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Articles 1 - 30 of 61
Full-Text Articles in Physical Sciences and Mathematics
Is Leed A True Leader? Studying The Effectiveness Of Leed Certification In Encouraging Green Building, Megan M. Turner
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
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
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.
Teaching Research: Encouraging Discoveries, Francis E. Su
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
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
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
"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
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
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
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 KN where N≥ 2. Let ZK be a union of varieties defined over K such that V ⊈ ZK. We prove the existence of a point of small height in V \ ZK, 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 ZK, where dependence on …
Glassy Dislocation Dynamics In 2d Colloidal Dimer Crystals, Sharon J. Gerbode, Ugmang Agarwal, Desmond C. Ong, Chekesha M. Liddell, Fernando Escobedo, Itai Cohen
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
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(nθ) = Tncos(θ),
where Tn 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
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, Tm(Tn(x)) = Tmn(x) and Um-1 (Tn(x))Un-1(x) = Umn-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
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 …
From Surface Operators To Non-Abelian Volume Operators In Puff Field Theory, Vatche Sahakian
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
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
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
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
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
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.
A Nonlinear Ode Model Of Tumor Growth And Effect Of Immunotherapy And Chemotherapy Treatment In Colorectal Cancer, Hannah P. Savage
A Nonlinear Ode Model Of Tumor Growth And Effect Of Immunotherapy And Chemotherapy Treatment In Colorectal Cancer, Hannah P. Savage
HMC Senior Theses
Colorectal cancer will kill approximately 50,000 people in the United States this year. Current treatment options, including surgery, chemotherapy, and radiation, are often able to force the cancer into remission, but better treatments are needed to help those who don't respond to current treatments. A new and promising treatment option, monoclonal-antibody therapy, has the potential to help reduce the deaths caused by colorectal cancer, but most monoclonal-antibody drugs are currently still in trial phases, and the variations in the dosing schedule of those currently approved for use have not been heavily explored. We have modified a nonlinear ODE tumor/treatment model …
A Multistage Incidence Estimation Model For Diseases With Differential Mortality, Alyssa W. Dray
A Multistage Incidence Estimation Model For Diseases With Differential Mortality, Alyssa W. Dray
HMC Senior Theses
According to theWorld Health Organization, surgically removable cataract remains the leading cause of blindness worldwide. In sub-Saharan Africa, cataract surgical rate targets should ideally be set based on cataract incidence (the number of new cataracts developed each year). Unfortunately, the longitudinal studies necessary to measure incidence have not yet been feasible in these areas. Our research instead proposes a method for estimating incidence based on available cataract prevalence data. We extend a method proposed by Podgor and Leske (1986) to estimate age-specific incidence from age-specific prevalence in single diseases with differential mortality. A two-stage disease extension is created in order …
Optimizing Restaurant Reservation Scheduling, Jacob Feldman
Optimizing Restaurant Reservation Scheduling, Jacob Feldman
HMC Senior Theses
We consider a yield-management approach to determine whether a restaurant should accept or reject a pending reservation request. This approach was examined by Bossert (2009), where the decision for each request is evaluated by an approximate dynamic program (ADP) that bases its decision on a realization of future demand. This model only considers assigning requests to their desired time slot. We expand Bossert's ADP model to incorporate an element of flexibility that allows requests to be assigned to a time slot that differs from the customer's initially requested time. To estimate the future seat utilization given a particular decision, a …
Understanding Voting For Committees Using Wreath Products, Stephen C. Lee
Understanding Voting For Committees Using Wreath Products, Stephen C. Lee
HMC Senior Theses
In this thesis, we construct an algebraic framework for analyzing committee elections. In this framework, module homomorphisms are used to model positional voting procedures. Using the action of the wreath product group S2[Sn] on these modules, we obtain module decompositions which help us to gain an understanding of the module homomorphism. We use these decompositions to construct some interesting voting paradoxes.
Kinematic Evidence For Superfast Locomotory Muscle In Two Species Of Teneriffiid Mites, Grace C. Wu, Jonathan C. Wright, Dwight L. Whitaker, Anna N. Ahn
Kinematic Evidence For Superfast Locomotory Muscle In Two Species Of Teneriffiid Mites, Grace C. Wu, Jonathan C. Wright, Dwight L. Whitaker, Anna N. Ahn
Pomona 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 …
Time To Get Real: A Food Assessment Of Dining At Pomona College, Samantha Meyer
Time To Get Real: A Food Assessment Of Dining At Pomona College, Samantha Meyer
Pomona Senior Theses
Pomona College is an institution deeply committed to sustainability and student well being; however these commitments are not reflected in the College’s food purchases. Before this study, an assessment of purchasing had not been conducted at Pomona College. Using the Real Food Calculator – a metric designed to evaluate food purchasing at academic institutions – I tracked all food purchased by one of the College’s dining halls over the course of one month. Each food item was assessed based on the potential health concerns of its ingredients and whether the item was locally produced, ecologically sound and/or humane to determine …
Not Empty, Lauren Orme
Not Empty, Lauren Orme
Scripps Senior Theses
Not Empty is a two- part exploration of the relationship between humans and nature. In this essay I intend to discuss the relationship Australian Aboriginal peoples have with their environment. Their many cultures are among the oldest surviving civilizations on the planet, and their natural history is rich and complex. I plan to compare the relationship Australian Aboriginal cultures have to their environment to that of a Western civilization, specifically the United States. Neither relationship is perfect, nor is one of them 'better.' Both have histories riddled with extinction, evolution, and the conquest of new lands. The struggle Aboriginal Australians …
Mixed Operators In Compressed Sensing, Matthew A. Herman, Deanna Needell
Mixed Operators In Compressed Sensing, Matthew A. Herman, Deanna Needell
CMC Faculty Publications and Research
Applications of compressed sensing motivate the possibility of using different operators to encode and decode a signal of interest. Since it is clear that the operators cannot be too different, we can view the discrepancy between the two matrices as a perturbation. The stability of L1-minimization and greedy algorithms to recover the signal in the presence of additive noise is by now well-known. Recently however, work has been done to analyze these methods with noise in the measurement matrix, which generates a multiplicative noise term. This new framework of generalized perturbations (i.e., both additive and multiplicative noise) extends the prior …
Signal Recovery From Inaccurate And Incomplete Measurements Via Regularized Orthogonal Matching Pursuit, Deanna Needell, Roman Vershynin
Signal Recovery From Inaccurate And Incomplete Measurements Via Regularized Orthogonal Matching Pursuit, Deanna Needell, Roman Vershynin
CMC Faculty Publications and Research
We demonstrate a simple greedy algorithm that can reliably recover a vector v ?? ??d from incomplete and inaccurate measurements x = ??v + e. Here, ?? is a N x d measurement matrix with Nv with O(n) nonzeros from its inaccurate measurements x in at most n iterations, where each iteration amounts to solving a least squares problem. The noise level of the recovery is proportional to ??{logn} ||e||2. In particular, if the error term e vanishes the reconstruction is exact.
Randomized Kaczmarz Solver For Noisy Linear Systems, Deanna Needell
Randomized Kaczmarz Solver For Noisy Linear Systems, Deanna Needell
CMC Faculty Publications and Research
The Kaczmarz method is an iterative algorithm for solving systems of linear equations Ax=b. Theoretical convergence rates for this algorithm were largely unknown until recently when work was done on a randomized version of the algorithm. It was proved that for overdetermined systems, the randomized Kaczmarz method converges with expected exponential rate, independent of the number of equations in the system. Here we analyze the case where the system Ax=b is corrupted by noise, so we consider the system where Ax is approximately b + r where r is an arbitrary error vector. We prove that in this noisy version, …