The Entangling Properties Of Knots And Links,
2016
Illinois Mathematics and Science Academy
The Entangling Properties Of Knots And Links, Eshan Mehrotra '17
IMSAloquium Student Investigation Showcase
It has been conjectured that quantum entanglement operators can be lifted to braiding operators by the way of the topological quantum field theory axioms set forth by Witten and Atiyah. Moreover, it can be readily shown that quantum link invariants need entanglement to construct topological invariants. Given these results and the already dense mathematical framework underlying topology and quantum field theory, we propose that, through the usage of quantum algebra and bracket models, we can identify a significant area of overlap where entangling R-matrix solutions to the Yang-Baxter equation can be used to construct invariants of knots and links. Such …
Essays On Strategy-Proofness And Implementation.,
2016
Indian Statistical Institute
Essays On Strategy-Proofness And Implementation., Sonal Yadav Dr.
Doctoral Theses
This thesis comprises of three chapters relating to strategy-proofness and implementation. We provide a brief description of each chapter below.1.1 A Hurwicz Type Result in a Model with Public Good Production We consider a two-good model with an arbitrary number of agents. One of the goods is a public good and the other is a private good. Each agent has an endowment of the private good and the private good can be converted into the public good using a well-behaved production function. A Social Choice Function (SCF) associates an allocation with each admissible preference profile. We impose the following requirements …
The Ko-Lee Key Exchange Protocol With Generalized Dihedral Groups,
2016
University of Mary Washington
The Ko-Lee Key Exchange Protocol With Generalized Dihedral Groups, Christopher Lloyd
Departmental Honors & Graduate Capstone Projects
Given an arbitrary abelian group A, one may form the generalized dihedral group D(A). As D(A) is usually non-abelian, this makes it a possible candidate for use with certain non-commutative key exchange protocols. Specifically, we examine the security of using D(A) with the Ko-Lee key exchange protocol. An appropriate presentation for D(A) is developed alongside methods for computing within the group in the context of the Ko-Lee protocol. Lastly we show that for such groups Ko-Lee is susceptible to a polynomial time attack.
Infinite Color Urn Models.,
2016
Indian Statistical Institute
Infinite Color Urn Models., Debleena Thacker Dr.
Doctoral Theses
In recent years, there has been a wide variety of work on random reinforcement models of various kinds. Urn models form an important class of random reinforcement models, with numerous applications in engineering and informatics and bioscience. In recent years there have been several works on different kinds of urn models and their generalizations. For occupancy urn models, where one considers recursive addition of balls into finite or infinite number of boxes, there are some works which introduce models with infinitely many colors, typically represented by the boxes.As observed in [51], the earliest mentions of urn models are in the …
A Comparison Of Methods To Fit A Model To Simultaneous Time Series,
2016
University of Mary Washington
A Comparison Of Methods To Fit A Model To Simultaneous Time Series, Victoria Marie Moore
Departmental Honors & Graduate Capstone Projects
This research project determines which methods are the most effective for finding a best fit model for simultaneous time series. The type of model used was an Autoregressive Integrated Moving Average (ARIMA) model. Two distinct methods were used when determining what order to assign to the ARIMA model: 1.) using the floor of the average number of autoregressive and moving average terms, and 2.) using the ceiling of the average number of autoregressive and moving average terms. After fitting the model, the Akaike Information Criterion (AIC) value for each method measured the goodness of fit to compare to fitting separate …
Dagum-Poisson Distribution: Model, Properties And Application,
2016
Georgia Southern University
Dagum-Poisson Distribution: Model, Properties And Application, Broderick O. Oluyede, Galelhakanelwe Motsewabagale, Shujiao Huang, Gayan Warahena-Liyanage, Marvis Pararai
Mathematical Sciences: Faculty Publications
A new four parameter distribution called the Dagum-Poisson (DP) distribution is introduced and studied. This distribution is obtained by compounding Dagum and Poisson distributions. The structural properties of the new distribution are discussed, including explicit algebraic formulas for its survival and hazard functions, quantile function, moments, moment generating function, conditional moments, mean and median deviations, Bonferroni and Lorenz curves, distribution of order statistics and R\'enyi entropy. Method of maximum likelihood is used for estimating the model parameters. A Monte Carlo simulation study is conducted to examine the bias, mean square error of the maximum likelihood estimators and width of the …
Blossom: A Language Built To Grow,
2016
Macalester College
Blossom: A Language Built To Grow, Jeffrey Lyman
Mathematics, Statistics, and Computer Science Honors Projects
No abstract provided.
Timely Curriculum Changes To An Undergraduate Actuarial Program,
2016
Bryant University
Timely Curriculum Changes To An Undergraduate Actuarial Program, Thomas Hartl, Kristin Kennedy, John Quinn
Mathematics Faculty Journal Articles
In the last decade mathematics departments in many universities around the country have established actuarial!science as a major concentration, or area of study. The profitable career choice of becoming an actuary has become well-known to parents and high school students, who are interested in mathematics, which at least partially drives a school to develop a program. Not all schools house the actuarial major in a mathematics department, but the number of universities, offering actuarial courses, has grown significantly in the last few years. At this time there are approximately 160 universities in the US alone offering this course of study? …
Measuring Dependence In Uncertainty Should Start In The Introduction To Probability And Statistics,
2016
Kettering University
Measuring Dependence In Uncertainty Should Start In The Introduction To Probability And Statistics, Boyan N. Dimitrov
Mathematics Presentations And Conference Materials
No abstract provided.
The Chromatic Number Of The Square Of Subcubic Planar Graphs,
2016
University of Colorado, Denver
The Chromatic Number Of The Square Of Subcubic Planar Graphs, Stephen Hartke, Sogol Jahanbekam, Brent Thomas
Faculty Publications
Wegner conjectured in 1977 that the square of every planar graph with maximum degree at most 3 is 7-colorable. We prove this conjecture using the discharging method and computational techniques to verify reducible configurations.
Introductory And Intermediate Algebra Mth 100x,
2016
University of Rhode Island
Introductory And Intermediate Algebra Mth 100x, Joanna Burkhardt
Library Impact Statements
No abstract provided.
Finite Math Mth 107,
2016
University of Rhode Island
Applied Calculus Mth 103x,
2016
University of Rhode Island
Applied Calculus Mth 103x, Joanna Burkhardt
Library Impact Statements
No abstract provided.
Drawing Numbers And Listening To Patterns,
2016
Georgia Southern University
Drawing Numbers And Listening To Patterns, Loren Zo Haynes
Honors College Theses
The triangular numbers is a series of number that add the natural numbers. Parabolic shapes emerge when this series is placed on a lattice, or imposed with a limited number of columns that causes the sequence to continue on the next row when it has reached the kth column. We examine these patterns and construct proofs that explain their behavior. We build off of this to see what happens to the patterns when there is not a limited number of columns, and we formulate the graphs as musical patterns on a staff, using each column as a line or space …
Pooling Strength Amongst Limited Datasets Using Hierarchical Bayesian Analysis, With Application To Pyroclastic Density Current Mobility Metrics,
2016
State University of New York at Buffalo
Pooling Strength Amongst Limited Datasets Using Hierarchical Bayesian Analysis, With Application To Pyroclastic Density Current Mobility Metrics, Sarah E. Ogburn, James Berger, Eliza S. Calder, Danilo Lopes, Abani K. Patra, E. Bruce Pitman, Regis Rutarindwa, Elaine Spiller, Robert L. Wolpert
Mathematics, Statistics and Computer Science Faculty Research and Publications
In volcanology, the sparsity of datasets for individual volcanoes is an important problem, which, in many cases, compromises our ability to make robust judgments about future volcanic hazards. In this contribution we develop a method for using hierarchical Bayesian analysis of global datasets to combine information across different volcanoes and to thereby improve our knowledge at individual volcanoes. The method is applied to the assessment of mobility metrics for pyroclastic density currents in order to better constrain input parameters and their related uncertainties for forward modeling. Mitigation of risk associated with such flows depends upon accurate forecasting of possible inundation …
Bivariate Barycentric-Coordinate Berstein-Bezier Polynomial & C1 Quadratic Vertex Spline,
2016
Illinois Wesleyan University
Bivariate Barycentric-Coordinate Berstein-Bezier Polynomial & C1 Quadratic Vertex Spline, Rui Jiang, Tian-Xiao He, Faculty Advisor
John Wesley Powell Student Research Conference
Poster presentation abstract.
Integer Antimagic Labeling For Cycle With One Chord,
2016
Illinois Wesleyan University
Integer Antimagic Labeling For Cycle With One Chord, Jinze Zheng, Daniel Roberts, Faculty Advisor
John Wesley Powell Student Research Conference
Poster presentation abstract.
Multidesigns For A Graph Pair Of Order 6,
2016
Illinois Wesleyan University
Multidesigns For A Graph Pair Of Order 6, Yizhe Gao, Daniel Roberts, Faculty Advisor
John Wesley Powell Student Research Conference
Oral presentation abstract.
Duals Of Bernoulli Numbers And Polynomials And Euler Numbers And Polynomials,
2016
Illinois Wesleyan University
Duals Of Bernoulli Numbers And Polynomials And Euler Numbers And Polynomials, Jinze Zheng, Tian-Xiao He, Faculty Advisor
John Wesley Powell Student Research Conference
Oral presentation abstract.
Multidecomposition Of Complete Directed Graphs Into Directed Graph Pairs Of Order 3 And 4,
2016
Illinois Wesleyan University
Multidecomposition Of Complete Directed Graphs Into Directed Graph Pairs Of Order 3 And 4, Jacob Henry, Daniel Roberts, Faculty Advisor
John Wesley Powell Student Research Conference
Oral presentation abstract.
