Physical Sciences and Mathematics | Open Access Articles

Whole Foods: Renewable Energy Credits, Green Business, And Capitalist Approaches To Climate Change, Samantha Kanofsky

Pomona Senior Theses

Dedication. Acknowledgements. Preface. Chapter 1: Introduction. Chapter 2: Green Business and Carbon Offsetting. Chapter 3A: Case Study. Chapter 3B: Interview. Chapter 4: Case Study. Chapter 5: Conclusion. Bibliography.

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Noisy Signal Recovery Via Iterative Reweighted L1-Minimization, Deanna Needell

CMC Faculty Publications and Research

Compressed sensing has shown that it is possible to reconstruct sparse high dimensional signals from few linear measurements. In many cases, the solution can be obtained by solving an L1-minimization problem, and this method is accurate even in the presence of noise. Recent a modified version of this method, reweighted L1-minimization, has been suggested. Although no provable results have yet been attained, empirical studies have suggested the reweighted version outperforms the standard method. Here we analyze the reweighted L1-minimization method in the noisy case, and provide provable results showing an improvement in the error bound over the standard bounds.

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Counting On Chebyshev Polynomials, Arthur T. Benjamin, Daniel Walton '07

All HMC Faculty Publications and Research

Chebyshev polynomials have several elegant combinatorial interpretations. Specificially, the Chebyshev polynomials of the first kind are defined by T₀(x) = 1, T₁(x) = x, and T_n(x) = 2x T_n-1(x) - T_n-2(x). Chebyshev polynomials of the second kind U_n(x) are defined the same way, except U₁(x) = 2x. T_n and U_n are shown to count tilings of length n strips with squares and dominoes, where the tiles are given weights and sometimes color. Using these interpretations, many identities satisfied by Chebyshev polynomials can be given …

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A Life Cycle Perspective On Online Community Success, Alicia Iriberri '06, Gondy Leroy

CGU Faculty Publications and Research

Using the information systems lifecycle as a unifying framework, we review online communities research and propose a sequence for incorporating success conditions during initiation and development to increase their chances of becoming a successful community, one in which members participate actively and develop lasting relationships. Online communities evolve following distinctive lifecycle stages and recommendations for success are more or less relevant depending on the developmental stage of the online community. In addition, the goal of the online community under study determines the components to include in the development of a successful online community. Online community builders and researchers will benefit …

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

All HMC Faculty Publications and Research

Optical refrigeration has been demonstrated by several groups of researchers, but the cooling elements have not been thermally linked to realistic heat loads in ways that achieve the desired temperatures. The ideal thermal link will have minimal surface area, provide complete optical isolation for the load, and possess high thermal conductivity. We have designed thermal links that minimize the absorption of fluoresced photons by the heat load using multiple mirrors and geometric shapes including a hemisphere, a kinked waveguide, and a tapered waveguide. While total link performance is dependent on additional factors, we have observed net transmission of photons with …

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An Undescribed Gecko (Gekkonidae: Cyrtodactylus) From Deer Cave, Gunung Mulu National Park, Sarawak, With Comments On The Distribution Of Bornean Cave Geckos, Donald A. Mcfarlane, Joyce Lundberg, Keith Christenson

WM Keck Science Faculty Papers

Geckos of the genus Cyrtodactylus are a speciose group in Southeast Asia, with at least nine species known from the island of Borneo (Das & Ismail, 2001; Das, 2006). Of these species, Cyrtodactylus cavernicolus has the smallest known range and is therefore the most vulnerable, a status that is reflected in the species having been designated a Totally Protected Species in Sarawak. Confirmed records of C. cavernicolus are known only from Niah Cave, located in an isolated limestone block known as the Gunung Subis massif, approximately 13 km² in extent. The Niah Cave Gecko is presumed to be dependent on …

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Bats And Bell Holes: The Microclimatic Impact Of Bat Roosting, Using A Case Study From Runaway Bay Caves, Jamaica, Joyce Lundberg, Donald A. Mcfarlane

WM Keck Science Faculty Papers

The microclimatic effect of bats roosting in bell holes (blind vertical cylindrical cavities in cave roofs) in Runaway Bay Caves, Jamaica, was measured and the potential impact of their metabolism on dissolution modelled. Rock temperature measurements showed that bell holes with bats get significantly hotter than those without bats during bat roosting periods (by an average of 1.1 °C). The relationship is clearest for bell holes with more than about 300 g aggregate bat body mass and for bell holes that are moderately wide and deep, of W:D ratio between 0.8 and 1.6. Measurement of temperature decay after abandonment showed …

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Why Did Lagrange "Prove" The Parallel Postulate?, Judith V. Grabiner

Pitzer Faculty Publications and Research

In 1806, Joseph-Louis Lagrange read a memoir "proving" Euclid's parallel postulate to the Institut de France in Paris. The memoir still exists in manuscript, and we’ll look at what it says. We ask why he tried to prove the postulate, and why he attacked the problem in the way that he did. We also look at how the ideas in this manuscript are related to such things as Lagrange’s philosophy of mathematics, artists’ ideas about space, Newtonian mechanics, and Leibniz's Principle of Sufficient Reason. Finally, we reflect on how this episode changes our views about eighteenth-century attitudes toward geometry, space, …

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Review: A Class Of Solutions To The Quantum Colored Yang-Baxter Equation, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

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Mathematical Model Creation For Cancer Chemo-Immunotherapy, Lisette G. De Pillis, K Renee Fister, Weiqing Gu, Craig Collins, Michael Daub, David Gross '08, James Moore '07, Benjamin Preskill '09

All HMC Faculty Publications and Research

One of the most challenging tasks in constructing a mathematical model of cancer treatment is the calculation of biological parameters from empirical data. This task becomes increasingly difficult if a model involves several cell populations and treatment modalities. A sophisticated model constructed by de Pillis et al., Mixed immunotherapy and chemotherapy of tumours: Modelling, applications and biological interpretations, J. Theor. Biol. 238 (2006), pp. 841–862; involves tumour cells, specific and non-specific immune cells (natural killer (NK) cells, CD8 T cells and other lymphocytes) and employs chemotherapy and two types of immunotherapy (IL-2 supplementation and CD8 T-cell infusion) as treatment modalities. …

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Stability Of Traveling Waves In Thin Liquid Films Driven By Gravity And Surfactant, Ellen Peterson, Michael Shearer, Thomas P. Witelski, Rachel Levy

All HMC Faculty Publications and Research

A thin layer of fluid flowing down a solid planar surface has a free surface height described by a nonlinear PDE derived via the lubrication approximation from the Navier Stokes equations. For thin films, surface tension plays an important role both in providing a significant driving force and in smoothing the free surface. Surfactant molecules on the free surface tend to reduce surface tension, setting up gradients that modify the shape of the free surface. In earlier work [12, 13J a traveling wave was found in which the free surface undergoes three sharp transitions, or internal layers, and the surfactant …

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On The Computational Complexity Of The Reticulate Cophylogeny Reconstruction Problem, Ran Libeskind-Hadas, Michael A. Charleston

All HMC Faculty Publications and Research

The cophylogeny reconstruction problem is that of finding minimal cost explanations of differences between evolutionary histories of ecologically linked groups of biological organisms. We present a proof that shows that the general problem of reconciling evolutionary histories is NP-complete and provide a sharp boundary where this intractability begins. We also show that a related problem, that of finding Pareto optimal solutions, is NP-hard. As a byproduct of our results, we give a framework by which meta-heuristics can be applied to find good solutions to this problem.

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Integral Orthogonal Bases Of Small Height For Real Polynomial Spaces, Lenny Fukshansky

CMC Faculty Publications and Research

Let P_N(R) be the space of all real polynomials in N variables with the usual inner product < , > on it, given by integrating over the unit sphere. We start by deriving an explicit combinatorial formula for the bilinear form representing this inner product on the space of coefficient vectors of all polynomials in P_N(R) of degree ≤ M. We exhibit two applications of this formula. First, given a finite dimensional subspace V of P_N(R) defined over Q, we prove the existence of an orthogonal basis for (V, < , >), consisting of polynomials of small height …

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Search Bounds For Zeros Of Polynomials Over The Algebraic Closure Of Q, Lenny Fukshansky

CMC Faculty Publications and Research

We discuss existence of explicit search bounds for zeros of polynomials with coefficients in a number field. Our main result is a theorem about the existence of polynomial zeros of small height over the field of algebraic numbers outside of unions of subspaces. All bounds on the height are explicit.

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The Pixtalk Communication System A Smartphone Application And Companion Website For The Improvement Of Communication Skills Of Children With Autism, Gondy Leroy, Gianluca De Leo

CGU Faculty Publications and Research

No abstract provided.

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Persuading Consumers To Form Precise Search Engine Queries, Gondy Leroy

CGU Faculty Publications and Research

Today’s search engines provide a single textbox for searching. This input method has not changed in decades and, as a result, consumer search behaviour has not changed either: few and imprecise keywords are used. Especially with health information, where incorrect information may lead to unwise decisions, it would be beneficial if consumers could search more precisely. We evaluated a new user interface that supports more precise searching by using query diagrams. In a controlled user study, using paper-based prototypes, we compared searching with a Google interface with drawing new or modifying template diagrams. We evaluated consumer willingness and ability to …

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Natural Medicine: Personal Responsibility And Self-Empowerment, Kimber Lopez

Pomona Senior Theses

Although most “alternative” medical practices have existed far longer than conventional healthcare, modern allopathic continues to be the dominant system of medicine used in the United States. Herbal medicine is one of the oldest healing practices known to humankind and continues to be practiced today despite the numerous challenges modern society poses. As Julie Stone and Joan Mathews illuminate in Complimentary Medicine and the Law, “Plant-based remedies have been the principal source of medicines in healing traditions around the world and, as the World health Organization is at pains to remind us, 80 percent of the world’s population still depends …

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Review: On Quantum Yang-Baxter Coherent Algebra Sheaves, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

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Mathematical Aids Epidemic Model: Preferential Anti-Retroviral Therapy Distribution In Resource Constrained Countries, Nadia Abuelezam

HMC Senior Theses

HIV/AIDS is one of the largest health problems the world is currently facing. Even with anti-retroviral therapies (ART), many resource-constrained countries are unable to meet the treatment needs of their infected populations. ART-distribution methods need to be created that prevent the largest number of future HIV infections. We have developed a compartment model that tracks the spread of HIV in multiple two-sex populations over time in the presence of limited treatment. The model has been fit to represent the HIV epidemic in rural and urban areas in Uganda. With the model we examine the spread of HIV among urban and …

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Review: Spectra Of Toeplitz Operators And Compositions Of Muckenhoupt Weights With Blaschke Products, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

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Truncated Toeplitz Operators: Spatial Isomorphism, Unitary Equivalence, And Similarity, Joseph A. Cima, Stephan Ramon Garcia, William T. Ross, Warren R. Wogen

Pomona Faculty Publications and Research

A truncated Toeplitz operator A φ : K Θ → K Θ is the compression of a Toeplitz operator T φ : H 2 → H 2 to a model space K Θ ≔ H 2 ⊖ Θ H 2 . For Θ inner, let T Θ denote the set of all bounded truncated Toeplitz operators on K Θ . Our main result is a necessary and sufficient condition on inner functions Θ 1 and Θ 2 which guarantees that T Θ 1 and T Θ 2 are spatially isomorphic (i.e., U T Θ 1 = T Θ 2 U …

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The Norm And Modulus Of A Foguel Operator, Stephan Ramon Garcia

Pomona Faculty Publications and Research

We develop a method for calculating the norm and the spectrum of the modulus of a Foguel operator. In many cases, the norm can be computed exactly. In others, sharp upper bounds are obtained. In particular, we observe several connections between Foguel operators and the Golden Ratio.

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Review: Dynamical Yang-Baxter Maps With An Invariance Condition, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

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Predicting The Drug Release Kinetics Of Matrix Tablets, Boris Baeumer, Lipika Chatterjee, Peter Hinow, Thomas Rades, Ami E. Radunskaya, Ian Tucker

Pomona Faculty Publications and Research

In this paper we develop two mathematical models to predict the release kinetics of a water soluble drug from a polymer/excipient matrix tablet. The first of our models consists of a random walk on a weighted graph, where the vertices of the graph represent particles of a drug, excipient and polymer, respectively. The graph itself is the contact graph of a multidisperse random sphere packing. The second model describes the dissolution and the subsequent diffusion of the active drug out of a porous matrix using a system of a partial differential equations. The predictions of both models show good qualitative …

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Review: Hankel And Toeplitz Transforms On H¹: Continuity, Compactness And Fredholm Properties, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

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Complex Symmetric Partial Isometries, Stephan Ramon Garcia, Warren R. Wogen

Pomona Faculty Publications and Research

An operator $T \in B(\h)$ is complex symmetric if there exists a conjugate-linear, isometric involution $C:\h\to\h$ so that $T = CT^*C$. We provide a concrete description of all complex symmetric partial isometries. In particular, we prove that any partial isometry on a Hilbert space of dimension $\leq 4$ is complex symmetric.

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Every Graph Has An Embedding In S³ Containing No Non-Hyperbolic Knot, Erica Flapan, Hugh Howards

Pomona Faculty Publications and Research

In contrast with knots, whose properties depend only on their extrinsic topology in S³ , there is a rich interplay between the intrinsic structure of a graph and the extrinsic topology of all embeddings of the graph in S³ . For example, it was shown by Conway and Gordon that every embedding of the complete graph K_7 in S³ contains a non-trivial knot. Later it was shown that for every m ∈ N there is a complete graph K_n such that every embedding of K_n in S³ contains a knot Q whose minimal crossing number is at least m. …

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Review: Graded Structure And Hopf Structures In Parabosonic Algebra. An Alternative Approach To Bosonisation, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

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Review: Solutions For The Constant Quantum Yang-Baxter Equation From Lie (Super)Algebras, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

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Review: Set-Theoretic Solutions Of The Yang-Baxter Equation, Graphs And Computations, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

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Full-Text Articles in Physical Sciences and Mathematics

Whole Foods: Renewable Energy Credits, Green Business, And Capitalist Approaches To Climate Change, Samantha Kanofsky

Pomona Senior Theses

Noisy Signal Recovery Via Iterative Reweighted L1-Minimization, Deanna Needell

CMC Faculty Publications and Research

Counting On Chebyshev Polynomials, Arthur T. Benjamin, Daniel Walton '07

All HMC Faculty Publications and Research

A Life Cycle Perspective On Online Community Success, Alicia Iriberri '06, Gondy Leroy

CGU Faculty Publications and Research

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

All HMC Faculty Publications and Research

An Undescribed Gecko (Gekkonidae: Cyrtodactylus) From Deer Cave, Gunung Mulu National Park, Sarawak, With Comments On The Distribution Of Bornean Cave Geckos, Donald A. Mcfarlane, Joyce Lundberg, Keith Christenson

WM Keck Science Faculty Papers

Bats And Bell Holes: The Microclimatic Impact Of Bat Roosting, Using A Case Study From Runaway Bay Caves, Jamaica, Joyce Lundberg, Donald A. Mcfarlane

WM Keck Science Faculty Papers

Why Did Lagrange "Prove" The Parallel Postulate?, Judith V. Grabiner

Pitzer Faculty Publications and Research

Review: A Class Of Solutions To The Quantum Colored Yang-Baxter Equation, Gizem Karaali

Pomona Faculty Publications and Research

Mathematical Model Creation For Cancer Chemo-Immunotherapy, Lisette G. De Pillis, K Renee Fister, Weiqing Gu, Craig Collins, Michael Daub, David Gross '08, James Moore '07, Benjamin Preskill '09

All HMC Faculty Publications and Research

Stability Of Traveling Waves In Thin Liquid Films Driven By Gravity And Surfactant, Ellen Peterson, Michael Shearer, Thomas P. Witelski, Rachel Levy

All HMC Faculty Publications and Research

On The Computational Complexity Of The Reticulate Cophylogeny Reconstruction Problem, Ran Libeskind-Hadas, Michael A. Charleston

All HMC Faculty Publications and Research

Integral Orthogonal Bases Of Small Height For Real Polynomial Spaces, Lenny Fukshansky

CMC Faculty Publications and Research

Search Bounds For Zeros Of Polynomials Over The Algebraic Closure Of Q, Lenny Fukshansky

CMC Faculty Publications and Research

The Pixtalk Communication System A Smartphone Application And Companion Website For The Improvement Of Communication Skills Of Children With Autism, Gondy Leroy, Gianluca De Leo

CGU Faculty Publications and Research

Persuading Consumers To Form Precise Search Engine Queries, Gondy Leroy

CGU Faculty Publications and Research

Natural Medicine: Personal Responsibility And Self-Empowerment, Kimber Lopez

Pomona Senior Theses

Review: On Quantum Yang-Baxter Coherent Algebra Sheaves, Gizem Karaali

Pomona Faculty Publications and Research

Mathematical Aids Epidemic Model: Preferential Anti-Retroviral Therapy Distribution In Resource Constrained Countries, Nadia Abuelezam

HMC Senior Theses

Review: Spectra Of Toeplitz Operators And Compositions Of Muckenhoupt Weights With Blaschke Products, Stephan Ramon Garcia

Pomona Faculty Publications and Research

Truncated Toeplitz Operators: Spatial Isomorphism, Unitary Equivalence, And Similarity, Joseph A. Cima, Stephan Ramon Garcia, William T. Ross, Warren R. Wogen

Pomona Faculty Publications and Research

The Norm And Modulus Of A Foguel Operator, Stephan Ramon Garcia

Pomona Faculty Publications and Research

Review: Dynamical Yang-Baxter Maps With An Invariance Condition, Gizem Karaali

Pomona Faculty Publications and Research

Predicting The Drug Release Kinetics Of Matrix Tablets, Boris Baeumer, Lipika Chatterjee, Peter Hinow, Thomas Rades, Ami E. Radunskaya, Ian Tucker

Pomona Faculty Publications and Research

Review: Hankel And Toeplitz Transforms On H¹: Continuity, Compactness And Fredholm Properties, Stephan Ramon Garcia

Pomona Faculty Publications and Research

Complex Symmetric Partial Isometries, Stephan Ramon Garcia, Warren R. Wogen

Pomona Faculty Publications and Research

Every Graph Has An Embedding In S³ Containing No Non-Hyperbolic Knot, Erica Flapan, Hugh Howards

Pomona Faculty Publications and Research

Review: Graded Structure And Hopf Structures In Parabosonic Algebra. An Alternative Approach To Bosonisation, Gizem Karaali

Pomona Faculty Publications and Research

Review: Solutions For The Constant Quantum Yang-Baxter Equation From Lie (Super)Algebras, Gizem Karaali

Pomona Faculty Publications and Research

Review: Set-Theoretic Solutions Of The Yang-Baxter Equation, Graphs And Computations, Gizem Karaali

Pomona Faculty Publications and Research