Digital Commons Network^™

Is Leed A True Leader? Studying The Effectiveness Of Leed Certification In Encouraging Green Building, Megan M. Turner

Pomona Senior Theses

Leadership in Energy and Environmental Design (or LEED) is the most commonly used green building rating system in the United States, bestowing upon LEED certified buildings the prestige of being considered more sustainable than their non-certified neighbors. The public often assumes that LEED certified buildings are completely sustainable or even net-zero with regards to greenhouse gas emissions, but in actuality buildings certified under the most popular version of LEED are only required to be 15% more energy efficient than required by most state building codes – a far cry from the energy usage cuts needed to stave off global warming. …

When Curiosity Kills More Than The Cat: The Perils Of Unchecked Scientific Inquiry, Jamie Shannon

Pomona Senior Theses

This work analyzes the ecological, physical, emotional and health impacts of the US nuclear testing done in the Marshall Islands in the mid-20th century.

Sums Of Evenly Spaced Binomial Coefficients, Arthur T. Benjamin, Bob Chen '10, Kimberly Kindred

All HMC Faculty Publications and Research

We provide a combinatorial proof of a formula for the sum of evenly spaced binomial coefficients. This identity, along with a generalization, are proved by counting weighted walks on a graph.

Intra-Industry Trade And The Open Economy, Sven W. Arndt

CMC Faculty Publications and Research

This paper explores the implications of cross-border production networks and vertical intra-industry trade for macroeconomic adjustment and for the effectiveness of monetary and fiscal stabilization policies. Vertical intra-industry trade introduces direct links between countries’ imports and exports and thereby affects the manner in which trade balances respond to variations in exchange rates and to global shocks more generally. The precise effects depend on whether the direct link runs from exports to imports or vice versa. In the U.S., for example, exports of auto parts and components rise with an increase of imports of passenger vehicles from Mexico. This produces a …

Between, Summer Janelle

CGU MFA Theses

My art evolves out of deep attentiveness to idiosyncratic aspects of mundane experience. These aspects of experience are manifested through body language, gestures, facial expressions, and the peripheral hunch. They arise from the awkward and pleasurable peculiarities of interacting with humanity on a daily basis. My work also touches upon fantasies and private thoughts that can determine behavior when individuals interact.Please see Download button in top right corner for the full statement.

Learning About Odes Using Interactive Online Modules, Kuva Jacobs, David Panton

CODEE Journal

This paper discusses the development and implementation of a set of online teaching and learning modules for the modeling and solution of simple linear Ordinary Differential Equations (ODEs). The paper describes how constructivist principles are used in the development of these modules and how in-built assessment has been used to enhance student learning. A discussion of the module structure is provided with particular emphasis on the concept of the module walk-through. Modules developed for the classical ODE problems of the simple pendulum and the mass on a spring are used to illustrate these module constructs. The paper concludes with a …

Teaching Research: Encouraging Discoveries, Francis E. Su

All HMC Faculty Publications and Research

What does it take to turn a learner into a discoverer? Or to turn a teacher into a co-adventurer? A handful of experiences—from teaching a middle-school math class to doing research with undergraduates—have changed the way that I would answer these questions. Some of the lessons I’ve learned have surprised me.

Engineering Flow States With Localized Forcing In A Thin, Marangoni-Driven Inclined Film, Rachel Levy, Stephen Rosenthal '09, Jeffrey Wong '11

All HMC Faculty Publications and Research

Numerical simulations of lubrication models provide clues for experimentalists about the development of wave structures in thin liquid films. We analyze numerical simulations of a lubrication model for an inclined thin liquid film modified by Marangoni forces due to a thermal gradient and additional localized forcing heating the substrate. Numerical results can be explained through connections to theory for hyperbolic conservation laws predicting wave fronts from Marangoni-driven thin films without forcing. We demonstrate how a variety of forcing profiles, such as Gaussian, rectangular, and triangular, affect the formation of downstream transient structures, including an N wave not commonly discussed in …

Compressed Sensing With Coherent And Redundant Dictionaries, Emmanuel J. Candès, Yonina C. Eldar, Deanna Needell, Paige Randall

CMC Faculty Publications and Research

This article presents novel results concerning the recovery of signals from undersampled data in the common situation where such signals are not sparse in an orthonormal basis or incoherent dictionary, but in a truly redundant dictionary. This work thus bridges a gap in the literature and shows not only that compressed sensing is viable in this context, but also that accurate recovery is possible via an ℓ₁-analysis optimization problem. We introduce a condition on the measurement/sensing matrix, which is a natural generalization of the now well-known restricted isometry property, and which guarantees accurate recovery of signals that are …

"Toward Integration: From Quantitative Biology To Mathbio-Biomath?", Pat Marsteller, Lisette G. De Pillis, Ann Findley, Karl Joplin, John Pelesko, Karen Nelson, Katerina Thompson, David Usher, Joseph Watkins

All HMC Faculty Publications and Research

In response to the call of BIO2010 for integrating quantitative skills into undergraduate biology education, 30 Howard Hughes Medical Institute (HHMI) Program Directors at the 2006 HHMI Program Directors Meeting established a consortium to investigate, implement, develop, and disseminate best practices resulting from the integration of math and biology. With the assistance of an HHMI-funded mini-grant, led by Karl Joplin of East Tennessee State University, and support in institutional HHMI grants at Emory and University of Delaware, these institutions held a series of summer institutes and workshops to document progress toward and address the challenges of implementing a more quantitative …

Dislocations And Vacancies In Two-Dimensional Mixed Crystals Of Spheres And Dimers, Sharon J. Gerbode, Desmond C. Ong, Chekesha M. Liddell, Itai Cohen

All HMC Faculty Publications and Research

In colloidal crystals of spheres, dislocation motion is unrestricted. On the other hand, recent studies of relaxation in crystals of colloidal dimer particles have demonstrated that the dislocation dynamics in such crystals are reminiscent of glassy systems. The observed glassy dynamics arise as a result of dislocation cages formed by certain dimer orientations. In the current study, we use experiments and simulations to investigate the transition that arises when a pure sphere crystal is doped with an increasing concentration of dimers. Specifically, we focus on both dislocation caging and vacancy motion. Interestingly, we find that any nonzero fraction of dimers …

Existence Of Solutions For A Semilinear Wave Equation With Non-Monotone Nonlinearity, Alfonso Castro, Benjamin Preskill '09

All HMC Faculty Publications and Research

For double-periodic and Dirichlet-periodic boundary conditions, we prove the existence of solutions to a forced semilinear wave equation with asymptotically linear nonlinearity, no resonance, and non-monotone nonlinearity when the forcing term is not flat on characteristics. The solutions are in L^∞ when the forcing term is in L^∞ and continous when the forcing term is continuous. This is in contrast with the results in [4], where the non-enxistence of continuous solutions is established even when forcing term is of class C^∞ but is flat on a characteristic.

Algebraic Points Of Small Height Missing A Union Of Varieties, Lenny Fukshansky

CMC Faculty Publications and Research

Let K be a number field, Q, or the field of rational functions on a smooth projective curve over a perfect field, and let V be a subspace of K^N where N≥ 2. Let Z_K be a union of varieties defined over K such that V ⊈ Z_K. We prove the existence of a point of small height in V \ Z_K, providing an explicit upper bound on the height of such a point in terms of the height of V and the degree of hypersurface containing Z_K, where dependence on …

Impulsivity, Impulsive And Reflective Processes And The Development Of Alcohol Use And Misuse In Adolescents And Young Adults, Reinout W. Wiers, Susan L. Ames, Wilhelm Hofmann, Marvin Krank, Alan W. Stacy

CGU Faculty Publications and Research

This paper contrasts dual-process and personality approaches in the prediction of addictive behaviors and related risk behaviors. In dual-process models, behavior is described as the joint outcome of qualitatively different “impulsive” (or associative) and “reflective” processes. There are important individual differences regarding both types of processes, and the relative strength of both in a specific situation is influenced by prior behavior and state variables (e.g., fatigue, alcohol use). From this perspective, a specific behavior (e.g., alcohol misuse) can be predicted by the combined indices of the behavior-related impulsive processes (e.g., associations with alcohol), and reflective processes, including the ability to …

Scriptures, Vincent L. Wimbush

CGU Faculty Publications and Research

Introduction

Interchangeable with holy/sacred book, “scriptures” is the English language term that is still popularly used to refer to a text or collection of texts deemed to be of special if not unique origins, authority and power. Users of the term also tend to assume that “the Bible” of the Jewish and Christian traditions represents either the only instance of such or the example par excellence among some others. A popular linguistic and rhetorical placeholder among cultures of Indo-European origins, the English term originally simply meant (from the Greek graphe/-ai, ta biblia; Latin, scriptura/-ae; Hebrew, ketav/-uvim) and continues to mean …

Teaching Introductory Differential Equations With Scicoslab, Stephen Campbell, Ramine Nikoukhah

CODEE Journal

Perhaps the largest and most capable open source software for doing applied mathematics is the open source package Scicoslab. Widely used in Europe and Asia it is less well known in the United States. In this article we will explain how ScicosLab can be easily used to help teach differential equations and to also introduce students to a software package that they can take with them for the rest of their careers.

Neural Reuse As A Source Of Developmental Homology, David S. Moore, Chris Moore

Pitzer Faculty Publications and Research

Neural reuse theories should interest developmental psychologists because these theories can potentially illuminate the developmental relations among psychological characteristics observed across the lifespan. Characteristics that develop by exploiting pre-existing neural circuits can be thought of as developmental homologues. And, understood in this way, the homology concept that has proven valuable for evolutionary biologists can be used productively to study psychological/behavioral development.

Glassy Dislocation Dynamics In 2d Colloidal Dimer Crystals, Sharon J. Gerbode, Ugmang Agarwal, Desmond C. Ong, Chekesha M. Liddell, Fernando Escobedo, Itai Cohen

All HMC Faculty Publications and Research

Although glassy relaxation is typically associated with disorder, here we report on a new type of glassy dynamics relating to dislocations within 2D crystals of colloidal dimers. Previous studies have demonstrated that dislocation motion in dimer crystals is restricted by certain particle orientations. Here, we drag an optically trapped particle through such dimer crystals, creating dislocations. We find a two-stage relaxation response where initially dislocations glide until encountering particles that cage their motion. Subsequent relaxation occurs logarithmically slowly through a second process where dislocations hop between caged configurations. Finally, in simulations of sheared dimer crystals, the dislocation mean squared displacement …

Combinatorial Trigonometry With Chebyshev Polynomials, Arthur T. Benjamin, Larry Ericksen, Pallavi Jayawant, Mark Shattuck

All HMC Faculty Publications and Research

We provide a combinatorial proof of the trigonometric identity cos(n_{θ) =} T_ncos(θ),
where T_n is the Chebyshev polynomial of the first kind. We also provide combinatorial proofs of other trigonometric identities, including those involving Chebyshev polynomials of the second kind.

Combinatorially Composing Chebyshev Polynomials, Arthur T. Benjamin, Daniel Walton '07

All HMC Faculty Publications and Research

We present a combinatorial proof of two fundamental composition identities associated with Chebyshev polynomials. Namely, for all m, n ≥ 0, T_m(T_n(x)) = T_mn(x) and U_m-1 (T_n(x))U_n-1(x) = U_mn-1(x).

Kinematic Evidence For Superfast Locomotory Muscle In Two Species Of Teneriffiid Mites, Grace C. Wu, Jonathan C. Wright, Dwight L. Whitaker, Anna N. Ahn

All HMC Faculty Publications and Research

Locomotory muscles typically operate over a narrow range of contraction frequencies, characterized by the predominant fiber types and functional roles. The highest documented frequencies in the synchronous sound-producing muscles of insects (550 Hz) and toadfish (200 Hz) far exceed the contraction frequencies observed in weight-bearing locomotory muscles, which have maximum documented frequencies below 15-30 Hz. Laws of scaling, however, predict that smaller arthropods may employ stride frequencies exceeding this range. In this study we measured running speed and stride frequency in two undescribed species of teneriffiid mites from the coastal sage scrub of southern California. Relative speeds of both species …

Teaching Differential Equations With Modeling And Visualization, Mike Huber

CODEE Journal

In this article, I explain the history of using Interdisciplinary Lively Applications Projects (ILAPs) in an ordinary differential equations course. Students want to learn methods to "solve real world problems," and incorporating ILAPs into the syllabus has been an effective way to apply solution methods to situations that students may encounter in other disciplines. Feedback has been positive and will be shared. Examples of ILAPs currently used will be referenced. For more information about how to develop ILAPs, see Huber and Myers (in "Innovative Approaches to Undergraduate Mathematics Courses Beyond Calculus," 2005). Included with this document are three Interdisciplinary Lively …

Review: Michael C. Carhart, The Science Of Culture In Enlightenment Germany, Andre Wakefield

Pitzer Faculty Publications and Research

This is a book review of The Science of Culture in Enlightenment Germany, by Michael C. Carhart. It is an entertaining book. Its chapters are organized around a series of vignettes: Carsten Niebuhr on camelback negotiating with his Bedouin guides; feral French children skinning rabbits with their bare hands; English gentlemen in Syrian deserts; Captian Cooks lieutenants carving "steaks" from teh severed heads of war victims. In case you've lost your bearings, let me assure you that The Science of Culture in Enlightenment Germany is indeed about Enlightenment Germany. But as the structure of the chapters suggests, Michael Carhart …

Review: Karin Hartbecke, Zwischen Fürstenwillkür Und Menschheitswohl: Gottfried Wilhelm Leibniz Als Bibliothekar, Andre Wakefield

Pitzer Faculty Publications and Research

This is a book review of Zwischen Fürstenwillkür und Menschheitswohl: Gottfried Wilhelm Leibniz als Bibliothekar, edited by Karin Hartbecke. The title of the volume—at least the part before the colon—is misleading. This is not really a book about the tension between human welfare and absolute monarchy. It is instead an extended effort to reconstruct Leibniz's practices of categorizing and acquiring books; it is also about the relationship between Leibniz's written reflections on categorizing books and those practices.

From Surface Operators To Non-Abelian Volume Operators In Puff Field Theory, Vatche Sahakian

All HMC Faculty Publications and Research

Puff field theory (PFT) is a low energy decoupling regime of string theory that still retains the nonlocal attributes of the parent theory—while preserving isotropy for its nonlocal degrees of freedom. It realizes an extended holographic dictionary at strong coupling and dynamical nonlocal states akin to defects or the surface operators of local gauge theories. In this work, we probe the nonlocal features of PFT using D3 branes. We find supersymmetric configurations that end on defects endowed with non-Abelian degrees of freedom. These are 2+1 dimensional defects in the 3+1 dimensional PFT that may be viewed as volume operators. We …

Arithmetic On Specializable Continued Fractions, Ross C. Merriam

HMC Senior Theses

No abstract provided.

Minimal Circuits For Very Incompletely Specified Boolean Functions, Richard Strong Bowen

HMC Senior Theses

In this report, asymptotic upper and lower bounds are given for the minimum number of gates required to compute a function which is only partially specified and for which we allow a certain amount of error. The upper and lower bounds match. Hence, the behavior of these minimum circuit sizes is completely (asymptotically) determined.

Combinatorial Proofs Using Complex Weights, Bo Chen

HMC Senior Theses

In 1961, Kasteleyn, Fisher, and Temperley gave a result for the number of possible tilings of a 2m 2n checkerboard with dominoes. Their proof involves the evaluation of a complicated Pfaffian. In this thesis we investigate combinatorial strategies to evaluate the sum of evenly spaced binomial coefficients, and present steps towards a purely combinatorial proof of the 1961 result.

Computational Feasibility Of Increasing The Visibility Of Vertices In Covert Networks, Yaniv J. Ovadia

HMC Senior Theses

Disrupting terrorist and other covert networks requires identifying and capturing key leaders. Previous research by Martonosi et al. (2009) defines a load metric on vertices of a covert network representing the amount of communication in which a vertex is expected to participate. They suggest that the visibility of a target vertex can be increased by removing other, more accessible members of the network. This report evaluates the feasibility of efficiently calculating the optimal subset of vertices to remove. We begin by proving that the general problem of identifying the optimally load maximizing vertex set removal is NP-complete. We then consider …

Group Frames And Partially Ranked Data, Kwang B. Ketcham

HMC Senior Theses

We give an overview of finite group frames and their applications to calculating summary statistics from partially ranked data, drawing upon the work of Rachel Cranfill (2009). We also provide a summary of the representation theory of compact Lie groups. We introduce both of these concepts as possible avenues beyond finite group representations, and also to suggest exploration into calculating summary statistics on Hilbert spaces using representations of Lie groups acting upon those spaces.