Modeling Contagion In The Eurozone Crisis Via Dynamical Systems,
2015
New York University
Modeling Contagion In The Eurozone Crisis Via Dynamical Systems, Giuseppe Castellacci, Youngna Choi
Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works
We recently (Castellacci and Choi, 2013) formulated a theoretical framework for the modeling of financial instability contagion using the theories of dynamical systems. Here, our main goal is to model the Eurozone financial crisis within that framework. The underlying system comprises many economic agents that belong to several subsystems. In each instantiation of this framework, the hierarchy and nesting of the subsystems is dictated by the nature of the problem at hand. We describe in great detail how a suitable model can be set up for the Eurozone crisis. The dynamical system is defined by the evolution of the wealths …
The Coupled Within- And Between-Host Dynamics In The Evolution Of Hiv/Aids In China,
2015
Shanghai University
The Coupled Within- And Between-Host Dynamics In The Evolution Of Hiv/Aids In China, Jie Lou, Hongna Zhou, Dong Liang, Zhen Jin, Baojun Song
Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works
In this work, we develop and analyze mathematical models for the coupled within-host and between-host dynamics caricaturing the evolution of HIV/AIDS. The host population is divided into susceptible, the infected without receiving treatment and the infected receiving ART treatment in accordance with China’s Four-Free-One-Care Policy. The within-host model is a typical ODE model adopted from literatures. The between-host model incorporates age-since-infection described by a system of integrodifferential equations. The two models are coupled via the viral load and number of CD4+ T cells of within the hosts. For the between-host model with an arbitrarily selected HIV infected individual, we focus …
A Survey Of Mathematical Models Of Dengue Fever,
2015
Georgia Southern University
A Survey Of Mathematical Models Of Dengue Fever, Iurii Bakach
College of Graduate Studies: Theses & Dissertations
In this paper, we compare and contrast five models of Dengue fever. We evaluate each model using different scenarios and identify the strenghts and wecknesses of each of the model
Solutions Of Inequality Constrained Spline Optimization Problems With The Active Set Method,
2015
Georgia Southern University
Solutions Of Inequality Constrained Spline Optimization Problems With The Active Set Method, Joshua A. Holloway
College of Graduate Studies: Theses & Dissertations
We solve the problem of finding a near-interpolant curve, subject to constraints, which minimizes the bending energy of the curve. Using B-splines as our tools, we give a brief overview of spline properties and develop several different cases of inequality constrained optimization problems of this type. In particular, we develop the active set method and use it to solve these problems, emphasizing the fact that this algorithm will converge to a solution in finite iterations. Our solution will solve an open problem regarding near-interpolant spline curves. Furthermore, we supplement this with an iterative technique for better choosing data sites so …
Topological Dynamics On Compact Phase Spaces,
2015
Louisiana State University and Agricultural and Mechanical College
Topological Dynamics On Compact Phase Spaces, Lieth Abdalateef Majed
LSU Doctoral Dissertations
Our main focus will be to investigate the various facets of what are commonly called dynamical systems or flows, which are triples $(S,X,\pi)$, where $X$ is a compact Hausdorff space and $\pi:S \times X \longrightarrow X$ is a separately continuous action of a semigroup $S$ on $X$. Historically, as was introduced by R.Ellis 1960, the enveloping semigroup, which is a closure of the set of continuous functions on a compact space $X$, was discovered to be an important tool to study dynamical systems. Soon, a realization of the existence of a universal compactification of a phase semigroup with an extended …
Mathematical Modeling Of Emiliania Huxleyi And A Host-Specific Virus,
2015
Colby College
Mathematical Modeling Of Emiliania Huxleyi And A Host-Specific Virus, Julia Middleton
Honors Theses
The world’s oceans provide the basis for life on the planet. One microscopic algae, the coccolithophores, and Emiliania huxleyi in particular, is a major source of carbon drawdown in the context of the global carbon cycle and account for a significant amount of the primary production in oceanic ecosystems. We know that the oceans are packed with marine viruses and they have an important role in the rise and fall of plankton populations but current mathematical models do not accurately account for virus-host interactions when predicting plankton blooms. Therefore I am using model optimization and comparison techniques to evaluate current …
Stochastic Approximation Algorithms With Applications To Particle Swarm Optimization, Adaptive Optimization, And Consensus,
2015
Wayne State University
Stochastic Approximation Algorithms With Applications To Particle Swarm Optimization, Adaptive Optimization, And Consensus, Quan Yuan
Wayne State University Dissertations
In this dissertation, we present three problems arising in recent applications of stochastic approximation methods. In Chapter 2, we use stochastic approximation to analyze Particle Swarm Optimization (PSO) algorithm. We introduce four coefficients and rewrite the PSO procedure as a stochastic approximation type iterative algorithm. Then we analyze its convergence using weak convergence method. It is proved that a suitably scaled sequence of swarms converge to the solution of an ordinary differential equation. We also establish certain stability results. Moreover, convergence rates are ascertained by using weak convergence method. A centered and scaled sequence of the estimation errors is shown …
On The Dynamics Of Internal Waves Interacting With The Equatorial Undercurrent,
2015
Technological University Dublin
On The Dynamics Of Internal Waves Interacting With The Equatorial Undercurrent, Alan Compelli, Rossen Ivanov
Articles
The interaction of the nonlinear internal waves with a nonuniform current with a specific form, characteristic for the equatorial undercurrent, is studied. The current has no vorticity in the layer, where the internal wave motion takes place. We show that the nonzero vorticity that might be occuring in other layers of the current does not affect the wave motion. The equations of motion are formulated as a Hamiltonian system.
Conditions For Deterministic Limits Of Markov Jump Processes : The Kurtz Theorem In Chemistry,
2015
University at Albany, State University of New York
Conditions For Deterministic Limits Of Markov Jump Processes : The Kurtz Theorem In Chemistry, Ada Anna Sedova
Legacy Theses & Dissertations (2009 - 2024)
A theorem by Kurtz on convergence of Markov jump processes is presented as it relates
The Pascal Matrix Function And Its Applications To Bernoulli Numbers And Bernoulli Polynomials And Euler Numbers And Euler Polynomials,
2015
Illinois Wesleyan University
The Pascal Matrix Function And Its Applications To Bernoulli Numbers And Bernoulli Polynomials And Euler Numbers And Euler Polynomials, Tian-Xiao He, Jeff Liao, Peter Shiue
Scholarship
A Pascal matrix function is introduced by Call and Velleman in [3]. In this paper, we will use the function to give a united approach in the study of Bernoulli numbers and Bernoulli polynomials. Many well-known and new properties of the Bernoulli numbers and polynomials can be established by using the Pascal matrix function. The approach is also applied to the study of Euler numbers and Euler polynomials.
Clique Topology Reveals Intrinsic Geometric Structure In
Neural Correlations,
2015
University of Pennsylvania
Clique Topology Reveals Intrinsic Geometric Structure In Neural Correlations, Chad Giusti, Eva Pastalkova, Carina Curto, Vladimir Itskov
Department of Mathematics: Faculty Publications
Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a 2D environment, and confirmed that our method is able to detect geometric organization using …
The Interplay Between Wnt Mediated
Expansion And Negative Regulation Of
Growth Promotes Robust Intestinal Crypt
Structure And Homeostasis,
2015
University of California, Irvine
The Interplay Between Wnt Mediated Expansion And Negative Regulation Of Growth Promotes Robust Intestinal Crypt Structure And Homeostasis, Huijing Du, Qing Nie, William R. Holmes
Department of Mathematics: Faculty Publications
The epithelium of the small intestinal crypt, which has a vital role in protecting the underlying tissue from the harsh intestinal environment, is completely renewed every 4–5 days by a small pool of stem cells at the base of each crypt. How is this renewal controlled and homeostasis maintained, particularly given the rapid nature of this process? Here, based on the recent observations from in vitro “mini gut” studies, we use a hybrid stochastic model of the crypt to investigate how exogenous niche signaling (from Wnt and BMP) combines with auto-regulation to promote homeostasis. This model builds on the sub-cellular …
A Hamiltonian Approach To Wave-Current Interactions In Two-Layer Fluids,
2015
Technological University Dublin
A Hamiltonian Approach To Wave-Current Interactions In Two-Layer Fluids, Adrian Constantin, Rossen Ivanov
Articles
We provide a Hamiltonian formulation for the governing equations describing the two-dimensional nonlinear interaction between coupled surfacewaves, internalwaves, and an underlying current with piecewise constant vorticity, in a two-layered fluid overlying a flat bed. This Hamiltonian structure is a starting point for the derivation of simpler models, which can be obtained systematically by expanding the Hamiltonian in dimensionless parameters. These enable an in-depth study of the coupling between the surface and internal waves, and how both these wave systems interact with the background current.
A Class Of High-Order Runge-Kutta-Chebyshev Stability Polynomials,
2015
Technological University Dublin
A Class Of High-Order Runge-Kutta-Chebyshev Stability Polynomials, Stephen O'Sullivan
Articles
The analytic form of a new class of factorized Runge-Kutta-Chebyshev (FRKC) stability polynomials of arbitrary order N is presented. Roots of FRKC stability polynomials of degree L = MN are used to construct explicit schemes comprising L forward Euler stages with internal stability ensured through a sequencing algorithm which limits the internal amplification factors to ~ L2. The associated stability domain scales as M2 along the real axis. Marginally stable real-valued points on the interior of the stability domain are removed via a prescribed damping procedure. By construction, FRKC schemes meet all linear order conditions; for nonlinear …
Will Oscillating Wave Surge Converters Survive Tsunamis?,
2015
Technological University Dublin
Will Oscillating Wave Surge Converters Survive Tsunamis?, Laura Cooke, P. Christodoulides, E. Renzi, T. Stefanakis, F. Dias
Articles
With an increasing emphasis on renewable energy resources, wave power technology is becoming one of the realistic solutions. However, the 2011 tsunami in Japan was a harsh reminder of the ferocity of the ocean. It is known that tsunamis are nearly undetectable in the open ocean but as the wave approaches the shore its energy is compressed, creating large destructive waves. The question posed here is whether an oscillating wave surge converter (OWSC) could withstand the force of an incoming tsunami. Several tools are used to provide an answer: an analytical 3D model developed within the framework of linear theory, …
A Heterogeneous Multiscale Method For Poroelasticity,
2015
University of Texas at El Paso
A Heterogeneous Multiscale Method For Poroelasticity, Paul M. Delgado
Open Access Theses & Dissertations
In this Thesis, we develop and analyze a heterogeneous multiscale model for coupled fluid flow and solid deformation in porous media based on operator splitting and finite volume method. The splitting method results in two elliptic multiscale PDE's in the form of a reaction diffusion equation and a linear elasticity equation. We extend our previous multiscale method from 1D to higher dimensions and develop new approaches for the inclusion of mixed boundary conditions and source terms. We derive an error estimate for our multiscale method and analyze the stability of our splitting method. We also test the effectiveness of our …
Stability Of A Circular System With Multiple Asymmetric Laplacians,
2015
Czech Technical University, Prague
Stability Of A Circular System With Multiple Asymmetric Laplacians, Ivo Herman, Dan Martinec, J. J. P. Veerman, Michael Sebek
Mathematics and Statistics Faculty Publications and Presentations
We consider an asymptotic stability of a circular system where the coupling Laplacians are different for each state used for synchronization. It is shown that there must be a symmetric coupling in the output state to guarantee the stability for agents with two integrators in the open loop. Systems with agents having three or more integrators cannot be stabilized by any coupling. In addition, recent works in analysis of a scaling in vehicular platoons relate the asymptotic stability of a circular system to a string stability. Therefore, as confirmed by simulations in the paper, our results have an application also …
Singular Value Computation And Subspace Clustering,
2015
University of Kentucky
Singular Value Computation And Subspace Clustering, Qiao Liang
Theses and Dissertations--Mathematics
In this dissertation we discuss two problems. In the first part, we consider the problem of computing a few extreme eigenvalues of a symmetric definite generalized eigenvalue problem or a few extreme singular values of a large and sparse matrix. The standard method of choice of computing a few extreme eigenvalues of a large symmetric matrix is the Lanczos or the implicitly restarted Lanczos method. These methods usually employ a shift-and-invert transformation to accelerate the speed of convergence, which is not practical for truly large problems. With this in mind, Golub and Ye proposes an inverse-free preconditioned Krylov subspace method, …
Analysis And Constructions Of Subspace Codes,
2015
University of Kentucky
Analysis And Constructions Of Subspace Codes, Carolyn E. Troha
Theses and Dissertations--Mathematics
Random network coding is the most effcient way to send data across a network, but it is very susceptible to errors and erasures. In 2008, Kotter and Kschischang introduced subspace codes as an algebraic approach to error correcting in random network coding. Since this paper, there has been much work in constructing large subspace codes, as well as exploring the properties of such codes. This dissertation explores properties of one particular construction and introduces a new construction for subspace codes. We begin by exploring properties of irreducible cyclic orbit codes, which were introduced in 2011 by Rosenthal et al. As …
The Krylov Subspace Methods For The Computation Of Matrix Exponentials,
2015
University of Kentucky
The Krylov Subspace Methods For The Computation Of Matrix Exponentials, Hao Wang
Theses and Dissertations--Mathematics
The problem of computing the matrix exponential etA arises in many theoretical and practical problems. Many methods have been developed to accurately and efficiently compute this matrix function or its product with a vector, i.e., etAv. In the past few decades, with the increasing need of the computation for large sparse matrices, iterative methods such as the Krylov subspace methods have proved to be a powerful class of methods in dealing with many linear algebra problems. The Krylov subspace methods have been introduced for computing matrix exponentials by Gallopoulos and Saad, and the corresponding error bounds …
