Physical Sciences and Mathematics Commons^™

Echolocation On Manifolds, Kerong Wang

Honors Theses

We consider the question asked by Wyman and Xi [WX23]: ``Can you hear your location on a manifold?” In other words, can you locate a unique point x on a manifold, up to symmetry, if you know the Laplacian eigenvalues and eigenfunctions of the manifold? In [WX23], Wyman and Xi showed that echolocation holds on one- and two-dimensional rectangles with Dirichlet boundary conditions using the pointwise Weyl counting function. They also showed echolocation holds on ellipsoids using Gaussian curvature.

In this thesis, we provide full details for Wyman and Xi's proof for one- and two-dimensional rectangles and we show that …

Particle Swarm Optimization For High Rigidity Spectrometer, Yicheng Wang

Honors Theses

The goal of this project is to find reliable parameter settings for a multi-dimensional global optimizer to optimize the performance of a large acceptance ion optical system for the requirements of nuclear physics experiments. We develop and test the Particle Swarm Optimization (PSO), a global optimization algorithm designed for continuous multi-dimensional problems, on a large acceptance particle beam separator, the High Rigidity Spectrometer (HRS) at the Facility for Rare Isotope Beams (FRIB), which is a laboratory specializing in the production and experimental study of short-lived nuclear matter. We split the HRS into two sections, the High-Transmission Beamline (HTBL) and the …

Graphs, Adjacency Matrices, And Corresponding Functions, Yang Hong

Honors Theses

Stable polynomials, in the context of this research, are two-variable polynomials like $p(z_1,z_2) = 2 - z_1 - z_2$ that are guaranteed to be non-zero if both input variables have an absolute value less than one in the complex plane. Stable polynomials are used in a variety of mathematical fields, thus finding ways to construct stable polynomials is valuable. An important property of these polynomials is whether they have boundary zeros, which are points in the complex plane where the polynomial equals zero and both variables have an absolute value of 1. Overall, it is challenging to find stable polynomials …

The Implementation Of Augmented Reality And Low Latency Protocols In Musical Instrumental Collaborations, Qixiao Zhu

Honors Theses

Past projects involving musical software have been completely virtual, while these software do well in entertainment and education, there is the question of whether these software are playable to the same extent as physical musical instruments. The software presented in this paper, "AR Jam", utilizes various software and hardware tools to form a networked mixed reality system for the users to play music on. The intention of this project is to seek new ways to explore more playable musical instruments in the digital world. The paper presents the software's implementation, challenges such as optimization problems of the synthesizer, and the …

Long-Range And Chaotic Active Mixing Of Swimming Microbes In A Vortex Chain Flow, Nghia Le

Honors Theses

We present experiments studying the motion and active mixing of swimming mi- crobes in laminar, vortex-dominated fluid flows. We are testing a theory that predicts the existence of swimming invariant manifolds (SwIMs) - invisible, one-way barriers blocking the paths of self-propelled tracers in the flow in one direction. We also pro- pose that the SwIMs together can form chute structures in three-dimensional phase space that facilitate cross-vortex transport of the microbes. We also observe evidence of how these structures promote long-range transport at different non-dimensional velocities (microbe’s velocity relative to flow velocity). Long-range transport is quan- tified by measuring the …

Environmental Racism In Baltimore: A Geographical Study Into The Connections Between Environmental Toxins And Public Health, Genevieve Block

Honors Theses

An investigation into the relationship between environmental toxins and environmental racism in Baltimore City, Maryland.

A Contraction Based Approach To Tensor Isomorphism, Anh Kieu

Honors Theses

Tensor isomorphism is a hard problem in computational complexity theory. Tensor isomorphism arises not just in mathematics, but also in other applied fields like Machine Learning, Cryptography, and Quantum Information Theory (QIT). In this thesis, we develop a new approach to testing (non)-isomorphism of tensors that uses local information from "contractions" of a tensor to detect differences in global structures. Specifically, we use projective geometry and tensor contractions to create a labelling data structure for a given tensor, which can be used to compare and distinguish tensors. This contraction labelling isomorphism test is quite general, and its practical potential remains …

Evaluating The Relationship Between Floodplain Topography And Channel Avulsion: Evidence From The Devonian Catskill Formation, North-Central Pennsylvania, Usa, Molly O'Halloran

Honors Theses

Topographic complexity on floodplains can route flow, control sediment dispersal, and influence channel behavior, but studying floodplain-channel interactions in modern rivers is challenging because of human modifications and the short timescales of observable data. This project assesses the link between different types of floodplain microtopography and avulsion style in the Devonian Catskill Formation, north-central Pennsylvania, where thick stacks of fluvial strata provide a lengthy record of channel-floodplain interaction. Using a combination of field observations and computer modeling, this study identifies sedimentary features indicative of floodplain complexity and analyzes their impact on avulsion style at fourteen Catskill Formation outcrops.

Based on …

Perceptually Improved Medical Image Translations Using Conditional Generative Adversarial Networks, Anurag Vaidya

Honors Theses

Magnetic resonance imaging (MRI) can help visualize various brain regions. Typical MRI sequences consist of T1-weighted sequence (favorable for observing large brain structures), T2-weighted sequence (useful for pathology), and T2-FLAIR scan (useful for pathology with suppression of signal from water). While these different scans provide complementary information, acquiring them leads to acquisition times of ~1 hour and an average cost of $2,600, presenting significant barriers. To reduce these costs associated with brain MRIs, we present pTransGAN, a generative adversarial network capable of translating both healthy and unhealthy T1 scans into T2 scans. We show that the addition of non-adversarial …

Ethics, Privacy And Data Collection: A Complex Intersection, Matthew S. Brown

Honors Theses

The technology around us enables incredible abilities such as high-resolution video calls and the ability to stay connected with everyone we care about through social media. This technology also comes with a hidden cost in the form of data collection.

This work explores what privacy means and how users understand what data social media companies collect and monetize. This thesis also proposes a more ethical business model that addresses privacy concerns from an individual perspective.

Crystalline Architecture And Stratigraphy Of Coral Skeletal Density Banding: A Geobiological Record Of Changing Coral Reef Ecology, Kyle Fouke

Honors Theses

Coral skeletal density banding (CSDB), composed of alternating high density band (HDB) and low density band (LDB) layers that comprise the CaCO₃ (aragonite) skeleton of scleractinian corals, are used as chronometers for global paleoclimatic reconstructions of sea surface temperature (SST). Scleractinian coral skeletons have been intensively studied for centuries with detail analysis of the macro- and microscale skeletal structure to establish taxonomic and evolutionary relationships of coral species, mechanisms of biomineralization, and seafloor physical, chemical and biological alteration (diagenesis) of the skeleton. This study is the first to determine the crystalline architecture of HDBs and CSDB stratigraphic …

Fluvial Sedimentology And Architecture Of Two Latest Devonian Lower Huntley Mountain Formation Outcrops, North-Central Pennsylvania, Usa, Evan W. Filion

Honors Theses

Thick successions of river deposits accumulated in the north-central Pennsylvania region of the Appalachian foreland basin during Late Devonian time (~380-360 Ma). The properties and morphologies of these paleorivers are not well characterized. Latest Devonian tectonic, climatic, and eustatic controls on river dynamics and basin infilling also remain unclear. This study assesses the sedimentology, facies architecture, paleochannel depths, and grain size of a 133 m thick section of fluvial strata exposed across two outcrops, Blossburg South (older) and Blossburg West (younger), mapped as lower Huntley Mountain Formation near Blossburg, Pennsylvania. Field-based lithofacies observations, high-resolution panoramic photography, terrestrial lidar scanning, and …

Sedimentological, Architectural, And Paleoenvironmental Analysis Of The Fluvial Upper Devonian Catskill Formation, North-Central Pennsylvania, Usa, Matylda Zaklicki

Honors Theses

During the Late Devonian time period, sediments eroded from the Acadian mountains were transported westward and deposited in fluvial environments, but the morphology of the rivers, avulsion style, and controls on basin infilling remain unclear. This study assesses the sedimentology, channel geometry, stratigraphic architecture, and avulsion style of the paleochannels and floodplains of the uppermost 80 meters of the Catskill Formation near Blossburg, Pennsylvania, using field-based lithofacies observations, high-resolution panoramic photographs, and terrestrial lidar scanning.

Upper Catskill Formation strata at Blossburg Middle consist of sandy channel and muddy floodplain deposits. Floodplain deposits were categorized into either proximal floodplain deposits or …

Linked-Cluster Expansions For Lattice Spin Models, Yuyi Wan

Honors Theses

Similar to various series expansions that are used to approximate mathematical func- tions, the linked-cluster expansion is an approximation method that allows us to approach the actual values of a very large physical system’s different physical quan- tities by systematically studying smaller systems embedded in this larger system. The main concept in linked-cluster expansion, weight, represents the additional con- tribution to a certain physical quantity by increasing the system size by one unit. These weights are used to eventually build up the result on a larger system. In our case, we focus on the partition function, a quantity that can …

Contextualizing Sexual Assault Data Collection On College Campuses: A Socio-Technical Approach, Anushikha Sharma

Honors Theses

Sexual assault is a rampant issue on college campuses in the United States. Colleges and universities use a variety of survey instruments to collect data regarding sexual assault as a means to improve campus culture, policies, and resources. These instruments contain a wealth of associated information in the form of metadata, that is, data about data.

This project takes a human-centered socio-technical approach to understanding the data collection processes associated with sexual assault, specifically, on the campus of Bucknell University. By identifying the underlying metadata within the data collection processes, this research contextualizes and critiques the process of data collection, …

Positivity Among P-Partition Generating Functions Of Partially Ordered Sets, Nate Lesnevich

Honors Theses

We find necessary and separate sufficient conditions for the difference between two labeled partially ordered set's (poset) partition generating functions to be positive in the fundamental basis. We define the notion of a jump sequence for a poset and show how different conditions on the jump sequences of two posets are necessary for those posets to have an order relation in the fundamental basis. Our sufficient conditions are of two types. First, we show how manipulating a poset's Hasse diagram produces a poset that is greater according to the fundamental basis. Secondly, we also provide tools to explain posets that …

Bridging Act-R And Project Malmo, Developing Models Of Behavior In Complex Environments, David M. Schwartz

Honors Theses

Cognitive architectures such as ACT-R provide a system for simulating the mind and human behavior. On their own they model decision making of an isolated agent. However, applying a cognitive architecture to a complex environment yields more interesting results about how people make decisions in more realistic scenarios. Furthermore, cognitive architectures enable researchers to study human behavior in dangerous tasks which cannot be tested because they would harm participants. Nonetheless, these architectures aren’t commonly applied to such environments as they don’t come with one. It is left to the researcher to develop a task environment for their model. The difficulty …

Late Devonian Sedimentary Record Of Appalachian Tectonics And Erosion: Geochronology And Geochemistry Of Detrital Muscovite And Zircon From Central Pennsylvania Strata, Cole T. Gardner

Honors Theses

Foreland basin sediment deposition in North-Central Pennsylvania during Late Devonian time records erosion of hinterland source terranes exhumed during regional plate convergence, including the collisional Acadian orogeny. The Catskill clastic wedge preserves a coarsening-upwards stratigraphic succession from marine to fluvial environments associated with sediment progradation and sea-level regression, yet depositional timescales and quantitative provenance data are largely unconstrained.

Detailed facies analysis of eight outcrops spanning >2 km of stratigraphy in Lycoming Co., Pennsylvania documents distinct upsection changes, interpreted to reflect changes in depositional environments consistent with previous sedimentology of the Catskill clastic wedge. Stratigraphy displays a transition from nearshore marine …

Extensions Of The Morse-Hedlund Theorem, Eben Blaisdell

Honors Theses

Bi-infinite words are sequences of characters that are infinite forwards and backwards; for example "...ababababab...". The Morse-Hedlund theorem says that a bi-infinite word f repeats itself, in at most n letters, if and only if the number of distinct subwords of length n is at most n. Using the example, "...ababababab...", there are 2 subwords of length 3, namely "aba" and "bab". Since 2 is less than 3, we must have that "...ababababab..." repeats itself after at most 3 letters. In fact it does repeat itself every two letters. …

Launch-Explore-Summarize In High School Calculus, Nate Mattis

Honors Theses

Current research on high school calculus instruction indicates that students often possess a procedural knowledge of differentiation and integration as opposed to a conceptual knowledge (Orton, 1983; Ferrini-Mundy & Graham, 1994). Given the prominence of traditional lecture and textbook-based calculus classes in the United States, students are not always given the opportunity to expand their conceptual knowledge of essential calculus concepts. This project introduces calculus students to a more active and communal method of teaching: Launch-Explore-Summarize (LES) (CMP, n.d.). This methodology places students at the center of their learning and emphasizes inquiry-based thinking during a class. Specifically, two LES lessons …

On A Problem Of Burnside, Matthew Mizuhara

Honors Theses

Burnside posed the question as to whether or not there exist groups having an external automorphism that behaves in a certain, specific way like an inner automorphism: we shall define such automorphisms to be nearly-inner.

NI-groups are fairly rare. With the aid of the computer algebra system Magma - in particular with the aid of its small group database - we set out to test this hypothesis.

Utilization Of Probabilistic Models In Short Read Assembly From Second-Generation Sequencing, Matthew W. Segar

Honors Theses

With the advent of cheaper and faster DNA sequencing technologies, assembly methods have greatly changed. Instead of outputting reads that are thousands of base pairs long, new sequencers parallelize the task by producing read lengths between 35 and 400 base pairs. Reconstructing an organism’s genome from these millions of reads is a computationally expensive task. Our algorithm solves this problem by organizing and indexing the reads using n-grams, which are short, fixed-length DNA sequences of length n. These n-grams are used to efficiently locate putative read joins, thereby eliminating the need to perform an exhaustive search over all possible read …

Verifying Harder's Conjecture For Classical And Siegel Modular Forms, David Sulon

Honors Theses

A conjecture by Harder shows a surprising congruence between the coefficients of “classical” modular forms and the Hecke eigenvalues of corresponding Siegel modular forms, contigent upon “large primes” dividing the critical values of the given classical modular form.

Harder’s Conjecture has already been verified for one-dimensional spaces of classical and Siegel modular forms (along with some two-dimensional cases), and for primes p 37. We verify the conjecture for higher-dimensional spaces, and up to a comparable prime p.

Sedimentology, Depositional Age, And Provenance Of Sedimentary And Volcanic Rocks Exposed Along Willow Creek, Eastern Susitna Basin, South-Central Alaska: Implications For Modification Of A Forearc Basin By Spreading Ridge Subduction, Erin E. Donaghy

Honors Theses

This is the first detailed study of the westernmost portion of the outcrop belt, which extends along the western flank of the Talkeetna Mountains and includes thick, well-exposed outcrops along Willow Creek in the eastern Susitna basin. New sedimentologic, compositional, and geochronologic data were obtained from stratigraphic sections within Arkose Ridge Formation strata at Willow Creek. This data combined with new geologic mapping and geochronologic data from Willow Bench and Kashwitna River Bluff (north of Willow Creek), and from the Government Peak area (east of Willow Creek), help constrain depositional processes and source terranes that provided detritus to the westernmost …

Behavioral Economics And Physician Behavior, Allyssa S. Ward

Honors Theses

This study seeks to answer whether the availability heuristic leads physicians to utilize more medical care than is economically efficient. Do rare, salient events alter physicians' perceptions about the probability of patient harm? Do these events lead physicians to overutilize certain medical procedures? This study uses Pennsylvania inpatient hospital admissions data from 2009 aggregated at the physician level to investigate these questions. The data come from the 2009 Pennsylvania Health Care Cost Containment Council (PHC4).

The study is divided into two parts. In Part I, we examine whether bad outcomes during childbirth (defined as maternal mortality, an obstetric fistula or …

Mesoproterozoic Deposition, Regional Metamorphism And Deformation In North-Central New Mexico: Evidence From Metamorphic Monazite And Detrital Zircon Geochronology In The Picuris Mountains, Lily S. Pfeifer

Honors Theses

Detrital zircon and metamorphic monazite ages from the Picuris Mountains, north central New Mexico, were used to confirm the depositional age of the Marquenas Formation, to document the depositional age of the Vadito Group, and to constrain the timing of metamorphism and deformation in the region.

Detrital zircon 207Pb/206Pb ages were obtained with the LA-MC-ICPMS from quartzites collected from the type locality of the Marquenas Formation exposed at Cerro de las Marquenas, and from the lower Vadito Group in the southern and eastern Picuris Mountains. The Marquenas Formation sample yields 113 concordant ages including a Mesoproterozoic age population with four …

Evaluating Bucknell's Waste Stream, Hallie S. Kennan

Honors Theses

This thesis examines three questions regarding the content of Bucknell University‟s waste stream and the contributors to campus recycling and solid waste disposal. The first asks, “What does Bucknell‟s waste stream consist of?” To answer this question, I designed a campus-wide waste audit procedure that sampled one dumpster from each of the eleven „activity‟ types on campus in order to better understand Bucknell‟s waste composition. The audit was implemented during the Fall semester of the 2011-2012 school year. The waste from each dumpster was sorted into several recyclable and non-recyclable categories and then weighed individually. Results showed the Bison and …

A Framework For The Automation Of Discrete-Event Simulation Experiments, Bryan Ward

Honors Theses

Simulation is an important resource for researchers in diverse fields. However, many researchers have found flaws in the methodology of published simulation studies and have described the state of the simulation community as being in a crisis of credibility. This work describes the project of the Simulation Automation Framework for Experiments (SAFE), which addresses the issues that undermine credibility by automating the workflow in the execution of simulation studies. Automation reduces the number of opportunities for users to introduce error in the scientific process thereby improvingthe credibility of the final results. Automation also eases the job of simulation users and …

Equality Of P-Partition Generating Functions, Ryan Ward

Honors Theses

To every partially ordered set (poset), one can associate a generating function, known as the P-partition generating function. We find necessary conditions and sufficient conditions for two posets to have the same P-partition generating function. We define the notion of a jump sequence for a labeled poset and show that having equal jumpsequences is a necessary condition for generating function equality. We also develop multiple ways of modifying posets that preserve generating function equality. Finally, we are able to give a complete classification of equalities among partially ordered setswith exactly two linear extensions.

Provenance Signature Of A Forearc Basin Modified By Spreading Ridge Subduction: Detrital Zircon Geochronology And Detrital Modes From The Paleogene Arkose Ridge Formation, Southern Alaska, Cullen Kortyna

Honors Theses

Upper Paleocene–Eocene boulder conglomerate, cross-stratified sandstone, and laminated carbonaceous mudstone of the Arkose Ridge Formation exposed in the southern Talkeetna Mountains record fluvial-lacustrine deposition proximal to the volcanic arc in a forearc basin modified by Paleogene spreading ridge subduction beneath southern Alaska. U-Pb ages of detrital zircon grains and modal analyses were obtained from stratigraphic sections spanning the 2,000 m thick Arkose Ridge Formation in order to constrain the lithology, age, and location of sediment sources that provided detritus. Detrital modes from 24 conglomerate beds and 54 sandstone thin sections aredominated by plutonic and volcanic clasts and plagioclase feldspar with …