Applied Mathematics Commons^™

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.

How To Detect Future Einsteins: Towards Systems Approach, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Talents are rare. It is therefore important to detect and nurture future talents as early as possible. In many disciplines, this is already being done -- via gifted and talented programs, Olympiads, and other ways to select kids with unusually high achievements. However, the current approach is not perfect: some of the kids are selected simply because they are early bloomers, they do not grow into unusually successful researchers; on the other hand, many of those who later become very successful are not selected since they are late bloomers. To avoid these problems, we propose to use systems approach: to …

Which Classes Of Bi-Intervals Are Closed Under Addition?, Olga Kosheleva, Vladik Kreinovich, Jonatan Contreras

Departmental Technical Reports (CS)

In many practical situations, uncertainty with which we know each quantity is described by an interval. In processing such data, it is useful to know that the sum of two intervals is always an interval. In some cases, however, the set of all possible value of a quantity is described by a bi-interval -- i.e., by a union of two intervals. It is known that the sum of two bi-intervals is not always a bi-interval. In this paper, we describe all the class of bi-intervals which are closed under addition -- i.e., for which the sum of bi-intervals is a …

Preference For Boys Does Not Necessarily Lead To A Gender Disbalance: A Realistic Example, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Intuitively, it seems that cultural preference for boys should lead to a gender disbalance -- more boys than girls. This disbalance is indeed what is often observed, and this disbalance is what many models predict. However, in this paper, we show, on a realistic example, that preference for boys does not necessarily lead to a gender disbalance: in our simplified example, boys are clearly preferred, but still there are exactly as many girls as there are boys.

Healthy Lifestyle Decreases The Risk Of Alzheimer Disease: A Possible Partial Explanation Of An Empirical Dependence, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

A recent paper showed that for people who follow all five healthy lifestyle recommendations, the risk of Alzheimer disease is only 40% of the risk for those who do not follow any of these recommendations, and that for people two or three of these recommendations, the risk is 63% of the not-followers risk. In this paper, we show that a relation between the two numbers -- namely, that 0.40 is the square of 0.63 -- can be naturally explained by a simple model.

When Can We Be Sure That Measurement Results Are Consistent: 1-D Interval Case And Beyond, Hani Dbouk, Steffen Schön, Ingo Neumann, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, measurements are characterized by interval uncertainty -- namely, based on each measurement result, the only information that we have about the actual value of the measured quantity is that this value belongs to some interval. If several such intervals -- corresponding to measuring the same quantity -- have an empty intersection, this means that at least one of the corresponding measurement results is an outlier, caused by a malfunction of the measuring instrument. From the purely mathematical viewpoint, if the intersection is non-empty, there is no reason to be suspicious, but from the practical viewpoint, if …

What If Not All Interval-Valued Fuzzy Degrees Are Possible?, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the applications of intervals is in describing experts' degrees of certainty in their statements. In this application, not all intervals are realistically possible. To describe all realistically possible degrees, we end up with a mathematical question of describing all topologically closed classes of intervals which are closed under the appropriate minimum and maximum operations. In this paper, we provide a full description of all such classes.

Common-Sense-Based Theoretical Explanation For An Empirical Formula Estimating Road Quality, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich

Departmental Technical Reports (CS)

The quality of a road is usually gauged by a group of trained raters; the resulting numerical value is known as the Present Serviceability Index (PSI). There are, however, two problems with this approach. First, while it is practical to use trained raters to gauge the quality of major highways, there are also numerous not-so-major roads, and there is not enough trained raters to gauge the quality of all of them. Second, even for skilled raters, their estimates are somewhat subjective: different groups of raters may estimate the quality of the same road segment somewhat differently. Because of these two …

Structure For Regular Inclusions. Ii Cartan Envelopes, Pseudo-Expectations And Twists, David R. Pitts

Department of Mathematics: Faculty Publications

We introduce the notion of a Cartan envelope for a regular inclusion (C,Ɗ). When a Cartan envelope exists, it is the unique, minimal Cartan pair into which (C,Ɗ) regularly embeds. We prove a Cartan envelope exists if and only if (C,Ɗ) has the unique faithful pseudo-expectation property and also give a characterization of the Cartan envelope using the ideal intersection property.

For any covering inclusion, we construct a Hausdorff twisted groupoid using appropriate linear functionals and we give a description of the Cartan envelope for (C,Ɗ) in terms of a twist …

A Study Of The Design Of Adaptive Camber Winglets, Justin J. Rosescu

Master's Theses

A numerical study was conducted to determine the effect of changing the camber of a winglet on the efficiency of a wing in two distinct flight conditions. Camber was altered via a simple plain flap deflection in the winglet, which produced a constant camber change over the winglet span. Hinge points were located at 20%, 50% and 80% of the chord and the trailing edge was deflected between -5° and +5°. Analysis was performed using a combination of three-dimensional vortex lattice method and two-dimensional panel method to obtain aerodynamic forces for the entire wing, based on different winglet camber configurations. …

On The Socles Of Fully Inert Subgroups Of Abelian P-Groups, Andrey R. Chekhlov, Peter V. Danchev, Brendan Goldsmith

Articles

We define the so-called fully inert socle-regular and weakly fully inert socle-regular Abelian p-groups and study them with respect to certain of their numerous interesting properties. For instance, we prove that in the case of groups of length ! these two group classes coincide but that in the case of groups of length ! + 1 they differ. Some structural and characterization results are also obtained. The work generalizes concepts which have been of interest recently in the theory of entropy in algebra and builds on recent investigations by the second and third named authors in Arch. Math. Basel (2009) …

Dynamical Behavior Of A Malaria Relapse Model With Insecticide Treated Nets (Itns) As Protection Measure, Reuben I. Gweryina, Anande R. Kimbir

Applications and Applied Mathematics: An International Journal (AAM)

Malaria is a tropical disease which is mainly spread by plasmodium falciparum which has been the principal enemy to the existence of mankind till date. In this paper a version of a malaria model incorporating the use of treated mosquito nets as a disease control strategy is proposed and then transformed into proportions, so as to assess the global impact of ITNs on the prevalence of malaria. Constructing a Lyapunov function using matrix-theoretic approach, a malaria-free equilibrium state is obtained, which is globally asymptotically stable if the control reproduction number, 𝑅_𝑚<1. This means that malaria can be controlled or eradicated under such a threshold quantity, 𝑅𝑚. On the other hand, a malaria-persistence equilibrium state exists which is globally stable when 𝑅_𝑚>1, using geometric theoretic method with Lozoskii …

Stability Of Regular Thin Shell Wormholes Supported By Vdw Quintessence, A. Eid

Applications and Applied Mathematics: An International Journal (AAM)

The dynamical equations of motion for a thin shell wormhole from regular black holes that are supported by Van der Waals (VDW) quintessence equation of state (EoS) are constructed, through cut and -paste technique. The linearized stability of regular wormhole is derived. The presences of unstable and stable static solutions with different value of some parameters are analyzed.