A Celebration of Student Projects Presentation Day May 2, 2016 | Theses

A Celebration of Student Achievement Student research is an integral part of the Harvey Mudd College experience. During Presentation Days each spring, the entire College community is invited to celebrate students’ original projects in design or research. This celebration of student achievement includes Presentation Days (May 2 and 4), a showcase of senior thesis research and class projects, and Projects Day (May 3), a showcase of projects in the Clinic Program. Our students grapple with real-world problems through individual and group research projects across all disciplines. Our professors use research as a powerful teaching tool that promotes learning well beyond the classroom and the laboratory. For many Harvey Mudd students, these intense research opportunities spark a lifelong love for a previously unconsidered field, help them lead diverse teams of varied disciplines and provide them with the flexibility to change careers over time. Each year, more than 200 students participate in Presentation Days, and every department at the College is well represented. From groundbreaking individual research done by graduating seniors to engaging and eye-opening design projects done by firstyear students, the emphasis throughout Presentation Days is on student achievement. You’ll find presentations listed by room and then by time. The 2016 Presentation Days Committee members are Dan Stoebel, Lisette de Pillis, Mary Cardenas, Theresa Lynn, Elizabeth Sweedyk, Darryl Wright and Gerald Van Hecke ’61.

Support Fellow Mudders and Win Receive a raffle ticket for each session you attend. Deposit your tickets in designated receptacles by Wednesday at 6 p.m. A drawing will take place to select three tickets, and winners will be announced via email Friday, May 6. First prize – $500 Apple Store gift card Second prize – Item of your choice from the HMC Store Third prize – $50 in Claremont Cash

Monday, May 2 | Shanahan Center Auditorium 9 a.m.

B460

B480 (Recital Hall)

Refreshments available on Shanahan patio

9:30 a.m.

Amzi Jeffs

Casey Cannon

Max Frenkel

9:45 a.m.

Joana Perdomo

Xin Zhang

Kate Arriola

Alec Dunton

Amber Cai

Naomi Epstein

10:15 a.m.

Madeleine Weinstein

Caleb Eades

Shannon Wetzler

10:30 a.m.

Ryan Jones

Jim Wu

10 a.m.

10:45 a.m. 11 a.m.

Break Margaux Hujoel

A. Sophie Blee-Goldman

Suzy Kim

11:15 a.m.

Kennedy Agwamba

Victor Shang

Allison Lim

11:30 a.m

John Phillpot

Siddarth Srinivasan

Maddi Hartley

11:45 a.m

Bo Li

Morgan Mastrovich

Isabell Lee

12-1:30 p.m.

Lunch

1:30 p.m

Matthew Dannenberg

1:45 p.m.

Weerapat Pittayakanchit

2 p.m.

Matthew Wilber

Miranda Thompson

Arthur Chang

2:15 p.m.

Matthew Lin

Philip Jahl

Justin Lee

2:30 p.m.

Joyce Yang

Miriam Bell

Mikaela Kosich

Robert Bennett

Shifrah Aron-Dine

Prudence Hong

3:15 p.m.

Casey Chu

Aaron Batker Pritzker

Angeline Cai

3:30 p.m.

Cheng Wai Koo

Shanel Wu and Lin Yang

Kevin Heath

3:45 p.m.

Patrick Tierney

2:45 p.m. 3 p.m.

Biology

Break

Chemistry

Humanities, Social Sciences, and the Arts

Samuel Woodman

Computer Science

Engineering

Mathematics

Physics

Symbols denote major or majors of student speakers. 1

Monday, May 2 | Morning 9 a.m.

Refreshments on patio

Shanahan Center, Drinkward Recital Hall (B480)

Chemistry and Biology

9:30 a.m. Max Frenkel: Mobility of the Human L1 Retrotransposon in

Drosophila melanogaster Advisor: Jae Hur, assistant professor of biology

More than 40 percent of the human genome consists of ancient mobile genetic elements known as retrotransposons. These selfish genes replicate by copying and pasting indiscriminately throughout their host genome. Humans (and almost every form of life) have accordingly evolved mechanisms to silence transposons. Because repressive mechanisms are imperfect and falter with aging, it is conceivable that excessive transposition contributes to aging-associated phenotypes like neurodegeneration. To test this, I seek to conditionally express the human L1 retrotransposon in Drosophila neurons. Assessing human L1 mobility in Drosophila will reveal host-specific factors during transposition and may provide means to study L1 mobility in aging-related human diseases. 9:45 a.m. Katie L. Arriola: Developing Bio-inspired Catalysts for

Dechlorination Advisor: Katherine Van Heuvelen, assistant professor of chemistry Halogenated waste generated as a byproduct of industrial processes poses a threat to the environment and to human health. Trichloroethylene (TCE), a carcinogenic byproduct of degreasing procedures, is of particular concern. We are developing an environmentally friendly catalyst to dechlorinate TCE to a benign form. Our catalyst is modeled on cobalamin, a cofactor known to exhibit dechlorination activity. We are investigating cobalamin’s poorly understood dechlorination mechanism using cobalt tetramethylcyclam (Co(TMC)) as a biomimetic model. Preliminary results indicate that Co(TMC) is able to dechlorinate perchloroethylene. Insights into this reactivity will be used to optimize reaction conditions for maximal dechlorination activity.

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10 a.m. Naomi Epstein: The Enzymatic Activity of hOGG1, a DNA Repair

Enzyme Advisor: Karl Haushalter, associate professor of chemistry and biology

DNA is our shared genetic code, and the order in which the four DNA bases appear is crucial to proper function of our cells. When certain DNA bases are mutated, they can cause a cell to become cancerous. The human body has mechanisms to ensure that when DNA bases are mutated, they are fixed before the mutation propagates. One of these mechanisms uses the enzyme human 8-oxoguanine DNA glycosylase (hOGG1) to repair oxidatively damaged DNA. Mutant versions of hOGG1 have been previously identified and associated with cancer in some human tissues. I purified mutant forms of hOGG1 and assayed their enzymatic activity to determine whether there is a mechanistic link between mutated hOGG1 and decreased activity. If this is the case, cancer could plausibly be linked with mutant hOGG1. 10:15 a.m. Shannon P. Wetzler: Biomimetic Diels-Alder Reactions to

Cryptobeilic Tetracycles Advisor: David Vosburg, associate professor of chemistry

Cryptobeilic acid D is an antimalarial natural product from Beilschmiedia cryptocaryoides. We have achieved a concise synthesis of cryptobeilic acid cores using iterative Suzuki-Miyaura couplings between boronic acids and MIDA-protected boronates to create a conjugated (E,Z,Z,E) tetraene, triggering an 8π-6π electrocyclization cascade. An intramolecular Diels-Alder reaction furnishes a fused or bridged tetracycle, depending upon whether the tethered diene acts as a diene or a dienophile. We have found that the fused product is favored, though not exclusively, in the Diels-Alder reaction leading to cryptobeilic acid D ethyl ester. We are optimizing the synthesis of natural tetracycles and examining the effects of varied conditions on Diels-Alder selectivities.

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10:45 a.m. Break 11 a.m. Suzy Kim: Metallating Ligands in Catalyst Development for

Carcinogens in Groundwater Advisor: Katherine Van Heuvelen, assistant professor of chemistry Trichloroethylene (TCE) is a volatile organic pollutant and also a carcinogen that has been found in groundwater. A safer way to dispose of TCE is to reduce it to ethylene before it reaches the groundwater. Metalloenzymes found in natural systems catalyze the dechlorination of chlorinated hydrocarbons like TCE, but their mechanism is not well understood. We have prepared biomimetic complexes that resemble these compounds by synthesizing three cyclam derivatives, which we reacted with cobalt or nickel salts to yield novel metal complexes. We then use UV-visible spectroscopy to monitor the reaction of our compounds with TCE to understand how the supporting ligand affects reactivity. The ultimate goal is to design catalysts that effectively treat TCE using environmentally friendly materials. 11:15 a.m. Allison Lim: Dual-layer Zinc Oxide Nanostructures for Dye-

Sensitized Solar Cells Advisor: Hal Van Ryswyk, John Stauffer Professor of Chemistry Dye-sensitized solar cells (DSSC) provide an efficient and economical alternative to conventional silicon solar cells. However, current DSSCs are limited by poor light absorption and interception of photogenerated electrons by the electrolyte. This project aimed to address both limitations by combining dual-layer zinc oxide nanostructures, PbS quantum dots and conventional dyes. The resulting DSSCs showed improved performance attributed to the light-scattering properties of the zinc oxide nanostructure and PbS quantum dots’ ability to inhibit interception of electrons. More importantly, the single-step electrodeposition of ZnO and successive ionic layer absorption and reaction (SILAR) of PbS led to a facile, replicable recipe for improving DSSCs.

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11:30 a.m. Maddi Hartley: Theoretical and Experimental Analyses of a

Subset of Ketal Claisen Rearrangements With Multiple Distinct Transition State Pathways Advisors: Robert Cave, professor of chemistry, and William Daub, Seeley Wintersmith Mudd Professor of Chemistry Ketal Claisen (KC) rearrangements are one of many types of organic intramolecular carbon-carbon bond shifting reactions that have a wide variety of applications. However, a subset of reactions (using cinnamyl alcohols and ketals as reagents) has posed a challenge to chemists attempting to understand the mechanisms behind these rearrangements. These reactions have the possibility to produce three distinct products through six different transition states. While the three products can be distinguished experimentally, the six pathways cannot. However, theoretical modeling methods such as Density Functional Theory (DFT) may be able to predict the favored pathways. Using DFT, we have modeled the transition states for each pathway to compare to experimental data as a test of theory. 11:45 a.m. Isabell Lee: Analysis of Irrigation Water From Oil Production

Sources Advisors: Lelia Hawkins, Barbara Stokes Dewey Assistant Professor of Chemistry, and Tanja Srebotnjak, Hixon Professor of Sustainable Environmental Design As the historic Californian drought continues, more farmers are using waste-water from oil and gas production to supplement their irrigation water. The Cawelo Water District, which provides the irrigation water for 34,000 acres of cropland in Kern County, California, has been using this waste-water for decades but has recently increased its deliveries, sometimes without any freshwater dilution. Both government agencies and environmental nonprofits have raised safety concerns about this water. My thesis project aims to address these safety concerns by quantifying chemical and physical parameters of the irrigation water, including pH, concentrations of organic compounds associated with petroleum production, and the concentrations of heavy metals that endanger crops and/or human health. Noon– 1:30 p.m.

Lunch

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Shanahan Auditorium Mathematics 9.30 a.m. Amzi Jeffs: Convexity of Neural Codes

Advisors: Mohamed Omar, assistant professor of mathematics, and Nora Youngs, teaching and research postdoctoral fellow An important task in neuroscience is stimulus reconstruction: Given activity in the brain, what stimulus could have caused it? We build on previous literature which uses neural codes to approach this problem mathematically. We consider neural codes arising from place cells, which are neurons that track an animal’s position in space, and attempt to classify which codes arise as a result of place cells with convex receptive fields. In this talk we will describe an algebraic approach to understanding these codes, including an interesting correspondence between algebraic transformations (homomorphisms) and geometric modifications of receptive fields. 9:45 a.m. Joana L. Perdomo: Mathematical Models of Blood Coagulation

Advisors: Lisette de Pillis, Norman F. Sprague Jr. Professor of Life Sciences and Professor of Mathematics – chair, Department of Mathematics; and Darryl Yong ’96, professor of mathematics

Blood coagulation is a series of biochemical reactions that take place to form a blood clot. Abnormalities in coagulation, such as under-clotting or over-clotting, can lead to significant blood loss, cardiac arrest, damage to vital organs or even death. Thus, understanding quantitatively how blood coagulation works is important in informing clinical decisions about treating deficiencies and disorders. Quantifying blood coagulation is possible through mathematical modeling. This review presents different mathematical models that have been developed in the last 30 years to describe the biochemistry, biophysics and clinical applications of blood coagulation research. This review includes the strengths and limitations of models, as well as suggestions for future work.  lec M. Dunton: Topological Data Analysis for Systems of A Coupled Oscillators Advisors: Andrew Bernoff, Kenneth A. and Diana G. Jonsson Professor of Mathematics, Harvey Mudd College; and Chad Topaz, professor of mathematics, Macalester College 10 a.m.

Coupled oscillators, such as groups of fireflies or clusters of neurons, are found throughout nature and are frequently modeled in the applied mathematics literature. Earlier work by

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Kuramoto, Strogatz and others has led to a deep understanding of the emergent behavior of systems of such oscillators using traditional dynamical systems methods. In this project we outline the application of techniques from topological data analysis to understanding the dynamics of systems of coupled oscillators. This includes the examination of partitions, partial synchronization and attractors. By looking for clustering in a data space consisting of the phase change of oscillators over a set of time delays, we hope to reconstruct attractors and identify members of clusters. 10:15 a.m. Madeleine Weinstein: Adinkras and Arithmetical Graphs

Advisors: Dagan Karp, associate professor of mathematics and associate department chair, Harvey Mudd College; and Charles Doran, professor of mathematics, University of Alberta Adinkras encode representations of supersymmetry algebras as colored bipartite graphs with certain additional structures. Arithmetical graphs arise in algebraic and arithmetic geometry and have a rich theory and many interesting properties. We will discuss what happens when we define an arithmetical graph structure on an adinkra. What can we learn about adinkras when we use the tools of algebraic geometry? 10:30 a.m. Ryan C. Jones: Hopper Bands: Locust Aggregation Advisors: Andrew Bernoff, Kenneth A. and Diana G. Jonsson Professor of Mathematics, Harvey Mudd College; and Chad Topaz, professor of mathematics, Macalester College Locust swarms cause extreme famine and hunger in parts of SubSaharan Africa as they travel across croplands and eat vegetation. Current models start with biological properties of locusts and analyze the macro-behavior of the system. These models exhibit the desired migratory behavior, but do so with too many parameters. To account for this, a new model, the Alignment and Intermittent Motion model, is derived with minimal assumptions. AIM is constructed with regards to locust biology, allowing it to elicit biologically correct locust behavior. A particle-in cell method is used to optimize simulations, allowing for runs of large numbers of locusts over reasonable timescales. We analyze how the swarms behave in the presence of a food source as well as study metrics related to swarm density. 10:45 a.m. Break

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11 a.m. Margaux L. Hujoel: Assessment of Chlamydia Procedures for

Treatment and Screening Advisor: Lisette de Pillis, Norman F. Sprague Jr. Professor of Life Sciences and Professor of Mathematics and chair, Department of Mathematics Chlamydia trachomatis infections are a sexually transmitted infection in the United States in which a majority of cases are asymptomatic. Due to this asymptomatic nature, as well as the serious health issues arising from untreated infections in women, the Centers for Disease Control and Prevention recommends a screening policy that annually targets women under 25 or older women with risk factors. There is little evidence supporting the efficacy of only screening women. Through a stochastic epidemiological model, we investigate a variety of screening policies within a college setting and evaluate their impact on infection prevalence. We developed a MATLAB code using an individual-based modeling approach to evaluate screening procedures. We will present a statistical analysis of the outcome. 11:15 a.m. Kennedy Agwamba: Computational Exploration of

Integrodifference Population Models Advisor: Jon Jacobsen, professor of mathematics and vice president for student affairs Mathematical modeling of population dynamics can provide novel insight to the growth and dispersal patterns of species populations and has become vital to the preservation of biodiversity. These growth and dispersal stages can be modeled using discretetime, continuous-space integrodifference equations. Previous studies have identified metrics that can determine whether a given species will persist or go extinct under certain model parameters. However, a need for computational tools to compute these metrics has limited the scope and analysis within many of these studies. We aim to create computational tools necessary to numerically examine a number of associated integrodifference equations, allowing modelers to explore results using a selection of models under a robust parameter set. 11:30 a.m. John Phillpot: Line-of-sight Pursuit and Evasion Games on

Polytopes in Rn Advisors: Ran Libeskind-Hadas, R. Michael Shanahan Professor of Computer Science and chair, Computer Science Department; and Nicholas Pippenger, professor of mathematics We study line-of-sight Pursuit and Evasion games in (n > 2)-dimensional polygons. In these games, a point Pursuer

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and Evader take turns moving up to unit distance within a n-dimensional polygon. The Pursuer aims to capture the Evader by ending their turn within unit distance of the Evader, while the Evader hopes to avoid capture indefinitely. We are interested in determining which shapes permit a Pursuer strategy guaranteed to capture the Evader in finite time. The challenge comes from the line-of-sight restriction: The Pursuer only knows the location of the Evader if the line connecting them is contained in the shape (if the Pursuer can “see” the Evader). We adapt a proven Pursuer strategy for 2-dimensional polygons to show that a large class of n-dimensional shapes admit Pursuer victory. 11:45 a.m. Bo Li: Math 197 Senior Thesis

Advisors: Alfonso Castro, professor of mathematics, and Ivan Ventura, visiting assistant professor of mathematics I consider a model for the control of criminality in cities. The model was developed during my REU at UCLA. The model is a system of partial differential equations that simulates the behavior of criminals and where they may accumulate—hot spots. I have proved a prior bounds for the partial differential equations in both one-dimensional and higher dimensional cases, which proves the attractiveness and density of criminals in the given area will not be unlimitedly high. I will also discuss my work on the bifurcation of solutions around constant steady states. Noon– 1:30 p.m.

Lunch

Shanahan B460 Physics 9:30 a.m. Casey B. Cannon: Computational Models of Optical Traps

Advisor: Tom Donnelly, professor of physics

An optical trap is a trapping laser which we use to levitate a micron scale sphere. This is useful for isolating targets for studies on stochastic heating: a process with possible applications to laserdriven nuclear fusion. I develop a model for loading these traps with spheres which has options for different trapping laser modes and spheres.

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9:45 a.m. Xin Zhang: Computational Modeling of Multi-Pass Stochastic

Heating Advisor: Tom Donnelly, professor of physics

Multi-pass stochastic heating is one of the proposed mechanisms through which laser energy is coupled into solid targets. In this study, we present a theoretical analysis of the basic physics of the stochastic heating processes and a simplified numerical model that simulates the heating of the plasma through single electron dynamics. With this model, we investigated the dependency of heating efficiency with various parameters. Through statistical sampling of single electrons, we were able to obtain energy spectrums after the laser irradiation of a micro-plasma and showed that the energy gain of hot electrons has a quadratic dependency on the frequency of the laser and the radius of the plasma. These results agree with published analytical predictions. 10 a.m. Amber Cai: Preparing Laser Targets for Studies of Multi-pass Stochastic Heating Advisor: Tom Donnelly, professor of physics Multi-pass stochastic heating is a mechanism in which a highintensity laser field couples its energy efficiently to spherical plasmas of wavelength-size scale. This work discusses methods for placing wavelength scale targets in the focus of a laser pulse. One promising method works through evaporation of a colloidal solution of polystyrene nanospheres onto silicon substrates followed by plasma etching. Results of this approach will be discussed. 10:15 a.m. Caleb Eades: Developing and Characterizing an Ideal Plasma Target Delivery Method for Small-Scale Fusion Studies Advisor: Tom Donnelly, professor of physics Small-scale fusion could provide a fruitful clean energy source in the future. A proposed method of heating electrons in plasma to induce such fusion with a Coulomb explosion is stochastic heating. To investigate this, an isolated nanosphere plasma target must be placed in the focus of a terawatt, femtosecond-laser pulse. Continuing from previous results, we have developed a method of consistently delivering these plasma targets to a precise spatial location in a specified time interval. Our two-stage deposition process of drying and oxygen plasma etching ensures the targets are suitable for ablation, whereby the spheres are scattered into the focus of the terawatt laser. Experimental data and numerical modeling demonstrate the reliability of our target delivery method.

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10:30 a.m. Jim Wu: Spectral Tuning of the Rhodopsin-Retinal Complex

Advisor: Robert Cave, professor of chemistry

The chromophore retinal mediates mammalian vision, and the rhodopsin protein and solvents play crucial roles in spectrally tuning this molecule. Numerous conflicting studies have used quantum chemistry and molecular mechanics methods to investigate the underlying tuning mechanisms, but incorrectly neglected the effects of a warm biological environment. In light of this, we will use multiple thermally accessible states of the rhodopsin-retinal complex to generate an averaged absorption spectrum and also modify retinal molecules in our model to elucidate the importance of certain functional groups in spectral tuning. We present results from initial calculations using a model of the complex and discuss the next steps and challenges toward a complete characterization of this system. 10:45 a.m. Break 11 a.m. A. Sophie Blee-Goldman: Synthesis and Collection of

Antibacterial Chitosan Nanoparticles for a Tissue-Engineered Brain Patch Advisor: Tom Donnelly, professor of physics Traumatic brain injury is responsible for 1-2 percent of all deaths. To replace lost tissue and fight both inflammation and infection, we tissue-engineered a “Brain Patch.” Antibacterial and anti-inflammatory properties can be imparted by embedding chitosan nanoparticles in the patch. These are synthesized using evaporative ultrasonic atomization, which allows for direct control of the final particle size. A nanoparticle powder is then collected using a Nylon membrane filter. Preliminary testing has demonstrated the antibacterial properties of 500 nm particles. Once we determine the optimal nanoparticle concentration and size with further testing, we can begin to integrate the nanoparticles into the Brain Patch. 11:15 a.m. Victor Shang: Computational Progress Towards Maximum

Distinguishability of Bell States by Linear Evolution and Local Measurement Advisor: Theresa Lynn, associate professor of physics Many quantum information protocols rely on distinguishing entangled states, or Bell states, between two particles. Theoretical upper bounds have been established for the maximal number of Bell states that can be distinguished using linear evolution and local measurement (LELM) devices. However, for the

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general qudit case, it is not known whether these upper bounds are achievable. I will present computational progress toward determining the maximal distinguishability of qutrit and qubit x qutrit Bell states. The number of cases to check has been reduced by defining equivalence classes of sets of Bell states. Applying distinguishability conditions to these sets then yields a system of polynomial equations whose Gröbner basis can determine whether the sets of Bell states are distinguishable. 11:30 a.m. Siddarth Srinivasan: Improving Measurements of OAM-

entangled Photons Advisor: Theresa Lynn, associate professor of physics

Quantum communication tasks can achieve higher information rates by encoding more information per photon. Light carries orbital angular momentum (OAM), which comes from the spatial pattern of the electric field. This is similar to but distinct from spin angular momentum, or polarization, which comes from the electric field direction. Unlike the 2-dimensional basis of polarization, however, OAM has an infinite-dimensional basis for encoding information. In my thesis I generate and test pairs of OAM entangled photons with the goal of trying to improve their measurements. I investigate sources of error in the current measurements, particularly the alignment of a hologram used to manipulate OAM. I present my progress in aligning the apparatus to improve measurements of OAM-entangled photons. 11:45 a.m. Morgan A. Mastrovich: Experimental Realization of

Entanglement Between Photon Orbital Angular Momentum and Polarization Advisor: Theresa Lynn, associate professor of physics Communication security can be improved by encoding messages in quantum-mechanically entangled photons. Photons have both orbital angular momentum (OAM) and polarization quantum states; using entanglement between these states can increase the information capacity of quantum communication schemes. In my thesis, I worked to build a q-plate, an optical element that uses the spatial orientation of liquid crystal molecules to manipulate the OAM of incident photons based on their polarization. The q-plate can act on superpositions of photon polarizations to create entanglement between that photon’s polarization and OAM states. Using this property, I investigated a single-photon state entangled across different variables and two-photon entangled states that contain more than two quantum bits. Noon–1:30 p.m. Lunch 12

Monday, May 2 | Afternoon Shanahan Center, Drinkward Recital Hall (B480)

Chemistry and Biology

2 p.m. Arthur Chang: The BD/CareFusion Clinic Project

Advisor: Liz Orwin ’95, James Howard Kindelberger Professor of Engineering and chair, Department of Engineering The BD/CareFusion Clinic team designed an intravenous infusion device that helps nurses deliver secondary-mode infusions with improved simplicity and reliability. The device achieves this by automating complex, non-intuitive manual operations. It will benefit hospitalized patients who receive intravenous medications. 2:15 p.m. Justin Lee: Advanced Toolkit for Adaptive Particle Simulations

Advisor: Jeff Amelang, visiting assistant professor of computer science

The objective of the Clinic project is to develop an alternative to a Voronoi tesselation package called voro++ to be used for mesh-free particle methods calculations. This includes efficiently matching existing functionality for identifying neighbors and calculating particle volumes. On top of this, the project will be able to support group specifications to be able to run calculations on subsets of the particles. The tesselator will interface with the meshfree particle methods package created by Sandia called MOAB. 2:30 p.m. Mikaela Kosich: Mechanistic Investigation of Tantalum

Amide-alkoxide Catalyzed Asymmetric Hydroamination of Aminoallenes Advisor: Adam Johnson, professor of chemistry Hydroamination is an atom economical process by which an N-H bond is added across a C-C multiple bond. Our laboratory studies the intramolecular hydroamination of aminoallenes using early transition metal amide-alkoxide catalysts. The products of this class of reactions, in this case tetrahydropyridines, have numerous potential applications, particularly in the pharmaceutical industry. The mechanism by which the reaction proceeds is dependent on the catalyst and substrate used, but little mechanistic work has been done for the tantalum catalyzed reaction. We monitor the reactions at regular intervals by 1H NMR spectroscopy. We will present mechanistic studies of the tantalum catalyzed reaction, comparing them to previous work by Bergman on the titanium catalyzed reaction. 13

2:45–3 p.m. Break

3 p.m. Prudence Hong: TSS Repression of Meristem Growth Through ERF Transcription Factors Advisor: Xuelin Wu, visiting assistant professor of biology In higher plants, primary structures, leaves, stems and roots develop post-embryonically via two main stem cell-containing structures – the shoot and the root apical meristems. Vital to our understanding of stem cell behavior in plants is how cell division in the meristem is regulated. In Arabidopsis thaliana, the loss of the STIMPY (STIP) gene results in meristem growth failure, while a mutation in TPR-Domain Suppressor of STIMPY (TSS) is able to partially rescue the stip mutant phenotype. The goal of this thesis is to understand the role of TSS in meristem growth regulation. In this study we test the hypothesis that TSS carries out its function by interacting with a group of ERF transcription factors, using genetic and bimolecular fluorescence complementation (BiFC) assays. 3:15 p.m. Angeline Cai: A Study of Locomotion on Inclined Surfaces With

the Rusty Lizard, Sceloporus olivaceus Advisor: Stephen Adolph, Stuart Mudd Professor of Biology and chair, Department of Biology

Lizards live in various habitats with different characteristics, including temperature, substrate and incline, but previous studies of lizard locomotion have generally focused on the effects of temperature. However, arboreal lizards like Sceloporus olivaceus need to negotiate both shallow and steep surfaces, including vertical ones. As slope may also affect locomotor behavior, more insight into how angle affects locomotion could capture more of the ecologically relevant performance of arboreal lizards. This study examines how velocity changes as slope increases from 0° to 90° in increments of 15° and whether the expected drop in speed is different for lizards of varying sizes. To do this, I use a racetrack and a mounted camera to obtain the performances of the lizards at each incline.

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3:30 p.m. Kevin N. Heath: Computational Approach to Identifying

Widespread Horizontal Gene Transfer Events Advisor: Eliot Bush, associate professor of biology

Horizontal gene transfer (HGT) events play an important role in the evolution of bacteria. While a large portion of the genes in bacteria have a history of being horizontally transferred, no methods exist to systematically identify HGT events in a clade of closely related strains. To facilitate the identification of novel HGT events, I am developing a pipeline to do this in large bacterial clades. I have developed a greedy algorithm that identifies families of related genes and proceeds to merge those that are likely to have resulted from a single HGT event. 3:45 p.m. Samuel M. Woodman: The Importance of Communication in

Honeybee Colonies Relative to Colony Size Advisor: Matina Donaldson-Matasci, assistant professor of biology In nature, organisms that have a communication system often are more fit than organisms that do not communicate. For instance, honeybees use a waggle dance to inform other foragers about the direction to, distance to and quality of a resource in the environment. Studies have shown that honeybees collect more nectar in environments that are sparse, patchy and of varying resource quality when they use communication than when they do not. However, studies on whether communication is more important in larger colonies than smaller colonies in these same environments have been inconclusive. I created a simulation that I used to examine whether larger honeybee colonies are more successful than smaller honeybee colonies in specific environments, with success measured by per capita nectar intake.

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Shanahan Auditorium Mathematics 1:30 p.m. Matthew Dannenberg: Pattern Recognition in High-Dimensional

Data Advisor: Weiqing Gu, Avery Professor of Mathematics

Hyperspectral imaging is a recent innovation allowing for massive amounts of spectral information to be contained in a single image. While these images contain vast amounts of data, not all of this data easily equates to useful information: Extracting information from large amounts of high-dimensional data is nontrivial. Using machine learning techniques, we can identify patterns, particularly geometric patterns, in this high-dimensional data. These identified patterns allow for the significant information contained therein to be understood and enable more effective decision-making. By using the intrinsic geometry of Grassmann manifolds to carry out dimensional reductions, an effective and efficient method to recognize and classify objects in hyperspectral images has been developed. 1:45 p.m. Weerapat Pittayakanchit: Global Stability of Equilibria in a Model

of Swarming Advisors: Andrew Bernoff, Kenneth A. and Diana G. Jonsson Professor of Mathematics, Harvey Mudd College; and Chad Topaz, professor of mathematics, Macalester College Flocks of sheep, schools of fish and even crowds of people form groups, called swarms, that mathematicians strive to understand. The most popular mathematical models characterize these swarms as a minimizer of the Morse potential for which an exact solution is known in one dimension. We verified the local stability of this solution analytically and numerically using the calculus of variations and eigenvalue analysis. We then changed our perspective on the problem and showed that minimizers for the quadratic energy for the density of individuals can relate to minimizers for a linear function of the auto-correlation of the density. Convex relaxation techniques for this new problem imply that local stability of the exact solution is equivalent to global stability.

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2 p.m. Matthew Wilber: Building a History of Horizontal Gene Transfer

in E. coli Advisor: Eliot Bush, associate professor of biology

Bacteria’s ability to pass entire genes between one another, a process called Horizontal Gene Transfer (HGT), is a major cause of bacterial evolution. In an ongoing project at Harvey Mudd, computational methods have been used to catalogue the HGT events that have impacted a group of closely related bacteria. My work builds on that project, by improving our ability to identify groups of genes in different strains that are related. Previously, similarity was measured only by comparing two genes’ DNA sequences, ignoring their positions on the organism’s DNA. My research leverages genes’ relative position to make a better measurement of gene similarity. These improved similarity measurements will improve the existing pipeline’s ability to identify HGT events. 2:15 p.m. Matthew S. Lin: Graph Cohomology

Advisor: Dagan Karp, associate professor of mathematics and associate chair What is the cohomology of a graph? Cohomology is a topological invariant and encodes such information as genus and euler characteristic. Graphs are combinatorial objects which may not a priori admit a natural and isomorphism invariant cohomology ring. In this project, given any finite graph G, we constructively define a cohomology H*(G) ring of G. Our method uses graph associahedra and toric varieties. Given a graph, there is a canonically associated convex polytope, called the graph associahedron, constructed from G. In turn, a convex polytope uniquely determines a toric variety. We synthesize these results and describe the cohomology of the associated permutohedral variety directly in terms of the graph G itself. 2:30 p.m. Joyce C. Yang: Interval Graphs Advisor: Nicholas Pippenger, professor of mathematics Interval graphs are undirected graphs whose vertices correspond to intervals of real numbers and whose edges correspond to nonempty intersections between intervals. We study several aspects of interval graphs, including their application to the dynamic storage allocation problem. 2:45–3 p.m. Break

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 obert Bennett: The Fibonomial Coefficients and Other UpR Down Tilings Advisor: Arthur Benjamin, Smallwood Family Professor of Mathematics

3 p.m.

The Fibonomial coefficients are a generalization of the binomial coefficients with a rather nice combinatorial interpretation. While the ordinary binomial coefficients count lattice paths in a grid, the Fibonomial coefficients count the number of ways to draw a lattice path in a grid and then Fibonacci-tile the regions above and below the path in a particular way. We may forgo a literal tiling interpretation and, instead of the Fibonacci numbers, use an arbitrary function to count the number of ways to “tile” the regions of the grid delineated by the lattice path. When the function is a combinatorial sequence such as the Lucas numbers or the q-numbers, the total number of “tilings” is some multiple of a generalized binomial coefficient corresponding to the sequence chosen. 3:15 p.m. Casey Chu: Probing Big Data Using Differential Geometry Advisor: Weiqing Gu, Avery Professor of Mathematics The spectacular increase in data in the modern world has created a need for new mathematical techniques to analyze this data. It turns out that much of today’s data, from the movements of the stock market to your Netflix watching habits, can be viewed as living on a low-dimensional surface embedded in a high-dimensional space. This makes differential geometry, the study of surfaces using calculus, a natural choice for such analysis. This talk will explain how data can be viewed this way and attempt to define a so-called Riemannian metric on the high-dimensional space, providing a novel but intuitive way to probe the data for insight. 3:30 p.m. Cheng Wai Koo: A Bound on the Number of Spanning Trees in

Bipartite Graphs Advisor: Mohamed Omar, assistant professor of mathematics

Given any graph, we can represent its structure in a matrix. Spectral graph theory, then, is the study of how the graph’s properties relate to the matrix’s eigenvalues. We will explore a conjecture by Richard Ehrenborg that gives an upper bound on the number of spanning trees in a bipartite graph. As we do so, we will witness the power of spectral graph theory to bridge graph theory and linear algebra.

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3:45 p.m. Patrick N. Tierney: Constructing the 2-Associahedron

Advisor: Satyan Devadoss, visiting professor of mathematics The associahedron, an object generated by the space of particle collisions on a line, has appeared in numerous contexts throughout the field of mathematics. By representing the associahedron as a poset of tubings, Michael Carr (Brandeis University) and Devadoss were able to create a generalization called graph associahedron. We consider an alternative generalization through the space of particle collisions on quilted spheres. We will explore multiple representations of this space and propose a method for constructing this object from truncations of convex polytopes.

Shanahan B460 Physics 2 p.m. Miranda L. Thompson: Determination of the Anisotropy

Energies in CoNi Magnetic Multilayers Advisors: James Eckert, professor of physics, and Patricia Sparks, professor of physics I investigated the magnetic properties of CoNi thin-film multilayers. The bulk magnetic properties of both cobalt and nickel are well known, but those properties change significantly when the two metals are layered in thin films. The structure of the samples was Si / Ta(4 nm) / Pd(4 nm) / [Co (0.2 nm) / Ni (Y)] x 10 / Ta (4 nm) with 0.2 nm ≤ Y ≤ 1.4 nm. I found the magnetization and coercive field of each sample, which allowed me to calculate the anisotropy energy – the energy required to force perpendicular magnetization back into the plane of the material. I also used the Anomalous Hall Effect (AHE) to determine the magnetic compensation point where the AHE vanishes. 2:15 p.m. Philip E. Jahl: Density Functional Theory Predictions of High

Entropy Alloy Phase Diagrams Advisor: Lori Bassman, professor of engineering

The Laspa Fellowship research group works to develop novel metallic high entropy alloys (HEAs). Current HEAs have demonstrated excellent mechanical properties compared to traditional alloys; however the structures of these complex alloys and their improved properties are not well understood. A first step in creating new HEAs is to find atomic compositions that form a single-phase solid solution. In order to decrease the development time of new HEAs we are developing methods based on density functional theory to predict alloy phase behavior. The model I have developed has been expanded to include the effects of vibrational entropy. Early results show promise for use of simulations for future material design. 19

2:30 p.m. Miriam Bell: Modeling Morning Glory Flower Motion

Advisor: Sharon Gerbode, Iris and Howard Critchell Assistant Professor of Physics Nature has already solved many of the problems that remain mysteries to humans. We can capitalize on these natural insights by studying and replicating natural phenomena. In the context of extreme mechanics, Morning Glory flower’s twisting and rolling motions can serve as a model for complex motion and for large deformations that are often difficult to solve with traditional numerical or analytic methods. We worked to determine the physical basis for the flower’s mechanisms of twisting open and rolling closed. Using time lapse footage and different physical experiments, we address previous hypotheses on the motion and present our own theories based on our observations. 2:45–3 p.m. Break 3 p.m. Shifrah Aron-Dine: First Principles Study of Lattice Disordering

in CuNiMnAl and CuNiMnSn Heusler Alloys Advisors: Lori Bassman, professor of engineering, Harvey Mudd College; Greg Pomrehn, The Boeing Company; Aurora PribramJones, Lawrence Livermore National Lab; Kevin Laws, University of New South Wales Heusler alloys have enormous potential for application in spintronic devices due to their high spin polarization, magnetization and Curie temperature. In addition, they are less expensive and have better mechanical properties than other alloys currently used in spintronic applications. Disordering in the lattice structure of a Heusler alloy negatively impacts the favorable band structure. In this work I present a new method for characterizing the probability for atomic disordering of the lattice structure based on density functional theory calculations. These calculations were carried out on two new four-component equiatomic Heusler alloys, CuNiMnAl and CuNiMnSn.

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3:15 p.m. Aaron Batker Pritzker: Rigorous Coupled-Wave Analysis of Thin-

Film Solar Cells Advisor: Peter Saeta, professor of physics and chair, Department of Physics

Thin-film solar cells can potentially be made cheaper and more efficient than traditional solar cells by confining light within the cell. This confinement occurs when light scatters off nanostructures within the cell and is redirected to travel along the cell’s plane. I present a computational tool, based on the accurate and flexible rigorous coupled-wave analysis method, to model the way light scatters from these nanostructures. This tool can be used to engineer optimal scattering structures and enhance the amount of electricity generated in thin-film solar cells. 3:30 p.m. Shanel Wu and Lin Yang: Spin-State Transitions in Metal-

Organic Magnets Advisor: James Eckert, professor of physics Sponsor: Vivien Zapf, Los Alamos National Laboratory

Metal-organic magnets show magnetic phenomena distinct from those of inorganics. In particular, they can undergo spin-state transitions (SSTs) that create changes in their crystal lattice. These structural transitions alter the magnetic and electric properties of these materials to produce magneto-electric coupling (MEC). Because current methods to produce MEC require excessive power and dissipate heat, SSTs are emerging as one of the most important magnetic phenomena in metal-organic materials. We observed SSTs in metal-organic materials prepared by Los Alamos National Laboratory by using a physical property measurement system (PPMS) to conduct calorimetry and vibrating sample magnetometry (VSM) measurements.

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