Applied Mathematics Commons^™

Identification Of Control Targets In Boolean Molecular Network Models Via Computational Algebra, David Murrugarra, Alan Veliz-Cuba, Boris Aguilar, Reinhard Laubenbacher

Mathematics Faculty Publications

Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment. The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. This paper focuses on processes at the molecular level that determine the state of an individual cell, involving signaling or gene regulation. The mathematical model type considered …

Finland's Economic Freeze, Shivang Mehta

Claremont-UC Undergraduate Research Conference on the European Union

Abstract

The Eurozone sovereign debt crisis has been well documented and so has Germany’s booming manufacturing economy but these events are relatively easy to explain. Greece’s troubles can easily be traced to its social security structure and lack of land registry while Germany’s success is a result of labour reforms, an undervalued currency and an emphasis on small scale businesses which form the backbone of the economy. A relatively paradoxical case has been that of Finland; ranked second for global innovation by the World Economic Forum and with over $1.8 billion being invested by the government in the country’s tech …

Essays In Market Structure And Liquidity, Adrian J. Walton

Electronic Thesis and Dissertation Repository

Market structure concerns the mechanisms for negotiating trades and the composition of trading participants, and can affect liquidity and price efficiency. More gains from trade can be realized from an asset that is more liquid, and a better allocation of risk and capital can be achieved when an asset’s price is more efficient so it is important to understand market structure. This thesis uses theory and empirical methods to examine the effects of a few specific aspects of market structure.

In Chapter 1, we study a novel market structure on the New York Stock Exchange (NYSE), the Retail Liqudity Program …

Synergistic Effects Of Phase Folding And Wavelet Denoising With Applications In Light Curve Analysis, Andrew M. Armstrong

Theses and Dissertations

The growing size of cosmological data sets is causing the current human-centric approach to cosmology to become impractical. Autonomous data analysis techniques need to be developed in order to advance the field of cosmology. This research examines the benefits of combining two signal analysis techniques, namely phase folding and wavelet denoising, into a newly-developed suite of autonomous light curve analysis tools which includes aspects of component extraction and period detection. The improvements these tools provide, with respect to autonomy and signal quality, are demonstrated using both simulated and real-world light curve data. Although applied to light curve data, the suite …

Time Domain Analysis Of Electromagnetic Scattering From Multiple Cavities Embedded In A Ground Plane, Richard P. Uber

Theses and Dissertations

This work examines the scattered fields produced when a transient wave is reflected from an infinite perfect electric conductor (PEC) ground plane with multiple embedded cavities. Incident and reflected waves will be decomposed into transverse magnetic to the z direction (TMz) and transverse electric to the z direction (TEz) polarizations, with primary focus given to the TMz. Cavities may be unfilled, partially filled, or fully filled with non-magnetic dielectric material and no assumptions are made regarding similarity, regularity, or periodicity. The Newmark method is used to discretize time and a variational formulation is presented for each time step. The principle …

Skyrmions, Rational Maps & Scaling Identities, E. G. Charalampidis, T. A. Ioannidou, N. S. Manton

Efstathios Charalampidis

Starting from approximate Skyrmion solutions obtained using the rational map ansatz, improved approximate Skyrmions are constructed using scaling arguments. Although the energy improvement is small, the change of shape clarifies whether the true Skyrmions are more oblate or prolate.

Rogue Waves In Nonlinear Schrodinger Models With Variable Coefficients : Application To Bose Einstein Condensates, J. S. He, E. G. Charalampidis, P. G. Kevrekidis, D. J. Frantzeskasis

Efstathios Charalampidis

We explore the form of rogue waves solution sin a select set of case examples of non linear Schrodinger equations with variable coefficients. We focus on systems with constant dispersion, and present three different models that describe atomic Bose Einstein condensates in different experimentally relevant settings. For these models, we identify exact rogue waves solutions. Our analytical findings are corroborated by direct numerical integration of the original equations, performed by two different schemes. Very good agreement between numerical results and analytical predictions for the emergence of the rogue waves is identified. Additionally, the nontrivial fate of small numerically induced perturbations …

Dark Bright Solitons In Coupled Nonlinear Schrodinger Equations With Unequal Dispersion Coefficients, E. G. Charalampidis, P. G. Kevrekidis, D. J. Frantzeskaki, B. A. Malomed

Efstathios Charalampidis

We study a two component nonlinear Schrodinger system with equal, repulsive cubic interactions and different dispersion coefficients in the two components. We consider states that have a dark solitary wave in one component. Treating it as a frozen one, we explore the possibility of the formation of bright solitonic structures in the other component. We identify bifurcation points at which such states emerge in the bright component in the linear limit and explore their continuation into the nonlinear regime. An additional analytically tractable limit is found to be that of vanishing dispersion of the bright component. We numerically identify regimes …

Vector Rogue Waves And Dark Bright Boomeronic Solitons In Autonomous And Non Autonomous Settings, R. Babu Mareeswaran, E. G. Charalampidis, T. Kanna, P. G. Kevrekidis, D. J. Frantzeskakis

Efstathios Charalampidis

In this work, we consider the dynamics of vector rogue waves and ark bright solitons in two component nonlinear Schrodinger equations with various physically motivated time dependent non linearity coefficients, as well as spatio temporally dependent potentials. A similarity transformation is utilized to convert the system into the integrable Manakov system and subsequently the vector rogue and dark bright boomeron like soliton solutions of the latter are converted back into ones of the original non autonomous model. Using direct numerical simulations we find that, in most cases, the rogue waves formation is rapidly followed by a modulational instability that leads …

Breakdown Of Itcz-Like Pv Patterns, Ajay Raghavendra, Thomas A. Guinn

Beyond: Undergraduate Research Journal

The Inter-Tropical Convergence Zone (ITCZ) is a zonal belt of intense convection, responsible for the genesis of over 80% of all tropical cyclones. This region of intense diabatic heating and shear results in a maximum of Ertel's potential vorticity (PV) meeting Rayleigh's necessary condition for barotropic instability. A fundamental issue is understanding the necessary precursor events leading to the breakdown of the ITCZ and subsequent formation of tropical cyclones. Our research examines the non-linear PV dynamics of the breakdown of both finite-length and infinite-length vorticity strips of varying widths and shapes, simulating the ITCZ found near the tropical eastern Pacific …

On Abstraction And Equivalence In Software Patent Doctrine: A Response To Bessen, Meurer And Klemens, Andrew Chin

Journal of Intellectual Property Law

No abstract provided.

The Subject Librarian Newsletter, Mathematics, Fall 2016, Patti Mccall

Libraries' Newsletters

No abstract provided.

Takagi-Sugeno Fuzzy Model Based Discrete Time Model Predictive Control For A Hypersonic Re-Entry Vehicle, Ben Margolis

Applied Mathematics Master's Theses

In this thesis, we present a control algorithm for a hypersonic re-entry vehicle during a Martian aerocapture maneuver. The proposed algorithm utilizes a discrete-time model predictive control technique with a Takagi-Sugeno fuzzy model of the vehicle to control the re-entry vehicle along an arbitrary trajectory using bank angle modulation. Simulations using model parameters and initial conditions from a Martian aerocapture mission demonstrate the stability, performance, and robustness of the proposed controller.

Ermakov Equation And Camassa-Holm Waves, Haret C. Rosu, S.C. Mancas

Publications

From the works of authors of this article, it is known that the solution of the Ermakov equation is an important ingredient in the spectral problem of the Camassa-Holm equation. Here, we review this interesting issue and consider in addition more features of the Ermakov equation which have an impact on the behavior of the shallow water waves as described by the Camassa-Holm equation.

Transients In The Synchronization Of Asymmetrically Coupled Oscillator Arrays, Carlos E. Cantos, David K. Hammond, J.J.P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We consider the transient behavior of a large linear array of coupled linear damped harmonic oscillators following perturbation of a single element. Our work is motivated by modeling the behavior of flocks of autonomous vehicles. We first state a number of conjectures that allow us to derive an explicit characterization of the transients, within a certain parameter regime Ω. As corollaries we show that minimizing the transients requires considering non-symmetric coupling, and that within Ω the computed linear growth in N of the transients is independent of (reasonable) boundary conditions.

On The Expression Of Higher Mathematics In American Sign Language, John Tabak

Journal of Interpretation

Abstract

The grammar and vocabulary of higher mathematics are different from the grammar and vocabulary of conversational English and conversational American Sign Language (ASL). Consequently, mathematical language presents interpreters with a unique set of challenges. This article characterizes those aspects of mathematical grammar that are peculiar to the subject. (A discussion of mathematical vocabulary and its expression in ASL can be found elsewhere (Tabak, 2014).) An increased awareness of the grammar of mathematical language will prove useful to those interpreters for the deaf and deaf mathematics professionals seeking to express higher mathematics in ASL.

In this article one will, for …

Prediction And Optimal Scheduling Of Advertisements In Linear Television, Mark J. Panaggio, Pak-Wing Fok, Ghan S. Bhatt, Simon Burhoe, Michael Capps, Christina J. Edholm, Fadoua El Moustaid, Tegan Emerson, Star-Lena Estock, Nathan Gold, Ryan Halabi, Madelyn Houser, Peter R. Kramer, Hsuan-Wei Lee, Qingxia Li, Weiqiang Li, Dan Lu, Yuzhou Qian, Louis F. Rossi, Deborah Shutt, Vicky Chuqiao Yang, Yingxiang Zhou

Mathematical Sciences Faculty Research

Advertising is a crucial component of marketing and an important way for companies to raise awareness of goods and services in the marketplace. Advertising campaigns are designed to convey a marketing image or message to an audience of potential consumers and television commercials can be an effective way of transmitting these messages to a large audience. In order to meet the requirements for a typical advertising order, television content providers must provide advertisers with a predetermined number of "impressions" in the target demographic. However, because the number of impressions for a given program is not known a priori and because …

Studying Both Direct And Indirect Effects In Predator-Prey Interaction, Xiaoying Wang

Electronic Thesis and Dissertation Repository

Studying and modelling the interaction between predators and prey have been one of the central topics in ecology and evolutionary biology. In this thesis, we study two different aspects of predator-prey interaction: direct effect and indirect effect.

Firstly, we study the direct predation between predators and prey in a patchy landscape.

Secondly, we study indirect effects between predators and prey.

Thirdly, we extend our previous model by incorporating a stage-structure into prey.

Finally, we further extend our previous model by incorporating spatial structures into modelling.

Bacteria-Phage Models With A Focus On Prophage As A Genetic Reservoir, Alina Nadeem

Electronic Thesis and Dissertation Repository

Temperate bacteriophages have the ability to incorporate their genetic material in the host's DNA, which may be utilized by later generations of phage to overcome the host's receptor-based defences. This effect of temperance can have major implications for the long-term survival of the phages as well as on bacteria-phage community evolution. To study the impact of prophage on microbial communities we have developed models simulating lytic and lysogenic infection and host and phage coevolution with a focus on prophage-phage recombination. Our results show that recombination can be crucial for the phage to survive host diversification, and a higher incidence of …

A Comparison Of Solution Methods For Mandelbrot-Like Polynomials, Eunice Y. S. Chan

Electronic Thesis and Dissertation Repository

We compare two different root-finding methods, eigenvalue methods and homotopy methods, using three test problems: Mandelbrot polynomials, Fibonacci-Mandelbrot polynomials, and Narayana-Mandelbrot polynomials. For the eigenvalue methods, using both MATLAB and Maple, we computed the eigenvalues of a specialized recursively-constructed, supersparse, upper Hessenberg matrix, inspired by Piers Lawrence's original construction for the Mandelbrot polynomials, for all three families of polynomials. This led us to prove that this construction works in general. Therefore, this construction is genuinely a new kind of companion matrix. For the homotopy methods, we used a special-purpose homotopy, in which we used an equivalent differential equation to solve …