Mathematics Commons^™

Functional Singular Spectrum Analysis, Hossein Haghbin, Seyed Morteza Najibi, Rahim Mahmoudvand, Jordan Trinka, Mehdi Maadooliat

Mathematical and Statistical Science Faculty Research and Publications

In this paper, we develop a new extension of the singular spectrum analysis (SSA) called functional SSA to analyze functional time series. The new methodology is constructed by integrating ideas from functional data analysis and univariate SSA. Specifically, we introduce a trajectory operator in the functional world, which is equivalent to the trajectory matrix in the regular SSA. In the regular SSA, one needs to obtain the singular value decomposition (SVD) of the trajectory matrix to decompose a given time series. Since there is no procedure to extract the functional SVD (fSVD) of the trajectory operator, we introduce a computationally …

Tractor Connections For Killing Tensors And Their Generalizations, Benjamin D. Shaw

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We create new symbolic software tools for the analysis of Killing tensors. Central to our work is the construction of the tractor connection defined on the tractor bundle, which allows one to obtain information about the space of Killing tensors without solving the Killing equations–an approach termed the tractor approach. We give a new application of the tractor approach which allows one to more easily check explicitly for linear independence of a given set of Killing tensors. We develop software to implement such methods in the case of rank 2 Killing tensors; similarly, we develop software to implement analogous methods …

On The Geometry Of The Moduli Space Of Certain Lattice Polarized K3 Surfaces And Their Picard-Fuchs Operators, Michael T. Schultz

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

K3 surfaces have a long and rich study in mathematics, and more recently in physics via string theory. Often, K3 surfaces come in multiparameter families - the parameters describing these surfaces fit together to form their own geometric space, a so-called moduli space. In particular, the moduli spaces of K3 surfaces equipped with a lattice polarization can sometimes be constructed explicitly, which subsequently reveals important information about the original K3 surface.

In this work, we construct such families explicitly from certain rational elliptic surfaces via the so-called mixed-twist construction of Doran & Malmendier, which in turn produces the moduli …

Finite Groups In Which The Number Of Cyclic Subgroups Is 3/4 The Order Of The Group, James Alexander Cayley

Graduate Theses/Dissertations

Let $G$ be a finite group, c(G) denotes the number of cyclic subgroups of G and α(G) = c(G)/|G|. In this thesis we go over some basic properties of alpha, calculate alpha for some families of groups, with an emphasis on groups with α(G) = 3/4, as all groups with α(G) > 3/4 have been classified by Garonzi and Lima (2018). We find all Dihedral group with this property, show all groups with α(G) = 3/4 have at least |G|/2-1 involutions, and discuss existing work by Wall (1970) and Miller (1919) classifying all such groups.

A Statistical Comparison Of Covid-19 In The United States Across Political Affiliations And Census Regions, Margarito Torres

Theses and Dissertations

In mid-January 2020, the United States reported their first cases of the coronavirus disease (COVID-19) from a passenger returning from Wuhan, China. Initially, the situation wasn’t very alarming as in China and European countries, but the situation began to worsen in March 2020 when the number of cases began to multiply. Then, in a matter of a few months, the United States became the number one country in terms of total cases and total deaths from COVID-19. We have been closely observing the United States and the world since July 2020. Our study aims to compare the political affiliations and …

Linear Algebra For Computer Science, M. Thulasidas

Research Collection School Of Computing and Information Systems

This textbook introduces the essential concepts and practice of Linear Algebra to the undergraduate student of computer science. The focus of this book is on the elegance and beauty of the numerical techniques and algorithms originating from Linear Algebra. As a practical handbook for computer and data scientists, LA4CS restricts itself mostly to real fields and tractable discourses, rather than deep and theoretical mathematics.

Consolidation Of Mobile Sands With Ameliorants And Phytomelioration, Sharibay Toremuratov, Bakhtiyar Ismailov

Karakalpak Scientific Journal

The results of even a few experiments show the possibility of obtaining a tangible effect when jointly carrying out chemical reclamation and phytomelioration. Reliable habitation of plants is a guarantee of further long-term stopping of the movement of sand and improvement of the ecological situation.

Thus, the sand-fixing crust obtained by this method simultaneously performs several functions: it stops the movement of sand, reduces dust removal, creates favorable conditions for the growth and development of vegetation, contributes to the emergence of soil structures, the accumulation of humus, etc.

Conceptual Replication And Extension Of The Relation Between The Number Line Estimation Task And Mathematical Competence Across Seven Studies, Alexa Ellis, María Inés Susperreguy, David J. Purpura, Pamela E. Davis-Kean

Purdue Center for Early Learning Faculty and Staff Publications

A recent meta-analysis demonstrated the overall correlation between the number line estimation (NLE) task and children’s mathematical competence was r = .44 (positively recoded), and this relation increased with age. The goal of the current study was to conceptually replicate and extend these results by further synthesizing this correlation utilizing studies not present in the meta-analysis. Across seven studies, 954 participants, ranging from 3 to 11 years old (Age M = 6.02 years, SD = 1.57), the overall estimation-competence correlations were similar to those of the meta-analysis and ranged from r = −.40 to −.35. The current conceptual replication demonstrated …

Some Nonparametric Hybrid Predictive Models : Asymptotic Properties And Applications., Tanujit Chakraborty Dr.

Doctoral Theses

Prediction problems like classification, regression, and time series forecasting have always attracted both the statisticians and computer scientists worldwide to take up the challenges of data science and implementation of complicated models using modern computing facilities. But most traditional statistical and machine learning models assume the available data to be well-behaved in terms of the presence of a full set of essential features, equal size of classes, and stationary data structures in all data instances, etc. Practical data sets from the domain of business analytics, process and quality control, software reliability, and macroeconomics, to name a few, suffer from various …

Behavior Of Entanglement Entropy Near Periodic Orbits In A Hamiltonian Dynamical System, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

Entanglement entropy growth is studied under a form of dynamics that is based on iteration. This approach allows the investigation of the role of decoherence in producing increases of entropy. This has important consequences as far as the study of decoherence is concerned. It is indicated that results are generally independent of Hilbert space partitioning. It is seen that a deep relationship between classical dynamical entropy and the growth of entanglement entropy exists in this kind of model. The former acts to bound the latter and in the asymptotic region, they tend to a common limit.

Practical Geometry, Christopher Clavius S.J., John B. Little

Holy Cross Bookshelf

John B. Little is the translator.

This is a Latin to English translation of Geometria Practica by Chrisopher Clavius, S.J. (1538-1612), the preeminent Jesuit mathematician and mathematical astronomer of his time. The first edition of Geometria Practica appeared in 1604. This translation is of the second edition from 1606, produced by the printshop of Johann Albin in Mainz.

In preparing this translation we have made use of the electronic version of the 1606 edition of the Geometria Practica maintained by the Bayerische StaatsBibliothek. In particular, all of the figures have been copied from the scanned images here. The typesetting was …

Evaluation Of The United States Covid-19 Vaccine Allocation Strategy, Md Rafiul Islam, Tamer Oraby, Audrey Mccombs, Mohammad Mihrab Chowdhury, Mohammad Al-Mamun, Michael G. Tyshenko, Claus Kadelkai

School of Mathematical & Statistical Sciences Faculty Publications

Background: Anticipating an initial shortage of vaccines for COVID-19, the Centers for Disease Control (CDC) in the United States developed priority vaccine allocations for specific demographic groups in the population. This study evaluates the performance of the CDC vaccine allocation strategy with respect to multiple potentially competing vaccination goals (minimizing mortality, cases, infections, and years of life lost (YLL)), under the same framework as the CDC allocation: four priority vaccination groups and population demographics stratified by age, comorbidities, occupation and living condition (congested or non-congested).

Methods and findings: We developed a compartmental disease model that incorporates key elements of the …

Distinct Circadian Assessments From Wearable Data Reveal Social Distancing Promoted Internal Desynchrony Between Circadian Markers, Yitong Huang, Caleb Mayer, Olivia J. Walch, Clark Bowman, Srijan Sen, Cathy Goldstein, Jonathan Tyler, Daniel B. Forger

Mathematics Sciences: Faculty Publications

Mobile measures of human circadian rhythms (CR) are needed in the age of chronotherapy. Two wearable measures of CR have recently been validated: one that uses heart rate to extract circadian rhythms that originate in the sinoatrial node of the heart, and another that uses activity to predict the laboratory gold standard and central circadian pacemaker marker, dim light melatonin onset (DLMO). We first find that the heart rate markers of normal real-world individuals align with laboratory DLMO measurements when we account for heart rate phase error. Next, we expand upon previous work that has examined sleep patterns or chronotypes …

A Complete Characterisation Of Vertex-Multiplications Of Trees With Diameter 5, Willie Han Wah Wong, Eng Guan Tay

Theory & Applications of Graphs

For a connected graph G, let D(G) be the family of strong orientations of G; and for any D ∈ D(G), we denote by d(D) the diameter of D. The orientation number of G is defined as d(G)=min{d(D) | D ∈ D(G)}. In 2000, Koh and Tay introduced a new family of graphs, G vertex-multiplications, and extended the results on the orientation number of complete n-partite graphs. Suppose G has the vertex set V(G)={v₁,v₂,… v_n}. For any sequence of n positive integers (s …

An Efficient High-Order Meshless Method For Advection-Diffusion Equations On Time-Varying Irregular Domains, Varun Shankar, Grady B. Wright, Aaron L. Fogelson

Mathematics Faculty Publications and Presentations

We present a high-order radial basis function finite difference (RBF-FD) framework for the solution of advection-diffusion equations on time-varying domains. Our framework is based on a generalization of the recently developed Overlapped RBF-FD method that utilizes a novel automatic procedure for computing RBF-FD weights on stencils in variable-sized regions around stencil centers. This procedure eliminates the overlap parameter δ, thereby enabling tuning-free assembly of RBF-FD differentiation matrices on moving domains. In addition, our framework utilizes a simple and efficient procedure for updating differentiation matrices on moving domains tiled by node sets of time-varying cardinality. Finally, advection-diffusion in time-varying domains …

Covering By Homothets And Illuminating Convex Bodies, Alexey Glazyrin

School of Mathematical & Statistical Sciences Faculty Publications

The paper is devoted to coverings by translative homothets and illuminations of convex bodies. For a given positive number α and a convex body B, gα⁡(B) is the infimum of α-powers of finitely many homothety coefficients less than 1 such that there is a covering of B by translative homothets with these coefficients. hα⁡(B) is the minimal number of directions such that the boundary of B can be illuminated by this number of directions except for a subset whose Hausdorff dimension is less than α. In this paper, we prove that gα⁡(B)≤hα⁡(B), find upper and lower bounds for both numbers, …

Image-Based Microbiome Profiling Differentiates Gut Microbial Metabolic States, Sarwesh Rauniyar

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Rippled Almost Periodic Behavior In An Epilepsy Model, David Chan, Candace Kent

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Topology And Ecology: Deducing States Of The Upper Mississippi River System, Killian Davis

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Connecting People To Food: A Network Approach To Alleviating Food Deserts, Anna Sisk

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.