems And Related Inequalities, Stephan Ramon Garcia

Pomona Faculty Publications and Research

If T is a complex symmetric operator on a separable complex Hilbert space H, then the spectrum σ ( |T| ) of √(T*T) can be characterized in terms of a certain approximate antilinear eigenvalue problem. This approach leads to a general inequality (applicable to any bounded operator T : H → H ), in terms of the spectra of the self-adjoint operators Re T and Im T, restricting the possible location of elements of σ ( |T| ) . A sharp inequality for the operator norm is produced, and the extremal operators are shown …

Intrinsic Linking And Knotting Are Arbitrarily Complex, Erica Flapan, Blake Mellor, Ramin Naimi

Pomona Faculty Publications and Research

We show that, given any n and alpha, any embedding of any sufficiently large complete graph in R³ contains an oriented link with components Q₁,...,Q_n such that for every i not equal to j, Ilk(Q_i,Q_j)I greater than or equal to alpha and la₂(Q_i)l greater than or equal to alpha, where a₂(Q_i) denotes the second coefficient of the Conway polynomial of Q_i.

Review: On Rank-One Perturbations Of Normal Operators, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Review: Hypercyclic Pairs Of Coanalytic Toeplitz Operators, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Review: Shift-Type Invariant Subspaces Of Contractions, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Interpolation And Complex Symmetry, Stephan Ramon Garcia, Mihai Putinar

Pomona Faculty Publications and Research

In a separable complex Hilbert space endowed with an isometric conjugate-linear involution, we study sequences orthonormal with respect to an associated bilinear form. Properties of such sequences are measured by a positive, possibly unbounded angle operator which is formally orthogonal as a matrix. Although developed in an abstract setting, this framework is relevant to a variety of eigenvector interpolation problems arising in function theory and in the study of differential operators.

Review: Some Remarks On Quantized Lie Superalgebras Of Classical Type, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Review: Degenerate Series Representations Of The Q-Deformed Algebra Soq′(R,S), Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Mathematicians Playing A Role In Math Education: What We Learned At The Ime/Mime Workshop, Anna Bargagliotti, Rama Chidambaram, Gizem Karaali

Pomona Faculty Publications and Research

In Hollywood, some actors are regularly cast as mean, others as sweet and endearing, and some typically play innocent big-eyed youths who inevitably succeed after awakening to the particular facts of life that their producer wants them to awaken to. It is unusual and difficult for actors to cross the bridge between different types on a regular basis. However, there are always exceptions to the rule.

In the seemingly unrelated world of academics, mathematics faculty may find themselves playing different roles. People with different skills and interests strive to balance their careers in ways that will be uniquely fulfilling to …