Bounded, Asymptotically Stable, And L^1 Solutions Of Caputo Fractional Differential Equations,
2015
University of Dayton
Bounded, Asymptotically Stable, And L^1 Solutions Of Caputo Fractional Differential Equations, Muhammad Islam
Mathematics Faculty Publications
The existence of bounded solutions, asymptotically stable solutions, and L1 solutions of a Caputo fractional differential equation has been studied in this paper. The results are obtained from an equivalent Volterra integral equation which is derived by inverting the fractional differential equation. The kernel function of this integral equation is weakly singular and hence the standard techniques that are normally applied on Volterra integral equations do not apply here. This hurdle is overcomed using a resolvent equation and then applying some known properties of the resolvent. In the analysis Schauder's fixed point theorem and Liapunov's method have been employed. …
Why Lattice-Valued Fuzzy Values? A Mathematical Justification,
2015
Chiang Mai University
Why Lattice-Valued Fuzzy Values? A Mathematical Justification, Rujira Ouncharoen, Vladik Kreinovich, Hung T. Nguyen
Departmental Technical Reports (CS)
To take into account that expert's degrees of certainty are not always comparable, researchers have used partially ordered set of degrees instead of the more traditional linearly (totally) ordered interval [0,1]. In most cases, it is assumed that this partially ordered set is a lattice, i.e., every two elements have the greatest lower bound and the least upper bound. In this paper, we prove a theorem explaining why it is reasonable to require that the set of degrees is a lattice.
Solutions Of A Logistic Equation On Varying Time Scales: A Quantitative And Qualitative Analysis,
2015
Marshall University
Solutions Of A Logistic Equation On Varying Time Scales: A Quantitative And Qualitative Analysis, Alexandria Amity Amorim
Theses, Dissertations and Capstones
Time Scale Calculus, introduced by Dr. Stefan Hilger in 1988, combines the study of differential and difference equations into a single topic. We begin with an introduction of sets used in this field, time scales, and build up to the definition of the exponential function on a time scale. The main focus of this work is a study of the solutions of a particular logistic dynamic equation on varying time scales. We study both the analytical and graphical solutions of this equation. Analytical solutions are worked out using theorems from Time Scale Calculus, including properties of the exponential function. Graphical …
Firing Rate Dynamics In Recurrent Spiking Neural Networks With Intrinsic And Network Heterogeneity,
2015
Virginia Commonwealth University
Firing Rate Dynamics In Recurrent Spiking Neural Networks With Intrinsic And Network Heterogeneity, Cheng Ly
Statistical Sciences and Operations Research Publications
Heterogeneity of neural attributes has recently gained a lot of attention and is increasing recognized as a crucial feature in neural processing. Despite its importance, this physiological feature has traditionally been neglected in theoretical studies of cortical neural networks. Thus, there is still a lot unknown about the consequences of cellular and circuit heterogeneity in spiking neural networks. In particular, combining network or synaptic heterogeneity and intrinsic heterogeneity has yet to be considered systematically despite the fact that both are known to exist and likely have significant roles in neural network dynamics. In a canonical recurrent spiking neural network model, …
Algae Population Self-Replenishment,
2015
George Fox University
Algae Population Self-Replenishment, R. Corban Harwood
Faculty Publications - Department of Mathematics
This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, in 1994. After reading a summary of news articles on the incident, students create an ODE system model from a verbal description of the factors, visualize this system using an executable Java applet (PPLANE) to predict overall behavior, and then analyze the nonlinear system using the Jacobian matrix, eigenvalues, phase plane, and feasibility conditions on parameters to fully describe the system behavior. Students are expected to be familiar with systems of differential equations, equilibria, jacobian matrices, and eigenvalues. Students will learn modeling from qualitative descriptions, nondimensionalization, applying …
Minimax Portfolio Optimization Under Interval Uncertainty,
2015
Waseda University
Minimax Portfolio Optimization Under Interval Uncertainty, Meng Yuan, Xu Lin, Junzo Watada, Vladik Kreinovich
Departmental Technical Reports (CS)
In the 1950s, Markowitz proposed to combine different investment instruments to design a portfolio that either maximizes the expected return under constraints on volatility (risk) or minimizes the risk under given expected return. Markowitz's formulas are still widely used in financial practice. However, these formulas assume that we know the exact values of expected return and variance for each instrument, and that we know the exact covariance of every two instruments. In practice, we only know these values with some uncertainty. Often, we only know the bounds of these values -- i.e., in other words, we only know the intervals …
Almost Sure Asymptotic Stabilization Of Differential Equations With Time-Varying Delay By Lévy Noise,
2015
Nanjing University of Science and Technology
Almost Sure Asymptotic Stabilization Of Differential Equations With Time-Varying Delay By Lévy Noise, Dezhi Liu, Weiqun Wang, Jose Luis Menaldi
Mathematics Faculty Research Publications
This paper aims to determine that the Lévy noise can stabilize the given differential equations with time-varying delay, which has generalized the Brownian motion case. An analysis is developed and sufficient conditions on the stabilization for stochastic differential equations with time-varying delay are presented. Our stabilization criteria is in terms of linear matrix inequalities (LMIs), whence the feedback controls can be designed more easily in practice.
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 …
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 …
Process Design, Dynamics, And Techno-Economic Analysis Of A Sustainable Coal, Wind, And Small Modular Nuclear Reactor Hybrid Energy System,
2015
Missouri University of Science and Technology
Process Design, Dynamics, And Techno-Economic Analysis Of A Sustainable Coal, Wind, And Small Modular Nuclear Reactor Hybrid Energy System, Kyle Lee Buchheit
Doctoral Dissertations
"The availability of cheap electricity is one of the biggest factors for improving quality of life. With the debate on the effects of carbon dioxide emissions continuing, several countries have either implemented or are considering the reduction of emissions through various economic means. The inclusion of a monetary penalty on carbon emissions would increase the prices of electricity produced by carbon-based sources. The push for large-scale renewable sources of energy has met problems with regards to energy storage and availability. The proposed coal, wind, and nuclear hybrid energy system would combine a renewable energy source, wind, with traditional and stable …
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 …
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
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 …
An Exposition And Calibration Of The Ho-Lee Model Of Interest Rates,
2015
Claremont McKenna College
An Exposition And Calibration Of The Ho-Lee Model Of Interest Rates, Benjamin I. Lawson
CMC Senior Theses
The purpose of this paper is to create an easily understandable version of the Ho-Lee interest rate model. The first part analyzes the model in detail, and the second part calibrates it to demonstrate how it can be applied to real market data.
One-Bit Compressive Sensing With Partial Support Information,
2015
Claremont McKenna College
One-Bit Compressive Sensing With Partial Support Information, Phillip North
CMC Senior Theses
This work develops novel algorithms for incorporating prior-support information into the field of One-Bit Compressed Sensing. Traditionally, Compressed Sensing is used for acquiring high-dimensional signals from few linear measurements. In applications, it is often the case that we have some knowledge of the structure of our signal(s) beforehand, and thus we would like to leverage it to attain more accurate and efficient recovery. Additionally, the Compressive Sensing framework maintains relevance even when the available measurements are subject to extreme quantization. Indeed, the field of One-Bit Compressive Sensing aims to recover a signal from measurements reduced to only their sign-bit. This …
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 …
