Physical Sciences and Mathematics Commons^™

Pattern Recognition In High-Dimensional Data, Matthew Dannenberg

HMC Senior Theses

Vast amounts of data are produced all the time. Yet this data does not easily equate to useful information: extracting information from large amounts of high dimensional data is nontrivial. People are simply drowning in data. A recent and growing source of high-dimensional data is hyperspectral imaging. Hyperspectral images allow for massive amounts of spectral information to be contained in a single image. In this thesis, a robust supervised machine learning algorithm is developed to efficiently perform binary object classification on hyperspectral image data by making use of the geometry of Grassmann manifolds. This algorithm can consistently distinguish between a …

Realizing The 2-Associahedron, Patrick N. Tierney

HMC Senior Theses

The associahedron has appeared in numerous contexts throughout the field of mathematics. By representing the associahedron as a poset of tubings, Michael Carr and Satyan L. Devadoss were able to create a gener- alized version of the associahedron in the graph-associahedron. We seek to create an alternative generalization of the associahedron by considering a particle-collision model. By extending this model to what we dub the 2- associahedron, we seek to further understand the space of generalizations of the associahedron.

Steady State Solutions For A System Of Partial Differential Equations Arising From Crime Modeling, Bo Li

HMC Senior Theses

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 case, which proves the attractiveness and density of criminals in the given area will not be unlimitedly high. In addition, I have found some local bifurcation points in the model.

Topological Data Analysis For Systems Of Coupled Oscillators, Alec Dunton

HMC Senior Theses

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 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 …

Line-Of-Sight Pursuit And Evasion Games On Polytopes In R^N, John Phillpot

HMC Senior Theses

We study single-pursuer, line-of-sight Pursuit and Evasion games in polytopes in $\mathbb{R}^n$. We develop winning Pursuer strategies for simple classes of polytopes (monotone prisms) in Rⁿ, using proven algorithms for polygons as inspiration and as subroutines. More generally, we show that any Pursuer-win polytope can be extended to a new Pursuer-win polytope in more dimensions. We also show that some more general classes of polytopes (monotone products) do not admit a deterministic winning Pursuer strategy. Though we provide bounds on which polytopes are Pursuer-win, these bounds are not tight. Closing the gap between those polytopes known to be …

Graph Cohomology, Matthew Lin

HMC Senior Theses

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 ring H*(G) 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 …

Interval Graphs, Joyce C. Yang

HMC Senior Theses

We examine the problem of counting interval graphs. We answer the question posed by Hanlon, of whether the formal power series generating function of the number of interval graphs on n vertices has a positive radius of convergence. We have found that it is zero. We have obtained a lower bound and an upper bound on the number of interval graphs on n vertices. We also study the application of interval graphs to the dynamic storage allocation problem. Dynamic storage allocation has been shown to be NP-complete by Stockmeyer. Coloring interval graphs on-line has applications to dynamic storage allocation. The …

Fibonomial Tilings And Other Up-Down Tilings, Robert Bennett

HMC Senior Theses

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 …

Adinkras And Arithmetical Graphs, Madeleine Weinstein

HMC Senior Theses

Adinkras and arithmetical graphs have divergent origins. In the spirit of Feynman diagrams, adinkras encode representations of supersymmetry algebras as graphs with additional structures. Arithmetical graphs, on the other hand, arise in algebraic geometry, and give an arithmetical structure to a graph. In this thesis, we will interpret adinkras as arithmetical graphs and see what can be learned.

Our work consists of three main strands. First, we investigate arithmetical structures on the underlying graph of an adinkra in the specific case where the underlying graph is a hypercube. We classify all such arithmetical structures and compute some of the corresponding …

Convexity Of Neural Codes, Robert Amzi Jeffs

HMC Senior Theses

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. A neural code is a collection of binary vectors that record concurrent firing of neurons in the brain. We consider neural codes arising from place cells, which are neurons that track an animal's position in space. We examine algebraic objects associated to neural codes, and completely characterize a certain class of maps between these objects. Furthermore, we show that such maps have natural geometric implications related to …

Hopper Bands: Locust Aggregation, Ryan C. Jones

HMC Senior Theses

Locust swarms cause famine and hunger in parts of Sub-Saharan Africa as they travel across croplands and eat vegetation. Current models start with biological properties of locusts and analyze the macroscopic 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 (AIM) model, is derived with minimal assumptions. AIM is constructed with regards to locust biology, allowing it to elicit biologically correct locust behavior: the most noteworthy being the fingering of hopper bands. A Particle-in-Cell method is used to optimize …

Archean Geodynamic Conditions Using P-T Constraints Of The East Pilbara Craton Ttgs, Andrew Kody Webb

LSU Master's Theses

We know very little about the tectonic setting present during the Hadean, but based on studies of surviving Hadean zircons, we know that a Hadean protocrust must have been established by at least 4.4 Ga (Kemp et al. 2010), and it must have also been able to accommodate minimum melt conditions (Harrison 2005). Tectonic models for Earth during the Hadean and Archean follow two trends: uniformitarianism and non-uniformitarianism. Uniformitarian models (following the famed geological concept that the present is the key to the past) argue that Hadean zircons and Archean rocks formed via processes akin to modern-style oceanic crust production …

Applying Deep Learning Techniques To The Analysis Of Android Apks, Robin Andrew Nix

LSU Master's Theses

Malware targeting mobile devices is a pervasive problem in modern life and as such tools to detect and classify malware are of great value. This paper seeks to demonstrate the effectiveness of Deep Learning Techniques, specifically Convolutional Neural Networks, in detecting and classifying malware targeting the Android operating system. Unlike many current detection techniques, which require the use of relatively rigid features to aid in detection, deep neural networks are capable of automatically learning flexible features which may be more resilient to obfuscation. We present a parsing for extracting sequences of API calls which can be used to describe a …

Using Tourmaline As An Indicator Of Provenance: Development And Application Of A Statistical Approach Using Random Forests, Erin Lael Walden

LSU Master's Theses

Tourmaline is a petrologic indicator mineral that is the major repository of boron in the earth’s crust. It forms readily when boron is present, accommodating multiple cations and anions with multiple possible substitutions for each site in the crystal structure. It is stable over a wide variety of pressures and temperatures, from near-surface P/T conditions to greater than 950 C and 7 GPa. It records information about conditions of formation, as well as pressure and temperature. Due to its resistance to chemical or physical weathering, and the negligible diffusion of elements in the crystal lattice, information about provenance is preserved. …

Fishes Associated With Oil And Gas Platforms In Louisiana's River-Influenced Nearshore Waters, Ryan Thomas Munnelly

LSU Master's Theses

A distinctive feature of coastal Louisiana is the unrivaled network of oil and gas installations (platforms) extending from inshore waters to the deep Gulf of Mexico. Since 2007 there has been a 38% reduction in platform numbers with the highest removal rates occurring in shallow (< 18 m) nearshore waters. Many fishes and invertebrates are attracted to platforms, presenting a unique opportunity to study detailed species-specific responses to the river-influenced hydrographic characteristics of Louisiana’s nearshore zone (5–25 km water depth). Prior studies of fishes around platforms focused on a few relatively large platforms in water depths ≥ 18 m. However, about one-third of all platforms are small, unmanned and non-drilling platforms located in waters < 18 m depth. Paired video and hydrographic data were collected at 150 small platforms in < 18 m water depth during the summers of 2013–2014. Fifty-four species of fishes were associated with small platforms. The assemblage(s) included juveniles of 29 species, indicating the importance of nearshore platforms as diverse nursery habitat. The coastal zone was divided into three regions based on broad-scale interactions between freshwater input and bathymetry driving major distinctions in interregional hydrography and fish assemblages. Co-occurring within this expansive artificial reef network is the second largest hypoxic area (dissolved oxygen (DO) < 2.0 mg l−1) on Earth. Platforms offer reef-like habitat features in the upper water column that may offer refugia for some reef-associated species during hypoxic events. Significant intraregional differences in physicochemical features were related to the presence of hypoxia (defined as DO < 50% saturation), as well as the distribution of sandy shoals. Eleven species accounted for most of the assemblage dissimilarities, composing ~93% of fishes observed. Habitat suitability indices for these 11 species provided information about habitat selection across horizontal and vertical physicochemical gradients throughout the coastal zone, and within hypoxic and well-oxygenated stratified water columns. East Bay, near the outlet of the Mississippi River, exhibited less hypoxia and a distinct fauna that included four adult goliath grouper (Epinephelus itajara). This endangered fish was observed during spawning season (summer), suggesting that East Bay might support a spawning aggregation.

Nonlinear Model And Qualitative Analysis For Coupled Axial/Torsional Vibrations Of Drill String, Fushen Ren, Baojin Wang, Suli Chen, Zhigang Yao, Baojun Bai

Geosciences and Geological and Petroleum Engineering Faculty Research & Creative Works

A nonlinear dynamics model and qualitative analysis are presented to study the key effective factors for coupled axial/torsional vibrations of a drill string, which is described as a simplified, equivalent, flexible shell under axial rotation. Here, after dimensionless processing, the mathematical models are obtained accounting for the coupling of axial and torsional vibrations using the nonlinear dynamics qualitative method, in which excitation loads and boundary conditions of the drill string are simplified to a rotating, flexible shell. The analysis of dynamics responses is performed by means of the Runge-Kutta-Fehlberg method, in which the rules that govern the changing of the …

Evidence For The Drainage Of A Superglacial Lake As The Source Of Seismic Waves Recorded At A Regional Distance, Erik J. Orantes

Dissertations and Theses

Surface melting during the summer leads to the formation of lakes on the Greenland Ice Sheet surface, known as supraglacial lakes. Some of these lakes drain through cracks in their beds and release the water into the ice sheet. Previous studies suggest that some of the water reaches the bedrock, enabling basal sliding, which could potentially increase glacial discharge (Sundal et al., 2009). Das et al. (2008) showed that supraglacial lake drainage can be accompanied by seismic activity, but little work has been done on the regional detection of such waves. The present study analyzes seismic data for the period …

Revised Distributional Estimates For The Recently Discovered Olinguito (Bassaricyon Neblina), Using Museum And Science Records, Beth E. Gerstner

Dissertations and Theses

In the context of global change, a necessary first step for the conservation of species is gaining a good understanding of their distributional limits. This is especially important for biodiversity hotspots with high endemism such as the Northern Andes. The olinguito (Procyonidae: Bassaricyon neblina) is a recently described, medium-sized carnivoran found in Northern Andean cloud forests. A preliminary distributional model was published along with the original description, and I here provide revised distributional estimates using updated locality records and more current ENM methods. I build ecological niche models in Maxent using occurrence data (georeferenced museum records and citizen science-derived photo-vouchers) …

Julia-Kocienski Approach To 4-Substituted 1- Alkenyl-1h-1,2,3-Triazoles, Kunga Tsetan

Dissertations and Theses

A modular approach to the synthesis of 4-substituted N-vinyltriazoles was
developed. The triazole cores were assembled by copper-catalyzed 1,3-dipolar
cycloaddition of 1-phenyl-1H-tetrazol-5-yl (PT) azidomethyl sulfide with: pmethoxyphenyl, 2-pyridyl, and triisopropylsilyl alkynes. Subsequent oxidation of the sulfides furnished 4-substituted triazoles with a Julia-Kocienski olefination handle attached at the N1 atom of the triazole. Olefination reactions of triazole-derived Julia-Kocienski reagents with paraformaldehyde gave 1-ethenyl-1H-1,2,3-triazoles. Heck reactions of these products with phenyl or p-methoxyphenyl iodide led to further functionalization of the terminal carbon, with E/Z-olefin ratios ≥ 92%. Heck reaction with p-cyanophenyl iodide gave low conversion, and that with 2-thienyl iodide did not …

Assessing The Utility Of Imaging Radar For Identifying White Sand Vegetation Structure, Jessica Rosenqvist

Dissertations and Theses

White sand vegetation communities are wide spread across South America; found in Peru, Venezuela, Brazilian Amazon and Guyana. They are distributed in patches ranging from <1 km2 to greater than tens of square kilometers and their origins and locations are still not well understood. The communities are related to a variety of factors (soil type, flooding, nutrient content and fire); hence a precise definition for the ecosystem is still not fully defined. Nevertheless, the result of these variations creates a unique environment for endemic plant and animal species to thrive. Furthermore, analysis of these areas has been very scattered and identification of local white sand areas (<1 km2) have not been accomplished. In addition, identification of these locations has currently only used optical satellite imagery (Landsat, MODIS). Hence, in this project, we have attempted to use synthetic aperture radar to create a classification system to locate the white sand vegetation systems. The goal is to be able to apply this method to identify white sand vegetation distribution across South America. The region of focus for this thesis has been in Aracá, a large white sand area located in Brazil in the State of Amazonas. Due to the lack of ground reference data, a classified map by Capurucho et al. (2013), generated using Landsat data, was used as a comparison and reference. JAXA’s ALOS-1 PALSAR (L-band), ESA’s Sentinel-1A (C-band) and NASA’s SRTM sensors were used for land classification. As microwave signals penetrate clouds and haze, the advantage of using sensors with this wavelength allows for an unobstructed coverage of the landscape all year round. Different combinations of polarizations and wavelengths were used during the analysis to try and separate the white sand vegetation from water and terra firme forest. The resulting classification images showed a 30% agreement with the classification map by Capurucho et al. It is important to note, that this number is in fact an agreement percentage as the map used was a classification image and coarse in resolution (due to the lack of reference data). Therefore, this value does not imply a bad classification. Future work will include time-series data, precise ground reference points and data from other sensors such as ALOS-2 PALSAR, to improve the classification accuracy.

Evaluating Distributed Word Representations For Predicting Missing Words In Sentences, Saniya Saifee

Dissertations and Theses

In recent years, the distributed representation of words in vector space or word embeddings have become very popular as they have shown significant improvements in many statistical natural language processing (NLP) tasks as compared to traditional language models like Ngram. In this thesis, we explored various state-of-the-art methods like Latent Semantic Analysis, word2vec, and GloVe to learn the distributed representation of words. Their performance was compared based on the accuracy achieved when tasked with selecting the right missing word in the sentence, given five possible options. For this NLP task we trained each of these methods using a training corpus …

An Approach To Automatic Detection Of Suspicious Individuals In A Crowd, Satabdi Mukherjee

Dissertations and Theses

This paper describes an approach to identify individuals with suspicious objects in a crowd. It is based on a well-known image retrieval problem as applied to mobile visual search. In many cases, the process of building a hierarchical tree uses k-means clustering followed by geometric verification. However, the number of clusters is not known in advance, and sometimes it is randomly generated. This may lead to a congested clustering which can cause problems in grouping large real-time data. To overcome this problem we have applied the Indian Buffet stochastic process approach in this paper to the clustering problem. We present …

Technetium: Productivity Tracking For Version Control Systems, David Leonard

Dissertations and Theses

In recent years, the City College of New York has seen its Computer Science program grow immensely, to the point of overcrowding. This has negative implications for both students and professors, particularly in introductory computer science courses in which constant feedback, iteration and collaboration with others is key to success. In this paper we propose various models for collaboration among students in all course levels using distributed version control systems and implement a secure and efficient tool for visualizing collaborative efforts by observing past work [5]. Lastly, we lay the foundation for future work around additional collaborative metrics, features and …

Vehicle Engine Classification Using Of Laser Vibrometry Feature Extraction, Chi Him Liu

Dissertations and Theses

Used as a non-invasive and remote sensor, the laser Doppler vibrometer (LDV) has been used in many different applications, such as inspection of aircrafts, bridge and structure and remote voice acquisition. However, using LDV as a vehicle surveillance device has not been feasible due to the lack of systematic investigations on its behavioral properties. In this thesis, the LDV data from different vehicles are examined and features are extracted. A tone-pitch indexing (TPI) scheme is developed to classify different vehicles by exploiting the engine’s periodic vibrations that are transferred throughout the vehicle’s body. Using the TPI with a two-layer feed-forward …

Relationship Between Sustainable Environmental Practices And Sustainable Value Creation: A Conceptual Study On Readymade Garments Industry Of Bangladesh, Mohammed S. Chowdhury, Zahurul Alam, Mizanur Rahaman Chowdhury

Graduate School of Business Publications and Research

Because of the increasing level of industrial contamination the demand for sustainable products and raw materials aligned with the ecological pollution has been on the rise in this horizon. This study theoretically explores the impact of sustainable environmental practices on financial performance of Ready-made Garment (RMG) companies of Bangladesh following the growing literature linking corporate sustainable environmental performance with revenue development and profitability. Various sustainable environmental practices have diverse effects on firm’s performance, as the literature review suggests. From literature review this paper reports four key areas (community, employee, environment and governance) of sustainable practices for sustainable financial performance that …

Effects Of The Green Life Nature Education Program For 4th Grade Students Who Attend Bay Area Title One Schools: A Mixed-Methods Study, Jessica Blundell

Doctoral Dissertations

This explanatory sequential design mixed-methods evaluation measures the effects of the GLNE program on (a) students’ personal and social skills (b) students’ stewardship of the environment (c) students’ knowledge and understanding of science concepts. Quantitative survey data and qualitative data from a phenomenologically-based study are analyzed and compared in order to understand the impact of attending Green Life Nature Education (GLNE) program, the only Bay Area Residential Outdoor School that serves urban youth with no-cost programing.

The quantitative data from student surveys implies that in general, attending GLNE has a neutral impact on students. While there were several negative impacts …

Reservoir Characterization Through Pre-Stack Seismic Analysis And Inversion In The Thrace Basin, Northwest Turkey, Emre Doguturk

Dissertations, Master's Theses and Master's Reports

This study analyzes hydrocarbon reservoirs by using Amplitude-Versus-Offset (AVO) analysis and different inversion methods to investigate hydrocarbon reservoir in the Thrace Basin which is located in northwest Turkey.

A 3D seismic survey containing prestack data was provided by Turkish Petroleum Corporation as true amplitude NMO corrected 3D gathers.

The quality of this land data was poor for AVO applications, and steps were taken to make it useful. Radon filtering proved to be extremely useful for this purpose. Although application of this filter affected the AVO characteristics differently depending on the parameters selected for the filter, relative AVO characteristics remained useful …

Defect-Deferred Correction Method For The Two-Domain Convection-Dominated Convection-Diffusion Problem, Dilek Erkmen

Dissertations, Master's Theses and Master's Reports

We present a method for solving a fluid-fluid interaction problem (two convection-dominated convection-diusion problems adjoined by an interface), which is a simplifed version of the atmosphere ocean coupling problem. The method resolves some of the issues that can be crucial to the fluid-fluid interaction problems: it is a partitioned time stepping method, yet it is of high order accuracy in both space and time (the two-step algorithm considered in this report provides second order accuracy); it allows for the usage of the legacy codes (which is a common requirement when resolving flows in complex geometries), yet it can be applied …

Can Seismic Velocity Stacking Errors Result In The Low-Frequency Shadow?, Umit Serhan Inan

Dissertations, Master's Theses and Master's Reports

The low-frequency shadow is the area on reflection seismic data, underneath gas reservoirs, that exhibits anomalously low frequency. This phenomenon has been related to the highly attenuating nature of the gas reservoir, which could explain the low-frequency shadows observed underneath extremely thick reservoirs, but not the ones underneath thin reservoirs. There are several other mechanisms that could be responsible, however detailed analysis of these possible explanations is yet to be found in the literature.

The main focus of this research is to test the possible contribution of stacking of offset seismic data, namely, their mis-stacking, to the generation of the …

Two Problems Of Gerhard Ringel, Adrian Pastine

Dissertations, Master's Theses and Master's Reports

Gerhard Ringel was an Austrian Mathematician, and is regarded as one of the most influential graph theorists of the twentieth century. This work deals with two problems that arose from Ringel's research: the Hamilton-Waterloo Problem, and the problem of R-Sequences.

The Hamilton-Waterloo Problem (HWP) in the case of C_m-factors and C_n-factors asks whether K_v, where v is odd (or K_v-F, where F is a 1-factor and v is even), can be decomposed into r copies of a 2-factor made entirely of m-cycles and s copies of a 2-factor made entirely of …