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Articles 1411 - 1440 of 2640

Full-Text Articles in Physical Sciences and Mathematics

Analytic And Numerical Studies Of A Simple Model Of Attractive-Repulsive Swarms, Andrew S. Ronan May 2011

Analytic And Numerical Studies Of A Simple Model Of Attractive-Repulsive Swarms, Andrew S. Ronan

HMC Senior Theses

We study the equilibrium solutions of an integrodifferential equation used to model one-dimensional biological swarms. We assume that the motion of the swarm is governed by pairwise interactions, or a convolution in the continuous setting, and derive a continuous model from conservation laws. The steady-state solution found for the model is compactly supported and is shown to be an attractive equilibrium solution via linear perturbation theory. Numerical simulations support that the steady-state solution is attractive for all initial swarm distributions. Some initial results for the model in higher dimensions are also presented.

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Continued Fractions: A New Form, Donald Lee Wiyninger Iii May 2011

Continued Fractions: A New Form, Donald Lee Wiyninger Iii

HMC Senior Theses

While the traditional form of continued fractions is well-documented, a new form, designed to approximate real numbers between 1 and 2, is less well-studied. This report first describes prior research into the new form, describing the form and giving an algorithm for generating approximations for a given real number. It then describes a rational function giving the rational number represented by the continued fraction made from a given tuple of integers and shows that no real number has a unique continued fraction. Next, it describes the set of real numbers that are hardest to approximate; that is, given a positive …

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Noise, Delays, And Resonance In A Neural Network, Austin Quan May 2011

Noise, Delays, And Resonance In A Neural Network, Austin Quan

HMC Senior Theses

A stochastic-delay differential equation (SDDE) model of a small neural network with recurrent inhibition is presented and analyzed. The model exhibits unexpected transient behavior: oscillations that occur at the boundary of the basins of attraction when the system is bistable. These are known as delay-induced transitory oscillations (DITOs). This behavior is analyzed in the context of stochastic resonance, an unintuitive, though widely researched phenomenon in physical bistable systems where noise can play in constructive role in strengthening an input signal. A method for modeling the dynamics using a probabilistic three-state model is proposed, and supported with numerical evidence. The potential …

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A Census Of Vertices By Generations In Regular Tessellations Of The Plane, Alice Paul '12, Nicholas Pippenger Apr 2011

A Census Of Vertices By Generations In Regular Tessellations Of The Plane, Alice Paul '12, Nicholas Pippenger

All HMC Faculty Publications and Research

We consider regular tessellations of the plane as infinite graphs in which q edges and q faces meet at each vertex, and in which p edges and p vertices surround each face. For 1/p + 1/q = 1/2, these are tilings of the Euclidean plane; for 1/p + 1/q < 1/2, they are tilings of the hyperbolic plane. We choose a vertex as the origin, and classify vertices into generations according to their distance (as measured by the number of edges in a shortest path) from the origin. For all p ≥ 3 and q ≥ 3 with 1/p + 1/q ≤ 1/2, we give simple combinatorial derivations of the rational generating functions for the number of vertices in each generation.

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Uniqueness Conditions For Low-Rank Matrix Recovery, Yonina C. Eldar, Deanna Needell, Yaniv Plan Mar 2011

Uniqueness Conditions For Low-Rank Matrix Recovery, Yonina C. Eldar, Deanna Needell, Yaniv Plan

CMC Faculty Publications and Research

Low-rank matrix recovery addresses the problem of recovering an unknown low-rank matrix from few linear measurements. Nuclear-norm minimization is a tractible approach with a recent surge of strong theoretical backing. Analagous to the theory of compressed sensing, these results have required random measurements. For example, m >= Cnr Gaussian measurements are sufficient to recover any rank-r n x n matrix with high probability. In this paper we address the theoretical question of how many measurements are needed via any method whatsoever --- tractible or not. We show that for a family of random measurement ensembles, m >= 4nr - 4r^2 …

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Acceleration Of Randomized Kaczmarz Method Via The Johnson-Lindenstrauss Lemma, Yonina C. Eldar, Deanna Needell Feb 2011

Acceleration Of Randomized Kaczmarz Method Via The Johnson-Lindenstrauss Lemma, Yonina C. Eldar, Deanna Needell

CMC Faculty Publications and Research

The Kaczmarz method is an algorithm for finding the solution to an overdetermined consistent system of linear equations Ax=b by iteratively projecting onto the solution spaces. The randomized version put forth by Strohmer and Vershynin yields provably exponential convergence in expectation, which for highly overdetermined systems even outperforms the conjugate gradient method. In this article we present a modified version of the randomized Kaczmarz method which at each iteration selects the optimal projection from a randomly chosen set, which in most cases significantly improves the convergence rate. We utilize a Johnson-Lindenstrauss dimension reduction technique to keep the runtime on the …

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Bounds For Solid Angles Of Lattices Of Rank Three, Lenny Fukshansky, Sinai Robins Feb 2011

Bounds For Solid Angles Of Lattices Of Rank Three, Lenny Fukshansky, Sinai Robins

CMC Faculty Publications and Research

We find sharp absolute constants C1 and C2 with the following property: every well-rounded lattice of rank 3 in a Euclidean space has a minimal basis so that the solid angle spanned by these basis vectors lies in the interval [C1,C2]. In fact, we show that these absolute bounds hold for a larger class of lattices than just well-rounded, and the upper bound holds for all. We state a technical condition on the lattice that may prevent it from satisfying the absolute lower bound on the solid angle, in which case we …

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What Do We Mean By Mathematical Proof?, Todd Cadwalladerolsker Jan 2011

What Do We Mean By Mathematical Proof?, Todd Cadwalladerolsker

Journal of Humanistic Mathematics

Mathematical proof lies at the foundations of mathematics, but there are several notions of what mathematical proof is, or might be. In fact, the idea of mathematical proof continues to evolve. In this article, I review the body of literature that argues that there are at least two widely held meanings of proof, and that the standards of proof are negotiated and agreed upon by the members of mathematical communities. The formal view of proof is contrasted with the view of proofs as arguments intended to convince a reader. These views are examined in the context of the various roles …

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Aesthetic Considerations In Mathematics, Nathalie Sinclair Jan 2011

Aesthetic Considerations In Mathematics, Nathalie Sinclair

Journal of Humanistic Mathematics

Drawing on some of the principles of humanistic mathematics first outlined by Alvin White, this paper seeks to examine the way in which value judgments are implicated in the growth of the mathematics discipline. After a short overview of some of the roles ascribed to the mathematical aesthetic historically, I turn to more contemporary positioning of the aesthetic in order to develop a framework that offers insight into the particular values, assumptions and desires that constrain what is done in mathematics, how it is done and why. My goal, at least in part, is to bring together under one umbrella …

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Welcome To The Journal Of Humanistic Mathematics, Mark Huber, Gizem Karaali Jan 2011

Welcome To The Journal Of Humanistic Mathematics, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

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Let It Be, Char Miller Jan 2011

Let It Be, Char Miller

Pomona Faculty Publications and Research

No abstract provided.

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Subaerial Freshwater Stromatolites In Deer Cave, Sarawak – A Unique Geobiological Cave Formation, Joyce Lundberg, Donald A. Mcfarlane Jan 2011

Subaerial Freshwater Stromatolites In Deer Cave, Sarawak – A Unique Geobiological Cave Formation, Joyce Lundberg, Donald A. Mcfarlane

WM Keck Science Faculty Papers

A suite of distinctive freshwater subaerial phosphatic stromatolites is developed close to the northeastern entrance of Deer Cave, Gunung Mulu National Park, Sarawak, Borneo, in conditions of very low light but ample supply of nutrients from guano. These stromatolites are not particulate; they are composed of alternating layers of more porous and more dense amorphous hydroxylapatite. This biomineralization occurs as moulds of coccoid (the majority) and filamentous (less abundant) cyanobacteria. Mineralization occurs at a pH of ~ 7.0 in the extracellular sheaths and in micro-domains of varying carbonate content in the surrounding mucus of the biofilm. The most recent surfaces …

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Effect Of Substrate Composition And Alignment On Corneal Cell Phenotype, Donna Phu '09, Lindsay S. Wray '08, Robert V. Warren '10, Richard C. Haskell, Elizabeth J. Orwin Jan 2011

Effect Of Substrate Composition And Alignment On Corneal Cell Phenotype, Donna Phu '09, Lindsay S. Wray '08, Robert V. Warren '10, Richard C. Haskell, Elizabeth J. Orwin

All HMC Faculty Publications and Research

Corneal blindness is a significant problem treated primarily by corneal transplants. Donor tissue supply is low, creating a growing need for an alternative. A tissue-engineered cornea made from patient-derived cells and biopolymer scaffold materials would be widely accessible to all patients and would alleviate the need for donor sources. Previous work in this lab led to a method for electrospinning type I collagen scaffolds for culturing corneal fibroblasts ex vivo that mimics the microenvironment in the native cornea. This electrospun scaffold is composed of small-diameter, aligned collagen fibers. In this study, we investigate the effect of scaffold nanostructure and composition …

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A Space-Filling, Nonregular Tetrahedron, Margaret Cagle, Joyce Frost, Christine Latulippe, Darryl H. Yong Jan 2011

A Space-Filling, Nonregular Tetrahedron, Margaret Cagle, Joyce Frost, Christine Latulippe, Darryl H. Yong

All HMC Faculty Publications and Research

This activity is an investigation of a special nonregular tetrahedron that can be arranged to fill space without leaving any internal gaps in the same way that certain planar figures tessellate the plane. These tetrahedra can be connected together with hinges to make fun and interesting puzzles. More background information can be found in the paper "An Amazing, Space-Filling, Non-Regular Tetrahedron" by Joyce Frost and Peg Cagle, published by the IAS/Park City Mathematics Institute (available at mathforum.org/pcmi/hstp/resources/dodeca/).

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Applications Of Convex And Algebraic Geometry To Graphs And Polytopes, Mohamed Omar Jan 2011

Applications Of Convex And Algebraic Geometry To Graphs And Polytopes, Mohamed Omar

All HMC Faculty Publications and Research

No abstract provided.

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A Primer Of Swarm Equilibria, Andrew J. Bernoff, Chad M. Topaz Jan 2011

A Primer Of Swarm Equilibria, Andrew J. Bernoff, Chad M. Topaz

All HMC Faculty Publications and Research

We study equilibrium configurations of swarming biological organisms subject to exogenous and pairwise endogenous forces. Beginning with a discrete dynamical model, we derive a variational description of the corresponding continuum population density. Equilibrium solutions are extrema of an energy functional and satisfy a Fredholm integral equation. We find conditions for the extrema to be local minimizers, global minimizers, and minimizers with respect to infinitesimal Lagrangian displacements of mass. In one spatial dimension, for a variety of exogenous forces, endogenous forces, and domain configurations, we find exact analytical expressions for the equilibria. These agree closely with numerical simulations of the underlying …

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Evidence Of The Harmonic Faraday Instability In Ultrasonic Atomization Experiments With A Deep, Inviscid Fluid, Andrew P. Higginbotham '09, Aaron Guillen '11, Nathan C. Jones '10, Thomas D. Donnelly, Andrew J. Bernoff Jan 2011

Evidence Of The Harmonic Faraday Instability In Ultrasonic Atomization Experiments With A Deep, Inviscid Fluid, Andrew P. Higginbotham '09, Aaron Guillen '11, Nathan C. Jones '10, Thomas D. Donnelly, Andrew J. Bernoff

All HMC Faculty Publications and Research

A popular method for generating micron-sized aerosols is to submerge ultrasonic (ω~MHz) piezoelectric oscillators in a water bath. The submerged oscillator atomizes the fluid, creating droplets with radii proportional to the wavelength of the standing wave at the fluid surface. Classical theory for the Faraday instability predicts a parametric instability driving a capillary wave at the subharmonic (ω/2) frequency. For many applications it is desirable to reduce the size of the droplets; however, using higher frequency oscillators becomes impractical beyond a few MHz. Observations are presented that demonstrate that smaller droplets may also be created by …

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Strong Nonnegativity And Sums Of Squares On Real Varieties, Mohamed Omar, Brian Osserman Jan 2011

Strong Nonnegativity And Sums Of Squares On Real Varieties, Mohamed Omar, Brian Osserman

All HMC Faculty Publications and Research

Motivated by scheme theory, we introduce strong nonnegativity on real varieties, which has the property that a sum of squares is strongly nonnegative. We show that this algebraic property is equivalent to nonnegativity for nonsingular real varieties. Moreover, for singular varieties, we reprove and generalize obstructions of Gouveia and Netzer to the convergence of the theta body hierarchy of convex bodies approximating the convex hull of a real variety.

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The Cophylogeny Reconstruction Problem Is Np-Complete, Yaniv J. Ovadia '10, Daniel Fielder '11, Chris Conow, Ran Libeskind-Hadas Jan 2011

The Cophylogeny Reconstruction Problem Is Np-Complete, Yaniv J. Ovadia '10, Daniel Fielder '11, Chris Conow, Ran Libeskind-Hadas

All HMC Faculty Publications and Research

The cophylogeny reconstruction problem arises in the study of host-parasite relationships. Specif- ically, we are given a host tree H, a parasite tree P, and a function ' mapping the leaves (extant taxa) of P to the leaves of H. Four biologically plausible operations are considered: cospeciation, duplication, host switching, and loss (Figure 1). A host switch is permitted in conjunction with a duplication event but not with a cospeciation event [1].

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Cultivating Youth Earth Connections Summer Internship Program (Yec): A Hands-On Environmental Justice Focused Farming Program At The High School Level, Samuel Lewis Jan 2011

Cultivating Youth Earth Connections Summer Internship Program (Yec): A Hands-On Environmental Justice Focused Farming Program At The High School Level, Samuel Lewis

Pomona Senior Theses

YEC’s main goal was to open dialogue with high school students from under resourced communities about environmental injustices and to create and explore positive alternatives. The summer program, which was funded by the 2010 Davis Projects for Peace and the Pomona College Summer Undergraduate Research Project Award, included a group of 11 high school students from Pomona, Montclair, La Puente, and Chino Hills, CA. The students were paid to participate in the program for 6 weeks in the summer of 2010, five days a week, for 30 hours each week. The program was designed to consistently connect movements for food …

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Sustainability Reporting Of Eighteen Fortune 500 General Merchandising Companies: How These Companies Address World Environmental And Social Issues, Jaclyn D'Arcy Jan 2011

Sustainability Reporting Of Eighteen Fortune 500 General Merchandising Companies: How These Companies Address World Environmental And Social Issues, Jaclyn D'Arcy

CMC Senior Theses

Climate change affects the health of people and the environment. The U.S. Environmental Protection Agency (EPA) has published research that explains the danger of greenhouse gas emissions on humans, wildlife, and the planet. Initiatives and policies are enacted every day to counter the harm that is done to the environment. Many companies now publish environmental impact reports or Corporate Sustainability Reports (CSR) to promote industry transparency. Participating in environmental and social initiatives is also a competitive advantage for these Fortune 500 companies. Customers can support a company based on their environmental friendliness or social responsibility. Companies are then encouraged to …

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Applying Localized Realized Volatility Modeling To Futures Indices, Luella Fu Jan 2011

Applying Localized Realized Volatility Modeling To Futures Indices, Luella Fu

CMC Senior Theses

This thesis extends the application of the localized realized volatility model created by Ying Chen, Wolfgang Karl Härdle, and Uta Pigorsch to other futures markets, particularly the CAC 40 and the NI 225. The research attempted to replicate results though ultimately, those results were invalidated by procedural difficulties.

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Discrete Variable Representation Of The Angular Variables In Quantum Three-Body Scattering, David Caballero Jan 2011

Discrete Variable Representation Of The Angular Variables In Quantum Three-Body Scattering, David Caballero

CGU Theses & Dissertations

There are many numerical methods to study the quantum mechanical three-body scattering system using the Schrodinger equation. Traditionally, a partial-wave decomposition of the total wave function is carried out first, allowing the scattering system to be solved one partial wave at a time. This is convenient when the interaction is central, causing the total angular momentum to be conserved during the collision process. This is not possible in the presence of a non-central interaction such as a laser field, where the total angular momentum is not conserved during the collision process. The Discrete Variable Representation is a new method for …

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Review: Massey Products On Cycles Of Projective Lines And Trigonometric Solutions Of The Yang-Baxter Equations, Gizem Karaali Jan 2011

Review: Massey Products On Cycles Of Projective Lines And Trigonometric Solutions Of The Yang-Baxter Equations, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

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Complete Graphs Whose Topological Symmetry Groups Are Polyhedral, Erica Flapan, Blake Mellor, Ramin Naimi Jan 2011

Complete Graphs Whose Topological Symmetry Groups Are Polyhedral, Erica Flapan, Blake Mellor, Ramin Naimi

Pomona Faculty Publications and Research

We determine for which m the complete graph Km has an embedding in S3 whose topological symmetry group is isomorphic to one of the polyhedral groupsA4, A5 or S4.

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Do Longer Delays Matter? The Effect Of Prolonging Delay In Ctl Activation, Angela Gallegos, Ami E. Radunskaya Jan 2011

Do Longer Delays Matter? The Effect Of Prolonging Delay In Ctl Activation, Angela Gallegos, Ami E. Radunskaya

Pomona Faculty Publications and Research

The activation of a specific immune response takes place in the lymphoid organs such as the spleen. We present here a simplified model of the proliferation of specific immune cells in the form of a single delay equation. We show that the system can undergo switches in stability as the delay is increased, and we interpret these results in the context of sustaining an effective immune response to a dendritic cell vaccine.

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Coalitions And Cliques In The School Choice Problem, Sinan Aksoy, Alexander Adam Azzam, Chaya Coppersmith, Julie Glass, Gizem Karaali, Xueying Zhao, Xinjing Zhu Jan 2011

Coalitions And Cliques In The School Choice Problem, Sinan Aksoy, Alexander Adam Azzam, Chaya Coppersmith, Julie Glass, Gizem Karaali, Xueying Zhao, Xinjing Zhu

Pomona Faculty Publications and Research

The school choice mechanism design problem focuses on assignment mechanisms matching students to public schools in a given school district. The well-known Gale Shapley Student Optimal Stable Matching Mechanism (SOSM) is the most efficient stable mechanism proposed so far as a solution to this problem. However its inefficiency is well-documented, and recently the Efficiency Adjusted Deferred Acceptance Mechanism (EADAM) was proposed as a remedy for this weakness. In this note we describe two related adjustments to SOSM with the intention to address the same inefficiency issue. In one we create possibly artificial coalitions among students where some students modify their …

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A Topological Approach To Molecular Chirality, Erica Flapan Jan 2011

A Topological Approach To Molecular Chirality, Erica Flapan

Pomona Faculty Publications and Research

Topology is the study of deformations of geometric figures. Chemistry is the study of molecular structures. At first glance these fields seem to have nothing in common. But let’s take a closer look to see how these fields come together in the study of molecular symmetries.

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Review: Nearly Invariant Subspaces For Backwards Shifts On Vector-Valued Hardy Spaces, Stephan Ramon Garcia Jan 2011

Review: Nearly Invariant Subspaces For Backwards Shifts On Vector-Valued Hardy Spaces, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

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Quotient Sets And Diophantine Equations, Stephan Ramon Garcia, Vincent Selhorst-Jones '09, Daniel E. Poore '11, Noah Simon '08 Jan 2011

Quotient Sets And Diophantine Equations, Stephan Ramon Garcia, Vincent Selhorst-Jones '09, Daniel E. Poore '11, Noah Simon '08

Pomona Faculty Publications and Research

Quotient sets U / U = {u / u¹: u, u¹ ϵ U} have been considered several times before in the MONTHLY. We consider more general quotient sets U / V and we apply our results to certain simultaneous Diophantine equations with side constraints.

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