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2016

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Articles 571 - 600 of 1329

Full-Text Articles in Mathematics

Computing The Optimal Path In Stochastic Dynamical Systems, Martha Bauver May 2016

Computing The Optimal Path In Stochastic Dynamical Systems, Martha Bauver

Theses, Dissertations and Culminating Projects

In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems it may be impossible to find an analytic form of the optimal path, and in high-dimensional systems, this is almost always the case. The optimal path is of great importance, since it represents the most likely path of a rare switching or escape event. For instance, the optimal path for an infectious disease model represents a switching from an infectious state to the extinction of the disease within …

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Adjusted Empirical Likelihood Method For Comparison Of Treatment Effects In Linear Model Setting, Xi Kang May 2016

Adjusted Empirical Likelihood Method For Comparison Of Treatment Effects In Linear Model Setting, Xi Kang

Theses, Dissertations and Culminating Projects

Empirical likelihood is a nonparametric method of statistical inference which was introduced by Owen. It allows the data analyst to use it without making distribution assumptions. Empirical likelihood method has been widely used not only for nonparametric models but also for semi-parametric models, with the effectiveness of the likelihood approach and good power properties. However, when the sample size is small or the dimension is high, the method is poorly calibrated, producing tests that generally have a higher type I error. In addition, it suffers from a limiting convex hull constraint. Many statisticians have proposed methods to address the performance. …

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Data Driven Sample Generator Model With Application To Classification, Alvaro Emilio Ulloa Cerna May 2016

Data Driven Sample Generator Model With Application To Classification, Alvaro Emilio Ulloa Cerna

Mathematics & Statistics ETDs

Despite the rapidly growing interest, progress in the study of relations between physiological abnormalities and mental disorders is hampered by complexity of the human brain and high costs of data collection. The complexity can be captured by machine learning approaches, but they still may require significant amounts of data. In this thesis, we seek to mitigate the latter challenge by developing a data driven sample generator model for the generation of synthetic realistic training data. Our method greatly improves generalization in classification of schizophrenia patients and healthy controls from their structural magnetic resonance images. A feed forward neural network trained …

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A Modularized Tablet-Based Approach To Preparation For Remedial Mathematics, Kenneth A. Parker May 2016

A Modularized Tablet-Based Approach To Preparation For Remedial Mathematics, Kenneth A. Parker

Publications and Research

Basic arithmetic forms the foundation of the math courses that students will face in their undergraduate careers. It is therefore crucial that students have a solid understanding of these fundamental concepts. At an open- access university offering both two-year and four-year degrees, incoming freshmen who were identified as lacking in basic arithmetic skills were engaged in an experimental technology-enhanced workshop designed to provide them with a deeper understanding of arithmetic prior to their initial remedial coursework. Customized online content was created specifically for this experiment, and the first implementation (n=27) yielded statistically significant improvement, not only from pretest to post- …

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Applications Of The Sierpiński Triangle To Musical Composition, Samuel C. Dent May 2016

Applications Of The Sierpiński Triangle To Musical Composition, Samuel C. Dent

Honors Theses

The present paper builds on the idea of composing music via fractals, specifically the Sierpiński Triangle and the Sierpiński Pedal Triangle. The resulting methods are intended to produce not just a series of random notes, but a series that we think pleases the ear. One method utilizes the iterative process of generating the Sierpiński Triangle and Sierpiński Pedal Triangle via matrix operations by applying this process to a geometric configuration of note names. This technique designs the largest components of the musical work first, then creates subsequent layers where each layer adds more detail.

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Completing Partial Latin Squares With One Nonempty Row, Column, And Symbol, Jaromy Kuhl, Michael W. Schroeder Apr 2016

Completing Partial Latin Squares With One Nonempty Row, Column, And Symbol, Jaromy Kuhl, Michael W. Schroeder

Mathematics Faculty Research

Let r,c,s ∈{1,2,…,n} and let PP be a partial latin square of order n in which each nonempty cell lies in row r, column c, or contains symbol s. We show that if n ∉ {3, 4, 5} and row r, column c, and symbol s can be completed in P, then a completion of P exists. As a consequence, this proves a conjecture made by Casselgren and Häggkvist. Furthermore, we show exactly when row r, column c, and symbol s can be completed.

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The Entangling Properties Of Knots And Links, Eshan Mehrotra '17 Apr 2016

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 …

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Infinite Color Urn Models., Debleena Thacker Dr. Apr 2016

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 …

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Essays On Strategy-Proofness And Implementation., Sonal Yadav Dr. Apr 2016

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 …

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The Ko-Lee Key Exchange Protocol With Generalized Dihedral Groups, Christopher Lloyd Apr 2016

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.

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A Comparison Of Methods To Fit A Model To Simultaneous Time Series, Victoria Marie Moore Apr 2016

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 …

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Blossom: A Language Built To Grow, Jeffrey Lyman Apr 2016

Blossom: A Language Built To Grow, Jeffrey Lyman

Mathematics, Statistics, and Computer Science Honors Projects

No abstract provided.

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Dagum-Poisson Distribution: Model, Properties And Application, Broderick O. Oluyede, Galelhakanelwe Motsewabagale, Shujiao Huang, Gayan Warahena-Liyanage, Marvis Pararai Apr 2016

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 …

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Timely Curriculum Changes To An Undergraduate Actuarial Program, Thomas Hartl, Kristin Kennedy, John Quinn Apr 2016

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? …

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Measuring Dependence In Uncertainty Should Start In The Introduction To Probability And Statistics, Boyan N. Dimitrov Apr 2016

Measuring Dependence In Uncertainty Should Start In The Introduction To Probability And Statistics, Boyan N. Dimitrov

Mathematics Presentations And Conference Materials

No abstract provided.

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The Chromatic Number Of The Square Of Subcubic Planar Graphs, Stephen Hartke, Sogol Jahanbekam, Brent Thomas Apr 2016

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.

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Introductory And Intermediate Algebra Mth 100x, Joanna Burkhardt Apr 2016

Introductory And Intermediate Algebra Mth 100x, Joanna Burkhardt

Library Impact Statements

No abstract provided.

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Finite Math Mth 107, Joanna Burkhardt Apr 2016

Finite Math Mth 107, Joanna Burkhardt

Library Impact Statements

No abstract provided.

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Applied Calculus Mth 103x, Joanna Burkhardt Apr 2016

Applied Calculus Mth 103x, Joanna Burkhardt

Library Impact Statements

No abstract provided.

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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 Apr 2016

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 …

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Drawing Numbers And Listening To Patterns, Loren Zo Haynes Apr 2016

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 …

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Bivariate Barycentric-Coordinate Berstein-Bezier Polynomial & C1 Quadratic Vertex Spline, Rui Jiang, Tian-Xiao He, Faculty Advisor Apr 2016

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.

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Integer Antimagic Labeling For Cycle With One Chord, Jinze Zheng, Daniel Roberts, Faculty Advisor Apr 2016

Integer Antimagic Labeling For Cycle With One Chord, Jinze Zheng, Daniel Roberts, Faculty Advisor

John Wesley Powell Student Research Conference

Poster presentation abstract.

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Multidecomposition Of Complete Directed Graphs Into Directed Graph Pairs Of Order 3 And 4, Jacob Henry, Daniel Roberts, Faculty Advisor Apr 2016

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.

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Multidesigns For A Graph Pair Of Order 6, Yizhe Gao, Daniel Roberts, Faculty Advisor Apr 2016

Multidesigns For A Graph Pair Of Order 6, Yizhe Gao, Daniel Roberts, Faculty Advisor

John Wesley Powell Student Research Conference

Oral presentation abstract.

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Duals Of Bernoulli Numbers And Polynomials And Euler Numbers And Polynomials, Jinze Zheng, Tian-Xiao He, Faculty Advisor Apr 2016

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.

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C7 And C7 Complement Multidecomposition Of Kn, Hang Phung, Daniel Roberts, Faculty Advisor Apr 2016

C7 And C7 Complement Multidecomposition Of Kn, Hang Phung, Daniel Roberts, Faculty Advisor

John Wesley Powell Student Research Conference

Poster presentation abstract.

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Generalized Catalan Numbers And Their Properties, Yuanziyi Zhang, Tian-Xiao He, Faculty Advisor Apr 2016

Generalized Catalan Numbers And Their Properties, Yuanziyi Zhang, Tian-Xiao He, Faculty Advisor

John Wesley Powell Student Research Conference

Poster presentation abstract.

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Usefulness Of Relative Hypochromia In Risk Stratification For Nonanemic Patients With Chronic Heart Failure, Muhammad Hammadah, Marie Luise Brennan, Yuping Wu, Stanley L. Hazen, W.H. Wilson Tang Apr 2016

Usefulness Of Relative Hypochromia In Risk Stratification For Nonanemic Patients With Chronic Heart Failure, Muhammad Hammadah, Marie Luise Brennan, Yuping Wu, Stanley L. Hazen, W.H. Wilson Tang

Mathematics and Statistics Faculty Publications

The purpose of this study is to investigate the impact of a reduction of hemoglobin (Hb) content in the erythrocytes as estimated by mean corpuscular hemoglobin concentration (MCHC) on long-term clinical outcomes in nonanemic patients with heart failure (HF). We prospectively enrolled 1,579 subjects with HF who underwent coronary angiography enrolled in the GeneBank study with 5-year follow-up of all-cause mortality. Levels of Hb and MCHC were assessed at enrollment and after 6 months of follow-up. Anemia was defined as Hb levels <13 g/dl in men and <12 g/dl in women. In our nonanemic cohort (n = 785, 49.7%), mean Hb and median MCHC were 13.8 ± 1.1 g/dl and 34.3 g/dL (interquartile range 33.6 to 35), respectively. Nonanemic patients with heart failure with lower MCHC had higher mortality risk (quartiles 1 vs 4, hazard ratio = 2.1, 95% confidence interval 1.4 to 3.3, p = 0.001). In a subset of nonanemic patients with persistent normal Hb on follow-up (n = 206), the mean time between baseline and follow-up MCHC levels was 169.3 ± 41.6 days. In comparison with patients with levels of MCHC more than the first quartile (≥33.6 g/dl) on baseline and follow-up, patients with persistently low MCHC (<33.6 g/dl) had a significantly increased mortality risk (log rank <0.001). All models remained significant even after adjusting for traditional cardiac risk factors, left ventricular ejection fraction, baseline Hb levels, and mean corpuscular volume. In conclusion, relative hypochromia is an independent predictor of increased mortality risk in patients with HF, even in the setting of normal Hb levels.

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Locally Convex Words And Permutations, Christopher Coscia, Jonathan Dewitt Apr 2016

Locally Convex Words And Permutations, Christopher Coscia, Jonathan Dewitt

Dartmouth Scholarship

We introduce some new classes of words and permutations characterized by the second difference condition pi(i - 1) + pi(i + 1) - 2 pi(i)

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