Mathematics Commons^™

Efficient Smooth Non-Convex Stochastic Compositional Optimization Via Stochastic Recursive Gradient Descent, Wenqing Hu, Chris Junchi Li, Xiangru Lian, Ji Liu, Huizhuo Yuan

Mathematics and Statistics Faculty Research & Creative Works

Stochastic compositional optimization arises in many important machine learning applications. The objective function is the composition of two expectations of stochastic functions, and is more challenging to optimize than vanilla stochastic optimization problems. In this paper, we investigate the stochastic compositional optimization in the general smooth non-convex setting. We employ a recently developed idea of Stochastic Recursive Gradient Descent to design a novel algorithm named SARAH-Compositional, and prove a sharp Incremental First-order Oracle (IFO) complexity upper bound for stochastic compositional optimization: 𝒪((n + m)^1/2ε^-2) in the finite-sum case and 𝒪(ε^-3) in the online case. …

A Pedagogic Analysis Of Linear Algebra Courses, Andrew Taylor

Mathematics & Statistics ETDs

This project is concerned with investigating the question, "Do our applied linear algebra courses (at the University of New Mexico) adequately prepare STEM students for future work in their respective fields?" In order to explore this, surveys were issued to three groups (sections) of students (among two different instructors) at the conclusion of their applied linear algebra course, as well as STEM professors/instructors from a variety of STEM fields. Students were surveyed regarding their perceived mastery of given topics/ideas from the course and professors/instructors were surveyed about the level of mastery they felt was necessary (referred to as ``desired mastery") …

Implications Of The Modifiable Areal Unit Problem For Wildfire Analyses, Timothy P. Nagle-Mcnaughton, Xi Gong, Jose A. Constantine

Geography and Environmental Studies Faculty Publications

Wildfires pose a danger to both ecologies and communities. To this end, many large-scale analyses of wildfire patterns and behavior rely on the aggregation of point data to polygons, typically those based on distinct disparate ecological areas. However, the sizes, shapes, andorientations of the polygons to which data are aggregated are not neutral factors in the resulting analysis. The influence of the aggregation polygons on calculated results is known as the modifiable areal unit problem (MAUP), which is well-documented in the spatial statistics literature. Despite the documentation of the MAUP, relatively few wildfire studies consider the effects of the MAUP …

The Negotiator's Role In A Buyer-Seller Game, Joseph Gaudy

Graduate Theses and Capstone Projects (excluding DNP)

In game theory, buyer-seller games rarely utilize a negotiating third party. Any negotiations are typically conducted by the buyer and seller. This study, motivated by the real estate market, uses sequentially and simultaneously played game models to explore the influence a self-interested, negotiating, third party has on player payoffs. For the sequential model, a game tree is utilized to demonstrate player actions, preferences, and outcomes. The weak sequential equilibrium is calculated using Gambit[1] and shows optimality in player payoffs to exist when the seller’s and realtor’s strategies align according to the current market. For the simultaneous model, expected payoff functions …

Approximation Dynamics, Ethan Akin

Mathematics and Statistics Faculty Research & Creative Works

We describe the approximation of a continuous dynamical system on a p.l. manifold or Cantor set by a tractable system. A system is tractable when it has a finite number of chain components and, with respect to a given full background measure, almost every point is generic for one of a finite number of ergodic invariant measures. The approximations we use are non-degenerate simplicial dynamical systems for p.l. manifolds and shift-like dynamical systems for Cantor Sets.

The Graphs That Have Antivoltages Using Groups Of Small Order, Vaidy Sivaraman, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a group Γ of order at most six, we characterize the graphs that have Γ-antivoltages and also determine the list of minor-minimal graphs that have no Γ-antivoltage. Our characterizations yield polynomial-time recognition algorithms for such graphs.

Reduced Bias For Respondent Driven Sampling: Accounting For Non-Uniform Edge Sampling Probabilities In People Who Inject Drugs In Mauritius, Miles Q. Ott, Krista J. Gile, Matthew T. Harrison, Lisa G. Johnston, Joseph W. Hogan

Statistical and Data Sciences: Faculty Publications

People who inject drugs are an important population to study in order to reduce transmission of blood-borne illnesses including HIV and Hepatitis. In this paper we estimate the HIV and Hepatitis C prevalence among people who inject drugs, as well as the proportion of people who inject drugs who are female in Mauritius. Respondent driven sampling (RDS), a widely adopted link-tracing sampling design used to collect samples from hard-to-reach human populations, was used to collect this sample. The random walk approximation underlying many common RDS estimators assumes that each social relation (edge) in the underlying social network has an equal …

"Big Ideas" In Secondary Mathematics Education Programs, Eryn Stehr, Hyunyi Jung, Jill Newton

Mathematical and Statistical Science Faculty Research and Publications

Although research and policy documents provide recommendations to inform secondary mathematics teacher preparation, no single study has addressed the “big ideas” of courses in multiple programs and how those big ideas may be interpreted through the lens of recent research and policy documents. To answer this need, we focused on big ideas and course objectives from three courses (i.e., Linear Algebra, Secondary Mathematics Methods, and Teaching in a Diversity Society) taught in four secondary mathematics programs. Major themes emerged related to mathematical content, pedagogy, and issues of equity. We describe findings related to big ideas, course objectives, and their connections …

Diabetes And Its Effect On Abdominal Aortic Aneurysm Growth Rate In Hispanic Patients, Monica Betancourt-Garcia, Kristina Vatcheva, Amrit Thakur, Prateek Gupta, Eugene Postevka, Ricardo Martinez, R. Armour Forse

School of Mathematical & Statistical Sciences Faculty Publications

Background

The growth rate of abdominal aortic aneurysms (AAA) can vary depending on age, baseline diameter, blood pressure, race, and history of smoking. Paradoxically, previous studies show evidence of a protective effect of diabetes on the rate of AAA expansion despite its well-established role in the morbidity and mortality of cardiovascular disease. This study aims to investigate the impact diabetes plays on AAA growth within a Hispanic population.

Methods

Data were collected from patients who were predominantly Mexican-American at a single hospital site. Baseline and follow-up measures for AAA diameter were obtained from serial imaging studies. Demographics, medical history, the …

A Multi-Step Approach To Modeling The 24-Hour Daily Profiles Of Electricity Load Using Daily Splines, Abdelmonaem Jornaz, V. A. Samaranayake

Mathematics and Statistics Faculty Research & Creative Works

Forecasting of real-time electricity load has been an important research topic over many years. Electricity load is driven by many factors, including economic conditions and weather. Furthermore, the demand for electricity varies with time, with different hours of the day and different days of the week having an effect on the load. This paper proposes a hybrid load-forecasting method that combines classical time series formulations with cubic splines to model electricity load. It is shown that this approach produces a model capable of making short-term forecasts with reasonable accuracy. In contrast to forecasting models that utilize a multitude of regressor …

Network Structure And Dynamics Of Biological Systems, Deena R. Schmidt

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Study On Discrete And Discrete Fractional Pharmacokinetics-Pharmacodynamics Models For Tumor Growth And Anti-Cancer Effects, Ferhan Atici, Ngoc Nguyen

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Toward Greater Reproducibility Of Undergraduate Behavioral Science Research, Bruce Evan Blaine

Mathematical and Computing Sciences Faculty/Staff Publications

Reproducibility crises have arisen in psychology and other behavioral sciences, spurring efforts to ensure research findings are credible and replicable. Although reforms are occurring at professional levels in terms of new publication parameters and open science initiatives, the credibility and reproducibility of undergraduate research deserves attention. Undergraduate behavioral science research projects that rely on small convenience samples of participants, overuse hypothesis testing for drawing meaning from data, and engage in opaque statistical computing are vulnerable to producing nonreproducible findings. These vulnerabilities are reviewed, and practical recommendations for improving the credibility and reproducibility of undergraduate behavioral science research are offered.

Quasilinearization And Boundary Value Problems At Resonance, Kareem Alanazi, Meshal Alshammari, Paul W. Eloe

Mathematics Faculty Publications

A quasilinearization algorithm is developed for boundary value problems at resonance. To do so, a standard monotonicity condition is assumed to obtain the uniqueness of solutions for the boundary value problem at resonance. Then the method of upper and lower solutions and the shift method are applied to obtain the existence of solutions. A quasilinearization algorithm is developed and sequences of approximate solutions are constructed, which converge monotonically and quadratically to the unique solution of the boundary value problem at resonance. Two examples are provided in which explicit upper and lower solutions are exhibited.

Mathematical Modeling Opportunities Reported By Secondary Mathematics Preservice Teachers And Instructors, Hyunyi Jung, Eryn Stehr, Jia He

Mathematical and Statistical Science Faculty Research and Publications

Engaging with mathematical modeling can support learners to collaboratively explore mathematics in integrated ways as well as generate mathematical ideas and representations that may be useful in everyday life. Although several studies provide diverse insights into teaching and learning mathematical modeling, research has yet to be conducted on the mathematical modeling learning opportunities available to secondary mathematics preservice teachers (PTs) in mathematics and education courses in teacher education programs. This study investigates the mathematical modeling learning opportunities reported by 48 instructors and ten focus groups of 37 PTs. Multiple data sources (e.g., interview transcripts, syllabi, tasks, and exams) collected from …

An Optimal Edg Method For Distributed Control Of Convection Diffusion Pdes, X. Zhang, Y. Zhang, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

We propose an embedded discontinuous Galerkin (EDG) method to approximate the solution of a distributed control problem governed by convection diffusion PDEs, and obtain optimal a priori error estimates for the state, dual state, their uxes, and the control. Moreover, we prove the optimize-then-discretize (OD) and discrtize-then-optimize (DO) approaches coincide. Numerical results confirm our theoretical results.

Three-Dimensional Rotation Of Paramagnetic And Ferromagnetic Prolate Spheroids In Simple Shear And Uniform Magnetic Field, Christopher A. Sobecki, Yanzhi Zhang, Cheng Wang

Mathematics and Statistics Faculty Research & Creative Works

We examine a time-dependent, three-dimensional rotation of magnetic ellipsoidal particles in a two-dimensional, simple shear flow and a uniform magnetic field. We consider that the particles have paramagnetic and ferromagnetic properties, and we compare their rotational dynamics due to the strengths and directions of the applied uniform magnetic field. We determine the critical magnetic field strength that can pin the particles' rotations. Above the critical field strength, the particles' stable steady angles were determined. In a weak magnetic regime (below the critical field strength), a paramagnetic particle's polar angle will oscillate toward the magnetic field plane while its azimuthal angle …

9th Annual Postdoctoral Science Symposium, University Of Texas Md Anderson Cancer Center Postdoctoral Association

Annual Postdoctoral Science Symposium Abstracts

The mission of the Annual Postdoctoral Science Symposium (APSS) is to provide a platform for talented postdoctoral fellows throughout the Texas Medical Center to present their work to a wider audience. The MD Anderson Postdoctoral Association convened its inaugural Annual Postdoctoral Science Symposium (APSS) on August 4, 2011.

The APSS provides a professional venue for postdoctoral scientists to develop, clarify, and refine their research as a result of formal reviews and critiques of faculty and other postdoctoral scientists. Additionally, attendees discuss current research on a broad range of subjects while promoting academic interactions and enrichment and developing new collaborations.

Fake News And Stem, Vikki French

The Liminal: Interdisciplinary Journal of Technology in Education

Based on over ten years teaching mathematics, statistics and science in universities, communities colleges, and for-profit universities, I have witnessed how Fake News is part of these disciplines and how students can easily be misled into accepting pseudoscience. This is a report of my findings.

On Nonoscillatory Solutions Of Three Dimensional Time-Scale Systems, Elvan Akin, Taher Hassan, Ozkan Ozturk, Ismail U. Tiryaki

Mathematics and Statistics Faculty Research & Creative Works

In this article, we classify nonoscillatory solutions of a system of three-dimensional time scale systems. We use the method of considering the sign of components of such solutions. Examples are given to highlight some of our results. Moreover, the existence of such solutions is obtained by Knaster's fixed point theorem.

The Ace1 Electrical Impedance Tomography System For Thoracic Imaging, Michelle M. Mellenthin, Jennifer L. Mueller, Erick Dario Leon Bueno De Camargo, Fernando Silva De Moura, Talles Batista Rattis Santos, Raul Gonzales Lima, Sarah J. Hamilton, Peter A. Muller, Melody Alsaker

Mathematical and Statistical Science Faculty Research and Publications

The design and performance of the active complex electrode (ACE1) electrical impedance tomography system for single-ended phasic voltage measurements are presented. The design of the hardware and calibration procedures allows for reconstruction of conductivity and permittivity images. Phase measurement is achieved with the ACE1 active electrode circuit which measures the amplitude and phase of the voltage and the applied current at the location at which current is injected into the body. An evaluation of the system performance under typical operating conditions includes details of demodulation and calibration and an in-depth look at insightful metrics, such as signal-to-noise ratio variations during …

An Hdg Method For Dirichlet Boundary Control Of Convection Dominated Diffusion Pdes, Gang Chen, John R. Singler, Yangwen Zhang

Mathematics and Statistics Faculty Research & Creative Works

We first propose a hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a convection dominated Dirichlet boundary control problem without constraints. Dirichlet boundary control problems and convection dominated problems are each very challenging numerically due to solutions with low regularity and sharp layers, respectively. Although there are some numerical analysis works in the literature on diffusion dominated convection diffusion Dirichlet boundary control problems, we are not aware of any existing numerical analysis works for convection dominated boundary control problems. Moreover, the existing numerical analysis techniques for convection dominated PDEs are not directly applicable for the Dirichlet boundary control …

Effective Statistical Energy Function Based Protein Un/Structure Prediction, Avdesh Mishra

LSU New Orleans Theses and Dissertations

Proteins are an important component of living organisms, composed of one or more polypeptide chains, each containing hundreds or even thousands of amino acids of 20 standard types. The structure of a protein from the sequence determines crucial functions of proteins such as initiating metabolic reactions, DNA replication, cell signaling, and transporting molecules. In the past, proteins were considered to always have a well-defined stable shape (structured proteins), however, it has recently been shown that there exist intrinsically disordered proteins (IDPs), which lack a fixed or ordered 3D structure, have dynamic characteristics and therefore, exist in multiple states. Based on …

The Topp-Leone Generalized Odd Log-Logistic Family Of Distributions: Properties, Characterizations And Applications, Mustafa Ç. Korkmaz, Haitham M. Yousof, Morad Alizadeh, Gholamhossein Hamedani

Mathematical and Statistical Science Faculty Research and Publications

A new family of distributions called the Topp-Leone generalized odd log-logistic-G family is introduced and studied. We provide some mathematical properties of the new family including ordinary and incomplete moments, generating function and order statistics. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of two simulation studies. Finally, the usefulness of the family is il lustrated by means of two real data sets. The new model provides consistently better fits than other competitive models for these data sets.

Mathematics Versus Statistics, Mindy B. Capaldi

Journal of Humanistic Mathematics

Mathematics and statistics are both important and useful subjects, but the former has maintained prominence in the American education system. On the other hand, statistics is more prevalent in daily life and is an increasingly marketable subject to know. This article gives a personal history of one mathematician’s bumpy road to learning and teaching statistics. Additionally, arguments for how and why to include statistics in the K-12 and college curricula are provided.

Choose Your Own Adventure: An Analysis Of Interactive Gamebooks Using Graph Theory, D'Andre Adams, Daniela Beckelhymer, Alison Marr

Journal of Humanistic Mathematics

"BEWARE and WARNING! This book is different from other books. You and YOU ALONE are in charge of what happens in this story." This is the captivating introduction to every book in the interactive novel series, Choose Your Own Adventure (CYOA). Our project uses the mathematical field of graph theory to analyze forty books from the CYOA book series for ages 9-12. We first began by drawing the digraphs of each book. Then we analyzed these digraphs by collecting structural data such as longest path length (i.e. longest story length) and number of vertices with outdegree zero (i.e. number …

Practical Modelling Of The Vanilla Option Volatility Smile, Jacob E. Shanley

Mathematics & Statistics ETDs

Many discussions on how best to model the standard American Option derivative focus solely upon the volatility smile modelling itself from a mathematical perspective. This thesis instead closely examines both the practical and mathematical implications of processing market data, modelling the volatility smile, and making real-world trading decisions from the results. In particular, it contains an analysis of market data processing algorithms, new volatility smile models, multiple empirically-driven weighting schemes, Gauss-Newton and Levenberg-Marquardt optimization algorithms, and various trading strategies. The top performing combinations found were those that involved the Smile and Twist volatility smile models, Volatility Width Vega Multiplier weighting …

A Deep Learning Approach To Uncertainty Quantification, Mst Afroja Akter

Mathematics & Statistics ETDs

In this thesis we consider ordinary differential equations (ODEs) with random parameters. We focus on Monte Carlo (MC) sampling for computing the statistics of some quantities of interest (QoIs) given by the solution of the ODE problems. We use the 4th order accurate Runge-Kutta (RK4) method as the deterministic ODE solver. We then develop a hybrid MC sampling method that combines RK4 with neural network models to efficiently compute the statistics of QoIs within a desired accuracy. We present several numerical examples to verify the accuracy and efficiency of the proposed hybrid method compared to classical MC sampling. The hybrid …

Taking Multiple Regression Analysis To Task: A Review Of Mindware: Tools For Smart Thinking, By Richard Nisbett (2015), Jason Makansi

Numeracy

Richard Nisbett. 2015. Mindware: Tools for Smart Thinking.(New York, NY: Farrar, Strauss, and Giroux). 336 pp. ISBN: 9780374536244

Nisbett, a psychologist, may not achieve his stated goal of teaching readers to “effortlessly” extend their common sense when it comes to quantitative analysis applied to everyday issues, but his critique of multiple regression analysis (MRA) in the middle chapters of Mindware is worth attention from, and contemplation by, the QL/QR and Numeracy community. While in at least one other source, Nisbett’s critique has been called a “crusade” against MRA, what he really advocates is that it not be used as …

On Continuous Images Of Ultra-Arcs, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

Any space homeomorphic to one of the standard subcontinua of the Stone-Čech remainder of the real half-line is called an ultra-arc. Alternatively, an ultra-arc may be viewed as an ultracopower of the real unit interval via a free ultrafilter on a countable set. It is known that any continuum of weight is a continuous image of any ultra-arc; in this paper we address the problem of which continua are continuous images under special maps. Here are some of the results we present.