An Optimal Threshold Strategy In The Two-Envelope Problem With Partial Information, 2015 SelectedWorks

#### An Optimal Threshold Strategy In The Two-Envelope Problem With Partial Information, Martin Egozcue, Luis Fuentes García

*Martin Egozcue*

No abstract provided.

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.

Partitioning Bipartite Graphs: A Modified Louvain, 2014 Yale University

#### Partitioning Bipartite Graphs: A Modified Louvain, Emily Diana

*Yale Day of Data*

Abstract

How do we find communities in a graph? How does this change if the graph is bipartite? The Louvain method maximizes links within communities and minimizes those between in order to determine an optimal grouping. Yet, because it may fail when bipartite restrictions are introduced, we have adjusted the null model so as to improve performance in these conditions.

Conclusion

Our Bipartite Louvain is more robust with respect to permutations of vertices than the standard Louvain. For our synthetic examples, Bipartite Louvain typically yields a higher modularity and uncovers the ground truth communities with a higher probability. In the ...

A Two-Light Version Of The Classical Hundred Prisoners And A Light Bulb Problem: Optimizing Experimental Design Through Simulations, 2014 Chapman University

#### A Two-Light Version Of The Classical Hundred Prisoners And A Light Bulb Problem: Optimizing Experimental Design Through Simulations, Alexander S. Barrett, Cyril Rakovski

*e-Research: A Journal of Undergraduate Work*

We propose five original strategies of successively increasing complexity and efficiency that address a novel version of a classical mathematical problem that, in essence, focuses on the determination of an optimal protocol for exchanging limited amounts of information among a group of subjects with various prerogatives. The inherent intricacy of the problem�solving protocols eliminates the possibility to attain an analytical solution. Therefore, we implemented a large-scale simulation study to exhaustively search through an extensive list of competing algorithms associated with the above-mentioned 5 generally defined protocols. Our results show that the consecutive improvements in the average amount of time ...

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)

Impacts Of Climate Change On The Evolution Of The Electrical Grid, 2014 University of Tennessee, Knoxville

#### Impacts Of Climate Change On The Evolution Of The Electrical Grid, Melissa Ree Allen

*Doctoral Dissertations*

Maintaining interdependent infrastructures exposed to a changing climate requires understanding 1) the local impact on power assets; 2) how the infrastructure will evolve as the demand for infrastructure changes location and volume and; 3) what vulnerabilities are introduced by these changing infrastructure topologies. This dissertation attempts to develop a methodology that will a) downscale the climate direct effect on the infrastructure; b) allow population to redistribute in response to increasing extreme events that will increase under climate impacts; and c) project new distributions of electricity demand in the mid-21^{st} century.

The research was structured in three parts. The first ...

Multistep Kinetic Monte Carlo, 2014 University of Tennessee, Knoxville

#### Multistep Kinetic Monte Carlo, Holly Nichole Johnson Clark

*Doctoral Dissertations*

Kinetic Monte Carlo (KMC) uses random numbers to simulate the time evolution of processes with well-defined rates. We analyze a multi-step KMC algorithm aimed at speeding up the single-step procedure and apply the algorithm to study a model for the growth of a surface dendrite. The growth of the dendrite is initiated when atoms diffusing on a substrate cluster due to lower hopping rates for highly coordinated atoms. The boundary of the cluster is morphologically unstable when the flux of new atoms is supplied in the far field, a scenario that could be generated by masking a portion of a ...

Spatial Dynamic Models For Fishery Management And Waterborne Disease Control, 2014 University of Tennessee, Knoxville

#### Spatial Dynamic Models For Fishery Management And Waterborne Disease Control, Michael Robert Kelly Jr.

*Doctoral Dissertations*

As the human population continues to grow, there is a need for better management of our natural resources in order for our planet to be able to produce enough to sustain us. One important resource we must consider is marine fish populations. We use the tool of optimal control to investigate harvesting strategies for maximizing yield of a fish population in a heterogeneous, finite domain. We determine whether these solutions include no-take marine reserves as part of the optimal solution. The fishery stock is modeled using a nonlinear, parabolic partial differential equation with logistic growth, movement by diffusion and advection ...