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On Degree Bound For Syzygies Of Polynomial Invariants, Zhao Gao
On Degree Bound For Syzygies Of Polynomial Invariants, Zhao Gao
Senior Independent Study Theses
Suppose G is a finite linearly reductive group. The degree bound for the syzygy ideal of the invariant ring of G is given in [2]. We develop the theory of commutative algebra and give the proof from [2] that the ideal of relations of the minimal set of generators of invariant ring of a finite linearly reductive group G is generated in degree at most 2|G|.
Grasping The Void: Immersion Tactics Using Gesture Controlled Physics Interaction Systems In Virtual Reality, Avery Rapson
Grasping The Void: Immersion Tactics Using Gesture Controlled Physics Interaction Systems In Virtual Reality, Avery Rapson
Senior Independent Study Theses
This thesis uses the HTC Vive in Unity to compare two different types of object interaction systems in order to determine the effectiveness of physics based interaction systems in a virtual environment. The research problem that motivates this project is the fact that there is no standardized method for defining successful object interaction techniques in VR. There are numerous interaction techniques in VR that fall short of simulating realistic object interaction. This project explores a physics based interaction system and examines how effective it is by comparing it to a non-physics based system. A model house with various interactable objects …
Legalization Of Prostitution And Its Impact On The Market For Human Trafficking, Varunavi Newar
Legalization Of Prostitution And Its Impact On The Market For Human Trafficking, Varunavi Newar
Senior Independent Study Theses
No abstract provided.
The Production And Manipulation Of Nonseparable Spin-Orbit Modes Of Light Under Hong-Ou-Mandel Interference Conditions, Maggie E. Lankford
The Production And Manipulation Of Nonseparable Spin-Orbit Modes Of Light Under Hong-Ou-Mandel Interference Conditions, Maggie E. Lankford
Senior Independent Study Theses
No abstract provided.
From Fantasy To Virtual Reality: An Exploration Of Modeling, Rigging And Animating Characters For Video Games, Sarah K. Williams
From Fantasy To Virtual Reality: An Exploration Of Modeling, Rigging And Animating Characters For Video Games, Sarah K. Williams
Senior Independent Study Theses
In the last few decades video games have quickly become one of the most popular forms of entertainment around the world. This can be linked to the improvement of computer systems and graphics which now allow for authentic and highly detailed computer generated characters. This project examines how these characters are modeled and developed. The examination of game characters entails a brief history of video games and their aesthetics. The foundations of character design are discussed and 3D modeling of a character is explored in detail. Finally, rigging or skeleton placement is investigated in order to animate the characters designed …
Optimal Placement Of Family Planning Centers, Kiera Dobbs
Optimal Placement Of Family Planning Centers, Kiera Dobbs
Senior Independent Study Theses
This project investigates and begins to solve the problem of access to family planning services in the United States. We research and implement methods in Operations Research to optimize the location of publicly funded family planning centers in the United States by minimizing travel distance. The solution begins with a designated number of family planning centers for the country. An apportionment integer programming algorithm is then exercised to allocate centers to all the states based on population, percent of population in poverty, and state square mileage. At the state level, we use apportionment again to distribute centers to counties. At …
I Don't Play Chess: A Study Of Chess Piece Generating Polynomials, Stephen R. Skoch
I Don't Play Chess: A Study Of Chess Piece Generating Polynomials, Stephen R. Skoch
Senior Independent Study Theses
This independent study examines counting problems of non-attacking rook, and non-attacking bishop placements. We examine boards for rook and bishop placement with restricted positions and varied dimensions. In this investigation, we discuss the general formula of a generating function for unrestricted, square bishop boards that relies on the Stirling numbers of the second kind. We discuss the maximum number of bishops we can place on a rectangular board, as well as a brief investigation of non-attacking rook placements on three-dimensional boards, drawing a connection to latin squares.
Learning Emotions: A Software Engine For Simulating Realistic Emotion In Artificial Agents, Douglas Code
Learning Emotions: A Software Engine For Simulating Realistic Emotion In Artificial Agents, Douglas Code
Senior Independent Study Theses
This paper outlines a software framework for the simulation of dynamic emotions in simulated agents. This framework acts as a domain-independent, black-box solution for giving actors in games or simulations realistic emotional reactions to events. The emotion management engine provided by the framework uses a modified Fuzzy Logic Adaptive Model of Emotions (FLAME) model, which lets it manage both appraisal of events in relation to an individual’s emotional state, and learning mechanisms through which an individual’s emotional responses to a particular event or object can change over time. In addition to the FLAME model, the engine draws on the design …
Keeping Your Options Open: An Introduction To Pricing Options, Ryan F. Snyder
Keeping Your Options Open: An Introduction To Pricing Options, Ryan F. Snyder
Senior Independent Study Theses
An option is a contract which gives the holder of the option the right, but not the obligation, to buy or sell a given security at a given price, which is called the strike price. For example, suppose Yahoo stock is currently trading at $10 per share. A person could buy an option that gives him or her the ability to purchase shares of Yahoo stock for $12 in one year. If the price of Yahoo stock is greater than $12 in one year, the holder of the option will make money. However, he or she will not use the …
A Bayesian Model Of Fertility Decisions In Relationship To Female Labor Force Participation, Rebecca C. Wardrop
A Bayesian Model Of Fertility Decisions In Relationship To Female Labor Force Participation, Rebecca C. Wardrop
Senior Independent Study Theses
Due to the increasing number of women in the labor force, opportunity costs associated with labor force participation are becoming an important factor in fertility decisions. Further, these decisions are assumed to be dynamic as the opportunity costs change as a woman progresses through her career. A Bayesian statistical model , which allows the distribution of the likelihood of having children to be updated as information is gathered, lends itself to the dynamicity of the decision-making process. A generalized model for fertility decisions in terms of labor force participation is created. I also discuss potentials for implementation and furthering the …
Generalist And Specialist Pollination Syndromes: When Are They Favoured? A Theoretical Approach To Predict The Conditions Under Which A Generalist Or Specialist Pollination Syndrome Is Favoured., Tyler L. Poppenwimer
Generalist And Specialist Pollination Syndromes: When Are They Favoured? A Theoretical Approach To Predict The Conditions Under Which A Generalist Or Specialist Pollination Syndrome Is Favoured., Tyler L. Poppenwimer
Senior Independent Study Theses
No abstract provided.
Markov Chain Theory With Applications To Baseball, Cal D. Thomay
Markov Chain Theory With Applications To Baseball, Cal D. Thomay
Senior Independent Study Theses
The applications of Markov chains span a wide range of fields to which models have been designed and implemented to simulate random processes. Markov chains are stochastic processes that are characterized by their memoryless property, where the probability of the process being in the next state of the system depends only on the current state and not on any of the previous states. This property is known as the Markov property. This thesis paper will first introduce the theory of Markov chains, along with explaining two types of Markov chains that will be beneficial in creating a model for analyzing …
A Not-So-Silent Spring: The Impacts Of Traffic Noise On Call Features Of The Bloody Bay Poison Frog (Mannophryne Olmonae), Catherine G. Clemmens
A Not-So-Silent Spring: The Impacts Of Traffic Noise On Call Features Of The Bloody Bay Poison Frog (Mannophryne Olmonae), Catherine G. Clemmens
Senior Independent Study Theses
No abstract provided.
The Analytic Hierarchy Process: A Mathematical Model For Decision Making Problems, Giang Huong Nguyen
The Analytic Hierarchy Process: A Mathematical Model For Decision Making Problems, Giang Huong Nguyen
Senior Independent Study Theses
The ability to make the right decision is an asset in many areas and lines of profession including social work, business, national economics, and international security. However, decision makers often have difficulty choosing the best option since they might not have a full understanding of their preferences, or lack a systematic approach to solve the decision making problems at hand. The Analytic Hierarchy Process (AHP) provides a mathematical model that helps the decision makers arrive at the most logical choice, based on their preferences. We investigate the theory of positive, reciprocal matrices, which provides the theoretical justification of the method …
The Machete Number, David Freund
The Machete Number, David Freund
Senior Independent Study Theses
Knot theory is a branch of topology that deals with the structure and properties of links. Employing a variety of tools, including surfaces, graph theory, and polynomials, we develop and explore classical link invariants. From this foundation, we de fine two novel link invariants, braid height and machete number, and investigate their properties and connection to classical invariants.
Let's Get In The Mood: An Exploration Of Data Mining Techniques To Predict Mood Based On Musical Properties Of Songs, Sarah Smith-Polderman
Let's Get In The Mood: An Exploration Of Data Mining Techniques To Predict Mood Based On Musical Properties Of Songs, Sarah Smith-Polderman
Senior Independent Study Theses
This thesis explores the possibility of predicting the mood a song will evoke in a person based on certain musical properties that the song exhibits. First, I introduce the topic of data mining and establish its significant relevance in this day and age. Next, I explore the several tasks that data mining can accomplish, and I identify classification and clustering as the two most relevant tasks for mood prediction based on musical properties of songs. Chapter 3 introduces in detail two specific classification techniques: Naive Bayes Classification and k-Nearest Neighbor Classification. Similarly, Chapter 4 introduces two specific clustering techniques: …
The Truth About Lie Symmetries: Solving Differential Equations With Symmetry Methods, Ruth A. Steinhour
The Truth About Lie Symmetries: Solving Differential Equations With Symmetry Methods, Ruth A. Steinhour
Senior Independent Study Theses
Differential equations are vitally important in numerous scientific fields. Oftentimes, they are quite challenging to solve. This Independent Study examines one method for solving differential equations. Norwegian mathematician Sophus Lie developed this method, which uses groups of symmetries, called Lie groups. These symmetries map one solution curve to another. They can be used to determine a canonical coordinate system for a given differential equation. Writing the differential equation in terms of a different coordinate system can make the equation simpler to solve. This I.S. explores techniques for finding a canonical coordinate system and using it to solve a given differential …
Ballistics Analysis Of Volcanic Ejecta: Miter Crater, Ice Springs Volcanic Field, Black Rock Desert, Utah, William Cary
Ballistics Analysis Of Volcanic Ejecta: Miter Crater, Ice Springs Volcanic Field, Black Rock Desert, Utah, William Cary
Senior Independent Study Theses
Ice Springs Volcanic Field, located in the Black Rock Desert west of Fillmore, Utah, is composed of three large craters, Crescent, Miter, and Terrace, and several smaller craters. Concern over the hazards of the volcanic field, ±660 years old, reactivating prompted the creation of a hazards model. This study focuses on Miter Crater in order to conduct a ballistic analysis of the blocks and bombs observed along the crater rim. Data analysis of Miter Crater ejecta was then used to create a hazards model for ballistic volcanic ejecta. Thirty-four blocks and bombs were recorded along the rim of Miter Crater. …
Tree-Ring Evidence Of North Pacific Volcanically Forced Cooling And Forcing Of The Pacific Decadal Oscillation (Pdo), Lauren Vargo
Tree-Ring Evidence Of North Pacific Volcanically Forced Cooling And Forcing Of The Pacific Decadal Oscillation (Pdo), Lauren Vargo
Senior Independent Study Theses
Two large undocumented volcanic eruptions in 1698/9 and 1809 have been previously identified in ice cores as sulfate peaks, and in tree-ring latewood density data as low-density rings. These eruptions can also be recognized using tree-ring width data, and can be identified in the tree-ring record as narrow rings for several consecutive years. The first part of this study uses tree-ring width data from the Gulf of Alaska to provide further evidence that these eruptions occurred. The two eruptions also provide a natural experiment for investigating the effects large volcanic eruptions have on North Pacific climate, including the Pacific Decadal …
Stratigraphy And Paleoenvironments Of The Soeginina Beds (Paadla Formation, Lower Ludlow, Upper Silurian) On Saaremaa Island, Estonia, Richa N. Ekka
Stratigraphy And Paleoenvironments Of The Soeginina Beds (Paadla Formation, Lower Ludlow, Upper Silurian) On Saaremaa Island, Estonia, Richa N. Ekka
Senior Independent Study Theses
The Soeginina Beds in the Paadla Formation on the island of Saaremaa, western Estonia, are a lower Ludlow (Upper Silurian) sequence of dolostones, marls, and stromatolites. They represent rocks just above the Wenlock/Ludlow boundary, which is distinguished by a major disconformity that can be correlated to a regional regression on the paleocontinent of Baltica. The depositional environments of the Soeginina Beds include a shelfal environment, restricted shallow marine setting, intertidal mudflat and finally a hypersaline supratidal setting. The evidence includes halite crystal molds, oscillation ripples, eurypterid fragments, stromatolites, ostracods, gastropods, Chondrites trace fossils, intraclasts and oncoids. Nautiloid conchs are common, …
Iteration Digraphs, Hannah Roberts
Iteration Digraphs, Hannah Roberts
Senior Independent Study Theses
No abstract provided.
Procedurally Generating Everything, Micah Caunter
Procedurally Generating Everything, Micah Caunter
Senior Independent Study Theses
This paper investigates using Perlin Noise in a three-dimensional environment. Perlin Noise has been previously used to simulate clouds, marble, wood, and other natural phenomena as well as to model virtual landscapes. The simulation created for the I.S. procedurally generates both static and animated textures and models virtual landscapes to create a virtual world. In order to keep up with the rapidly advancing graphics industry, the OpenGL API is utilized to generate the textures in real-time and to display the final product.
Geochemical And Field Relationships Of Pillow And Dike Units In A Subglacial Pillow Unit Undirhliđar Quarry, Southwest Iceland, Lindsey J. Bowman
Geochemical And Field Relationships Of Pillow And Dike Units In A Subglacial Pillow Unit Undirhliđar Quarry, Southwest Iceland, Lindsey J. Bowman
Senior Independent Study Theses
Undirhlíðar quarry is located on the Sveifluhals ridge, a Pleistocene subglacial pillow ridge within the NE-SW trending Krísuvík fissure swarm on the Reykjanes peninsula in Southwest Iceland. The walls of Undirhlíðar quarry provide excellent exposures of the internal architecture of the pillow ridge, yielding insights into the sequence of eruptive and intrusive events that construct subglacial ridges. In particular, the south and east walls expose at least 5 different pillow units and 3 dikes. Also seen in the east wall is a black, glassy breccia unit that appears on both the north and south sections of the east wall. Preliminary …