Physical Sciences and Mathematics Commons^™

Curvature: A Geometric Villain That Ruins Our Instinctive Perception Of Nature, Vehbi Emrah Paksoy

Mathematics Colloquium Series

Our perception of nature is based on evolutionary wiring of our brain and observations we make via our senses. But, in reality, many scientific and technological advancements are based on non-intuitive rules and principles that can only be explained by the ultimate abstraction that is embedded in mathematics. In this talk, I will discuss the concept of curvature and argue how it explains the “unexplainable”. We will see how the curvature proves that the earth is rotating, how good the soap bubbles are at proving profound mathematical results, and if the two dimensional residents can determine the shape of their …

Match-Making For Stability: A Survey Of The Stable Marriage Problem, Adam J. Hammett

Mathematics Colloquium

No abstract provided.

Bayes Multiple Binary Classifier - How To Make Decisions Like A Bayesian, Wensong Wu

Mathematics Colloquium Series

This presentation will start by a general introduction of Bayesian statistics, which has become popular in the era of big data. Then we consider a two-class classification problem, where the goal is to predict the class membership of M units based on the values of high-dimensional categorical predictor variables as well as both the values of predictor variables and the class membership of other N independent units. We focus on applying generalized linear regression models with Boolean expressions of categorical predictors. We consider a Bayesian and decision-theoretic framework, and develop a general form of Bayes multiple binary classification functions with …

P-38 On The Riemannian Submersion Invariant, Yun Myung Oh

Celebration of Research and Creative Scholarship

For a Riemannian submersion pi:Mⁿ->B^bwith totally geodesic fibers, the submersion invariant (see attached abstract for equation) was introduced using the integrability tensor of the submersion. B. Y. Chen has provided the inequality on this invariant if the manifold M admits an isometric immersion into a Riemannian manifold M^m. Some of the recent results on this invariant are included with examples. This is a continuation of the work published in 2013.

See attached abstract for full equations.

Flexible Gating Of Contextual Influences In Natural Vision, Odelia Schwartz

Mathematics Colloquium Series

An appealing hypothesis suggests that neurons represent inputs in a coordinate system that is matched to the statistical structure of images in the natural environment. I discuss theoretical work on unsupervised learning of statistical regularities in natural images. In the model, Bayesian inference amounts to a generalized form of divisive normalization, a canonical computation that has been implicated in many neural areas. In our framework, divisive normalization is flexible: it is recruited only when the image is inferred to contain dependencies, and muted otherwise. I particularly focus on recent work in which we have applied this approach to understanding spatial …

Using Nitrate, Chloride, Sodium, And Sulfate To Calculate Groundwater Age, Kimm Crawford, Terry Lee

Sinkhole Conference 2015

Regression analysis is used to identify monotonic trends to assign water age using ion data from two large well water databases from southeast Minnesota (SE MN). Nitrate (NO3-N), chloride (Cl), sodium (Na), and sulfate (SO4) ions in the commonly used aquifers in SE MN can be used as groundwater tracers since they are either entirely or partly anthropogenic in their sources, their loading occurs on a regional scale, and they are almost entirely conserved. Ion concentrations over time are used to establish six trend patterns. Two patterns are unchanging (background and stable above background), and four are changing (linear up, …

Learning From Lionfish: Modeling Marine Invaded Systems, Matthew Johnston

Mathematics Colloquium Series

Simulating marine invaded systems requires broad consideration of physical oceanographic processes, such as ocean circulation patterns and temperature, and biological traits of the invader, such as their reproductive strategy and tolerances to their environment. Through this understanding of baseline biological and oceanographic function, models can be developed in order to forecast the incursion patterns of marine invasive species - helpful both to predict their spread as well as forewarn of impacts. To facilitate this understanding, computer simulation is useful in order to quickly and efficiently assimilate large biological and oceanographic datasets into digestible products. Data derived from such simulations are …

Life As An Nfl Statistician, Dennis Lock

Mathematics Colloquium Series

Over the last few years, the fields of statistics and mathematics have become more prevalent and popular in professional sports (with the help of mainstream books and movies like Moneyball). The use of advanced (and non-advanced) statistical methods is growing across the sporting landscape from the front office to the media, and even into business and ticket sales. This talk will discuss Lock’s experiences building an analytics department with the Miami Dolphins as well as the general role of statistics in sports today. It will also including the recent analytics boom in the front office framework, the coinciding need for …

A Nonlinear Filter For Markov Chains And Its Effect On Diffusion Maps, Stefan Steinerberger

Yale Day of Data

Diffusion maps are a modern mathematical tool that helps to find structure in large data sets - we present a new filtering technique that is based on the assumption that errors in the data are intrinsically random to isolate and filter errors and thus boost the efficiency of diffusion maps. Applications include data sets from medicine (the Cleveland Heart Disease Data set and the Wisconsin Breast Cancer Data set) and engineering (the Ionosphere data set).

Computing Invariant Dynamics For Differential Equations: Spectral Methods, Errors, And Computer Assisted Proof, J. D. Mireles James

Mathematics Colloquium Series

The qualitative theory of dynamical systems is concerned with studying the long time behavior discrete and continuous time models such as nonlinear differential equations. The long time behavior of such models is organized by landmarks called invariant sets. For complicated nonlinear equations these invariant sets are difficult to study via pen and paper analysis, and we typically employ numerical simulations to gain insights into the dynamics. If we now think of these computer assisted insights as mathematical conjectures, then it is natural to ask how we might obtain proofs. Since the conjectures themselves originate with the computer it is not …

Generalizations And Algebraic Structures Of The Grøstl-Based Primitives, Dmitriy Khripkov, Nicholas Lacasse, Bai Lin, Michelle Mastrianni, Liljana Babinkostova (Mentor)

Idaho Conference on Undergraduate Research

With the large scale proliferation of networked devices ranging from medical implants like pacemakers and insulin pumps, to corporate information assets, secure authentication, data integrity and confidentiality have become some of the central goals for cybersecurity. Cryptographic hash functions have many applications in information security and are commonly used to verify data authenticity. Our research focuses on the study of the properties that dictate the security of a cryptographic hash functions that use Even-Mansour type of ciphers in their underlying structure. In particular, we investigate the algebraic design requirements of the Grøstl hash function and its generalizations. Grøstl is an …

Video Event Understanding With Pattern Theory, Fillipe Souza, Sudeep Sarkar, Anuj Srivastava, Jingyong Su

MODVIS Workshop

We propose a combinatorial approach built on Grenander’s pattern theory to generate semantic interpretations of video events of human activities. The basic units of representations, termed generators, are linked with each other using pairwise connections, termed bonds, that satisfy predefined relations. Different generators are specified for different levels, from (image) features at the bottom level to (human) actions at the highest, providing a rich representation of items in a scene. The resulting configurations of connected generators provide scene interpretations; the inference goal is to parse given video data and generate high-probability configurations. The probabilistic structures are imposed using energies that …

The Smallest Intersecting Ball Problem, Daniel J. Giles, Mau Nam Nguyen

Student Research Symposium

The smallest intersecting ball problem involves finding the minimal radius necessary to intersect a collection of closed convex sets. This poster discusses relevant tools of convex optimization and explores three methods of finding the optimal solution: the subgradient method, log-exponential smoothing, and an original approach using target set expansion. A fourth algorithm based on weighted projections is given, but its convergence is yet unproven. Numerical tests and comparison between methods are also presented.

Non-Orientable Objects As Gaming Surfaces, Haley P. Bourke, Paul Latiolais

Student Research Symposium

Developed in Python, Klein Space Fighter is an interactive learning tool and mathematically themed arcade game that allows the player to combat on different mathematical surfaces including a 2D Klein bottle. The app is available for Android and desktop devices, and will be made available for iOS in the future.

To receive an invitation to download the app through Google Play, contact me at HaleyoBourke@yahoo.com

On The Sum Of The Reciprocals Of Squares, Hussam Ibrahim

Celebration of Learning

The Fourier Series has always been a great tool by turning the most complicated functions into a simple approximation by several sine and cosine terms. However, given the fact that its called an approximation arouses the question of how accurate is this approximation, especially with functions that have a corner at x values. In this project, we will show how the series that is the sum of the reciprocals of squares arises in the study of Fourier series. We will discuss the convergence and the rate of convergence of this series. This result arose during exploration on mathematical software Sage. …

A Fixed-Inverse Binary Misclassification Model Under Possible False-Positive Misclassification, Asmerom Tesfamichael, Kent Riggs

Bright Ideas Conference

In this project, we develop a particular statistical model for binary data that allows for the possibility of false-positive misclassification. To account for the misclassification, the model incorporates a two-stage sampling scheme.

• Next, we apply maximum likelihood methods to find estimators of the primary prevalence parameter p as well as the false-positive misclassification rate parameter ϕ. In addition, we derive confidence intervals for p based on inverting Wald, score and likelihood ratio statistics.

• Also, we graphically compare coverage and width properties of the Wald-based, score-based, and likelihood ratio-based confidence intervals for p through a Monte Carlo simulation. The …

Packing Densities Of Colored And Non-Colored Patterns, Matthew R. Just

GS4 Georgia Southern Student Scholars Symposium

Pattern packing concerns finding an optimal permutation that contains the maximum number of occurrences of a given pattern and computing the corresponding packing density. In many instances such an optimal permutation can be characterized directly and the number of occurrences of the pattern in interest may be enumerated explicitly. In more complicated patterns a direct characterization may be more challenging, however computational results for long permutations can help provide an indirect characterization of the general form of an optimal permutation. Much work has been done on the study of pattern packing in layered patterns, as the optimal permutation of a …

Multidecompositions Of Complete Graphs Into A Graph Pair Of Order 6, Yizhe Gao, Mark Daniel Roberts, Faculty Advisor

John Wesley Powell Student Research Conference

A graph is a mathematical structure consisting of a set of objects called vertices and a set of 2-element subsets of vertices, called edges. The complete graph on n vertices is the graph with n vertices and an edge between any pair of distinct vertices. Let C₆ denote the cycle on 6 vertices. We are interested in partitioning the edges of the complete graph on n vertices into copies of C₆ and its complement with at least one copy of each graph. We provide necessary and sufficient conditions on n for the existence such a structure.

How Visualization Can Improve The Understanding Of Mathematics, Mariah Martin

Undergraduate Research Conference

High school students have a difficult time taking the new End-Of-Course exams in math. Why are students having this difficulty? This could be because students lack the understanding of visualization in mathematics. Visualization can be helpful to certain students who think this way, while also confusing to those same students, and others as well. However, to what extent do high stakes tests, such as the End-Of-Course exams in Algebra I and II, incorporate mathematical visualization? How can visualization help improve the understanding of mathematics? This review will explain the advantages and disadvantages of incorporating visualization in these exams, how students …

Analysis Of Accounting Wages Within The Largest Cities Of Texas, Zuleima Espino, Delyla Frederick, Allyson Gallier, Halee Morehead

Undergraduate Research Conference

No abstract provided.

Tamed And Compatible Symplectic Forms On Four-Dimensional Almost Complex Lie Algebras, Andres Cubas

Undergraduate Research at FIU (URFIU) Conference

We are able to give a complete description of four-dimensional Lie algebras g which satisfy the tame-compatible question of Donaldson for all almost complex structures J on g are completely described. As a consequence, examples are given of (non-unimodular) four-dimensional Lie algebras with almost complex structures which are tamed but not compatible with symplectic forms.? Note that Donaldson asked his question for compact four-manifolds. In that context, the problem is still open, but it is believed that any tamed almost complex structure is in fact compatible with a symplectic form. In this presentation, I will define the basic objects involved …

Session B-1: Pipelines And Oil Spills!, Patrick Young

Professional Learning Day

Don’t miss this hands-on approach to middle school math. Participants will construct an actual pipeline from inexpensive materials and record evidence of leakage. They will then conduct an experiment and create a model relating liquid volume and spill area. They will apply their model to determine how much liquid leaked from their pipeline.

Session B-3: Mathematical Games, Puzzles, And Diversions, Steven M. Condie

Professional Learning Day

Delve into the exciting world of math through games, puzzles and other sources! Participants shall try their luck and test their skill at these diversions. Participants will leave this session with a wealth of mathematical activities appropriate for students of all ages.

Session B-2: The “Roll” Of Statistics In Modeling - It All Adds Up, Richard Stalmack, Janice Krouse

Professional Learning Day

The common core practice standards ask us to teach students to propose mathematical models and test their viability. Participants will do an experiment, collect data and use technological tools to combine modeling, analysis and basic statistics. Participants should bring a laptop, if possible; otherwise, bring a graphing calculator.

Session A-2: From Polynomial To Rational Functions: Flip!, Ruth Dover

Professional Learning Day

Ah HA! Making the connection between polynomial functions, rational functions and using reciprocals! Join us to flip, not flop, with trig for your classroom.

Session C-2: Problem-Based Mathematics: You Reap What You Sow, Nicole Ross, Lindsey Herlehy

Professional Learning Day

Approach problem-based mathematics through a historical perspective! Join us to learn a fun, hands-on approach to examining the science behind crop rotation systems originally implemented during the Medieval Period. This activity requires students to mathematically evaluate the efficiency of a crop rotation system, strategically complete an integers-based crop puzzle, and evaluate crop yield and profit through data analysis. This activity integrates a variety of middle school mathematics concepts.

Session A-1: Implementing Common Core In Middle School Math, Karen Togliatti

Professional Learning Day

This session will focus on implementing Common Core Middle-School Mathematics Standards using student-centered activities. Participants will receive three hands-on activities (one each at grades six, seven, and eight) to take back to their classrooms.

2015 Oklahoma Research Day Full Program, Northeastern State University

Oklahoma Research Day Abstracts

This document contains all abstracts from the 2015 Oklahoma Research Day held at Northeastern State University.