Applied Mathematics Commons^™

Earthquake Magnitude Prediction Using Support Vector Machine And Convolutional Neural Network, Esther Amfo

Open Access Theses & Dissertations

A deep learning-based method Convolutional Neural Network (CNN) and Support Vector Machine (SVM) for earthquake prediction is proposed. Large-magnitude earthquakes triggered by earthquakes can kill thousands of people and cause millions of dollars worth of economic losses. The accurate prediction of large-magnitude earthquakes is a worldwide problem.

In recent years, deep learning technology that can automatically extract features from mass data has been applied in image recognition, natural language processing, object recognition, etc., with great success. We explore to apply deep learning technology to earthquake prediction, we propose a deep learning method for continuous earthquake prediction using historical seismic events. …

Some Transitivity-Like Concepts In Abelian Groups, Gabor Braun, Brendan Goldsmith, Ketao Gong, Lutz Strungmann

Articles

The classical notions of transitivity and full transitivity in Abelian p-groups have natural extensions to concepts called Krylov and weak transitivity. The interconnections between these four types of transitivity are determined for Abelian p-groups; there is a marked difference in the relationships when the prime p is equal to 2. In the final section the relationship between full and Krylov transitivity is examined in the case of mixed Abelian groups which are p-local in the sense that multiplication by an integer relatively prime to p is an automorphism.

Equatorial Wave–Current Interactions, Adrian Constantin, Rossen Ivanov

Articles

We study the nonlinear equations of motion for equatorial wave–current interactions in the physically realistic setting of azimuthal two-dimensional inviscid flows with piecewise constant vorticity in a two-layer fluid with a flat bed and a free surface. We derive a Hamiltonian formulation for the nonlinear governing equations that is adequate for structure-preserving perturbations, at the linear and at the nonlinear level. Linear theory reveals some important features of the dynamics, highlighting differences between the short- and long-wave regimes. The fact that ocean energy is concentrated in the long-wave propagation modes motivates the pursuit of in-depth nonlinear analysis in the long-wave …

Integrable Cosmological Model With Van Der Waals Gas And Matter Creation, Rossen Ivanov, Emil Prodanov

Articles

A cosmological model with van der Waals gas and dust has been studied in the context of a three-component autonomous non-linear dynamical system involving the time evolution of the particle number density, the Hubble parameter and the temperature. Due to the presence of a symmetry of the model, the temperature evolution law is determined (in terms of the particle number density) and with this the dynamical system reduces to a two-component one which is fully integrable. The globally conserved Hamiltonian is identified and, in addition to it, some special (second) integrals, defined and conserved on a lower-dimensional manifold, are found. …

Least Action Principle Applied To A Non-Linear Damped Pendulum, Katherine Rhodes

Theses, Dissertations and Culminating Projects

The principle of least action is a variational principle that states an object will always take the path of least action as compared to any other conceivable path. This principle can be used to derive the equations of motion of many systems, and therefore provides a unifying equation that has been applied in many fields of physics and mathematics. Hamilton’s formulation of the principle of least action typically only accounts for conservative forces, but can be reformulated to include non-conservative forces such as friction. However, it can be shown that with large values of damping, the object will no longer …

Optimization Methods For Learning Graph-Structured Sparse Models, Baojian Zhou

Legacy Theses & Dissertations (2009 - 2024)

Learning graph-structured sparse models has recently received significant attention thanks to their broad applicability to many important real-world problems. However, such models, of more effective and stronger interpretability compared with their counterparts, are difficult to learn due to optimization challenges. This thesis presents optimization algorithms for learning graph-structured sparse models under three different problem settings. Firstly, under the batch learning setting, we develop methods that can be applied to different objective functions that enjoy linear convergence guarantees up to constant errors. They can effectively optimize the statistical score functions in the task of subgraph detection; Secondly, under stochastic learning setting, …

Pawnee Dam Inflow Design Flood (Idf) Update And Stage-Frequency Curve Development Using Rmcrfa, Jennifer P. Christensen, Joshua J. Melliger

United States Geological Survey: Water Reports and Publications

Pawnee Dam is one of the ten Salt Creek Dams designed and built in the 1960s to mitigate flooding in Lincoln, Nebraska. This short paper illustrates the update of the Pawnee Dam inflow design flood (IDF) through calibration to recent high flow events and the development of its stage-frequency or hydrologic loading curve with the U.S. Army Corps of Engineers’ Risk Management Center Reservoir Frequency Analysis (RMC-RFA) model. The IDF update follows Engineering Regulation 1110-8-2, Inflow Design Flood for Dams and Reservoirs, including unit hydrograph peaking and two antecedent pool elevations. Background information on the original design of the dam …

Stabilize Chaotic Flows In A Coupled Triple-Loop Thermosyphon System, Haley N. Anderson

Honors College Theses

This study addresses the control of chaotic dynamic systems represented by three coupled Lorenz systems. In application, Lorenz systems are commonly used to describe the one-dimensional motion of fluids in a tube when heated below and cooled above. This system, in particular, reflects the fluid motion in a coupled triple-loop thermosyphon system. The goal is to derive a system of nonlinear differential equations to help us study various flow patterns governed by such a high-dimensional nonlinear model numerically. Once the driving parameter (Rayleigh number) values are identified corresponding to the chaotic regime, a minimal number of proportional controllers are designed …

Inverse Gaussian Ornstein-Uhlenbeck Applied To Modeling High Frequency Data, Emmanuel Kofi Kusi

Open Access Theses & Dissertations

With about 226050 estimated deaths worldwide in 2010, an earthquake is considered as one of the disasters that records a great number of deaths. This thesis develops a model for the estimation of magnitude of future seismic events.

We propose a stochastic differential equation arising on the Ornstein-Uhlenbeck processes driven by IG(a,b) process. IG(a,b) Ornstein-Uhlenbeck processes offers analytic flexibility and provides a class of continuous time processes capable of exhibiting long memory

behavior. The stochastic differential equation is applied to geophysics and financial stock markets by fitting the superposed IG(a,b) Ornstein-Uhlenbeck model to earthquake and financial time series.

On The Role Of Ill-Conditioning: Biharmonic Eigenvalue Problem And Multigrid Algorithms, Kasey Bray

Theses and Dissertations--Mathematics

Very fine discretizations of differential operators often lead to large, sparse matrices A, where the condition number of A is large. Such ill-conditioning has well known effects on both solving linear systems and eigenvalue computations, and, in general, computing solutions with relative accuracy independent of the condition number is highly desirable. This dissertation is divided into two parts.

In the first part, we discuss a method of preconditioning, developed by Ye, which allows solutions of Ax=b to be computed accurately. This, in turn, allows for accurate eigenvalue computations. We then use this method to develop discretizations that yield accurate computations …

An Inverse Eigenvalue Problem For The Schrödinger Equation On The Unit Ball Of R3, Maryam Ali Al Ghafli

Theses and Dissertations--Mathematics

The inverse eigenvalue problem for a given operator is to determine the coefficients by using knowledge of its eigenfunctions and eigenvalues. These are determined by the behavior of the solutions on the domain boundaries. In our problem, the Schrödinger operator acting on functions defined on the unit ball of $\mathbb{R}^3$ has a radial potential taken from $L^2_{\mathbb{R}}[0,1].$ Hence the set of the eigenvalues of this problem is the union of the eigenvalues of infinitely many Sturm-Liouville operators on $[0,1]$ with the Dirichlet boundary conditions. Each Sturm-Liouville operator corresponds to an angular momentum $l =0,1,2....$. In this research we focus on …

Quasilinearization And Boundary Value Problems For Riemann-Liouville Fractional Differential Equations, Paul W. Eloe, Jaganmohan Jonnalagadda

Mathematics Faculty Publications

We apply the quasilinearization method to a Dirichlet boundary value problem and to a right focal boundary value problem for a RiemannLiouville fractional differential equation. First, we sue the method of upper and lower solutions to obtain the uniqueness of solutions of the Dirichlet boundary value problem. Next, we apply a suitable fixed point theorem to establish the existence of solutions. We develop a quasilinearization algorithm and construct sequences of approximate solutions that converge monotonically and quadratically to the unique solution of the boundary value problem. Two examples are exhibited to illustrate the main result for the Dirichlet boundary value …

The Large Contraction Principle And Existence Of Periodic Solutions For Infinite Delay Volterra Difference Equations, Paul W. Eloe, Jaganmohan Jonnalagadda, Youssef Raffoul

Mathematics Faculty Publications

In this article, we establish sufficient conditions for the existence of periodic solutions of a nonlinear infinite delay Volterra difference equation. (See paper for equation.)

We employ a Krasnosel’skii type fixed point theorem, originally proved by Burton. The primary sufficient condition is not verifiable in terms of the parameters of the difference equation, and so we provide three applications in which the primary sufficient condition is verified.

Avery Fixed Point Theorem Applied To A Hammerstein Integral Equation, Paul W. Eloe, Jeffrey T. Neugebauer

Mathematics Faculty Publications

Abstract. We apply a recent Avery et al. fixed point theorem to the Hammerstein integral equation (see paper for equation). Under certain conditions on G, we show the existence of positive and positive symmetric solutions. Examples are given where G is a convolution kernel and where G is a Green’s function associated with different boundary-value problem.

Randomized Algorithms For Preconditioner Selection With Applications To Kernel Regression, Conner Dipaolo

HMC Senior Theses

The task of choosing a preconditioner M to use when solving a linear system Ax=b with iterative methods is often tedious and most methods remain ad-hoc. This thesis presents a randomized algorithm to make this chore less painful through use of randomized algorithms for estimating traces. In particular, we show that the preconditioner stability || I - M^-1A ||_F, known to forecast preconditioner quality, can be computed in the time it takes to run a constant number of iterations of conjugate gradients through use of sketching methods. This is in spite of folklore which …

Non-Marginal Decisions: A Novel Bayesian Multiple Testing Procedure, Noirrit Kiran Chandra, Sourabh Bhattacharya

Journal Articles

In this paper, we consider the problem of multiple testing where the hypotheses are dependent. In most of the existing literature, either Bayesian or non-Bayesian, the decision rules mainly focus on the validity of the test procedure rather than actually utilizing the dependency to increase efficiency. Moreover, the decisions regarding different hypotheses are marginal in the sense that they do not depend upon each other directly. However, in realistic situations, the hypotheses are usually dependent, and hence it is desirable that the decisions regarding the dependent hypotheses are taken jointly. In this article, we develop a novel Bayesian multiple testing …

Bayesian Hierarchical Meta-Analysis Of Asymptomatic Ebola Seroprevalence, Peter Brody-Moore

CMC Senior Theses

The continued study of asymptomatic Ebolavirus infection is necessary to develop a more complete understanding of Ebola transmission dynamics. This paper conducts a meta-analysis of eight studies that measure seroprevalence (the number of subjects that test positive for anti-Ebolavirus antibodies in their blood) in subjects with household exposure or known case-contact with Ebola, but that have shown no symptoms. In our two random effects Bayesian hierarchical models, we find estimated seroprevalences of 8.76% and 9.72%, significantly higher than the 3.3% found by a previous meta-analysis of these eight studies. We also produce a variation of this meta-analysis where we exclude …

Mathematically Modeling The Role Of Triglyceride Production On Leptin Resistance, Yu Zhao, Daniel Burkow, Baojun Song

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Diet-induced obesity is becoming more common all over the world, which is increasing the prevalence of obesity-induced chronic diseases such as diabetes, coronary heart disease, cancer, and sleep apnea. Many experimental results show that obesity is often associated with an elevated concentration of plasma leptin and triglycerides. Triglycerides inhibit the passage of leptin across the blood–brain barrier (BBB) to signal the hypothalamus to suppress appetite. However, it is still not clear how triglyceride concentration affects leptin transport across the BBB and energy balance. In this paper, we propose a novel ordinary differential equations model describing the role of leptin in …

A Family Of Cantorvals, John Ferdinands, Timothy Ferdinands

University Faculty Publications and Creative Works

The set of subsums of the series Σn=1∞ xn is known to be one of three types: a finite union of intervals, homeomorphic to the Cantor set, or of the type known as a Cantorval. Bartoszewicz, Filipczak and Szymonik have described a family of series which contained all known examples of subsum sets which are Cantorvals. We construct another family of series which produces new examples of subsum sets which are Cantorvals.

An Approach To Determining Customer Satisfaction In Traditional Serbian Restaurants, Florentin Smarandache, Dragisa Stanujkic, Darjan Karabasevic, Edmundas Kazimieras Zavadskas, F. Cavallaro

Branch Mathematics and Statistics Faculty and Staff Publications

The aim of this paper is to make a proposal for an easy–to–use approach to the evaluation of customer satisfaction in restaurants. In order to provide a reliable way to collect respondents’ real attitudes, an approach based on the use of smaller number of evaluation criteria and interactive questionnaire created in a spreadsheet file is proposed in this paper, whereby an easy-to-understand and simple-touse procedure is proposed for determining weights of criteria. In addition to the said, the proposed approach applies the simplified SERVQUAL-based approach, for which reason a simplified version of the Weighted Sum Method based on the decision …