Intelligent Firefly Algorithm For Global Optimization, 2014 SelectedWorks

#### Intelligent Firefly Algorithm For Global Optimization, Seif-Eddeen K. Fateen, Adrián Bonilla-Petriciolet

*Seif-Eddeen K Fateen*

Intelligent firefly algorithm (IFA) is a novel global optimization algorithm that aims to improve the performance of the firefly algorithm (FA), whichwas inspired by the flashing communication signals among firefly swarms. This chapter introduces the IFA modification and evaluates its performance in comparison with the original algorithm in twenty multi-dimensional benchmark problems. The results of those numerical experiments show that IFA outperformed FA in terms of reliability and effectiveness in all tested benchmark problems. In some cases, the global minimum could not have been successfully identified via the firefly algorithm, except with the proposed modification for FA.

Fast Estimation Of Time-Varying Transmission Rates For Infectious Diseases, 2014 McMaster University

#### Fast Estimation Of Time-Varying Transmission Rates For Infectious Diseases, Michelle S. Dejonge

*Open Access Dissertations and Theses*

Modelling and analysis of recurrent infectious disease epidemics often depends on the reconstruction of a time-varying transmission rate from historical reports of cases or deaths. Statistically rigorous estimation methods for time-varying transmission rates exist but are too computationally demanding to apply to a time series longer than a few decades. We present a computationally ecient estimation method that is suitable for very long data sets. Our method, which uses a discrete-time approximation to the SIR model for infectious diseases, is easy to implement and outperforms the classic Fine and Clarkson estimation method.

Parameter Identification For Ordinary And Delay Differential Equations By Using Flat Inputs, 2014 SelectedWorks

#### Parameter Identification For Ordinary And Delay Differential Equations By Using Flat Inputs, René Schenkendorf, Michael Mangold

*René Schenkendorf*

The concept of differential flatness has been widely used for nonlinear controller design. In this contribution, it is shown that flatness may also be a very useful property for parameter identification. An identification method based on flat inputs is introduced. The treatment of noisy measurements and the extension of the method to delay differential equations are discussed. The method is illustrated by two case studies: the well-known FitzHugh-Nagumo equations and a virus replication model with delays.

Simulating Burr Type Vii Distributions Through The Method Of L-Moments And L-Correlations, 2014 SelectedWorks

#### Simulating Burr Type Vii Distributions Through The Method Of L-Moments And L-Correlations, Mohan D. Pant, Todd C. Headrick

*Mohan Dev Pant*

Burr Type VII, a one-parameter non-normal distribution, is among the less studied distributions, especially, in the contexts of statistical modeling and simulation studies. The main purpose of this study is to introduce a methodology for simulating univariate and multivariate Burr Type VII distributions through the method of L-moments and L-correlations. The methodology can be applied in statistical modeling of events in a variety of applied mathematical contexts and Monte Carlo simulation studies. Numerical examples are provided to demonstrate that L-moment-based Burr Type VII distributions are superior to their conventional moment-based analogs in terms of distribution fitting and estimation. Simulation results ...

Analytical Solution Of The Symmetric Circulant Tridiagonal Linear System, 2014 Rose-Hulman Institute of Technology

#### Analytical Solution Of The Symmetric Circulant Tridiagonal Linear System, Sean A. Broughton, Jeffery J. Leader

*Mathematical Sciences Technical Reports (MSTR)*

A circulant tridiagonal system is a special type of Toeplitz system that appears in a variety of problems in scientific computation. In this paper we give a formula for the inverse of a symmetric circulant tridiagonal matrix as a product of a circulant matrix and its transpose, and discuss the utility of this approach for solving the associated system.

Understanding Recurrent Disease: A Dynamical Systems Approach, 2014 Western University

#### Understanding Recurrent Disease: A Dynamical Systems Approach, Wenjing Zhang

*University of Western Ontario - Electronic Thesis and Dissertation Repository*

Recurrent disease, characterized by repeated alternations between acute relapse and long re- mission, can be a feature of both common diseases, like ear infections, and serious chronic diseases, such as HIV infection or multiple sclerosis. Due to their poorly understood etiology and the resultant challenge for medical treatment and patient management, recurrent diseases attract much attention in clinical research and biomathematics. Previous studies of recurrence by biomathematicians mainly focus on in-host models and generate recurrent patterns by in- corporating forcing functions or stochastic elements. In this study, we investigate deterministic in-host models through the qualitative analysis of dynamical systems, to ...

Observational Signatures From Self-Gravitating Protostellar Disks, 2014 Western University

#### Observational Signatures From Self-Gravitating Protostellar Disks, Alexander L. Desouza

*University of Western Ontario - Electronic Thesis and Dissertation Repository*

Protostellar disks are the ubiquitous corollary outcome of the angular momentum conserving, gravitational collapse of molecular cloud cores into stars. Disks are an essential component of the star formation process, mediating the accretion of material onto the protostar, and for redistributing excess angular momentum during the collapse. We present a model to explain the observed correlation between mass accretion rates and stellar mass that has been inferred from observations of intermediate to upper mass T Tauri stars. We explain this correlation within the framework of gravitationally driven torques parameterized in terms of Toomre’s Q criterion. Our models reproduce both ...

Estimation Of Hidden Markov Models And Their Applications In Finance, 2014 Western University

#### Estimation Of Hidden Markov Models And Their Applications In Finance, Anton Tenyakov

*University of Western Ontario - Electronic Thesis and Dissertation Repository*

Movements of financial variables exhibit extreme fluctuations during periods of economic crisis and times of market uncertainty. They are also affected by institutional policies and intervention of regulatory authorities. These structural changes driving prices and other economic indicators can be captured reasonably by models featuring regime-switching capabilities. Hidden Markov models (HMM) modulating the model parameters to incorporate such regime-switching dynamics have been put forward in recent years, but many of them could still be further improved. In this research, we aim to address some of the inadequacies of previous regime-switching models in terms of their capacity to provide better forecasts ...

One-Dimensional Weakly Nonlinear Model Equations For Rossby Waves, 2014 Dublin Institute of Technology

#### One-Dimensional Weakly Nonlinear Model Equations For Rossby Waves, David Henry, Rossen Ivanov

*Articles*

In this study we explore several possibilities for modelling weakly nonlinear Rossby waves in fluid of constant depth, which propagate predominantly in one direction. The model equations obtained include the BBM equation, as well as the integrable KdV and Degasperis-Procesi equations.

The Neural Ring: Using Algebraic Geometry To Analyze Neural Codes, 2014 University of Nebraska - Lincoln

#### The Neural Ring: Using Algebraic Geometry To Analyze Neural Codes, Nora Youngs

*Dissertations, Theses, and Student Research Papers in Mathematics*

Neurons in the brain represent external stimuli via neural codes. These codes often arise from stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer properties of a represented stimulus space without knowledge of the receptive fields, using only the intrinsic structure of the neural code. How does the brain do this? To address this question, it is important to determine what stimulus space features can - in principle - be extracted from neural codes. This motivates us to define the neural ring and a related neural ideal, algebraic objects that encode ...

Boundary Value Problems Of Nabla Fractional Difference Equations, 2014 University of Nebraska - Lincoln

#### Boundary Value Problems Of Nabla Fractional Difference Equations, Abigail M. Brackins

*Dissertations, Theses, and Student Research Papers in Mathematics*

In this dissertation we develop the theory of the nabla fractional self-adjoint difference equation,

∇_{a}^{ν}(p∇y)(t)+q(t)y(ρ(t)) = f(t),

where 0 < ν < 1.We begin with an introduction to the nabla fractional calculus. In the second chapter, we show existence and uniqueness of the solution to a fractional self-adjoint initial value problem. We find a variation of constants formula for this fractional initial value problem, and use the variation of constants formula to derive the Green's function for a related boundary value problem. We study the Green's function and its properties in several settings. For a simplified boundary value problem, we show that the Green's function is nonnegative and we find its maximum and the maximum of its integral. For a boundary value problem with generalized boundary conditions, we find the Green's function and show that it is a generalization of the first Green's function. In the third chapter, we use the Contraction Mapping Theorem to prove existence and uniqueness of a positive solution to a forced self-adjoint fractional difference equation with a finite limit. We explore modifications to the forcing term and modifications to the space of functions in which the solution exists, and we provide examples to demonstrate the use of these theorems.

Advisers: Lynn Erbe and Allan Peterson

Light Pollution Research Through Citizen Science, 2014 California Polytechnic State University

#### Light Pollution Research Through Citizen Science, John Kanemoto

*STEM Teacher and Researcher (STAR) Program Posters*

Light pollution (LP) can disrupt and/or degrade the health of all living things, as well as, their environments. The goal of my research at the NOAO was to check the accuracy of the citizen science LP reporting systems entitled: Globe at Night (GaN), Dark Sky Meter (DSM), and Loss of the Night (LoN). On the GaN webpage, the darkness of the night sky (DotNS) is reported by selecting a magnitude chart. Each magnitude chart has a different density/number of stars around a specific constellation. The greater number of stars implies a darker night sky. Within the DSM iPhone ...

Taylor’S Theorem And Taylor Series (Appendix A), 2014 Utah State University

#### Taylor’S Theorem And Taylor Series (Appendix A), Charles G. Torre

*Foundations of Wave Phenomena*

Taylor’s theorem and Taylor’s series constitute one of the more important tools used by mathematicians, physicists and engineers. They provides a means of approximating a function in terms of polynomials.

Vector Spaces (Appendix B), 2014 Utah State University

#### Vector Spaces (Appendix B), Charles G. Torre

*Foundations of Wave Phenomena*

Throughout this text we have noted that various objects of interest form a vector space. Here we outline the basic structure of a vector space. You may find it useful to refer to this Appendix when you encounter this concept in the text.

References And Suggestions For Further Reading (Appendix C), 2014 Utah State University

#### References And Suggestions For Further Reading (Appendix C), Charles G. Torre

*Foundations of Wave Phenomena*

References and Suggestions for Further Reading (Appendix C)

A Women In Mathematics, Computer Science, And Physics Course, 2014 College of Saint Benedict and Saint John’s University

#### A Women In Mathematics, Computer Science, And Physics Course, Jim Crumley, Kristen Nairn, Lynn Ziegler, Pamela L. Bacon, Yu Zhang

*MapCores Faculty Publications*

Increasing women's participation is a concern in disciplines beyond

physics. As part of our Mathematics, Physics, Computer Science

Research Scholars (MapCores) program, we teach a women in science

class covering these three areas. Our course is a special version of

our college's first year seminar, which is a course designed to

prepare our students to read, write, and speak at a college-level. We

structure our FYS to promote academic confidence and interest in our

disciplines for the women in MapCores. It covers not only contributions

that women have made and barriers that women face in these

disciplines, but ...

Options Pricing And Hedging In A Regime-Switching Volatility Model, 2014 Western University

#### Options Pricing And Hedging In A Regime-Switching Volatility Model, Melissa A. Mielkie

*University of Western Ontario - Electronic Thesis and Dissertation Repository*

Both deterministic and stochastic volatility models have been used to price and hedge options. Observation of real market data suggests that volatility, while stochastic, is well modelled as alternating between two states. Under this two-state regime-switching framework, we derive coupled pricing partial differential equations (PDEs) with the inclusion of a state-dependent market price of volatility risk (MPVR) term.

Since there is no closed-form solution for this pricing problem, we apply and compare two approaches to solving the coupled PDEs, assuming constant Poisson intensities. First we solve the problem using numerical solution techniques, through the application of the Crank-Nicolson numerical scheme ...

What Is Higher Mathematics? Why Is It So Hard To Interpret? What Can Be Done?, 2014 University of North Florida

#### What Is Higher Mathematics? Why Is It So Hard To Interpret? What Can Be Done?, John Tabak

*Journal of Interpretation*

Courses and seminars in higher mathematics are some of the most challenging assignments faced by academic interpreters. Difficulties interpreting higher mathematics can adversely impact the academic and professional aspirations of deaf mathematics students and professionals. This paper discusses the nature of higher mathematics with the goal of identifying what distinguishes higher mathematics from other subjects; it then reviews the history of attempts to sign/interpret higher mathematics with particular attention to current challenges associated with expressing higher mathematics in sign. The final part of the paper discusses strategies for more effectively expressing higher mathematics in American Sign Language.

Monte Carlo Simulation: When Should A Contestant Stop Spinning?, 2014 Governors State University

#### Monte Carlo Simulation: When Should A Contestant Stop Spinning?, Gregory Horn

*Student Theses*

Every episode of the popular game show *The Price Is Right* contains two rounds called The Showcase Showdown or The Big Wheel. During these rounds, three contestants spin a large wheel that consists of monetary values from five cents through one dollar in 5 cent increments. The object of this game is to get closest to one dollar without going over in one or a combination of two spins. The two winners of these rounds get to compete for the most valuable prizes at the end of each show. Monte Carlo simulation will be used to find the range of ...

A Discrete Density-Dependent Model Of The Solanum Virus, 2014 Governors State University

#### A Discrete Density-Dependent Model Of The Solanum Virus, James Morgan

*Student Theses*

Compartmental modeling has been used to model infectious diseases for roughly 100 years. Since 2009, several papers have modeled zombie outbreak using this method with various results. This paper will develop a unique model for the spread of the *The Walking Dead* zombie virus throughout the contiguous United States. Frequency dependent and density dependent transmission will be discussed, and density dependent transmission will be shown to be the appropriate choice for this model. Constant parameters, such as birth rate, bite rate, death rate, and turning rate will be determined using real-world and fictional data. After developing a basic model, modifications ...