Applied Mathematics Commons^™

Projecting The Covid-19 Weekly Deaths And Hospitalizations For Jefferson County, Kentucky, Seyed Karimi, Natalie Dupre, W. Paul Mckinney, Bert B. Little, Naiya Patel, Sarah Moyer

The University of Louisville Journal of Respiratory Infections

Introduction: The trends in the numbers of active hospitalizations and fatalities caused by the COVID-19 in Jefferson County, Kentucky, were projected over the period May 7 to August 20, 2020.

Methods: The projections provided in this report are from a susceptible-exposed-infectious-recovered (SEIR) model. The model was calibrated using the COVID-19 transmission dynamics parameters from relevant literature and clinical dynamics parameters from the county’s data. The model was used to measure the impact of public health policy interventions designed to contain the infection. The policy was modeled by its intervention day and impact on the transmission of the virus such that …

An Improved Method For Spectroscopic Quality Classification, Elizabeth G. Mayer

Mathematics & Statistics ETDs

Spectral quality classification is a vital step in data cleaning before the

analysis of magnetic resonance spectroscopy (MRS) data can be done. This

analysis compares five methods of quality classification; three of these are

legacy methods, Maudsley et al. (2006), Zhang et al. (2018), and

Bustillo et al. (2020), and two newly created methods that used a random forests

classifier (RFC) to inform their classifications. We found that the random forest

classifier was the most accurate at predicting spectra quality (balanced

accuracy for RF of 88% vs legacy of 70%, 72%, or 72%). A

Random-Forests-Informed Filtering method (RFIFM) for quality …

A Study Of The Efficacy Of Machine Learning For Diagnosing Obstructive Coronary Artery Disease In Non-Diabetic Patients, Demond Larae Handley

Theses and Dissertations

According to the Centers for Disease Control and Prevention, about 18.2 million adults age 20 and older have Coronary Artery Disease in the United States. Early diagnosis is therefore of crucial importance to help prevent debilitating consequences, and principally death for many patients. In this study we use data containing gene expression values from peripheral blood samples in 198 non-diabetic patients, with the goal of developing an age and sex gene expression model for diagnosis of Coronary Artery Disease. We employ machine learning methods to obtain a classification based on genetic information, age and sex. Our implementation uses feed forward …

Distributed Control Of Multiagent Systems Under Heterogeneity, Selahattin Burak Sarsilmaz

USF Tampa Graduate Theses and Dissertations

The overarching objective of this work is to propose solutions to quite a few distributed control problems arising from networks of heterogeneous agents or the heterogeneous nature of multiagent systems. Each problem with its solutions is concisely summarized below.

We consider the cooperative output regulation problem of heterogeneous linear multiagent systems over fixed directed communication graphs. The purpose of this problem is to design a distributed control law such that the overall closed-loop stability is ensured and the tracking error of each agent converges to zero asymptotically for a class of reference inputs and disturbances generated by a so-called exosystem. …

Covid-19 Peak Immunity Values Seem To Follow Lognormal Distribution, Julio Urenda, Olga Kosheleva, Vladik Kreinovich, Tonghui Wang

Departmental Technical Reports (CS)

For the current pandemic, an important open problem is immunity: do people who had this disease become immune against further infections? In the immunity study, it is important to know how frequent are different levels of immunity, i.e., what is the probability distribution of the immunity levels. Different people have different rates of immunity dynamics: for some, immunity gets to the level faster, for others the immunity effect is slower. Similarly, in some patients, immunity stays longer, it others, it decreases faster. In view of this, an important characteristic is peak immunity. A recent study provides some statistics on the …

Gifted And Talented: With Others? Separately? Mathematical Analysis Of The Problem, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Crudely speaking, there are two main suggestions about teaching gifted and talented student: we can move them to a separate class section, or we can mix them with other students. Both options have pluses and minuses. In this paper, we formulate this problem in precise terms, we solve the corresponding mathematical optimization problem, and we come up with a somewhat unexpected optimal solution: mixing, but with an unusual twist.

Grading Homeworks, Verifying Code: How Thorough Should The Feedback Be?, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the ideal world, we should assign many homeworks and give a thorough feedback for each homework. However, in reality, the instructor's time is limited, so we can either assign few homeworks and give a detailed feed back for all of them, or we can assign many homeworks, but give a less thorough feedback. What is the optimal thoroughness? A similar question can be raised for code verification: what is the optimal amount of feedback that should be provided to each programmer? In this paper, we provide answers to these questions.

Let Us Use Negative Examples In Regression-Type Problems Too, Jonatan Contreras, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich, Martine Ceberio

Departmental Technical Reports (CS)

In many practical situations, we need to reconstruct the dependence between quantities x and y based on several situations in which we know both x and y values. Such problems are known as regression problems. Usually, this reconstruction is based on positive examples, when we know y -- at least, with some accuracy. However, in addition, we often also know some examples in which we have negative information about y -- e.g., we know that y does not belong to a certain interval. In this paper, we show how such negative examples can be used to make the solution …

Why Quadratic Log-Log Dependence Is Ubiquitous And What Next, Sean R. Aguilar, Vladik Kreinovich, Uyen Pham

Departmental Technical Reports (CS)

In many real-life situations ranging from financial to volcanic data, growth is described either by a power law -- which is linear in log-log scale, or by a quadratic dependence in the log-log scale. In this paper, we use natural scale invariance requirement to explain the ubiquity of such dependencies. We also explain what should be a reasonable choice of the next model, if quadratic turns out to be not too accurate: it turns out that under scale invariance, the next class of models are cubic dependencies in the log-log scale, then fourth order dependencies, etc.

It Is Important To Take All Available Information Into Account When Making A Decision: Case Of The Two Envelopes Problem, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In situations when we know the probabilities of all possible consequences, traditional decision theory recommends selecting the action that maximizes expected utility. In many practical situations, however, we only have partial information about the corresponding probabilities. In this case, for different possible probability distributions, we get different values of expected utility. In general, possible values of expected utility form an interval. One way to approach this situation is to use the optimism-pessimism approach proposed by Nobelist Leo Hurwicz. Another approach is to select one of the possible probability distributions -- e.g., the one that has the largest possible entropy. Both …

How To Decide Which Cracks Should Be Repaired First: Theoretical Explanation Of Empirical Formulas, Edgar Daniel Rodriguez Velasquez, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Due to stress, cracks appear in constructions: cracks appear in buildings, bridges, pavements, among other structures, cracks appear in pavements, etc. In the long run, cracks need to be repaired. However, our resources are limited, so we need to decide which cracks are more dangerous. For this, we need to be able to predict how different cracks will grow. There are several empirical formulas describing crack growth. In this paper, we show that by using scale invariance, we can provide a theoretical explanation for these empirical formulas.

Euclidean Distance Between Intervals Is The Only Representation-Invariant One, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

An interval can be represented as a point in a plane, e.g., as a point with its endpoints as coordinates. We can thus define distance between intervals as the Euclidean distance between the corresponding points. Alternatively, we can describe an interval by its center and radius, which leads to a different definition of distance. Interestingly, these two definitions lead, in effect, to the same distance -- to be more precise, these two distances differ by a multiplicative constant. In principle, we can have more general distances on the plane. In this paper, we show that only for Euclidean distance, the …

The Less We Love A Woman, The More She Likes Us: Pushkin's Observation Explained, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Alexander Pushkin, the most famous Russian poet, made this observation in "Eugene Onegin", his novel in verse which is most known to non-Russian readers via Tchaikovsky's opera. This observation may not be an absolute truth -- there are counterexamples -- but the fact that it is still widely cited shows that there is some truth in this statement. In this paper, we recall the usual utility-based explanation for a similar statement, and propose a new explanation, which is even more fundamental -- it is on the biological level.

An Application Of The Unscented Kalman Filter For Spacecraft Attitude Estimation On Real And Simulated Light Curve Data, Kent A. Rush

Master's Theses

In the past, analyses of lightcurve data have been applied to asteroids in order to determine their axis of rotation, rotation rate and other parameters. In recent decades, these analyses have begun to be applied in the domain of Earth orbiting spacecraft. Due to the complex geometry of spacecraft and the wide variety of parameters that can influence the way in which they reflect light, these analyses require more complex assumptions and a greater knowledge about the object being studied. Previous investigations have shown success in extracting attitude parameters from unresolved spacecraft using simulated data. This paper presents a focused …

Optimal Allocation Of Two Resources In Annual Plants, David Mcmorris

Department of Mathematics: Dissertations, Theses, and Student Research

The fitness of an annual plant can be thought of as how much fruit is produced by the end of its growing season. Under the assumption that annual plants grow to maximize fitness, we can use techniques from optimal control theory to understand this process. We introduce two models for resource allocation in annual plants which extend classical work by Iwasa and Roughgarden to a case where both carbohydrates and mineral nutrients are allocated to shoots, roots, and fruits in annual plants. In each case, we use optimal control theory to determine the optimal resource allocation strategy for the plant …

Dynamics Of Discontinuities In Elastic Solids, Arkadi Berezovski, Mihhail Berezovski

Publications

The paper is devoted to evolving discontinuities in elastic solids. A discontinuity is represented as a singular set of material points. Evolution of a discontinuity is driven by the configurational force acting at such a set. The main attention is paid to the determination of the velocity of a propagating discontinuity. Martensitic phase transition fronts and brittle cracks are considered as representative examples.

An A Posteriori Error Analysis Of Stationary Incompressible Magnetohydrodynamics, Ari E. Rappaport

Mathematics & Statistics ETDs

Adjoint based a posteriori error analysis is a technique to produce exact error repre- sentations for quantities of interests that are functions of the solution of systems of partial differential equations (PDE). The tools used in the analysis consist of duality arguments and compatible residuals. In this thesis we apply a posteriori error anal- ysis to the magnetohydrodynamics (MHD) equations . MHD provides a continuum level description of conducting fluids in the presence of electromagnetic fields. The MHD system is therefore a multi-physics system, capturing both fluid and electro- magnetic effects. Mathematically, The equations of MHD are highly nonlinear and …

Numerical Solution Of Ordinary Differential Equations Using Continuous Runge-Kutta Methods (Feldberg Of Order Four And Five), Madeha Yousif

Emirates Journal for Engineering Research

In this paper the continuous Runge-Kutta method (Runge-Kutta Feldberg method of order four and five) have been used to find the numerical solution of ordinary differential equation not only at the mesh points but also the all points between them. the results are computed using matlab program..

Multigrid Methods For Elliptic Optimal Control Problems, Sijing Liu

LSU Doctoral Dissertations

In this dissertation we study multigrid methods for linear-quadratic elliptic distributed optimal control problems.

For optimal control problems constrained by general second order elliptic partial differential equations, we design and analyze a $P_1$ finite element method based on a saddle point formulation. We construct a $W$-cycle algorithm for the discrete problem and show that it is uniformly convergent in the energy norm for convex domains. Moreover, the contraction number decays at the optimal rate of $m^{-1}$, where $m$ is the number of smoothing steps. We also prove that the convergence is robust with respect to a regularization parameter. The robust …

2n-Dimensional Canonical Systems And Applications, Andrei Ludu, Keshav Baj Acharya

Publications

We study the 2N-dimensional canonical systems and discuss some properties of its fundamental solution. We then discuss the Floquet theory of periodic canonical systems and observe the asymptotic behavior of its solution. Some important physical applications of the systems are also discussed: linear stability of periodic Hamiltonian systems, position-dependent effective mass, pseudo-periodic nonlinear water waves, and Dirac systems.