Physical Sciences and Mathematics Commons^™

Structural Analysis And Fluid Flow Modeling Of The Kapuni Field, New Zealand, Jarret Taylor Baldwin

Masters Theses

"The Taranaki Basin is the largest hydrocarbon producing basin in New Zealand. A total area of over 330,000 km

Automated Design Of Boolean Satisfiability Solvers Employing Evolutionary Computation, Alex Raymond Bertels

Masters Theses

"Modern society gives rise to complex problems which sometimes lend themselves to being transformed into Boolean satisfiability (SAT) decision problems; this thesis presents an example from the program understanding domain. Current conflict-driven clause learning (CDCL) SAT solvers employ all-purpose heuristics for making decisions when finding truth assignments for arbitrary logical expressions called SAT instances. The instances derived from a particular problem class exhibit a unique underlying structure which impacts a solver's effectiveness. Thus, tailoring the solver heuristics to a particular problem class can significantly enhance the solver's performance; however, manual specialization is very labor intensive. Automated development may apply hyper-heuristics …

Composite Model Representation For Computer Aided Design Of Functionally Gradient Materials, Fangquan Wang

Masters Theses

"Functionally Gradient Materials (FGMs) feature smooth transition from one material to another within a single object. FGMs modeling is considered to be one of the new challenges in Computer Aided Design (CAD) area. To overcome this challenge, this thesis presents a composite approach to model FGMs. The input in STL format can be meshed and voxelized in FGMs modeling system. The material composition in each voxel can be generated from multiple different types of control features. And LTI filters including Gaussian Filter and Average Filter are applied to blur default material features in order to generate FGMs inside models. The …

Fluid Flow Through Deformation Band, Huining Zhang

Masters Theses

"Cataclastic deformation bands, which are common in porous sandstone, have the potential to restrict fluid flow. Geological studies have shown that permeability of deformation band shear zones can be one to five orders of magnitude less than for the sandstone host rock. However, recent studies based on simplified analytical estimates have shown that fluid flow in jointed deformation bands may not be retarded since joints play an important role in conducting fluids. In this study, 2 dimensional finite element analysis (FEA) is used to simulate the total discharge flow rate through jointed deformations. Variations of single planar and conjugate jointed …

Lose Big, Win Big, Sum Big: An Exploration Of Ranked Voting Systems, Erin Else Stuckenbruck

Senior Projects Spring 2016

Senior Project submitted to The Division of Science, Mathematics and Computing of Bard College.

The Schur Factorization Property As It Applies To Subsets Of The General Laguerre Polynomials, Christopher A. Gunnell

Senior Projects Spring 2016

Senior Project submitted to The Division of Science, Mathematics and Computing of Bard College.

Integer Generalized Splines On The Diamond Graph, Emmet Reza Mahdavi

Senior Projects Spring 2016

In this project we extend previous research on integer splines on graphs, and we use the methods developed on n-cycles to characterize integer splines on the diamond graph. First, we find an explicit module basis consisting of flow-up classes. Then we develop a determinantal criterion for when a given set of splines forms a basis.

Analogy: A Decomposition Of Space And Time, David Gordon Shoemaker Jr

Senior Projects Spring 2016

The written part of this project is divided into two sections, with the first section focusing on the human eye as a biological tool for gathering and processing physical information. The second section strives to provide a model of human vision by utilizing Fourier Analysis. Out of this model came a focus on Fourier Analysis as not only a model, but as a methodology that can be applied in a variety of ways. The Fourier methodology provided a conceptual bridge that allowed me to more thoroughly explore art, physics, and how these two fields can contribute to each other.

Radical Recognition In Off-Line Handwritten Chinese Characters Using Non-Negative Matrix Factorization, Xiangying Shuai

Senior Projects Spring 2016

In the past decade, handwritten Chinese character recognition has received renewed interest with the emergence of touch screen devices. Other popular applications include on-line Chinese character dictionary look-up and visual translation in mobile phone applications. Due to the complex structure of Chinese characters, this classification task is not exactly an easy one, as it involves knowledge from mathematics, computer science, and linguistics.

Given a large image database of handwritten character data, the goal of my senior project is to use Non-Negative Matrix Factorization (NMF), a recent method for finding a suitable representation (parts-based representation) of image data, to detect specific …

Mckay Graphs And Modular Representation Theory, Polina Aleksandrovna Vulakh

Senior Projects Spring 2016

Ordinary representation theory has been widely researched to the extent that there is a well-understood method for constructing the ordinary irreducible characters of a finite group. In parallel, John McKay showed how to associate to a finite group a graph constructed from the group's irreducible representations. In this project, we prove a structure theorem for the McKay graphs of products of groups as well as develop formulas for the graphs of two infinite families of groups. We then study the modular representations of these families and give conjectures for a modular version of the McKay graphs.

Associativity Of Binary Operations On The Real Numbers, Samuel Joseph Audino

Senior Projects Spring 2016

It is known that there is an agreed upon convention of how to go about evaluating expressions in the real numbers. We colloquially call this PEMDAS, which is short for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. It is also called the Order of Operations, since it is the order in which we execute the operators of a given expression. When we remove this convention and begin to execute the operators in every possible order, we begin to see that this allows for many different values based on the order in which the operations are executed. We will investigate this question …

Providing Hands-On Training With Bioinformatics Databases: A Collaboration Between Vcu Libraries & Wright Center For Clinical And Translational Research, Karen H. Gau, Julie A. Arendt, Amy Olex, Aaron R. Wolen

VCU Libraries Faculty and Staff Presentations

Background
With the goal of increasing specialized services for researchers, Virginia Commonwealth University (VCU) Libraries sent its basic science librarians to an intensive training on bioinformatics databases, “A Librarian’s Guide to NCBI.” VCU’s Wright Center for Clinical and Translational Research (Wright CCTR) was expanding the educational component of its bioinformatics support around the same time. This year, the librarians partnered with the Wright CCTR to offer an introductory bioinformatics database workshop introducing researchers to genetic/genomic databases.

Methods
For one week in June, sessions were conducted introducing up to 30 faculty and staff to The Cancer Genome Atlas and NCBI’s Gene, …

Incorporating Field Studies Into Species Distribution And Climate Change Modelling: A Case Study Of The Koomal Trichosurus Vulpecula Hypoleucus (Phalangeridae), Shaun Molloy, Robert Davis, Eddie Van Etten

Research outputs 2014 to 2021

Species distribution models (SDMs) are an effective way of predicting the potential distribution of species and their response to environmental change. Most SDMs apply presence data to a relatively generic set of predictive variables such as climate. However, this weakens the modelling process by overlooking the responses to more cryptic predictive variables. In this paper we demonstrate a means by which data gathered from an intensive animal trapping study can be used to enhance SDMs by combining field data with bioclimatic modelling techniques to determine the future potential distribution for the koomal (Trichosurus vulpecula hypoleucus). The koomal is a geographically …

Oxidative Dehydrogenation Of Light Alkanes With Carbon Dioxide, Marktus A. Atanga

Masters Theses

”Most experts studying the global ecosystem and climate suggest that rising anthropogenic CO₂ emissions have contributed to significant global climate change in the last half-century. The development of effective strategies that convert CO₂ into energy, fuels, and chemicals are greatly preferable to oceanic or geologic sequestration options because they offer the potential to create new commercially-viable products from renewable carbon feedstock. On the other hand, the selective oxidative dehydrogenation of light alkanes (C₂-C₄) to corresponding olefins, methane reforming, and methane coupling are the major challenges for producing valuable and versatile feedstocks. The oxidative dehydrogenation …

Real Complex Functions, Stephan Ramon Garcia, Javad Mashreghi, William T. Ross

Department of Math & Statistics Faculty Publications

We survey a few classes of analytic functions on the disk that have real boundary values almost everywhere on the unit circle. We explore some of their properties, various decompositions, and some connections these functions make to operator theory.

Development In Normal Mixture And Mixture Of Experts Modeling, Meng Qi

Theses and Dissertations--Statistics

In this dissertation, first we consider the problem of testing homogeneity and order in a contaminated normal model, when the data is correlated under some known covariance structure. To address this problem, we developed a moment based homogeneity and order test, and design weights for test statistics to increase power for homogeneity test. We applied our test to microarray about Down’s syndrome. This dissertation also studies a singular Bayesian information criterion (sBIC) for a bivariate hierarchical mixture model with varying weights, and develops a new data dependent information criterion (sFLIC).We apply our model and criteria to birth- weight and gestational …

Multi-State Models With Missing Covariates, Wenjie Lou

Theses and Dissertations--Statistics

Multi-state models have been widely used to analyze longitudinal event history data obtained in medical studies. The tools and methods developed recently in this area require the complete observed datasets. While, in many applications measurements on certain components of the covariate vector are missing on some study subjects. In this dissertation, several likelihood-based methodologies were proposed to deal with datasets with different types of missing covariates efficiently when applying multi-state models.

Firstly, a maximum observed data likelihood method was proposed when the data has a univariate missing pattern and the missing covariate is a categorical variable. The construction of the …

New Hampshire Beaches: Sediment Characterization, Larry G. Ward, Kaitlyn A. Mcpherran, Zachary S. Mcavoy, Maxlimer Coromoto Vallee-Anziani

Center for Coastal and Ocean Mapping

The grain size of the natural sediment composing the major New Hampshire beaches under summer equilibrium conditions was determined as a first step in assessing the optimal sediment size that would be needed for beach nourishment. In summer, 2015, seven major beaches including Wallis Sands, Foss Beach, Jenness Beach, North Hampton Beach, North Beach, Hampton Beach, and Seabrook Beach were sampled along three to five transects extending from the dunes or engineering structures (e.g., seawalls) to the low water line. In addition, the beach cross-section was profiled using a rover GPS system or the Emery method (profile rods and the …

Solutions To The LP Mixed Boundary Value Problem In C1,1 Domains, Laura D. Croyle

Theses and Dissertations--Mathematics

We look at the mixed boundary value problem for elliptic operators in a bounded C^1,1(ℝⁿ) domain. The boundary is decomposed into disjoint parts, D and N, with Dirichlet and Neumann data, respectively. Expanding on work done by Ott and Brown, we find a larger range of values of p, 1 < p < n/(n-1), for which the L^p mixed problem has a unique solution with the non-tangential maximal function of the gradient in L^p(∂Ω).

The Bourgain Spaces And Recovery Of Magnetic And Electric Potentials Of Schrödinger Operators, Yaowei Zhang

Theses and Dissertations--Mathematics

We consider the inverse problem for the magnetic Schrödinger operator with the assumption that the magnetic potential is in C^λ and the electric potential is of the form p₁ + div p₂ with p₁, p₂ ∈ C^λ. We use semiclassical pseudodifferential operators on semiclassical Sobolev spaces and Bourgain type spaces. The Bourgain type spaces are defined using the symbol of the operator h²Δ + hμ ⋅ D. Our main result gives a procedure for recovering the curl of the magnetic field and the electric potential from the Dirichlet to Neumann …

Thermal Effects On Spin Currents In Non-Local Metallic Spin Valves, Alex Hojem

Electronic Theses and Dissertations

The study of non-local spin valves (NLSVs) has recently proven to be a fertile area for both applied and fundamental research in nanomagnetism due to the unique ability to separate charge currents and spin currents. NLSVs may also prove essential for a new class of high-density hard disk read heads due to their favorable scalability. Recent studies have shown thermal effects created by high current densities play a significant role in the response of NLSVs. These thermal effects also provide the opportunity to create a pure spin current from thermal gradients via a mechanism call the spin dependent Seebeck effect …

A Revision Of Megalocraerus Lewis, 1902 (Coleoptera, Histeridae: Exosternini), Michael S. Caterino, Alexey K. Tishechkin

Publications

The formely monotypic Neotropical genus Megalocraerus Lewis is revised to include five species, known from southeastern Brazil to Costa Rica: M. rubricatus Lewis, M. mandibularis sp. n., M. chico sp. n., M. madrededios sp. n., and M. tiputini sp. n. We describe the species, map their distributions, and provide a key for their identification. Their subcylindrical body form and emarginate mesosternum have previously hindered placement to tribe, although their curent assignment to Exosternini now appears well supported by morphological evidence. Nothing is known of the natural history of the species.

Towards On Demand Road Condition Monitoring Using Mobile Phone Sensing As A Service, Wael Alrahal Alorabi, Sawsan Abdul Rahman, May El Barachi, Azzam Mourad

All Works

© 2016 The Authors. With the increased need for mobility and the overcrowding of cities, the area of Intelligent Transportation aims at improving the efficiency, safety, and productivity of transportation systems by relying on communication and sensing technologies. One of the main challenges faced in Intelligent Transportation Systems (ITS) pertains to the real time collection of traffic and road related data, in a cost effective, efficient, and scalable manner. The current approaches still suffer from problems related to the energy consumption of mobile devices and overhead in terms of communications and processing. We have previously proposed the concept of Mobile …

Alexander And Writhe Polynomials For Virtual Knots, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

We give a new interpretation of the Alexander polynomial Δ₀ for virtual knots due to Sawollek and Silver and Williams, and use it to show that, for any virtual knot, Δ₀ determines the writhe polynomial of Cheng and Gao (equivalently, Kauffman's affine index polynomial). We also use it to define a second-order writhe polynomial, and give some applications.

Colorings, Determinants And Alexander Polynomials For Spatial Graphs, Terry Kong, Alec Lewald, Blake Mellor, Vadim Pigrish

Mathematics, Statistics and Data Science Faculty Works

A {\em balanced} spatial graph has an integer weight on each edge, so that the directed sum of the weights at each vertex is zero. We describe the Alexander module and polynomial for balanced spatial graphs (originally due to Kinoshita \cite{ki}), and examine their behavior under some common operations on the graph. We use the Alexander module to define the determinant and p-colorings of a balanced spatial graph, and provide examples. We show that the determinant of a spatial graph determines for which p the graph is p-colorable, and that a p-coloring of a graph corresponds to a representation of …

Involutory Quandles Of (2,2,R)-Montesinos Links, Jim Hoste, Patrick D. Shanahan

Mathematics, Statistics and Data Science Faculty Works

In this paper we show that Montesinos links of the form L(1/2, 1/2, p/q;e), which we call (2,2,r)-Montesinos links, have finite involutory quandles. This generalizes an observation of Winker regarding the (2, 2, q)-pretzel links. We also describe some properties of these quandles.

Links With Finite N-Quandles, Jim Hoste, Patrick D. Shanahan

Mathematics, Statistics and Data Science Faculty Works

We prove a conjecture of Przytycki which asserts that the n-quandle of a link L in the 3-sphere is finite if and only if the fundamental group of the n-fold cyclic branched cover of the 3-sphere, branched over L, is finite.

The Regularity Of The Boundary Of A Multidimensional Aggregation Patch, Andrea L. Bertozzi, John B. Garnett, Thomas Laurent, Joan Verdera

Mathematics, Statistics and Data Science Faculty Works

We consider solutions to the aggregation equation with Newtonian potential where the initial data are the characteristic function of a domain with boundary of class $C^{1+\gamma}$ ,$0<\gamma<1$. Such initial data are known to yield a solution that, going forward in time, retains a patch-like structure with a constant time-dependent density inside an evolving region, which collapses on itself in a finite time, and which, going backward in time, converges in an $L^1$ sense to a self-similar expanding ball solution. In this work, we prove $C^{1+\gamma}$ regularity of the domain's boundary on the time interval on which the solution exists as an $L^\infty$ patch, up to the collapse time going forward in time and for all finite times going backward in time.

The Segal–Shale–Weil Representation, The Indices Of Kashiwara And Maslov, And Quantum Mechanics, Michael C. Berg

Mathematics, Statistics and Data Science Faculty Works

We produce a connection between the Weil 2-cocycles defining the local and adèlic metaplectic groups defined over a global field, i.e. the double covers of the attendant local and adèlic symplectic groups, and local and adèlic Maslov indices of the type considered by Souriau and Leray. With the latter tied to phase integrals occurring in quantum mechanics, we provide a formulation of quadratic reciprocity for the underlying field, first in terms of an adèlic phase integral, and then in terms of generalized time evolution unitary operators.

Generalized Local And Nonlocal Master Equations For Some Stochastic Processes, Yanping Ma

Mathematics, Statistics and Data Science Faculty Works

In this paper, we present a study on generalized local and nonlocal equations for some stochastic processes. By considering the net flux change in a region determined by the transition probability, we derive the master equation to describe the evolution of the probability density function. Some examples, such as classical Fokker-Planck equations, models for Lévy process, and stochastic coagulation equations, are provided as illustrations. A particular application is a consistent derivation of coupled dynamical systems for spatially inhomogeneous stochastic coagulation processes.