Mathematics Commons^™

Machine Learning Approach To Predict Mortality Rates Based On Hospital Clinical Data, Rebecca Smith

Theses and Dissertations

This thesis integrates fundamental concepts from conventional statistics with the more explanatory, algorithmic, and computational techniques offered by machine learning to predict early mortality risk of surgical patients. Well-known classification methods, including Random Forest, Decision Trees, Nearest Neighbor, Stochastic Gradient Descent, Logistic Regression, Na¨ıve Bayes, Bayes Network, Neural Networks, and Support Vector Machines, are utilized to predict mortality risk of elective general surgical patients treated between January 2005 and September 2010 at the Cleveland Clinic [33]. Clinical factors include surgery type, age, gender, race, BMI, underlying chronic conditions, surgical risk indices, surgical timing predictors, the 30-day mortality, and in-hospital complication …

Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang

Electronic Theses and Dissertations

While the "path integral" formulation of quantum mechanics is both highly intuitive and far reaching, the path integrals themselves often fail to converge in the usual sense. Richard Feynman developed regularization as a solution, such that regularized path integrals could be calculated and analyzed within a strictly physics context. Over the past 50 years, mathematicians and physicists have retroactively introduced schemes for achieving mathematical rigor in the study and application of regularized path integrals. One such scheme was introduced in 2007 by the mathematicians Klaus Kirsten and Paul Loya. In this thesis, we reproduce the Kirsten and Loya approach to …

Defect Detection In Atomic Resolution Transmission Electron Microscopy Images Using Machine Learning, Philip Cho, Aihua W. Wood, Krishnamurthy Mahalingam, Kurt Eyink

Faculty Publications

Point defects play a fundamental role in the discovery of new materials due to their strong influence on material properties and behavior. At present, imaging techniques based on transmission electron microscopy (TEM) are widely employed for characterizing point defects in materials. However, current methods for defect detection predominantly involve visual inspection of TEM images, which is laborious and poses difficulties in materials where defect related contrast is weak or ambiguous. Recent efforts to develop machine learning methods for the detection of point defects in TEM images have focused on supervised methods that require labeled training data that is generated via …

Ramanujan Type Congruences For Quotients Of Level 7 Klein Forms, Timothy Huber, Dongxi Ye

School of Mathematical & Statistical Sciences Faculty Publications

Klein forms are used to construct generators for the graded algebra of modular forms of level 7. Dissection formulas for the series imply Ramanujan type congruences modulo powers of 7 for a family of generating functions that subsume the counting function for 7-core partitions. The broad class of arithmetic functions considered here enumerate colored partitions by weights determined by parts modulo 7. The method is a prototype for similar analysis of modular forms of level 7 and at other prime levels. As an example of the utility of the dissection method, the paper concludes with a derivation of novel congruences …

Constructions & Optimization In Classical Real Analysis Theorems, Abderrahim Elallam

Electronic Theses and Dissertations

This thesis takes a closer look at three fundamental Classical Theorems in Real Analysis. First, for the Bolzano Weierstrass Theorem, we will be interested in constructing a convergent subsequence from a non-convergent bounded sequence. Such a subsequence is guaranteed to exist, but it is often not obvious what it is, e.g., if an = sin n. Next, the H¨older Inequality gives an upper bound, in terms of p ∈ [1,∞], for the the integral of the product of two functions. We will find the value of p that gives the best (smallest) upper-bound, focusing on the Beta and Gamma integrals. …

Exploring The Choiceless Cardinal Hierarchy, David Linkletter

UNLV Theses, Dissertations, Professional Papers, and Capstones

In 1971, Kunen proved that the Axiom of Choice imposes a ceiling on the large cardinal hierarchy [7]. Much like the assumption V ≠ L unlocks measurable cardinals and beyond, dropping the Axiom of Choice enables Reinhardt cardinals and stronger cardinals to be explored. Some major notions of large cardinals beyond choice have recently been standardized by Woodin et. al. [2], with questions raised regarding their interconnectedness. Part 1 of this dissertation partially answers two of those questions, while conjecturing, with a partial solution, a much stronger answer which would simplify the existing cardinal charts - that Regular Berkeley Cardinals …

Symmetric Presentation Of Finite Groups, And Related Topics, Marina Michelle Duchesne

Electronic Theses, Projects, and Dissertations

We have discovered original symmetric presentations for several finite groups, including 2²:^.(2⁴:(2^.S₃)), M₁₁, 3:(PSL(3,3):2), S₈, and 2^.M₁₂. We have found homomorphic images of several progenitors, including 2^*18:((6x2):6), 2^*24:(2^.S₄), 2^*105:A₇, 3^*3:_m(2³:3), 7^*8:_m(PSL(2,7):2), 3^*4:_m(4²:2²), 7^*5:(2xA₅), and 5^*6:_mS₅. We have provided the isomorphism type of …

Visualization Of Exact Invariant Solutions Associated With Atmospheric Waves In A Thin Circular Layer, Ranis N. Ibragimov, Lauren D. Mongrain, Benjamin Stimmel, Olga Trozkaya, Guang Lin, Sheng Zhang, Vesselin Vatchev, Daniel Stankiewicz

School of Mathematical & Statistical Sciences Faculty Publications

The purpose of the research was to investigate the exact solutions of nonlinear shallow water equations associated with planetary equatorial waves corresponding to the Cauchy-Poisson free boundary problem describing the nonstationary motion of an incompressible perfect fluid propagating around a solid circle. We consider water waves for which the ratio of the depth of fluid above the circular bottom to the radius of the circle is small (shallow water).

Coordinating Stem Core Courses For Student Success, Cristina Villalobos, Hyung Won Kim, Timothy J. Huber, Roger Knobel, Shaghayegh Setayesh, Lekshmi Sasidharan, Anahit Galstyan, Andras Balogh

School of Mathematical & Statistical Sciences Faculty Publications

Research indicates multi-section coordination improves the academic performance of students in STEM education. This paper describes the process of coordination in Precalculus, Calculus 1, and Calculus 2 courses undertaken by a large department that grew from the merger of two institutions through a pilot program, and a project grant. Components introduced in the project courses are documented, including collaborative problem-solving sessions, student learning assistants, Q&A sessions, and additional technology resources. Preliminary data is provided on the impacts of the initiative on student success. The study findings provide a template for coordination, faculty buy-in, and increased student engagement at similar institutions …

On The Socles Of Fully Inert Subgroups Of Abelian P-Groups, Andrey R. Chekhlov, Peter V. Danchev, Brendan Goldsmith

Articles

We define the so-called fully inert socle-regular and weakly fully inert socle-regular Abelian p-groups and study them with respect to certain of their numerous interesting properties. For instance, we prove that in the case of groups of length ω, these two group classes coincide, but that in the case of groups of length ω+1, they differ. Some structural and characterization results are also obtained. The work generalizes concepts which have been of interest recently in the theory of entropy in algebra and builds on recent investigations by Danchev and Goldsmith (Arch Math (3) 92:191–199, 2009; J Algebra 323:3020–3028, 2010).

On The Socles Of Characteristically Inert Subgroups Of Abelian P-Groups, Andrey R. Chekhlov, Peter V. Danchev, Brendan Goldsmith

Articles

We define the notion of a characteristically inert socle-regular Abelian p-group and explore such groups by focussing on their socles, thereby relating them to previously studied notions of socle-regularity. We show that large classes of p-groups, including all divisible, totally projective and torsion-complete p-groups, share this property when the prime p is odd. The present work generalizes notions of full inertia intensively studied recently by several authors and is a development of a recent work of the authors published in Mediterranean J. Math. (2021).

An Introduction To Obstacle Problems, Calvin Reedy

Honors Theses

The obstacle problem can be used to predict the shape of an elastic membrane lying over an obstacle in a domain Ω. In this paper we introduce and motivate a mathematical formulation for this problem, and give an example to demonstrate the need to search for solutions in non-classical settings. We then introduce Sobolev spaces as the proper setting for solutions, and prove that unique solutions exist in W1,2(Ω).

Overdose Prevention Sites Placement Informed By Simulation, Jing Dong

Honors Theses

In Philadelphia, people are experiencing the greatest opioid crisis in a century. Plac- ing the Overdose Prevention Site (OPS) can alleviate this crisis. However, the journey to the successful launch of the first OPS in the USA is rough. It was first accused of having a collision with federal drug laws. While Safehouse won the lawsuit and the OPS was judged to be legal in 2020, other pressure rose afterward such as the against from the public and the COVID19, which delayed the plan to open the OPS. Without solid research on the effectiveness of OPS, we thought it is …

How Risk-Related Statistics, As Reported In News And Social Media, Are Linked To The Use Of The Public Transit System, Prashiddhi Pokhrel

Thinking Matters Student Research Symposium

Due to the pandemic, people have started relying more on televisions, news, social media, and other news outlets for guidance. Moreover, with the increasing amount of news, data, and information there is also an increase in the amount of misleading statistics. People’s opinions and decisions significantly depend on the data, statistics, and information that they are exposed to, as well as their sources. For this project, we want to look at how information and its sources are affecting the decision made by the general public for the usage of the Portland Transit System. It is very important to know why …

The Impact Of Decriminalizing Marijuana In Rhode Island On The Number Of Narcotic Related Arrests And Quantities Seized, Abigail Kojoian

Mathematics & Computer Science Student Scholarship

Major: Mathematics
Minor: Classics
Faculty Mentor: Dr. Asta Shomberg, Mathematics

Solving Parabolic Interface Problems With A Finite Element Method, Henry Brown

Mathematics Student Work

Partial differential equations (PDEs) dominate mathematical models given their effectiveness and accuracy at modeling the physical realities which govern the world. Though we have these powerful tools, analytic solutions can only be found in the simplest of cases due to the complexity of PDE models. Thus, efficient and accurate computational methods are needed to approximate solutions to PDE models. One class of these methods are finite element methods which can be used domain to provide close approximations to the PDE model in a finite domain. In this presentation, we discuss the use of a Discontinuous Galerkin (DG) Finite Element Methods …

Modeling The Problem Of Integral Geometry On A Family Of Hyperbolic And Spherical Curves, Azamat Pirimbetov, N. Uteuliev, G. Djaykov

Karakalpak Scientific Journal

The problems of integral geometry in a strip on a family of curves of hyperbolic and spherical type are considered which have numerous applications in problems of geophysics, thermoacoustic and photoacoustic tomography. Explicit formulas are obtained for the Fourier image of the solution of integral geometry problems in the class of smooth compactly supported functions. Further, the obtained formulas are investigated for stability using numerical methods. To solve the problems, algorithms are constructed. Numerical and graphical results of applying these algorithms to solving the problems are presented.

Markov Chains And Their Applications, Fariha Mahfuz

Math Theses

Markov chain is a stochastic model that is used to predict future events. Markov chain is relatively simple since it only requires the information of the present state to predict the future states. In this paper we will go over the basic concepts of Markov Chain and several of its applications including Google PageRank algorithm, weather prediction and gamblers ruin.

We examine on how the Google PageRank algorithm works efficiently to provide PageRank for a Google search result. We also show how can we use Markov chain to predict weather by creating a model from real life data.

Bang The Can Slowly: An Investigation Into The 2017 Houston Astros, Ryan Elmore, Gregory J. Matthews

Mathematics and Statistics: Faculty Publications and Other Works

This article is a statistical investigation into the 2017 Major League Baseball scandal involving the Houston Astros, the World Series championship winner that the same year. The Astros were alleged to have stolen their opponents’ pitching signs in order to provide their batters with a potentially unfair advantage. This work finds compelling evidence that the Astros on-field performance was significantly affected by their sign-stealing ploy and quantifies the effects. The three main findings in the article are (i) the Astros’ odds of swinging at a pitch were reduced by approximately 27% (OR: 0.725, 95% CI: (0.618, 0.850)) when the sign …

Studies On Diagnostic Coverage And X-Sensitivity In Logic Circuits., Manjari Pradhan Dr.

Doctoral Theses

Today’s integrated circuits comprise billions of interconnected transistors assembled on a tiny silicon chip, and testing them to ensure functional and timing correctness continues to be a major challenge to designers and test engineers with further downscaling of transistors. Although substantial progress has been witnessed during the last five decades in the area of algorithmic test generation and fault diagnosis, applications of combinatorial and machinelearning (ML) techniques to solve these problems remain largely unexplored till date. In this thesis, we study three problems in the context of digital logic test and diagnosis. The first problem is that of fault diagnosis …