Physical Sciences and Mathematics Commons^™

Scroll Waves In The Presence Of Slowly Varying Anisotropy With Application To The Heart, S. Setayeshgar, Andrew J. Bernoff

All HMC Faculty Publications and Research

We consider the dynamics of scroll waves in the presence of rotating anisotropy, a model of the left ventricle of the heart in which the orientation of fibers in successive layers of tissue rotates. By choosing a coordinate system aligned with the fiber rotation and studying the phase dynamics of a straight but twisted scroll wave, we derive a Burgers’ equation with forcing associated with the fiber rotation rate. We present asymptotic solutions for scroll twist, verified by numerics, using a realistic fiber distribution profile. We make connection with earlier numerical and analytical work on scroll dynamics.

A Local Inversion Principle Of The Nash-Moser Type, Alfonso Castro, J. W. Neuberger

All HMC Faculty Publications and Research

We prove an inverse function theorem of the Nash-Moser type. The main difference between our method and that of [J. Moser, Proc. Nat. Acad. Sci. USA, 47 (1961), pp. 1824-1831] is that we use continuous steepest descent while Moser uses a combination of Newton-type iterations and approximate inverses. We bypass the loss of derivatives problem by working on finite dimensional subspaces of infinitely differentiable functions.

Meeting Medical Terminology Needs: The Ontology-Enhanced Medical Concept Mapper, Gondy Leroy, Hsinchun Chen

CGU Faculty Publications and Research

This paper describes the development and testing of the Medical Concept Mapper, a tool designed to facilitate access to online medical information sources by providing users with appropriate medical search terms for their personal queries. Our system is valuable for patients whose knowledge of medical vocabularies is inadequate to find the desired information, and for medical experts who search for information outside their field of expertise. The Medical Concept Mapper maps synonyms and semantically related concepts to a user's query. The system is unique because it integrates our natural language processing tool, i.e., the Arizona (AZ) Noun Phraser, with human-created …

Meeting Medical Terminology Needs: The Ontology-Enhanced Medical Concept Mapper, Gondy Leroy, Hsinchun Chen

CGU Faculty Publications and Research

This paper describes the development and testing of the Medical Concept Mapper, a tool designed to facilitate access to online medical information sources by providing users with appropriate medical search terms for their personal queries. Our system is valuable for patients whose knowledge of medical vocabularies is inadequate to find the desired information, and for medical experts who search for information outside their field of expertise. The Medical Concept Mapper maps synonyms and semantically related concepts to a user's query. The system is unique because it integrates our natural language processing tool, i.e., the Arizona (AZ) Noun Phraser, with human-created …

Modeling Control Of Hiv Infection Through Structured Treatment Interruptions With Recommendations For Experimental Protocol, Shannon Kubiak, Heather Lehr, Rachel Levy, Todd Moeller, Albert Parker, Edward Swim

All HMC Faculty Publications and Research

Highly Active Anti-Retroviral Therapy (HAART) of HIV infection has significantly reduced morbidity and mortality in developed countries. However, since these treatments can cause side effects and require strict adherence to treatment protocol, questions about whether or not treatment can be interrupted or discontinued with control of infection maintained by the host immune system remain to be answered. We present sensitivity analysis of a compartmental model for HIV infection that allows for treatment interruptions, including the sensitivity of the compartments themselves to our parameters as well as the sensitivity of the cost function used in parameter estimation. Recommendations are made about …

Transformation Of Statistics In Fractional Quantum Hall Systems, John J. Quinn, Arkadiusz Wojs, Jennifer J. Quinn, Arthur T. Benjamin

All HMC Faculty Publications and Research

A Fermion to Boson transformation is accomplished by attaching to each Fermion a tube carrying a single quantum of flux oriented opposite to the applied magnetic field. When the mean field approximation is made in Haldane’s spherical geometry, the Fermion angular momentum l_F is replaced by l_B =l_F − 1/2 (N −1). The set of allowed total angular momentum multiplets is identical in the two different pictures. The Fermion and Boson energy spectra in the presence of many body interactions are identical only if the pseudopotential V (interaction energy as a function of pair angular …

Distinguishing Surface And Bulk Contributions To Third-Harmonic Generation In Silicon, Peter N. Saeta, Nathan A. Miller '01

All HMC Faculty Publications and Research

We report measurements of third-harmonic generation from ultrathin crystalline silicon layers of gradually varying thickness. Both the angular and thickness dependence of the third-harmonic light generated in transmission at normal incidence are consistent with negligible surface contribution to third-harmonic generation in silicon, even under tight focusing. This work illustrates a method for distinguishing surface and bulk contributions to harmonic generation.

Monotone Solutions Of A Nonautonomous Differential Equation For A Sedimenting Sphere, Andrew Belmonte, Jon T. Jacobsen, Anandhan Jayaraman

All HMC Faculty Publications and Research

We study a class of integrodifferential equations and related ordinary differential equations for the initial value problem of a rigid sphere falling through an infinite fluid medium. We prove that for creeping Newtonian flow, the motion of the sphere is monotone in its approach to the steady state solution given by the Stokes drag. We discuss this property in terms of a general nonautonomous second order differential equation, focusing on a decaying nonautonomous term motivated by the sedimenting sphere problem

Math Major, Math Major, Arthur T. Benjamin

All HMC Faculty Publications and Research

Sung to the tune of "Matchmaker" from Fiddler on the Roof:

Math major, math major, make me some math.

Find me a prime, sketch me a path.

Math major, math major look through your books,

And make me some perfect math.

Puerto Rican Karst - A Vital Resource, Ariel E. Lugo, Leopoldo Miranda Castro, Abel Vale, Tania Del Mar López, Enrique Hernández Prieto, Andrés García Martinó, Alberto R. Puente Rolón, Adrianne G. Tossas, Donald A. Mcfarlane, Tom Miller, Armando Rodríguez, Joyce Lundberg, John Thomlinson, José Colón, Johannes H. Schellekens, Olga Ramos, Eileen Helmer

WM Keck Science Faculty Papers

The limestone region of Puerto Rico covers about 27.5 percent of the island's surface and is subdivided into the northern, southern, and dispersed limestone areas. All limestone areas have karst features. The karst belt is that part of the northern limestone with the most spectacular surficial karst landforms. It covers 142,544 ha or 65 percent of the northern limestone. The karst belt is the focus of this publication, although reference is made to all limestone regions. The northern limestone contains Puerto Rico's most extensive freshwater aquifer, largest continuous expanse of mature forest, and largest coastal wetland, estuary, and underground cave …

An Inverse Function Theorem Via Continuous Newton’S Method, Alfonso Castro, J. W. Neuberger

All HMC Faculty Publications and Research

We prove an inverse function theorem of the Nash-Moser type. The main difference between our method and that of [4] is that we use continuous steepest descent while [4] uses a combination of Newton type iterations and approximate inverses. We bypass the loss of derivatives problem by working on finite dimensional subspaces of infinitely differentiable functions.

Transcribing Spacetime Data Into Matrices, Vatche Sahakian

All HMC Faculty Publications and Research

In certain supergravity backgrounds, D0 branes may polarize into higher dimensional Dp branes. We study this phenomenon in some generality from the perspective of a local inertial observer and explore polarization effects resulting from tidal-like forces. We find D2 brane droplets made of D0 branes at an extremum of the Born-Infeld action even in scenarios where the RR fields may be zero. These solutions lead us to a local formulation of the UV-IR correspondence. A holographic Planck scale bound on the number of D0 branes plays an important role in the analysis. We focus on the impact of higher order …

Uniqueness Of Volume-Minimizing Submanifolds Calibrated By The First Pontryagin Form, Daniel A. Grossman, Weiqing Gu

All HMC Faculty Publications and Research

One way to understand the geometry of the real Grassmann manifold G_k(R^k+n) parameterizing oriented k-dimensional subspaces of R^k+n is to understand the volume-minimizing subvarieties in each homology class. Some of these subvarieties can be determined by using a calibration. In previous work, one of the authors calculated the set of 4-planes calibrated by the first Pontryagin form p₁ on G_k(R^k+n) for all k,n ≥4, and identified a family of mutually congruent round 4-spheres which are consequently homologically volume-minimizing. In the present work, we associate to the family of calibrated …

Mathematical Constance (A Poem Dedicated To Constance Reid), Arthur T. Benjamin

All HMC Faculty Publications and Research

Mathematical Constance (A Poem Dedicated to Constance Reid)

I think that I shall never see

A constant lovelier than e,

Whose digits are too great too state,

They're 2.71828…

And e has such amazing features

It's loved by all (but mostly teachers).

With all of e's great properties

Most integrals are done with … ease.

Theorems are proved by fools like me

But only Euler could make an e.

I suppose, though, if I had to try

To choose another constant, I

Might offer i or phi or pi.

But none of those would satisfy.

Of all the …

On D0 Brane Polarization By Tidal Forces, Vatche Sahakian

All HMC Faculty Publications and Research

Gravitational tidal forces may induce polarization of D0-branes, in analogy to the same effects arising in the context of constant background gauge fields. Such phenomena can teach us about the correspondence between smooth curved spacetime and its underlying non-commutative structure. However, unlike polarization by gauge fields, the gravitational counterpart involves concerns regarding the classical stability of the corresponding polarized states. In this work, we study this issue with respect to the solutions presented in hepth0010237 and find that they are classically unstable. The instability however appears with intricate features with all but a few decay channels being lifted. Through a …

Large-Scale Synchrony In Weakly Interacting Automata, Eric J. Friedman, Adam S. Landsberg

WM Keck Science Faculty Papers

We study the behavior of two spatially distributed (sandpile) models which are weakly linked with one another. Using a Monte Carlo implementation of the renormalization-group and algebraic methods, we describe how large-scale correlations emerge between the two systems, leading to synchronized behavior.

Proof With Words: 2 + 11 - 1 = 12, Arthur T. Benjamin

All HMC Faculty Publications and Research

Proof with words: 2 + 11 – 1 = 12

TWo ELeVEn

Phase Modulation At 125 Khz In A Michelson Interferometer Using An Inexpensive Piezoelectric Stack Driven At Resonance, Barbara M. Hoeling, Andrew D. Fernandez, Richard C. Haskell, Daniel C. Petersen

All HMC Faculty Publications and Research

Fast phase modulation has been achieved in a Michelson interferometer by attaching a lightweight reference mirror to a piezoelectric stack and driving the stack at a resonance frequency of about 125 kHz. The electrical behavior of the piezo stack and the mechanical properties of the piezo-mirror arrangement are described. A displacement amplitude at resonance of about 350 nm was achieved using a standard function generator. Phase drift in the interferometer and piezo wobble were readily circumvented. This approach to phase modulation is less expensive by a factor of roughly 50 than one based on an electro-optic effect.

Spectral Equivalence Of Bosons And Fermions In One-Dimensional Harmonic Potentials, Michael Crescimanno, Adam S. Landsberg

WM Keck Science Faculty Papers

Recently, Schmidt and Schnack [Physica A 260, 479 (1998)], following earlier references, reiterate that the specific heat of N noninteracting bosons in a one-dimensional harmonic well equals that of N noninteracting fermions in the same potential. We show that this peculiar relationship between heat capacities results from a more dramatic equivalence between Bose and Fermi systems. Namely, we prove that the excitations of such Bose and Fermi systems are spectrally equivalent. Two complementary proofs of this equivalence are provided; one based on a combinatoric argument, the other from analysis of the underlying dynamical symmetry group.

Discrepancy Convergence For The Drunkard's Walk On The Sphere, Francis E. Su

All HMC Faculty Publications and Research

We analyze the drunkard's walk on the unit sphere with step size θ and show that the walk converges in order C/sin²(θ) steps in the discrepancy metric (C a constant). This is an application of techniques we develop for bounding the discrepancy of random walks on Gelfand pairs generated by bi-invariant measures. In such cases, Fourier analysis on the acting group admits tractable computations involving spherical functions. We advocate the use of discrepancy as a metric on probabilities for state spaces with isometric group actions.

Particle Size Determination: An Undergraduate Lab In Mie Scattering, I. Weiner '01, M. Rust '01, Thomas D. Donnelly

All HMC Faculty Publications and Research

A technique for determining the size of microscopic spherical particles using light scattering is presented as an undergraduate physics lab. Scatterer size is determined from angular scattering distribution measurements of laser light scattered from a dilute suspension of latex spheres with diameters of 4.99±0.05 and 6.038±0.045 μm. Previous experiments of this type used approximate theoretical corrections and required the construction of specialized sample cells to minimize complicating effects. As a significant improvement to these, we generate angular scattering distributions from Mie theory and, using an accurate numerical procedure, correct these distributions for Snell’s law and foreshortening effects. Scatterer size …

A New Species Of Extinct Oryzomyine Rodent From The Quaternary Of Curaçao, Netherlands Antilles, Donald A. Mcfarlane, Adolphe O. Debrot

WM Keck Science Faculty Papers

An extinct new species of Oryzomyine rodent, known since 1936 from the cave of Grot van Hato on the island of Curaçao, is described from abundant new specimens collected from owl-pellet deposits at three localities on the island.

Proof Without Words: The Pigeonhole Principle, Ran Libeskind-Hadas

All HMC Faculty Publications and Research

This article contains one image and no text.

Multicast Communication In Circuit-Switched Optical Networks, Ran Libeskind-Hadas, Rami Melhem

All HMC Faculty Publications and Research

In this paper we examine the problem of multicast routing in Wavelength-division multiplexed (WDM) optical networks. In particular, we examine wavelength and routing assignment problems in circuit-switched WDM networks. We show that although the routing and wavelength assignment (RWA) problem is NP-complete in general, the wavelength assignment (WA) problem can be solevd in a polynomial time.

Optimal Token Allocations In Solitaire Knock 'M Down, Arthur Benjamin, Matthew T. Fluet, Mark L. Huber

All HMC Faculty Publications and Research

In the game Knock ’m Down, tokens are placed in N bins. At each step of the game, a bin is chosen at random according to a fixed probability distribution. If a token remains in that bin, it is removed. When all the tokens have been removed, the player is done. In the solitaire version of this game, the goal is to minimize the expected number of moves needed to remove all the tokens. Here we present necessary conditions on the number of tokens needed for each bin in an optimal solution, leading to an asymptotic solution. MR Subject Classifications: …

Transient Anomalous Diffusion In Poiseuille Flow, Marco Latini '01, Andrew J. Bernoff

All HMC Faculty Publications and Research

We revisit the classical problem of dispersion of a point discharge of tracer in laminar pipe Poiseuille flow. For a discharge at the centre of the pipe we show that in the limit of small non-dimensional diffusion, D, tracer dispersion can be divided into three regimes. For small times (t [double less-than sign] D^−1/3), diffusion dominates advection yielding a spherically symmetric Gaussian dispersion cloud. At large times (t [dbl greater-than sign] D⁻¹), the flow is in the classical Taylor regime, for which the tracer is homogenized transversely across the pipe and diffuses with …

Enumeration Of Equicolourable Trees, Nicholas Pippenger

All HMC Faculty Publications and Research

A tree, being a connected acyclic graph, can be bicolored in two ways, which differ from each other by exchange of the colors. We shall say that a tree is equicolorable if these bicolorings assign the two colors to equal numbers of vertices. Labelled equicolored trees have been enumerated several times in the literature, and from this result it is easy to enumerate labelled equicolorable trees. The result is that the probability that a randomly chosen n-vertex labelled tree is equicolorable is asymptotically just twice the probability that its vertices would be equicolored if they were assigned colors by …

A Mathematical Tumor Model With Immune Resistance And Drug Therapy: An Optimal Control Approach, Lisette G. De Pillis, Ami E. Radunskaya

All HMC Faculty Publications and Research

We present a competition model of cancer tumor growth that includes both the immune system response and drug therapy. This is a four-population model that includes tumor cells, host cells, immune cells, and drug interaction. We analyze the stability of the drug-free equilibria with respect to the immune response in order to look for target basins of attraction. One of our goals was to simulate qualitatively the asynchronous tumor-drug interaction known as “Jeffs phenomenon.” The model we develop is successful in generating this asynchronous response behavior. Our other goal was to identify treatment protocols that could improve standard pulsed chemotherapy …

An Open Field, Char Miller

Pomona Faculty Publications and Research

It should have been during a similarly punishing and mercurial moment in late twentieth-century San Antonio, enveloped in a "furious storm of rain, of hail, or of snow," that I initially encountered Richard White's seminal historiographical essay. Such a convergence of art, life, and weather pattern might have defied reality, but it would have made for a fabulous narrative opening. That said, like the norther's rush, his article, which I read shortly after its publication in the August 1985 issue of the Pacific Historical Review, blew me away.