Dimension Reduction Techniques For High Dimensional And Ultra-High Dimensional Data, 2019 New Jersey Institute of Technology

#### Dimension Reduction Techniques For High Dimensional And Ultra-High Dimensional Data, Subha Datta

*Dissertations*

This dissertation introduces two statistical techniques to tackle high-dimensional data, which is very commonplace nowadays. It consists of two topics which are inter-related by a common link, dimension reduction.

The first topic is a recently introduced classification technique, the weighted principal support vector machine (WPSVM), which is incorporated into a spatial point process framework. The WPSVM possesses an additional parameter, a weight parameter, besides the regularization parameter. Most statistical techniques, including WPSVM, have an inherent assumption of independence, which means the data points are not connected with each other in any manner. But spatial data violates this assumption. Correlation between ...

Algorithms For Mappings And Symmetries Of Differential Equations, 2019 The University of Western Ontario

#### Algorithms For Mappings And Symmetries Of Differential Equations, Zahra Mohammadi

*Electronic Thesis and Dissertation Repository*

Differential Equations are used to mathematically express the laws of physics and models in biology, finance, and many other fields. Examining the solutions of related differential equation systems helps to gain insights into the phenomena described by the differential equations. However, finding exact solutions of differential equations can be extremely difficult and is often impossible. A common approach to addressing this problem is to analyze solutions of differential equations by using their symmetries. In this thesis, we develop algorithms based on analyzing infinitesimal symmetry features of differential equations to determine the existence of invertible mappings of less tractable systems of ...

Personalized Detection Of Anxiety Provoking News Events Using Semantic Network Analysis, 2019 Southern Methodist University

#### Personalized Detection Of Anxiety Provoking News Events Using Semantic Network Analysis, Jacquelyn Cheun Phd, Luay Dajani, Quentin B. Thomas

*SMU Data Science Review*

In the age of hyper-connectivity, 24/7 news cycles, and instant news alerts via social media, mental health researchers don't have a way to automatically detect news content which is associated with triggering anxiety or depression in mental health patients. Using the Associated Press news wire, a semantic network was built with 1,056 news articles containing over 500,000 connections across multiple topics to provide a personalized algorithm which detects problematic news content for a given reader. We make use of Semantic Network Analysis to surface the relationship between news article text and anxiety in readers who struggle ...

A Data Driven Approach To Forecast Demand, 2019 Southern Methodist University

#### A Data Driven Approach To Forecast Demand, Hannah Kosinovsky, Sita Daggubati, Kumar Ramasundaram, Brent Allen

*SMU Data Science Review*

Abstract. In this paper, we present a model and methodology for accurately predicting the following quarter’s sales volume of individual products given the previous five years of sales data. Forecasting product demand for a single supplier is complicated by seasonal demand variation, business cycle impacts, and customer churn. We developed a novel prediction using machine learning methodology, based upon a Dense neural network (DNN) model that implicitly considers cyclical demand variation and explicitly considers customer churn while minimizing the least absolute error between predicted demand and actual sales. Using parts sales data for a supplier to the oil and ...

Intermediate C∗-Algebras Of Cartan Embeddings, 2019 jonathan.henry.brown@gmail.com

#### Intermediate C∗-Algebras Of Cartan Embeddings, Jonathan H. Brown, Ruy Exel, Adam H. Fuller, David R. Pitts, Sarah A. Reznikoff

*Faculty Publications, Department of Mathematics*

Let A be a C*-algebra and let D be a Cartan subalgebra of A. We study the following question: if B is a C*-algebra such that D B A, is D a Cartan subalgebra of B? We give a positive answer in two cases: the case when there is a faithful conditional expectation from A onto B, and the case when A is nuclear and D is a C*-diagonal of A. In both cases there is a one-to-one correspondence between the intermediate C*-algebras B, and a class of open subgroupoids of the groupoid G, where ! G ...

Image Restoration Using Automatic Damaged Regions Detection And Machine Learning-Based Inpainting Technique, 2019 Chapman University

#### Image Restoration Using Automatic Damaged Regions Detection And Machine Learning-Based Inpainting Technique, Chloe Martin-King

*Computational and Data Sciences (PhD) Dissertations*

In this dissertation we propose two novel image restoration schemes. The first pertains to automatic detection of damaged regions in old photographs and digital images of cracked paintings. In cases when inpainting mask generation cannot be completely automatic, our detection algorithm facilitates precise mask creation, particularly useful for images containing damage that is tedious to annotate or difficult to geometrically define. The main contribution of this dissertation is the development and utilization of a new inpainting technique, region hiding, to repair a single image by training a convolutional neural network on various transformations of that image. Region hiding is also ...

Individual Based Model To Simulate The Evolution Of Insecticide Resistance, 2019 University of Nebraska - Lincoln

#### Individual Based Model To Simulate The Evolution Of Insecticide Resistance, William B. Jamieson

*Dissertations, Theses, and Student Research Papers in Mathematics*

Insecticides play a critical role in agricultural productivity. However, insecticides impose selective pressures on insect populations, so the Darwinian principles of natural selection predict that resistance to the insecticide is likely to form in the insect populations. Insecticide resistance, in turn, severely reduces the utility of the insecticides being used. Thus there is a strong economic incentive to reduce the rate of resistance evolution. Moreover, resistance evolution represents an example of evolution under novel selective pressures, so its study contributes to the fundamental understanding of evolutionary theory.

Insecticide resistance often represents a complex interplay of multiple fitness trade-offs for individual ...

Determinism Of Stochastic Processes Through The Relationship Between The Heat Equation And Random Walks, 2019 CUNY New York City College of Technology

#### Determinism Of Stochastic Processes Through The Relationship Between The Heat Equation And Random Walks, Gurmehar Singh Makker

*Publications and Research*

We study the deterministic characteristics of stochastic processes through investigation of random walks and the heat equation. The relationship is confirmed by discretizing the heat equation in time and space and determining the probability distribution function for random walks in dimension d = 1, 2. The existence of the relationship is presented both through theoretical analysis and numerical computation.

Joule's 19th Century Energy Conservation Meta-Law And The 20th Century Physics (Quantum Mechanics And General Relativity): 21st Century Analysis, 2019 University of Texas at El Paso

#### Joule's 19th Century Energy Conservation Meta-Law And The 20th Century Physics (Quantum Mechanics And General Relativity): 21st Century Analysis, Vladik Kreinovich, Olga Kosheleva

*Departmental Technical Reports (CS)*

Joule's Energy Conservation Law was the first "meta-law": a general principle that all physical equations must satisfy. It has led to many important and useful physical discoveries. However, a recent analysis seems to indicate that this meta-law is inconsistent with other principles -- such as the existence of free will. We show that this conclusion about inconsistency is based on a seemingly reasonable -- but simplified -- analysis of the situation. We also show that a more detailed mathematical and physical analysis of the situation reveals that not only Joule's principle remains true -- it is actually strengthened: it is no longer ...

Multi-Point Flux Approximations Via The O-Method, 2019 University of Southern Mississippi

#### Multi-Point Flux Approximations Via The O-Method, Christen Leggett

*Master's Theses*

When an oil refining company is drilling for oil, much of the oil gets left behind after the first drilling. Enhanced oil recovery techniques can be used to recover more of that oil, but these methods are quite expensive. When a company is deciding if it is worth their time and money to use enhanced oil recovery methods, simulations can be used to model oil flow, showing the behavior and location of the oil. While methods do exist to model this flow, these methods are often very slow and inaccurate due to a large domain and wide variance in coefficients ...

Function Space Tensor Decomposition And Its Application In Sports Analytics, 2019 East Tennessee State University

#### Function Space Tensor Decomposition And Its Application In Sports Analytics, Justin Reising

*Electronic Theses and Dissertations*

Recent advancements in sports information and technology systems have ushered in a new age of applications of both supervised and unsupervised analytical techniques in the sports domain. These automated systems capture large volumes of data points about competitors during live competition. As a result, multi-relational analyses are gaining popularity in the field of Sports Analytics. We review two case studies of dimensionality reduction with Principal Component Analysis and latent factor analysis with Non-Negative Matrix Factorization applied in sports. Also, we provide a review of a framework for extending these techniques for higher order data structures. The primary scope of this ...

Recover Data In Sparse Expansion Forms Modeled By Special Basis Functions, 2019 University of Missouri-St. Louis

#### Recover Data In Sparse Expansion Forms Modeled By Special Basis Functions, Abdulmtalb Mohamed Hussen

*Dissertations*

In data analysis and signal processing, the recovery of structured functions (in terms of frequencies and coefficients) with respect to certain basis functions from the given sampling values is a fundamental problem. The original Prony method is the main tool to solve this problem, which requires the equispaced sampling values.

In this dissertation, we use the equispaced sampling values in the frequency domain after the short time Fourier transform in order to reconstruct some signal expansions, such as the exponential expansions and the cosine expansions. In particular, we consider the case that the phase of the cosine expansion is quadratic ...

Optimal Relaxation Weights For Multigrid Reduction In Time (Mgrit), 2019 University of New Mexico

#### Optimal Relaxation Weights For Multigrid Reduction In Time (Mgrit), Masumi Sugiyama

*Mathematics & Statistics ETDs*

Based on current trends in computer architectures, faster compute speeds must come from increased parallelism rather than increased clock speeds, which are stagnate. This situation has created the well-known bottleneck for sequential time-integration, where each individual time-value (i.e., time-step) is computed sequentially. One approach to alleviate this and achieve parallelism in time is with multigrid. In this work, we consider the scheme known as multigrid-reduction-in-time (MGRIT), but note that there exist other parallel-in-time methods such as parareal and the parallel full approximation scheme in space and time (PFASST). MGRIT is a full multi-level method applied to the time dimension ...

The Frequency Response Modeling Of Linear Systems, 2019 University of North Georgia

#### The Frequency Response Modeling Of Linear Systems, Wynn Kwiatkowski

*Georgia Undergraduate Research Conference (GURC)*

The purpose of this project is to identify a general linear system based on certain sinusoidal inputs so we are able to understand the dynamics of a system. The concept previously mentioned, known as frequency response modeling, has many applications in chemistry, hospital science, mathematics, laser technology, and more. This project uses differential equations and the Laplace transform to model and solve linear systems based on a certain sinusoidal input. This project uses the transfer function of a linear system to create a mathematical identity to create two Bode plots of a general linear system. Complex numbers are also integrated ...

Investigations Of The Cohesion Of Nanoscale Bioactive With Titanium: A Molecular Dyanmics Approach Using Density Functional Theory And The Kohn-Sham Framework., 2019 University of North Georgia

#### Investigations Of The Cohesion Of Nanoscale Bioactive With Titanium: A Molecular Dyanmics Approach Using Density Functional Theory And The Kohn-Sham Framework., Jerry Magaña

*Georgia Undergraduate Research Conference (GURC)*

ABSTRACT: In order to overcome the complications evolved with certain kinds of bone-replacement surgeries, especial in the field of dentistry, it has become common for manufactures of bone-prosthetic to apply a nano-scale, bioactive coating that improves the rate of integration with the host bone tissue (a process known as osseointegration). The most frequently used bio-active compound is hydroxyapite, or HaP. These coatings are applied to a titanium substrate via one of several application methods. One of the most pressing issues with these coatings is the problem of mechanical stability of the implant, which is undermined by a weaker bond between ...

How Can We Explain Different Number Systems?, 2019 University of Texas at El Paso

#### How Can We Explain Different Number Systems?, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich

*Departmental Technical Reports (CS)*

At present, we mostly use decimal (base-10) number system, but in the past, many other systems were used: base-20, base-60 -- which is still reflected in how we divide an hour into minutes and a minute into seconds -- and many others. There is a known explanation for the base-60 system: 60 is the smallest number that can be divided by 2, by 3, by 4, by 5, and by 6. Because of this, e.g., half an hour, one-third of an hour, all the way to one-sixth of an hour all correspond to a whole number of minutes. In this paper ...

Deep Learning (Partly) Demystified, 2019 University of Texas at El Paso

#### Deep Learning (Partly) Demystified, Vladik Kreinovich, Olga Kosheleva

*Departmental Technical Reports (CS)*

Successes of deep learning are partly due to appropriate selection of activation function, pooling functions, etc. Most of these choices have been made based on empirical comparison and heuristic ideas. In this paper, we show that many of these choices -- and the surprising success of deep learning in the first place -- can be explained by reasonably simple and natural mathematics.

The Graphs That Have Antivoltages Using Groups Of Small Order, 2019 Wright State University - Main Campus

#### 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.

Model-Form Uncertainty Quantification For Predictive Probabilistic Graphical Models, 2019 University of Massachusetts Amherst

#### Model-Form Uncertainty Quantification For Predictive Probabilistic Graphical Models, Jinchao Feng

*Doctoral Dissertations*

In this thesis, we focus on Uncertainty Quantification and Sensitivity Analysis, which can provide performance guarantees for predictive models built with both aleatoric and epistemic uncertainties, as well as data, and identify which components in a model have the most influence on predictions of our quantities of interest.

In the first part (Chapter 2), we propose non-parametric methods for both local and global sensitivity analysis of chemical reaction models with correlated parameter dependencies. The developed mathematical and statistical tools are applied to a benchmark Langmuir competitive adsorption model on a close packed platinum surface, whose parameters, estimated from quantum-scale computations ...

Equators Have At Most Countable Many Singularities With Bounded Total Angle, 2019 University of Pennsylvania

#### Equators Have At Most Countable Many Singularities With Bounded Total Angle, Pilar Herreros, Mario Ponce, J.J.P. Veerman

*J. J. P. Veerman*

For distinct points p and q in a two-dimensional Riemannian manifold, one defines their mediatrix Lpq as the set of equidistant points to p and q. It is known that mediatrices have a cell decomposition consisting of a finite number of branch points connected by Lipschitz curves. In the case of a topological sphere, mediatrices are called equators and it can benoticed that there are no branching points, thus an equator is a topological circle with possibly many Lipschitz singularities. This paper establishes that mediatrices have the radial …