Physical Sciences and Mathematics Commons^™

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

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 …

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 …

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 …

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.

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.

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

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 …

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

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

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

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

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

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

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

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, …

An Extraordinary Example Of Photokarren In A Sandstone Cave, Cueva Charles Brewer, Chimantá Plateau, Venezuela: Biogeomorphology On A Small Scale, Joyce Lundberg, Donald A. Mcfarlane, Charles Brewer-Carias

WM Keck Science Faculty Papers

A distinctive suite of small-scale erosional forms that are oriented towards the light occur close to the entrance of Cueva Charles Brewer, a large cave in a sandstone tepui, in SE Venezuela. These are the third example of photokarren ever studied in the world, the other two being from Borneo and Ireland. They are the only photokarren ever described from sandstone, and the only example from a non-carbonate environment. The host rock is a poorly-lithified unit of the Precambrian quartz arenite of the Roraima Supergroup. The forms are all oriented towards the light at 30° regardless of rock surface orientation. …

A Unique Population Of Cave Bears (Carnivora: Ursidae) From The Middle Pleistocene Of Kents Cavern, England, Based On Dental Morphometrics, Donald A. Mcfarlane, Martin Sabol, Joyce Lundberg

WM Keck Science Faculty Papers

The ‘breccia’ stratum from Kents (we follow local tradition in using the form ‘Kents’, without an apostrophe) Cavern, England, has been well known for its rich yield of cave-bear material since excavations began in the mid-19th century. Recent work has established that the bears are of latest MIS 12 or earliest MIS 11 age. A life table based on a collection of 67 molariform teeth is consistent with the use of the cave as a hibernaculum. Univariate and morphological assessment of the teeth shows an unusual range of primitive and more derived characters. Multivariate morphometric analysis of cave-bear teeth from …

A Geographic Information Systems Approach To The 19th Century Excavation Of Brixham Cavern, Devon, England, Donald A. Mcfarlane, Joyce Lundberg, Warren Roberts

WM Keck Science Faculty Papers

The oldest known spatially-explicit archaeological excavation, conducted in Brixham cave, Devon, in 1858, is reconstructed using geographic information systems technology. Two dimensional plots of individual fossil taxa and flint artefacts demonstrate the utility of the technique for elucidating taphonomy and palaeobiology. The cave served as a den for hibernating brown bears, as a den for hyena and cave lion, and as a reliquary for their prey.

Review: The Semi-Dynamical Reflection Equation: Solutions And Structure Matrices, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Reduced Electronic Spaces For Modeling Donor/Acceptor Interactions, Robert J. Cave, Stephen T. Edwards '06, John A, Kouzelos '07, Marshall D. Newton

All HMC Faculty Publications and Research

Diabatic states for donor (D) and acceptor (A) interactions in electron transfer (ET) processes are formulated and evaluated, along with coupling elements (H_DA) and effective D/A separation distances (r_DA), for reduced electronic spaces of variable size, using the generalized Mulliken Hush model (GMH), applicable to an arbitrary state space and nuclear configuration, and encompassing Robin−Day class III and as well as class II situations. Once the electronic state space is selected (a set of n ≥ 2 adiabatic states approximated by an orbital space based on an effective 1-electron (1-e) Hamiltonian), the charge-localized GMH …

Jane: A New Tool For The Cophylogeny Reconstruction Problem, Chris Conow, Daniel Fielder '11, Yaniv J. Ovadia '10, Ran Libeskind-Hadas

All HMC Faculty Publications and Research

Background

This paper describes the theory and implementation of a new software tool, called Jane, for the study of historical associations. This problem arises in parasitology (associations of hosts and parasites), molecular systematics (associations of orderings and genes), and biogeography (associations of regions and orderings). The underlying problem is that of reconciling pairs of trees subject to biologically plausible events and costs associated with these events. Existing software tools for this problem have strengths and limitations, and the new Jane tool described here provides functionality that complements existing tools.

Results

The Jane software tool uses a polynomial time dynamic …

Voting In Agreeable Societies, Deborah E. Berg '06, Serguei Norine, Francis E. Su, Robin Thomas, Paul Wollan

All HMC Faculty Publications and Research

No abstract provided in this article.

Two-Player Envy-Free Multi-Cake Division, John Cloutier '03, Kathryn L. Nyman, Francis E. Su

All HMC Faculty Publications and Research

We introduce a generalized cake-cutting problem in which we seek to divide multiple cakes so that two players may get their most-preferred piece selections: a choice of one piece from each cake, allowing for the possibility of linked preferences over the cakes. For two players, we show that disjoint envy-free piece selections may not exist for two cakes cut into two pieces each, and they may not exist for three cakes cut into three pieces each. However, there do exist such divisions for two cakes cut into three pieces each, and for three cakes cut into four pieces each. The …

An Amazing Mathematical Card Trick, Arthur T. Benjamin

All HMC Faculty Publications and Research

A magician gives a member of the audience 20 cards to shuffle. After the cards are thoroughly mixed, the magician goes through the deck two cards at a time, sometimes putting the two cards face to face, sometimes back to back, and sometimes in the same direction. Before dealing each pair of cards into a pile, he asks random members of the audience if the pair should be flipped over or not. He goes through the pile again four cards at a time and before each group of four is dealt to a pile, the audience gets to decide whether …

Sex, Mixability, And Modularity, Adi Livnat, Christos Papadimitriou, Nicholas Pippenger, Marcus W. Feldman

All HMC Faculty Publications and Research

The assumption that different genetic elements can make separate contributions to the same quantitative trait was originally made in order to reconcile biometry and Mendelism and ever since has been used in population genetics, specifically for the trait of fitness. Here we show that sex is responsible for the existence of separate genetic effects on fitness and, more generally, for the existence of a hierarchy of genetic evolutionary modules. Using the tools developed in the process, we also demonstrate that in terms of their fitness effects, separation and fusion of genes are associated with the increase and decrease of the …

Stability And Dynamics Of Self-Similarity In Evolution Equations, Andrew J. Bernoff, Thomas P. Witelski

All HMC Faculty Publications and Research

A methodology for studying the linear stability of self-similar solutions is discussed. These fundamental ideas are illustrated on three prototype problems: a simple ODE with finite-time blow-up, a second-order semi-linear heat equation with infinite-time spreading solutions, and the fourth-order Sivashinsky equation with finite-time self-similar blow-up. These examples are used to show that self-similar dynamics can be studied using many of the ideas arising in the study of dynamical systems. In particular, the use of dimensional analysis to derive scaling invariant similarity variables is discussed, as well as the role of symmetries in the context of stability of self-similar dynamics. The …

Local Versus Global Search In Channel Graphs, A.H. Hunter, Nicholas Pippenger

All HMC Faculty Publications and Research

Previous studies of search in channel graphs has assumed that the search is global; that is, that the status of any link can be probed by the search algorithm at any time. We consider for the first time local search, for which only links to which an idle path from the source has already been established may be probed. We show that some well known channel graphs may require exponentially more probes, on the average, when search must be local than when it may be global.

Learning To Create Jazz Melodies Using Deep Belief Nets, Greg Bickerman '10, Sam Bosley, Peter Swire, Robert M. Keller

All HMC Faculty Publications and Research

We describe an unsupervised learning technique to facilitate automated creation of jazz melodic improvisation over chord sequences. Specifically we demonstrate training an artificial improvisation algorithm based on unsupervised learning using deep belief nets, a form of probabilistic neural network based on restricted Boltzmann machines. We present a musical encoding scheme and specifics of a learning and creational method. Our approach creates novel jazz licks, albeit not yet in real-time. The present work should be regarded as a feasibility study to determine whether such networks could be used at all. We do not claim superiority of this approach for pragmatically creating …