Physical Sciences and Mathematics Commons^™

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.

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.

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 …

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 …

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.

Well, It's About Time, Daniel David Gagné

Senior Projects Spring 2016

A clock can be thought of as anything that oscillates with a known and stable frequency, and is able to count its oscillations. Multivibrators are examples of such a device. Multivibrators resonate with a calculable resonant frequency, and this frequency is stable enough to be a standard by which time is kept. Though we assume clocks to be perfect timekeepers, however, this is not the case. Clocks not only have hardware imperfections, they are also susceptible to environmental noises---the combined effects of which leads to variations in timekeeping. This project will aim to explore and characterize the impact of environmental …

Winning Strategies In The Board Game Nowhere To Go, Najee Kahil Mcfarland-Drye

Senior Projects Spring 2016

Nowhere To Go is a two player board game played on a graph. The players take turns placing blockers on edges, and moving from vertex to vertex using unblocked edges and unoccupied vertices. A player wins by ensuring their opponent is on a vertex with all blocked edges. This project goes over winning strategies for Player 1 for Nowhere To Go on the standard board and other potential boards.

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.

Algorithmic Music Composition And Accompaniment Using Neural Networks, Daniel Wilton Risdon

Senior Projects Spring 2016

The goal of this project was to use neural networks as a tool for live music performance. Specifically, the intention was to adapt a preexisting neural network code library to work in Max, a visual programming language commonly used to create instruments and effects for electronic music and audio processing. This was done using ConvNetJS, a JavaScript library created by Andrej Karpathy.

Several neural network models were trained using a range of different training data, including music from various genres. The resulting neural network-based instruments were used to play brief pieces of music, which they used as input to create …

Constructing A Categorical Framework Of Metamathematical Comparison Between Deductive Systems Of Logic, Alex Gabriel Goodlad

Senior Projects Spring 2016

The topic of this paper in a broad phrase is “proof theory". It tries to theorize the general

notion of “proving" something using rigorous definitions, inspired by previous less general

theories. The purpose for being this general is to eventually establish a rigorous framework

that can bridge the gap when interrelating different logical systems, particularly ones

that have not been as well defined rigorously, such as sequent calculus. Even as far as

semantics go on more formally defined logic such as classic propositional logic, concepts

like “completeness" and “soundness" between the “semantic" and the “deductive system"

is too arbitrarily defined …

Optimizing Website Design Through The Application Of An Interactive Genetic Algorithm, Elijah Patton Mensch

Senior Projects Spring 2016

The goal of this project was to determine the efficacy and practicality of “optimizing” the design of a webpage through the application of an interactive genetic algorithm. Software was created to display a “population” of mutable designs, collect user feedback as a measure of fitness, and apply genetic operations in an ongoing evolutionary process. By tracking the prevalence of design parameters over multiple generations and evaluating their associated “fitness” values, it was possible to judge the overall performance of the algorithm when applied to this unique problem space.

A Variational Approach To The Moving Sofa Problem, Ningning Song

Senior Projects Spring 2016

The moving sofa problem is a two-dimensional idealisation of real-life furniture moving problems, and its goal is to find the biggest area that can be maneuvered around a L-shape hallway with unit width. In this project we will learn about Hammersly’s sofa ,Gerver’s sofa and adapt Hammersly’s sofa to non-right angle hallways. We will also use calculus of variations to maximize the area and find out Gerver’s sofa satisfied several conditions that the best sofa satisfies.

Abstractions And Analyses Of Grid Games, Taylor Rowan Boone

Senior Projects Spring 2016

In this paper, we define various combinatorial games derived from the NQueens Puzzle and scrutinize them, particularly the Knights Game, using combinatorial game theory and graph theory. The major result of the paper is an original method for determining who wins the Knights Game merely from the board's dimensions. We also inspect the Knights Game's structural similarities to the Knight's Tour and the Bishops Game, and provide some historical background and real-world applications of the material.

Photovoltaics: An Investigation Into The Origins Of Efficiency On All Scales, Jeremy Alexander Bannister

Senior Projects Spring 2016

This project is comprised of a set of parallel investigations, which share the common mo- tivation of increasing the efficiency of photovoltaics. First, the reader is introduced to core concepts of photovoltaic energy conversion via a semi-classical description of the phys- ical system. Second, a key player in photovoltaic efficiency calculations, the exciton, is discussed in greater quantum mechanical detail. The reader will be taken through a nu- merical derivation of the low-energy exciton states in various geometries, including a line segment, a circle and a sphere. These numerical calculations are done using Mathematica, a computer program which, due to …

Branching Boogaloo: Botanical Adventures In Multi-Mediated Morphologies, Diana Marie Ruggiero

Senior Projects Spring 2016

FormaLeaf is a software interface for exploring leaf morphology using parallel string rewriting grammars called L-systems. Scanned images of dicotyledonous angiosperm leaves removed from plants around Bard’s campus are displayed on the left and analyzed using the computer vision library OpenCV. Morphometrical information and terminological labels are reported in a side-panel. “Slider mode” allows the user to control the structural template and growth parameters of the generated L-system leaf displayed on the right. “Vision mode” shows the input and generated leaves as the computer ‘sees’ them. “Search mode” attempts to automatically produce a formally defined graphical representation of the input …

Orthogonal Projections Of Lattice Stick Knots, Margaret Marie Allardice

Senior Projects Spring 2016

A lattice stick knot is a closed curve in R³ composed of finitely many line segments, sticks, that lie parallel to the three coordinate axes in R³, such that the line segments meet at points in the 3-dimensional integer lattice. The lattice stick number of a knot is the minimal number of sticks required to realize that knot as a lattice stick knot. A right angle lattice projection is a projection of a knot in R³onto the plane such that the edges of the projection lie parallel to the two coordinate axes in the plane, …

Computing Language And Thinking: Analysis, Design, And Assessment Of Introductory Computer Science Workshops In The Liberal Arts Experience, Kathleen Teresa Burke

Senior Projects Spring 2016

This project seeks to assess and improve upon a new required introductory computer science workshop for first year students at Bard College. It addresses the design and implementation of the course itself, along with the improvements needed in order to continue the program. Many students are not offered computer science courses prior to college; this program has been designed to remedy that by requiring all students to learn key concepts in computer science as a part of their orientation. The program consists of a 90 minute lesson taught by professors with expertise in fields outside of computer science, in addition …

The Facilitation Of Sound Waves Using Mathematical And Scientific Methods Of Digital Signal Processing, Benjamin Rocco Moss

Senior Projects Spring 2016

Mathematics and music have been lifelong partners since the beginning of time. Rhythm and time are two fundamental aspects of music which rely solely on counting, an under-appreciated skill in mathematics, yet recognized by all mathematically-minded people as the foundation of some of the most important mathematical findings; as John B. Fraleigh would say, “Never underestimate a theorem that counts something!” However, music recordings have evolved through the use of technology further than merely possessing the capabilities to quantify and archive the notes that were played in the recording. In the days before digital recordings, the only way to ensure …

Flame-Turbulence Interaction For Deflagration To Detonation, Jessica Chambers

Honors Undergraduate Theses

Detonation is a high energetic mode of pressure gain combustion that exploits total pressure rise to augment high flow momentum and thermodynamic cycle efficiencies. Detonation is initiated through the Deflagration-to-Detonation Transition (DDT). This process occurs when a deflagrated flame is accelerated through turbulence induction, producing shock-flame interactions that generate violent explosions and a supersonic detonation wave. There is a broad desire to unravel the physical mechanisms of turbulence induced DDT. For the implementation of efficient detonation methods in propulsion and energy applications, it is crucial to understand optimum turbulence conditions for detonation initiation. The study examines the role of turbulence-flame …

The Effect Of Impurities On The Superconductivity Of Bscco-2212, John Vastola

Honors Undergraduate Theses

BSCCO-2212 is a high-temperature cuprate superconductor whose microscopic behavior is currently poorly understood. In particular, it is unclear whether its order parameter is consistent with s-wave or d-wave symmetry. It has been suggested that its order parameter might take one of several forms that are consistent with d-wave behavior. We present some calculations using the many-body theory approach to superconductivity that suggest that such order parameters would lead to a suppression of the critical temperature in the presence of impurities. Because some experiments have suggested the critical temperature of BSCCO-2212 is relatively independent of the concentration of impurities, this lends …

Eikonal Perturbation Theory In Photoionization, F. Cajiao Vélez, Katarzyna Krajewska, J. Z. Kamiński

Department of Physics and Astronomy: Faculty Publications

The eikonal perturbation theory is formulated and applied to photoionization by strong laser pulses. A special emphasis is put on the first order approximation with respect to the binding potential, which is known as the generalized eikonal approximation [2015 Phys. Rev. A 91 053417]. The ordinary eikonal approximation and its domain of applicability is derived from the generalized eikonal approximation. While the former approach is singular for the electron trajectories which return to the potential center, the generalized eikonal avoids this problem. This property makes it a promising tool for further investigations of rescattering and high-order harmonic generation processes.

Theory Of Magnon Motive Force In Chiral Ferromagnets, Utkan Güngördü, Alexey Kovalev

Department of Physics and Astronomy: Faculty Publications

We predict that magnon motive force can lead to temperature dependent, nonlinear chiral damping in both conducting and insulating ferromagnets. We estimate that this damping can significantly influence the motion of skyrmions and domain walls at finite temperatures. We also find that in systems with low Gilbert damping moving chiral magnetic textures and resulting magnon motive forces can induce large spin and energy currents in the transverse direction.

Spin Torque And Nernst Effects In Dzyaloshinskii-Moriya Ferromagnets, Alexey Kovalev, Vladimir Zyuzin

Department of Physics and Astronomy: Faculty Publications

We predict that a temperature gradient can induce a magnon-mediated intrinsic torque in systems with a nontrivial magnon Berry curvature. With the help of a microscopic linear response theory of nonequilibrium magnon-mediated torques and spin currents we identify the interband and intraband components that manifest in ferromagnets with Dzyaloshinskii-Moriya interactions and magnetic textures. To illustrate and assess the importance of such effects, we apply the linear response theory to the magnon-mediated spin Nernst and torque responses in a kagome lattice ferromagnet.

Stability Of Skyrmion Lattices And Symmetries Of Quasi-Two-Dimensional Chiral Magnets, Utkan Güngördü, Rabindra Nepal, Oleg A. Tretiakov, Kirill D. Belashchenko, Alexey Kovalev

Department of Physics and Astronomy: Faculty Publications

Recently there has been substantial interest in realizations of skyrmions, in particular in quasi-two-dimensional (2D) systems due to increased stability resulting from reduced dimensionality. A stable skyrmion, representing the smallest realizable magnetic texture, could be an ideal element for ultradense magnetic memories. Here we use the most general form of the quasi-2D free energy with Dzyaloshinskii-Moriya interactions constructed from general symmetry considerations reflecting the underlying system. We predict that the skyrmion phase is robust and it is present even when the system lacks the in-plane rotational symmetry. In fact, the lowered symmetry leads to increased stability of vortex-antivortex lattices with …

Magnetoelectric Domain Wall Dynamics And Its Implications For Magnetoelectric Memory, Kirill D. Belashchenko, Oleg Tchernyshyov, Alexey Kovalev, Oleg A. Tretiakov

Department of Physics and Astronomy: Faculty Publications

Domain wall dynamics in a magnetoelectric antiferromagnet is analyzed, and its implications for magnetoelectric memory applications are discussed. Cr₂O₃ is used in the estimates of the materials parameters. It is found that the domain wall mobility has a maximum as a function of the electric field due to the gyrotropic coupling induced by it. In Cr₂O₃, the maximal mobility of 0.1 m/(s Oe) is reached at E = 0.06 V/nm. Fields of this order may be too weak to overcome the intrinsic depinning field, which is estimated for B-doped Cr₂O_{3 …}

Measurement Of The Differential Cross Section And Charge Asymmetry For Inclusive Pp → W± + X Production At √S = 8 Tev, Ekaterina Avdeeva, Rachel Bartek, Kenneth A. Bloom, Suvadeep Bose, Daniel R. Claes, Aaron Dominguez, Caleb Fangmeier, Rebeca Gonzalez Suarez, Rami Kamalieddin, Daniel Knowlton, Ilya Kravchenko, Jose Monroy, F. Meier, F. Ratnikov, J. E. Siado, Gregory Snow, B. Stieger, Cms Collaboration

Department of Physics and Astronomy: Faculty Publications

The differential cross section and charge asymmetry for inclusive pp → W^± + X → μ^±ν + X production at √s = 8 TeV are measured as a function of muon pseudorapidity. The data sample corresponds to an integrated luminosity of 18.8 fb⁻¹ recorded with the CMS detector at the LHC. These results provide important constraints on the parton distribution functions of the proton in the range of the Bjorken scaling variable x from 10⁻³ to 10⁻¹.

Ecology Of Two Reintroduced Black Bear Populations In The Central Appalachians, Sean Mccarthy Murphy

Theses and Dissertations--Animal and Food Sciences

Reintroduced populations are vulnerable to demographic and environmental stochasticity, deleterious genetic effects, and reduced population fitness, all of which can increase extinction probability. Population viability is principle to determining the status of reintroduced populations and for guiding management decisions. To attempt to reestablish black bear (Ursus americanus) populations in the central Appalachians, two reintroductions using small founder groups occurred during the 1990s in the Big South Fork area along the Kentucky-Tennessee border (BSF) and in the Jefferson National Forest along the Kentucky-Virginia border (KVP). My objectives were to estimate demographic and genetic parameters, and to evaluate long-term viability …

Ua12/2/2 2016 Talisman - Life More Life, Wku Student Affairs

WKU Archives Records

2016 Talisman yearbook.

• Paris, Rachel. Dawn of Delta Zeta
• Ziege, Nicole. Kick It to the Limit – Soccer
• Paris, Rachel. Immersion: Band
• Houston, Emily. Immersion: Dance
• Paris, Rahcel. Immersion: ROTC
• Ziege, Nicole. Immersion: Theatre
• Holt, Delaney. Major Pride – WKU Majorette Style Dance Team
• Houston, Emily. Hollow Spike – Volleyball
• Moscoe, Carrie. The Intergallactic Tightrope – Elliott Talkington, Theatre & Dance
• Gilliam, Ashely. Tops on Top – Cheerleaders
• Young, Kreable. A Grand Adventure – Grand Canyon, Outdoor Recreation Activity Center
• Voorhees, Jessica. Home Team Advantage – Track & Field
• Homecoming
• Sproles, Katherine. Saddle School – Dylan Davis, Rodeo
• Sims, Bryna. …

Petrophysical And Empirical And Theoretical Rock Physics Modeling For The Moki Formation In Two Fields In The Taranaki Basin, New Zealand, Deniz Yener

Dissertations, Master's Theses and Master's Reports

This work consists of conventional petrophysical analysis and sonic response determination from empirical relations, rock physics modelling, and fluid substitution for six wells in the Moki formation of New Zealand’s Taranaki Basin. The project composed of three parts encompassing conventional log analysis, rock-physics modeling using empirical and theoretical approaches, and finally rock-physics modeling for shaley sands using semi-empirical adaptations to Gassmann fluid substitution. Finally, comparisons are made between results for the different wells, based on their depths and mineralogy.

The first part of this study is presented as a petrophysical analysis, including crossplot analysis, conventional 3-mineral identification approach, and determination …

Investigation Of The Resistance To Demagnetization In Bulk Rare-Earth Magnets Comprised Of Crystallographically-Aligned, Single-Domain Crystallites With Modified Intergranular Phase, Jie Li

Dissertations, Master's Theses and Master's Reports

The research presented in this dissertation investigates whether an increased coercivity of Neodymium-Iron-Boron (Nd2Fe14B) based bulk magnets at elevated temperature (160°C), which is now only obtainable by substituting ~7wt% dysprosium (Dy) for a portion of neodymium (Nd), can be achieved through specific microstructural modifications with decreased Dy concentrations. The approach is to reduce the size of individual crystallographically-aligned grains in the magnet so that each grain can only support a single magnetic domain and to simultaneously dilute the Nd-Fe inter-granular phase present in conventional magnets with a non-Fe-containing, Nd-rich phase (Nd-Cu alloy) in an attempt to partially magnetically isolate the …