Digital Commons Network^™

Mitigation Impact Of Statewide Non-Pharmaceutical Policies On Covid-19: An Application Of Infectious Disease Transmission Model And Partially Observed Markov Process To New Mexico, Xingya Ma

Mathematics & Statistics ETDs

This thesis is an application of epidemiological models for infectious disease transmission and the use of partially observed Markov process (POMP) for model fitting. It focuses on COVID-19 pandemic in the state of New Mexico. The analysis covered March 2020 to June 2021. Daily data of COVID19 cases and deaths and a daily index of eleven statewide government non-pharmaceutical intervention (NPI) policies were collected from six public sources and were validated. These data were integrated through the Susceptible-Exposed-Infected-Removed (SEIR) model. Estimated daily transmission rates between the model compartments quantify the impact of the mitigation policies, and show that transmission rates …

Convexity Of Regularized Optimal Transport Dissimilarity Measures For Signed Signals, Christian P. Fowler

Mathematics & Statistics ETDs

Debiased Sinkhorn divergence (DS divergence) is a distance function of

regularized optimal transport that measures the dissimilarity between two

probability measures of optimal transport. This thesis analyzes the advantages of

using DS divergence when compared to the more computationally expensive

Wasserstein distance as well as the classical Euclidean norm. Specifically, theory

and numerical experiments are used to show that Debiased Sinkhorn divergence

has geometrically desirable properties such as maintained convexity after data

normalization. Data normalization is often needed to calculate Sinkhorn

divergence as well as Wasserstein distance, as these formulas only accept

probability distributions as inputs and do not directly …

Statistical Methods For Differential Gene Expression Analysis Under The Case-Cohort Design, Lidong Wang

Mathematics & Statistics ETDs

Differential gene expression analysis has the potential to discover candidate biomarkers, therapeutic targets, and gene signatures. How to save money when using an unaffordable sample is a practical question. The case-cohort (CCH) study design can blend the economy of case-control studies with the advantages of cohort studies. But it has not been seen in the medical research literature where high-throughput genomic data were involved.

A score test does not need to fit the Cox PH model iteratively; hence, it can save computing time and avoid potential convergence issues. We developed a score test under the CCH design to identify DEGs …

Functional Data Analysis Of Covid-19, Nichole L. Fluke

Mathematics & Statistics ETDs

This thesis deals with Functional Data Analysis (FDA) on COVID data. The Data involves counts for new COVID cases, hospitalized COVID patients, and new COVID deaths. The data used is for all the states and regions in the United States. The data starts in March 1^st, 2020 and goes through March 31^st, 2021. The FDA smooths the data and looks to see if there are similarities or differences between the states and regions in the data. The data also shows which states and regions stand out from the others and which ones are similar. Also shown …

Music Genre Classification By Convolutional Neural Networks, Usame Suud

Mathematics & Statistics ETDs

In today’s world, deep learning models are widely used in a variety of fields. Audio

applications include speech recognition, audio classification, and music information

retrieval. In this paper, we will focus on the classification of music genres using an

artificial neural network. The development of audio machine learning techniques has

created an independence from traditional, more time-consuming signal processing

techniques. Starting with raw audio data, we will gain an understanding of what

audio is and its digital representation. Then, the focus will be on obtaining frequency

information from audio signals through the use of spectrograms. Transforming the

spectrograms into the …

Determining The Idealizers Of Principal Monomial Ideals Over A Rational Normal Curve, Perla A. Maldonado Cortez

Mathematics & Statistics ETDs

Given an ideal J generated by an element of the form sm1 tm2 , where
m1 ≥ 2 and m2 ≥ 0, we illustrate how to compute the idealizer I(J) over the ring
of the rational normal curve of degree n and we give a formula for it using the
graded pieces of the sets of differential operators.

Machine Learning Model Comparison And Arma Simulation Of Exhaled Breath Signals Classifying Covid-19 Patients, Aaron Christopher Segura

Mathematics & Statistics ETDs

This study compared the performance of machine learning models in classifying COVID-19 patients using exhaled breath signals and simulated datasets. Ground truth classification was determined by the gold standard Polymerase Chain Reaction (PCR) test results. A residual bootstrapped method generated the simulated datasets by fitting signal data to Autoregressive Moving Average (ARMA) models. Classification models included neural networks, k-nearest neighbors, naïve Bayes, random forest, and support vector machines. A Recursive Feature Elimination (RFE) study was performed to determine if reducing signal features would improve the classification models performance using Gini Importance scoring for the two classes. The top 25% of …

Robust Uncertainty Quantification With Analysis Of Error In Standard And Non-Standard Quantities Of Interest, Zachary Stevens

Mathematics & Statistics ETDs

This thesis derives two Uncertainty Quantification (UQ) methods for differential equations that depend on random parameters: (\textbf{i}) error bounds for a computed cumulative distribution function (\textbf{ii}) a multi-level Monte Carlo (MLMC) algorithm with adaptively refined meshes and accurately computed stopping-criteria. Both UQ approaches utilize adjoint-based \textit{a posteriori} error analysis in order to accurately estimate the error in samples of numerically approximated quantities of interest. The adaptive MLMC algorithm developed in this thesis relies on the adjoint-based error analysis to adaptively create meshes and accurately monitor a stopping criteria. This is in contrast to classical MLMC algorithms which employ either a …

Effect Of Phylogeny Misestimation On Estimating Trait Evolution Parameters, Tabytha Ariel Perez

Mathematics & Statistics ETDs

Biologists are interested in estimating trait evolution models from phylogenies. However, phylogenies are imperfectly estimated, generally from DNA sequence data. In this study, true phylogenies are simulated to understand whether errors in phylogeny estimation affect inference of the trait evolution model. Given the tree, DNA sequences as well as traits are then simulated from the true phylogeny; both are simulated independently from the other. After the simulation, the DNA sequences were used to estimate trees using the UPGMA method without utilizing the trait information. The estimated trees combined with the traits are used to infer the evolutionary trait models, specifically …

The Obata First Eigenvalue Theorem On A Seven Dimensional Quaternionic Contact Manifold, Abdelrahman Mohamed

Mathematics & Statistics ETDs

We prove an Obata-type rigidity result for the first eigenvalue of the sub-Laplacian on a compact seven dimensional quaternionic contact (QC) manifold which satisfies a Lichnerowicz-type bound on its QC-Ricci tensor, and has a non-negative Paneitz P -function. In particular, under the stated conditions, the lowest possible eigenvalue of the sub-Laplacian is achieved if and only if the manifold is QC-equivalent to the standard 3-Sasakian sphere.

Applications Of Machine Learning Algorithms In Materials Science And Bioinformatics, Mohammed Quazi

Mathematics & Statistics ETDs

The piezoelectric response has been a measure of interest in density functional theory (DFT) for micro-electromechanical systems (MEMS) since the inception of MEMS technology. Piezoelectric-based MEMS devices find wide applications in automobiles, mobile phones, healthcare devices, and silicon chips for computers, to name a few. Piezoelectric properties of doped aluminum nitride (AlN) have been under investigation in materials science for piezoelectric thin films because of its wide range of device applicability. In this research using rigorous DFT calculations, high throughput ab-initio simulations for 23 AlN alloys are generated.

This research is the first to report strong enhancements of piezoelectric properties …

Sparse Spectral-Tau Method For The Two-Dimensional Helmholtz Problem Posed On A Rectangular Domain, Gabriella M. Dalton

Mathematics & Statistics ETDs

Within recent decades, spectral methods have become an important technique in numerical computing for solving partial differential equations. This is due to their superior accuracy when compared to finite difference and finite element methods. For such spectral approximations, the convergence rate is solely dependent on the smoothness of the solution yielding the potential to achieve spectral accuracy. We present an iterative approach for solving the two-dimensional Helmholtz problem posed on a rectangular domain subject to Dirichlet boundary conditions that is well-conditioned, low in memory, and of sub-quadratic complexity. The proposed approach spectrally approximates the partial differential equation by means of …

Middle School Students Communicating Computational Thinking: A Systemic Functional Linguistics-Case Study Of Bilingual, Collaborative Teaching/Learning Of Computer Programming In Python, Jose Antonio Lecea Yanguas

Language, Literacy, and Sociocultural Studies ETDs

This dissertation presents the first Systemic Functional Linguistics-based analysis of the teaching/learning of computational thinking through computer programming and comprehensive analysis of discourse of a whole computer programming course at any educational level. The current educational research raises questions about the nature of authentic computational

vii

thinking teaching/learning environments and how they happen moment-to-moment. In one such environment, I examined the discourse of a facilitator, three students, and their Language Arts teacher in an introductory middle school after-school course (approximately 30 hours) in spring 2017 as students created a video in Python.

Methodologically, I show how a Systemic Functional Linguistics-based …

Eigenfunction Restriction Estimates For Curves With Nonvanishing Geodesic Curvatures In Compact Riemannian Surfaces With Nonpositive Sectional Curvatures, Chamsol Park

Mathematics & Statistics ETDs

For 2 ≤ p < 4, we study the Lp norms of restrictions of eigenfunctions of the Laplace-Beltrami operator on smooth compact 2-dimensional Riemannian manifolds. Burq, G\´erard, and Tzvetkov [12], and Hu [21] found eigenfunction restriction estimates for a curve with nonvanishing geodesic curvatures. We will explain how the proof of the known estimates helps us to consider the case where the given smooth compact Riemannian manifold has nonpositive sectional curvatures. For p = 4, we will also obtain a logarithmic analogous estimate, by using arguments in Xi and Zhang [37], Sogge [33], and Bourgain [10]. At the end of this dissertation, we will talk about a future work, which is a follow up study for higher dimensional analogues of the above curve cases.

Intra-Hour Solar Forecasting Using Cloud Dynamics Features Extracted From Ground-Based Infrared Sky Images, Guillermo Terrén-Serrano

Electrical and Computer Engineering ETDs

Due to the increasing use of photovoltaic systems, power grids are vulnerable to the projection of shadows from moving clouds. An intra-hour solar forecast provides power grids with the capability of automatically controlling the dispatch of energy, reducing the additional cost for a guaranteed, reliable supply of energy (i.e., energy storage). This dissertation introduces a novel sky imager consisting of a long-wave radiometric infrared camera and a visible light camera with a fisheye lens. The imager is mounted on a solar tracker to maintain the Sun in the center of the images throughout the day, reducing the scattering effect produced …

Soft Set Product Extended To Hypersoft Set And Indetermsoft Set Product Extended To Indetermhypersoft Set, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we define the Soft Set Product as a product of many soft sets and afterwards we extend it to the HyperSoft Set. Similarly, the IndetermSoft Product is extended to the IndetermHyperSoft Set. We also present several applications of the Soft Set Product to Fuzzy (and fuzzy-extensions) Soft Set Product and to IndetermSoft Set and IndetermHyperSoft Set.

Linguistic Matrices, W. B. Vasantha Kandasamy, K. Ilanthenral, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The authors build linguistic matrices only for those linguistic variables which yield a linguistic continuum or an ordered linguistic set. Most of the properties enjoyed by real and complex matrices are satisfied by these linguistic matrices. However, we see when we try to define operations on linguistic matrices that they behave in different ways. The possible operations defined on linguistic matrices are only the maximum and minimum. Further, we have different identities for min and max operations on these matrices for linguistic variable and its associated linguistic words.

On Neutrosophic Αψ -Supra Open Sets, Mani Parimala, Muthusamy Karthika, Harish Garg, Saeid Jafari, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic topological space is an extension of fuzzy topology. Neutrosophic topological space addresses each element’s membership, indeterminacy and non-membership grades. Dropping an axiom in the neutrosophic topological space produces a new topological space called neutrosophic supra topological space. Elements in this neutrosophic supra topology are neutrosophic sets. We established the neutrosophic αψ-supra open set in neutrosophic supra topological spaces in this paper. Also, we investigate the properties of the newly defined set. Neutrosophic αψ -supra continuity is introduced and studied subsequently.

Collected Papers (On Neutrosophic Theory And Its Applications In Algebra), Volume Ix, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This ninth volume of Collected Papers includes 87 papers comprising 982 pages on Neutrosophic Theory and its applications in Algebra, written between 2014-2022 by the author alone or in collaboration with 81 co-authors from 19 countries.

نيوتروسوفيك أوفرسيت ، نيوتروسوفيك أونديرست ، وإزاحة نيوتروسوفيك [Neutrosophic Overset, Neutrosophic Underset, And Neutrosophic Offset], Florentin Smarandache, Riad K Al-Hamido (Translator From English To Arabic)), Khaled Adnan Alabdullah (Translator From English To Arabic)

Branch Mathematics and Statistics Faculty and Staff Publications

تم تعريف Neutrosophic Over-/ Under- / Off-Set and -Logic لأول مرة بواسطة Smarandache في عام 1995 ونشر في عام 2007. وهي مختلفة تمامًا عن المجموعات / المنطق / الاحتمالات الأخرى. قام بتمديد مجموعة العدلات على التوالي إلى Neutrosophic Overset {عندما يكون بعض مكونات neutrosophic> 1} ، Neutrosophic Underset {عندما يكون بعض مكونات neutrosophic <0} ، وإلى إزاحة Neutrosophic {عندما تكون بعض مكونات العدلات خارج الفاصل الزمني [0 ، 1] ، أي بعض مكونات العدلات> 1 ومكونات أخرى نيوتروسوفيك <0}. هذا ليس مفاجئًا فيما يتعلق بالمجموعة / المنطق الغامض الكلاسيكي ، أو المجموعة / المنطق الغامض الحدسي ، أو الاحتمال الكلاسيكي / غير الدقيق ، حيث لا يُسمح بالقيم خارج الفاصل الزمني [0 ، 1] ، نظرًا لأن عالمنا الحقيقي به العديد من الأمثلة و تطبيقات المكونات الزائدة / السفلية / البعيدة عن العدلات

Neutrosophic Over-/Under-/Off-Set and -Logic were defined for the first time by Smarandache in 1995 and published in 2007. They are totally different from other sets/logics/probabilities. He extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is > 1}, Neutrosophic Underset {when …

Collected Papers (On Neutrosophic Theory And Applications), Volume Viii, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This eighth volume of Collected Papers includes 75 papers comprising 973 pages on (theoretic and applied) neutrosophics, written between 2010-2022 by the author alone or in collaboration with 102 co-authors from 24 countries.

Introduction To Plithogenic Sociogram With Preference Representations By Plithogenic Number, Nivetha Martin, Florentin Smarandache, R. Priya

Branch Mathematics and Statistics Faculty and Staff Publications

The theory of Plithogeny is gaining momentum in recent times as it generalizes the concepts of fuzzy, intuitionistic fuzzy, neutrosophy and other extended representations of fuzzy sets. The relativity of the comprehensive and accommodative nature of plithogenic sets in dealing with attributes shall be applied to handle the decision–making problems in the field of sociology. This paper introduces the concepts of Plithogenic Sociogram (PS) and Plithogenic Number (PN) where the former is the integration of plithogeny to the sociometric technique of sociogram and the latter is the generalization of fuzzy, intuitionistic fuzzy and neutrosophic numbers that shall be used in …

New Development Of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, And Neutrosophic Plithogenic Optimizations, Florentin Smarandache, Yanhui Guo

Branch Mathematics and Statistics Faculty and Staff Publications

This collective book presents state-of-the-art papers on new topics related to neutrosophic theories, such as neutrosophic algebraic structures, neutrosophic triplet algebraic structures, neutrosophic extended triplet algebraic structures, neutrosophic algebraic hyperstructures, neutrosophic triplet algebraic hyperstructures, neutrosophic n-ary algebraic structures, neutrosophic n-ary algebraic hyperstructures, refined neutrosophic algebraic structures, refined neutrosophic algebraic hyperstructures, quadruple neutrosophic algebraic structures, refined quadruple neutrosophic algebraic structures, neutrosophic image processing, neutrosophic image classification, neutrosophic computer vision, neutrosophic machine learning, neutrosophic artificial intelligence, neutrosophic data analytics, neutrosophic deep learning, and neutrosophic symmetry, as well as their applications in the real world.

Introduction To Superhyperalgebra And Neutrosophic Superhyperalgebra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we recall our concepts of n th-Power Set of a Set, SuperHyperOperation, SuperHyperAxiom, SuperHyperAlgebra, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom and Neutrosophic SuperHyperAlgebra. In general, in any field of knowledge, one actually encounters SuperHyperStructures (or more accurately (m, n)- SuperHyperStructures).

The Reciprocal Of The Butterfly Theorem, Ion Patrascu, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Linguistic Functions, W. B. Vasantha Kandasamy, K. Ilanthenral, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, the authors have proved the analogues of the Bolzano Weierstrass theorem for the linguistic version. Several concepts in the case of linguistic continuum are very distinct from the natural classical real continuum. Categorically, we have three linguistic variables: one leading to a continuum, some finite and orderable set, and some not orderable. We define a linguistic plane associated with linguistic variables and give graphs associated with linguistic functions.

Linguistic Graphs And Their Applications, W. B. Vasantha Kandasamy, K. Ilanthenral, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The authors define the notion of directed linguistic graphs and linguistic-weighted graphs.

The second chapter discusses all types of linguistic graphs, linguistic dyads, linguistic triads, linguistic wheels, complete linguistic graphs, connected linguistic graphs, disconnected linguistic graphs, and linguistic components of the graphs. Further we define the notion of linguistic subgraphs of a linguistic graph. The third chapter also introduces the notion of Linguistic Cognitive Maps (LCMs) analogous to Fuzzy Cognitive maps (FCMs). We also propose Linguistic relational Maps, which are analogous to Fuzzy Relational Maps. These models find applications in problems whose data is unsupervised, but the values are linguistic.

Linguistic Geometry And Its Applications, W. B. Vasantha Kandasamy, K. Ilanthenral, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The authors venture to define the notion of linguistic geometry in this book.

It is pertinent to keep on the record that linguistic geometry differs from the classical geometry.

Many fundamental concepts and notions of classical geometry are not valid or extendable in the case of linguistic geometry.

We discuss in dept the linguistic variables, graphs and geometry essential for social information networks.

And then develop the new notion of linguistic geometry and its related properties.

The concept of linguistic social information geometric networks is also developed.

Linguistic Semilinear Algebras And Linguistic Semivector Spaces, W. B. Vasantha Kandasamy, K. Ilanthenral, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This book introduces algebraic structures on linguistic sets associated with a linguistic variable.

The linguistics with single closed binary operations are only semigroups and monoids. Authors feel it is not possible to define the notion of linguistic group.

We describe the new notion of linguistic semirings, linguistic semifields, linguistic semivector spaces, and linguistic semilinear algebras defined over linguistic semifields.

We also define algebraic structures on linguistic subsets of a linguistic set associated with a linguistic variable.

Collected Papers (On Various Scientific Topics), Volume Xiii, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This thirteenth volume of Collected Papers is an eclectic tome of 88 papers in various fields of sciences, such as astronomy, biology, calculus, economics, education and administration, game theory, geometry, graph theory, information fusion, decision making, instantaneous physics, quantum physics, neutrosophic logic and set, non-Euclidean geometry, number theory, paradoxes, philosophy of science, scientific research methods, statistics, and others, structured in 17 chapters (Neutrosophic Theory and Applications; Neutrosophic Algebra; Fuzzy Soft Sets; Neutrosophic Sets; Hypersoft Sets; Neutrosophic Semigroups; Neutrosophic Graphs; Superhypergraphs; Plithogeny; Information Fusion; Statistics; Decision Making; Extenics; Instantaneous Physics; Paradoxism; Mathematica; Miscellanea), comprising 965 pages, published between 2005-2022 in different …