Applied Mathematics Commons^™

Grouping Algorithms For Informative Array Testing In Disease Surveillance, David Sokolov

Graduate Theses, Dissertations, and Problem Reports (ETD)

In order to maintain normal operations and prevent unnecessary morbidity and mortality during times of disease outbreak, institutions find a need to conduct frequent and widespread testing of their constituents, often under significantly limited testing resource constraints. Faced with the challenge of how best to allo- cate these limited resources to maximum effect, institutions are increasingly turning to group (or “pooled”) testing, which involves testing strategically-chosen groups of patient samples rather than individual samples, producing significant testing resource savings under certain regimes of disease prevalence. While group test- ing can be conducted without any a priori knowledge of individual disease …

Deterministic And Statistical Methods For Inverse Problems With Partial Data, Yanfang Liu

Dissertations, Master's Theses and Master's Reports

Inverse problems with partial data have many applications in science and engineering. They are more challenging than the complete data cases since the lack of data increases ill-posedness and nonlinearity. The use of only deterministic or statistical methods might not provide satisfactory results. We propose to combine the deterministic and statistical methods to treat such inverse problems. The thesis is organized as follows.

In Chapter 1, we briefly introduce the inverse problems and their applications. The classical deterministic methods and Bayesian inversion are discussed. The chapter is concluded with a summary of contributions.

Chapter 2 considers the reconstruction of the …

Optimal Construction Of A Layer-Ordered Heap And Its Applications, Jake Pennington

Graduate Student Theses, Dissertations, & Professional Papers

The layer-ordered heap (LOH) is a simple data structure used in algorithms that perform optimal top-$k$ on $X+Y$, algorithms with the best known runtime for top-$k$ on $X_1+X_2+\cdots+X_m$, and the fastest method in practice for computing the most abundant isotopologue peaks in a chemical compound. In the analysis of these algorithms, the rank, $\alpha$, has been treated as a constant and $n$, the size of the array, has been treated as the sole parameter. Here, we explore the algorithmic complexity of LOH construction with $\alpha$ as a parameter, introduce a few algorithms for constructing LOHs, analyze their complexity in both …

Implementing A Neural Network For Supervised Learning With A Random Configuration Of Layers And Nodes, Kane A. Phillips

College of Graduate Studies: Theses & Dissertations

Deep learning has a substantial amount of real-life applications, making it an increasingly popular subset of artificial intelligence over the last decade. These applications come to fruition due to the tireless research and implementation of neural networks. This paper goes into detail on the implementation of supervised learning neural networks utilizing MATLAB, with the purpose being to generate a neural network based on specifications given by a user. Such specifications involve how many layers are in the network, and how many nodes are in each layer. The neural network is then trained based on known sample values of a function …

Proper Orthogonal Decomposition: New Approximation Theory And A New Computational Approach, Sarah Katherine Locke

Doctoral Dissertations

“Proper orthogonal decomposition (POD) projection errors and error bounds for POD reduced order models of partial differential equations have been studied by many. In this research we obtain new results regarding POD data approximation theory and present a new difference quotient (DQ) approach for computing the POD modes of the data.

First, we improve on earlier results concerning POD projection errors by extending to a more general framework that allows for non-orthogonal POD projections and seminorms. We obtain new exact error formulas and convergence results for POD data approximation errors, and also prove new pointwise convergence results and error bounds …

Hands-On Developmental Playbook For Stem Clubs In Elementary Schools, James Lipuma, Bruce G. Bukiet, Cristo Leon

STEM for Success Resources

The following guide is the result of the work of NJIT researchers, staff, and student STEM role models along with the many public and private partners including Apple and the Us ARMY. The work was funded by the National Science Foundation through the NSF INCLUDES Life grant and support from Howmet Aerospace Foundation grants. The materials in the guide have been developed and tested with our New Jersey school district partners in Hillside, Long Branch, Morris Plains, Newark, Princeton, and Weehawken. See our strategic partners section for a more complete list of partners and collaborators.

Extending Critical Infrastructure Element Longevity Using Constellation-Based Id Verification, Christopher M. Rondeau, Michael A. Temple, J. Addison Betances, Christine M. Schubert Kabban

Faculty Publications

This work supports a technical cradle-to-grave protection strategy aimed at extending the useful lifespan of Critical Infrastructure (CI) elements. This is done by improving mid-life operational protection measures through integration of reliable physical (PHY) layer security mechanisms. The goal is to improve existing protection that is heavily reliant on higher-layer mechanisms that are commonly targeted by cyberattack. Relative to prior device ID discrimination works, results herein reinforce the exploitability of constellation-based PHY layer features and the ability for those features to be practically implemented to enhance CI security. Prior work is extended by formalizing a device ID verification process that …

A Learning Curve Model Accounting For The Flattening Effect In Production Cycles, Evan R. Boone, John J. Elshaw, Clay M. Koschnick, Jonathan D. Ritschel, Adedeji B. Badiru

Faculty Publications

We investigate production cost estimates to identify and model modifications to a prescribed learning curve. Our new model examines the learning rate as a decreasing function over time as opposed to a constant rate that is frequently used. The purpose of this research is to determine whether a new learning curve model could be implemented to reduce the error in cost estimates for production processes. A new model was created that mathematically allows for a “flattening effect,” which typically occurs later in the production process. This model was then compared to Wright’s learning curve, which is a popular method used …

Dances And Escape Of The Vortex Quartet, Brandon Behring

Dissertations

This dissertation considers the linear stability of a one-parameter family of periodic solutions of the four-vortex problem known as 'leapfrogging' orbits. These solutions, which consist of two pairs of identical yet oppositely-signed vortices, were known to W. Gröbli (1877) and A. E. H. Love (1883) and can be parameterized by a dimensionless parameter related to the geometry of the initial configuration. Simulations by Acheson and numerical Floquet analysis by Tophøj and Aref both indicate, to many digits, that the bifurcation occurs at a value related to the inverse square of the golen ratio. Acheson observed that, after an initial period …

Convergence Of The Boundary Integral Method For Interfacial Stokes Flow, Keyang Zhang

Dissertations

Boundary integral numerical methods are among the most accurate methods for interfacial Stokes flow, and are widely applied. They have the advantage that only the boundary of the domain must be discretized, which reduces the number of discretization points and allows the treatment of complicated interfaces. Despite their popularity, there is no analysis of the convergence of these methods for interfacial Stokes flow. In practice, the stability of discretizations of the boundary integral formulation can depend sensitively on details of the discretization and on the application of numerical filters. A convergence analysis of the boundary integral method for Stokes flow …

Visual Arts Enhance Instruction In Observation And Analysis Of Microscopic Forms In Developmental And Cell Biology, Max Ezin, Christina Noravian, Amira Mahomed, Adam Lyle, Aveleen Gill, Tamira Elul

The Transdisciplinary STEAM+ Journal

Two important skills for scientists in developmental and cell biology, as well as in fields such as neurobiology, histology and pathology, are: 1) observation of features and details in microscopic images of cells, and 2) quantification of cellular features observed in microscopic images. However, current training in developmental and cell biology does not emphasize observation and quantitative analysis of microscopic images, and it is unclear how best to teach students these skills. Here, we describe our experiences applying visual artistic approaches to instruct undergraduate and graduate students in how to observe and analyze cellular forms in microscopic images. At Loyola …

Algorithm And Application For Iot Based Real Time Patient Monitoring System, Hakimjon Zaynidinov, Sarvar Maxmudjonov, Ruzikulov R.A.

Bulletin of TUIT: Management and Communication Technologies

Among the applications that Internet of Things (IoT) facilitated to the world, Healthcare applications are most important. In general, IoT has been widely used to interconnect the advanced medical resources and to offer smart and effective healthcare services to the people. The advanced sensors can be either worn or be embedded into the body of the patients, so as to continuously monitor their health. The information collected in such manner, can be analyzed, aggregated and mined to do the early prediction of diseases. The processing algorithms assist the physicians for the personalization of treatment and it helps to make the …

The Family Of Bicircular Matroids Closed Under Duality, Vaidy Sivaraman, Daniel Slilaty

Mathematics and Statistics Faculty Publications

We characterize the 3-connected members of the intersection of the class of bicircular and cobi- circular matroids. Aside from some exceptional matroids with rank and corank at most 5, this class consists of just the free swirls and their minors.

Multigrid For The Nonlinear Power Flow Equations, Enrique Pereira Batista

Mathematics Theses and Dissertations

The continuously changing structure of power systems and the inclusion of renewable
energy sources are leading to changes in the dynamics of modern power grid,
which have brought renewed attention to the solution of the AC power flow equations.
In particular, development of fast and robust solvers for the power flow problem
continues to be actively investigated. A novel multigrid technique for coarse-graining
dynamic power grid models has been developed recently. This technique uses an
algebraic multigrid (AMG) coarsening strategy applied to the weighted
graph Laplacian that arises from the power network's topology for the construction
of coarse-grain approximations to …

Uncertainty Quantification Of Nonreflecting Boundary Schemes, Brian Citty

Mathematics Theses and Dissertations

Numerical methods have been developed to solve partial differential equations involving the far-field radiation of waves. In addition, there has been recent interest in uncertainty quantification- a burgeoning field involving solving PDEs where random variables are used to model uncertainty in the data. In this thesis we will apply uncertainty quantification methodology to the 1D and 2D wave equation with nonreflecting boundary. We first derive a boundary condition for the 1D wave equation assuming several models of the random wave speed. Later we use our result to compare to an asymptotic SDE approach, and finally we repeat our analysis for …

Modeling Fluid Phenomena In The Context Of The Constrained Vapor Bubble System, James Barrett

Mathematics Theses and Dissertations

This thesis focuses on the fluid phenomena observed within what is known as the constrained vapor bubble system. The constrained vapor bubble system is a closed system consisting of a quartz cuvette partially filled with liquid and used as a coolant device. Heat is applied to the heater end which causes the liquid to evaporate and condense on the cooled end of the cuvette. Liquid travels back to the heated end via capillary flow in the corners. A pure vapor bubble is formed in the center of the cuvette giving rise to the name of the experiment. The constrained vapor …

Multi-Level Small Area Estimation Based On Calibrated Hierarchical Likelihood Approach Through Bias Correction With Applications To Covid-19 Data, Nirosha Rathnayake

Theses & Dissertations

Small area estimation (SAE) has been widely used in a variety of applications to draw estimates in geographic domains represented as a metropolitan area, district, county, or state. The direct estimation methods provide accurate estimates when the sample size of study participants within each area unit is sufficiently large, but it might not always be realistic to have large sample sizes of study participants when considering small geographical regions. Meanwhile, high dimensional socio-ecological data exist at the community level, providing an opportunity for model-based estimation by incorporating rich auxiliary information at the individual and area levels. Thus, it is critical …

The Revised Nim For Solving The Non-Linear System Variant Boussinesq Equations And Comparison With Nim, Oday Ahmed Jasim

Karbala International Journal of Modern Science

This research aims to guide researchers to use a new method, and it is the Revised New Iterative Method (RNIM) to solve partial differential equation systems and apply them to solve problems in various disciplines such as chemistry, physics, engineering and medicine. In this paper, the numerical solutions of the nonlinear Variable Boussinesq Equation System (VBE) were obtained using a new modified iterative method (RNIM); this was planned by (Bhaleker and Datterder-Gejj). A numerical solution to the Variable Boussinesq Equation System (VBE) was also found using a widely known method, a new iterative method (NIM). By comparing the numerical solutions …

Two New Finite Element Schemes And Their Analysis For Modeling Of Wave Propagation In Graphene, Jichun Li

Mathematical Sciences Faculty Research

© 2020 The Author(s) In this paper, we investigate a system of governing equations for modeling wave propagation in graphene. Compared to our previous work (Yang et al., 2020), here we re-investigate the governing equations by eliminating two auxiliary unknowns from the original model. A totally new stability for the model is established for the first time. Since the finite element scheme proposed in Yang et al. (2020) is only first order in time, here we propose two new schemes with second order convergence in time for the simplified modeling equations. Discrete stabilities inheriting exactly the same form as the …

A Logical Method For Finding Maximum Compatible Subsystems Of Systems Of Boolean Equations, Anvar Kabulov, Erkin Urunbaev, Mansur Berdimurodov

Scientific Journal of Samarkand University

The problem of finding the maximum joint subsystem of Boolean equation systems is solved. An algorithm for finding the maximum upper zero of a monotone Boolean function is proposed. An efficient procedure for calculating the values of monotone functions on sets of a - dimensional cube is investigated and developed. An algorithm for solving systems of Boolean equations based on the search for the maximum upper zero of monotone functions of the logic algebra is developed.

Spectral Properties Of A Non-Compact Operator In Ecology, Matthew Reichenbach

Department of Mathematics: Dissertations, Theses, and Student Research

Ecologists have used integral projection models (IPMs) to study fish and other animals which continue to grow throughout their lives. Such animals cannot shrink, since they have bony skeletons; a mathematical consequence of this is that the kernel of the integral projection operator T is unbounded, and the operator is not compact. A priori, it is unclear whether these IPMs have an asymptotic growth rate λ, or a stable-stage distribution ψ. In the case of a compact operator, these quantities are its spectral radius and the associated eigenvector, respectively. Under biologically reasonable assumptions, we prove that the non-compact operators in …

Parametric Art, Shaun Pollard, Daanial Ahmad, Satyanand Singh

Publications and Research

Lissajous curves, named after Jules Antoine Lissajous (1822-1880) are generated by the parametric equations ��=��������(����) and ��=��������(����) in its simplistic form. Others have studied these curves and their applications like Nathaniel Bowditch in 1815, and they are often referred to as Bowditch curves as well. Lissajous curves are found in engineering, mathematics, graphic design, physics, and many other backgrounds. In this project entitled “Parametric Art” this project will focus on analyzing these types of equations and manipulating them to create art. We will be investigating these curves by answering a series of questions that elucidate their purpose. Using Maple, which …

Using Statistical Analysis To Examine Weather Variability In New York City, Ryan Chen, Yuhuang Wang, Jiehao Huang

Publications and Research

As the overall temperature of Earth continues to warm, atmospheric hazards (e.g. heatwaves, cyclones) may be driving increases in climatological trends. This study examines the daily precipitation and temperature record of the greater New York City region during the 1979-2014 period. Daily station observations from three greater New York City airports: John F. Kennedy (JFK), LaGuardia (LGA) and Newark (EWR), are used in this study. Climatological & statistical analyses are performed for the weather variability of New York City metro area to understand the impacts of climate change.The temperature climatology reveals a distinct seasonal cycle, while the precipitation climatology exhibits …

A Brief On Characteristic Functions, Austin G. Vandegriffe

Graduate Student Research & Creative Works

Characteristic functions (CFs) are often used in problems involving convergence in distribution, independence of random variables, infinitely divisible distributions, and stochastics. The most famous use of characteristic functions is in the proof of the Central Limit Theorem, also known as the Fundamental Theorem of Statistics. Though less frequent, CFs have also been used in problems of nonparametric time series analysis and in machine learning. Moreover, CFs uniquely determine their distribution, much like the moment generating functions (MGFs), but the major difference is that CFs always exists, whereas MGFs can fail, e.g. the Cauchy distribution. This makes CFs more robust in …

Stability Analysis Of Krylov Subspace Spectral Methods For The 1-D Wave Equation In Inhomogeneous Media, Bailey Rester

Master's Theses

Krylov subspace spectral (KSS) methods are high-order accurate, explicit time-stepping methods for partial differential equations (PDEs) that also possess the stability characteristic of implicit methods. Unlike other time-stepping approaches, KSS methods compute each Fourier coefficient of the solution from an individualized approximation of the solution operator of the PDE. As a result, KSS methods scale effectively to higher spatial resolution. This thesis will present a stability analysis of a first-order KSS method applied to the wave equation in inhomogeneous media.

Inference And Estimation In Change Point Models For Censored Data, Kristine Gierz

Mathematics & Statistics Theses & Dissertations

In general, the change point problem considers inference of a change in distribution for a set of time-ordered observations. This has applications in a large variety of fields and can also apply to survival data. With improvements to medical diagnoses and treatments, incidences and mortality rates have changed. However, the most commonly used analysis methods do not account for such distributional changes. In survival analysis, change point problems can concern a shift in a distribution for a set of time-ordered observations, potentially under censoring or truncation.

In this dissertation, we first propose a sequential testing approach for detecting multiple change …

Conical Orbital Mechanics: A Rework Of Classic Orbit Transfer Mechanics, Cian Anthony Branco

Mechanical & Aerospace Engineering Theses & Dissertations

Simple orbital maneuvers obeying Kepler’s Laws, when taken with respect to Newton’s framework, require considerable time and effort to interpret and understand. Instead of a purely mathematical approach relying on the governing relations, a graphical geometric conceptual representation provides a useful alternative to the physical realities of orbits. Conic sections utilized within the full scope of a modified cone (frustum) were employed to demonstrate and develop a geometric approach to elliptical orbit transformations. The geometric model in-question utilizes the rotation of a plane intersecting the orbital frustum at some angle β (and the change in this angle) in a novel …

On Subdiagonal Rational Pade Approximations And The Brenner-Thomee Approximation Theorem For Operator Semigroups, Frank Neubrander, Koray Ozer, Lee Windsperger

Faculty Publications

The computational powers of Mathematica are used to prove polynomial identities that are essential to obtain growth estimates for subdiagonal rational Pade approximations of the exponential function and to obtain new estimates of the constants of the Brenner-Thomee Approximation Theorem of Semigroup Theory.

Analytic Solutions For Diffusion On Path Graphs And Its Application To The Modeling Of The Evolution Of Electrically Indiscernible Conformational States Of Lysenin, K. Summer Ware

Boise State University Theses and Dissertations

Memory is traditionally thought of as a biological function of the brain. In recent years, however, researchers have found that some stimuli-responsive molecules exhibit memory-like behavior manifested as history-dependent hysteresis in response to external excitations. One example is lysenin, a pore-forming toxin found naturally in the coelomic fluid of the common earthworm Eisenia fetida. When reconstituted into a bilayer lipid membrane, this unassuming toxin undergoes conformational changes in response to applied voltages. However, lysenin is able to "remember" past history by adjusting its conformational state based not only on the amplitude of the stimulus but also on its previous …

Development Of An Effect Size To Classify The Magnitude Of Dif In Dichotomous And Polytomous Items, James D. Weese

Graduate Theses and Dissertations

A standardized effect size for the SIBTEST/POLYSIBTEST procedure is proposed, allowing for Differential Item Functioning (DIF) to be classified with a single set of DIF heuristics regardless of whether data are dichotomous or polytomous. This proposed standardized effect size accounts for both variability in responses and whether participants are included in the SIBTEST/POLYSIBTEST calculations. First, a new set of unstandardized effect size heuristics are established for dichotomous data that are more aligned with Educational Testing Service (ETS) standards using two and three parameter logistic (2PL and 3PL) models. Second, a standardized effect size is proposed and compared to other DIF …