Physical Sciences and Mathematics Commons^™

Constructing Diabatic States From Adiabatic States: Extending Generalized Mulliken–Hush To Multiple Charge Centers With Boys Localization, Joseph E. Subotnik, Robert J. Cave, Sina Yeganeh, Mark A. Ratner

All HMC Faculty Publications and Research

This article shows that, although Boys localization is usually applied to single-electron orbitals, the Boys method itself can be applied to many electron molecular states. For the two-state charge-transfer problem, we show analytically that Boys localization yields the same charge-localized diabatic states as those found by generalized Mulliken–Hush theory. We suggest that for future work in electron transfer, where systems have more than two charge centers, one may benefit by using a variant of Boys localization to construct diabatic potential energy surfaces and extract electronic coupling matrix elements. We discuss two chemical examples of Boys localization and propose a generalization …

Greedy Signal Recovery Review, Deanna Needell, Joel A. Tropp, Roman Vershynin

CMC Faculty Publications and Research

The two major approaches to sparse recovery are L1-minimization and greedy methods. Recently, Needell and Vershynin developed Regularized Orthogonal Matching Pursuit (ROMP) that has bridged the gap between these two approaches. ROMP is the first stable greedy algorithm providing uniform guarantees.

Even more recently, Needell and Tropp developed the stable greedy algorithm Compressive Sampling Matching Pursuit (CoSaMP). CoSaMP provides uniform guarantees and improves upon the stability bounds and RIC requirements of ROMP. CoSaMP offers rigorous bounds on computational cost and storage. In many cases, the running time is just O(NlogN), where N is the ambient dimension of the signal. This …

Mathematics In The Mountains: The Park City Mathematics Institute, Andrew J. Bernoff

All HMC Faculty Publications and Research

It's noon. A Fields medalist, master high school teachers from the US and abroad, aspiring undergraduate and graduate students, gifted expositors of mathematics, and mathematical artists gather at tables under a tent. Lunch and so much more is served at these meetings of the minds.

Evaluating Online Health Information: Beyond Readability Formulas, Gondy Leroy, Stephen Helmreich, James Cowie, Trudi Miller '08, Wei Zheng '08

CGU Faculty Publications and Research

Although understanding health information is important, the texts provided are often difficult to understand. There are formulas to measure readability levels, but there is little understanding of how linguistic structures contribute to these difficulties. We are developing a toolkit of linguistic metrics that are validated with representative users and can be measured automatically. In this study, we provide an overview of our corpus and how readability differs by topic and source. We compare two documents for three groups of linguistic metrics. We report on a user study evaluating one of the differentiating metrics: the percentage of function words in a …

Siegel’S Lemma Outside Of A Union Of Varieties, Lenny Fukshansky

CMC Faculty Publications and Research

Lecture given at the AMS Special Session on Number Theory, October 2008.

Tiling Proofs Of Recent Sum Identities Involving Pell Numbers, Arthur T. Benjamin, Sean S. Plott '08, James A. Sellers

All HMC Faculty Publications and Research

In a recent note, Santana and Diaz-Barrero proved a number of sum identities involving the well-known Pell numbers. Their proofs relied heavily on the Binet formula for the Pell numbers. Our goal in this note is to reconsider these identities from a purely combinatorial viewpoint. We provide bijective proofs for each of the results by interpreting the Pell numbers as enumerators of certain types of tilings. In turn, our proofs provide helpful insight for straightforward generalizations of a number of the identities.

The Biomechanics Of Ballistochory In Impatiens Pallida, Lua Del Campo

Pomona Senior Theses

This research is an analysis of the explosive seed dispersal of Impatiens pallida fruit. Data was taken using high-speed video and analyzed using LoggerPro video analysis software. From the videos we discerned a qualitative model for dehiscence, a description of how the process unfolds, and from our data we deduced quantitative values for the velocity, momentum, and energy of the system. We were also able to glean a lower bound of Young’s modulus E of the fruit tissue. These results and the tools of analysis that generate them are the foundation for the development of a theoretical model of the …

Borda Meets Pascal, Marie K. Jameson, Gregory Minton '08, Michael E. Orrison

All HMC Faculty Publications and Research

Every so often (especially in mathematics), unforeseen connections between different ideas arise and beg explanation. This happened to us when, in an effort to generalize the voting procedure known as the Borda count, we began to see vectors of the form (-1, 1), (1, -2, 1), (-1, 3, -3, 1), (1, -4, 6, -4, 1), and so on. As you might imagine, we were instantly intrigued by this unanticipated relationship with Pascal's triangle, and we quickly set out to find an explanation. This article describes some of our initial findings.

Synthesis And Assembly Of Nonspherical Hollow Silica Colloids Under Confinement, Stephanie H. Lee, Sharon J. Gerbode, Bettina S. John, Angie K. Wolfgang, Fernando A. Escobedo, Itai Cohen, Chekesha M. Liddell

All HMC Faculty Publications and Research

Hard peanut-shaped colloids were synthesized and organized into a degenerate crystal (DC), a phase previously observed only in simulations. In this structure, particle lobes tile a triangular lattice while their orientations uniformly populate the three underlying crystalline directions.

Restricted Dislocation Motion In Crystals Of Colloidal Dimer Particles, Sharon J. Gerbode, Stephanie H. Lee, Chekesha M. Liddell, Itai Cohen

All HMC Faculty Publications and Research

Received 2 April 2008; published 1 August 2008; corrected 1 October 2008

At high area fractions, monolayers of colloidal dimer particles form a degenerate crystal (DC) structure in which the particle lobes occupy triangular lattice sites while the particles are oriented randomly along any of the three lattice directions. We report that dislocation glide in DCs is blocked by certain particle orientations. The mean number of lattice constants between such obstacles is Z̅ _exp=4.6±0.2 in experimentally observed DC grains and Z̅ _sim=6.18±0.01 in simulated monocrystalline DCs. Dislocation propagation beyond these obstacles is observed to proceed through dislocation reactions. …

Imagine Math Day: Encouraging Secondary School Students And Teachers To Engage In Authentic Mathematical Discovery, Darryl H. Yong, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

Research mathematicians and school children experience mathematics in profoundly different ways. Ask a group of mathematicians what it means to “do mathematics” and you are likely to get a myriad of responses: mathematics involves analyzing and organizing patterns and relationships, reasoning and drawing conclusions about the world, or creating languages and tools to describe and solve important problems. Students of mathematics often report “doing mathematics” as performing calculations or following rules. It’s natural that they see mathematics as monolithic rather than an evolving, growing, socially constructed body of knowledge, because most mathematical training in primary and secondary schools consists of …

On Distribution Of Well-Rounded Sublattices Of Z², Lenny Fukshansky

CMC Faculty Publications and Research

A lattice is called well-rounded if its minimal vectors span the corresponding Euclidean space. In this paper we completely describe well-rounded full-rank sublattices of Z², as well as their determinant and minima sets. We show that the determinant set has positive density, deriving an explicit lower bound for it, while the minima set has density 0. We also produce formulas for the number of such lattices with a fixed determinant and with a fixed minimum. These formulas are related to the number of divisors of an integer in short intervals and to the number of its representations as a sum …

E-Transcript Web Services System Supporting Dynamic Conversion Between Xml And Edi, Myungjae Kwak '11, Woohyun Kang '14, Gondy Leroy, Samir Chatterjee

CGU Faculty Publications and Research

As XML becomes a standard for communications between distributed heterogeneous machines, many schools plan to implement Web Services systems using the XML e-transcript (electronic transcript) standard. We propose a framework that supports both XML e-transcript Web Services and existing EDI e-transcript systems. The framework uses the workflow engine to exploit the benefits of workflow management mechanisms. The workflow engine manages the e-transcript business process by enacting and completing the tasks and sub-processes within the main business process. We implemented the proposed framework by using various open source projects including Java, Eclipse, and Apache Software Foundation’s Web Services projects. Compared with …

Cosamp: Iterative Signal Recovery From Incomplete And Inaccurate Samples, Deanna Needell, J. A. Tropp

CMC Faculty Publications and Research

Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples. This paper describes a new iterative recovery algorithm calledCoSaMP that delivers the same guarantees as the best optimization-based approaches. Moreover, this algorithm offers rigorous bounds on computational cost and storage. It is likely to be extremely efficient for practical problems because it requires only matrix–vector multiplies with the sampling matrix. For compressible signals, the running time is just O(Nlog²N), where N is the length …

On Distribution Of Well-Rounded Sublattices Of Z², Lenny Fukshansky

CMC Faculty Publications and Research

Lecture given at Institut de Mathématiques in Bordeaux, France, June 2008.

Uniform Uncertainty Principle And Signal Recovery Via Regularized Orthogonal Matching Pursuit, Deanna Needell, Roman Vershynin

CMC Faculty Publications and Research

This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements—L1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized version of Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of L1-minimization. Our algorithm, ROMP, reconstructs a sparse signal in a number of iterations linear in the sparsity, and the reconstruction is exact provided the linear measurements satisfy the uniform uncertainty principle.

Smartphones To Facilitate Communication And Improve Social Skills Of Children With Severe Autism Spectrum Disorder: Special Education Teachers As Proxies, Gondy Leroy, Gianluca De Leo

CGU Faculty Publications and Research

We present an overview of the approach we used and the challenges we encountered while designing software for smartphones to facilitate communication and improve social skills of children with severe autism spectrum disorder (ASD). We employed participatory design, using special education teachers of children with ASD as proxies for our target population.

The Motivators And Benefits Of Sharing Knowledge To A Kms Repository In An Omani Organization, Kamla Al-Busaidi '05, Lorne Olfman, Terry Ryan, Gondy Leroy

CGU Faculty Publications and Research

Knowledge is a powerful resource that enables individuals and organizations to achieve several benefits such as improved learning and decisionmaking. Repository knowledge management system (KMS) assists organizations to efficiently capture their knowledge for later reuse. However, the breadth and depth of a knowledge management system depends on the magnitude of knowledge contributed to the system. This paper aimed to empirically investigate the motivators of knowledge sharing behavior and the individual benefits of such behavior in a culture where knowledge is perceived as power and private. Based on 104 employees in a major private petroleum organization in Oman and the partial …

H I Line Profiles Of Galaxies: Tilted Ring Models, Erica Nelson

Pomona Senior Theses

Two-dimensional information on the kinematics and spatial distribution of gas in spiral galaxies is encoded in radio observations of their one-dimensional 21-cm neutral hydrogen (HI) line profiles. More than ten thousand HI profiles have been published and are publicly available. In order to explore the parameter space mapped out by the 21-cm neutral hydrogen line pro file, we have modified and run a FORTRAN-based computer simulation code. We have identified 7 control parameters that define the morphology of the modelled galaxy: they describe the neutral hydrogen gas distribution (density and spatial location of the gas), characteristics of its rotation curve, …

A Study Of Interacanding And Companion Galaxies: Implications For Cosmology, Kristen Petrillo

Pomona Senior Theses

This paper examined a few different types of interacting galaxies and the implications the data has on cosmological theories. An analysis of the Holmberg Effect, Holmberg (1969)’s observation that companion galaxies tend to be near the poles of edge-on galaxies rather than in the planes, was done by reexamining the spirals viewed by Holmberg. Only using radial velocity confirmed companions to test for this effect showed that if anything, the opposite of the Holmberg effect is true. However, due to small number statistics, more edge-on spirals and their companions would have to be viewed in order to determine if this …

Shaping Graphene: An Alternative Approach, Ian W. Frank

Pomona Senior Theses

With experimentation on graphene (an atomic layer of graphite) becoming more and more common it is imperative that we have the capability to shape the material beyond the random manner in which it is deposited by mechanical exfoliation. This capability would be invaluable not only for the interesting electronic and optical properties that can be obtained, but also potentially for characterizing the mechanical resonators that we have been able to fabricate here at Pomona College by suspending few-layer graphene sheets over trenches in SiO2. We propose novel methods for etching graphene that should allow us to shape the material when …

An Alternate Approach To Alternating Sums: A Method To Die For, Arthur T. Benjamin, Jennifer J. Quinn

All HMC Faculty Publications and Research

No abstract provided in this article.

Reactivity Of Ptii "Pincer" Complexes With Carbon Monoxide, Margaret L. Scheuermann

Scripps Senior Theses

ABSTRACT Upon addition of carbon monoxide (CO) to a solution of (k-N, C, N-2, 6-bis(diethylaminomethyl)-phenyl)methyl platinum(II),[NCN]PtMe,(1), a ligand arm is displaced to form [SP-4-2] ((k-N,C-2,6-bis(diethylaminomethyl)-phenyl) carbonmethyl platinum(II), N[CN]Pt(CO)(Me),(2). Addition of CO to a THF solution of 2 results in the formation of [SP-4-3]((k-N,C-2,6-bis(diethylaminomethyl)-phenyl)acylcarbonyl platinum(II),N[CN]pt(Ac)(CO),(3). In THF ,2 partially isomerizes in the presence of CO to form [SP-4-4]((k-N,C-2,6-bis(diethylaminomethyl)-phenyl)carbonylmethyl platinum(II), N[CN]Pt(Me)(CO).(2’).in equilibrium with 2(K=ca.2 at 100 degree celcius). In the absence of CO, only trace isomerization was observed. Thermolysis of 3 results in the formation of 2 and 2’ , while a reaction of 3 with trimethylamine N-oxide results exclusively in the …

Bridging The Gender Gap In Quantum Physics, Gordon Stecklein

Pomona Senior Theses

Why is it important to study the gender gap in physics? Despite entering the workforce in increasing numbers over the last fifty years, women remain severely underrepresented in science and technology-related careers, particularly in positions of authority. Simultaneously, numerous studies verify that women have the ability to perform as well as – or better than – males in physics, and, when presented in certain lights, as many women as men show an interest in physics. Changes must be made in order to strive for equality and, given the changing demographic of the workforce, increase our country’s diminishing scientific prowess.

Acoustical Measurement Of The Human Vocal Tract: Quantifying Speech & Throat-Singing, Bryant R. Foresman

Pomona Senior Theses

The field of biological acoustics has witnessed a steady increase in the research into overtone singing, or “throat-singing,” in which a singer utilizes resonance throughout the vocal tract to sing melodies with the overtones created by a vocal drone. Recent research has explored both how a singer vocalizes in order to obtain rich harmonics from a vocal drone, as well as how further manipulations of the vocal apparatus function to filter and amplify selected harmonics. In the field of phonetics, vowel production is quantified by measuring the frequencies of vocal tract resonances, or formants, which a speaker manipulates to voice …

The Shapley Value Of Phylogenetic Trees, Claus-Jochen Haake, Akemi Kashiwada '05, Francis E. Su

All HMC Faculty Publications and Research

Every weighted tree corresponds naturally to a cooperative game that we call a tree game; it assigns to each subset of leaves the sum of the weights of the minimal subtree spanned by those leaves. In the context of phylogenetic trees, the leaves are species and this assignment captures the diversity present in the coalition of species considered. We consider the Shapley value of tree games and suggest a biological interpretation. We determine the linear transformation M that shows the dependence of the Shapley value on the edge weights of the tree, and we also compute a null space …

Traveling Waves And Shocks In A Viscoelastic Generalization Of Burgers' Equation, Victor Camacho '07, Robert D. Guy, Jon T. Jacobsen

All HMC Faculty Publications and Research

We consider traveling wave phenomena for a viscoelastic generalization of Burgers' equation. For asymptotically constant velocity profiles we find three classes of solutions corresponding to smooth traveling waves, piecewise smooth waves, and piecewise constant (shock) solutions. Each solution type is possible for a given pair of asymptotic limits, and we characterize the dynamics in terms of the relaxation time and viscosity.

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 …