American Spread Option Models And Valuation,
2013
Brigham Young University - Provo
American Spread Option Models And Valuation, Yu Hu
Theses and Dissertations
Spread options are derivative securities, which are written on the difference between the values of two underlying market variables. They are very important tools to hedge the correlation risk. American style spread options allow the holder to exercise the option at any time up to and including maturity. Although they are widely used to hedge and speculate in financial market, the valuation of the American spread option is very challenging. Because even under the classic assumptions that the underlying assets follow the log-normal distribution, the resulting spread doesn't have a distribution with a simple closed formula. In this dissertation, we …
The Mathematics Of A Successful Deconvolution: A Quantitative Assessment Of Mixture-Based Combinatorial Libraries Screened Against Two Formylpeptide Receptors,
2013
Torrey Pines Institute for Molecular Studies
The Mathematics Of A Successful Deconvolution: A Quantitative Assessment Of Mixture-Based Combinatorial Libraries Screened Against Two Formylpeptide Receptors, Radleigh Santos, Jon R. Appel, Marc Giulianotti, Bruce S. Edwards, Larry A. Sklar, Richard A. Houghten, Clemencia Pinilla
Mathematics Faculty Articles
In the past 20 years, synthetic combinatorial methods have fundamentally advanced the ability to synthesize and screen large numbers of compounds for drug discovery and basic research. Mixture-based libraries and positional scanning deconvolution combine two approaches for the rapid identification of specific scaffolds and active ligands. Here we present a quantitative assessment of the screening of 32 positional scanning libraries in the identification of highly specific and selective ligands for two formylpeptide receptors. We also compare and contrast two mixture-based library approaches using a mathematical model to facilitate the selection of active scaffolds and libraries to be pursued for further …
Al-Khwarizmi: Founder Of Classical Algebra,
2013
Dordt College
Al-Khwarizmi: Founder Of Classical Algebra, Calvin Jongsma
Faculty Work Comprehensive List
Adopting a historically defensible definition of “algebra,” we will begin by exploring a few examples of algebra prior to al-Khwarizmi. We will then examine what algebra became through al-Khwarizmi’s work. In conclusion, we will assess the historical importance of al-Khwarizmi’s contributions for developments in European algebra.
Schedule (2013),
2013
Taylor University
Schedule (2013), Association Of Christians In The Mathematical Sciences
ACMS Conference Proceedings 2013
Nineteenth Conference of the Association of Christians in the Mathematical Sciences
Table Of Contents (2013),
2013
Taylor University
Table Of Contents (2013), Association Of Christians In The Mathematical Sciences
ACMS Conference Proceedings 2013
Nineteenth Conference of the Association of Christians in the Mathematical Sciences
19th Conference Of The Associations Of Christians In The Mathematical Sciences,
2013
Taylor University
19th Conference Of The Associations Of Christians In The Mathematical Sciences, Association Of Christians In The Mathematical Sciences
ACMS Conference Proceedings 2013
Association of Christians in the Mathematical Sciences 19th Biennial Conference Proceedings, May 29 - June 1, 2011, Bethel University.
Iterative Statistical Verification Of Probabilistic Plans,
2013
Lawrence University
Iterative Statistical Verification Of Probabilistic Plans, Colin M. Potts
Lawrence University Honors Projects
Artificial intelligence seeks to create intelligent agents. An agent can be anything: an autopilot, a self-driving car, a robot, a person, or even an anti-virus system. While the current state-of-the-art may not achieve intelligence (a rather dubious thing to quantify) it certainly achieves a sense of autonomy. A key aspect of an autonomous system is its ability to maintain and guarantee safety—defined as avoiding some set of undesired outcomes. The piece of software responsible for this is called a planner, which is essentially an automated problem solver. An advantage computer planners have over humans is their ability to consider and …
Boundary Value Problems For Discrete Fractional Equations,
2013
University of Nebraska-Lincoln
Boundary Value Problems For Discrete Fractional Equations, Pushp R. Awasthi
Department of Mathematics: Dissertations, Theses, and Student Research
In this dissertation we develop certain aspects of the theory of discrete fractional calculus. The author begins with an introduction to the discrete delta calculus together with the fractional delta calculus which is used throughout this dissertation. The Cauchy function, the Green's function and some of their important properties for a fractional boundary value problem for are developed. This dissertation is comprised of four chapters. In the first chapter we introduce the delta fractional calculus. In the second chapter we give some preliminary definitions, properties and theorems for the fractional delta calculus and derive the appropriate Green's function and give …
Establishing Foundations For Investigating Inquiry-Oriented Teaching,
2013
Portland State University
Establishing Foundations For Investigating Inquiry-Oriented Teaching, Estrella Maria Salas Johnson
Dissertations and Theses
The Teaching Abstract Algebra for Understanding (TAAFU) project was centered on an innovative abstract algebra curriculum and was designed to accomplish three main objectives: to produce a set of multi-media support materials for instructors, to understand the challenges faced by mathematicians as they implemented this curriculum, and to study how this curriculum supports student learning of abstract algebra. Throughout the course of the project I took the lead investigating the teaching and learning in classrooms using the TAAFU curriculum. My dissertation is composed of three components of this research. First, I will report on a study that aimed to describe …
Near-Optimal Compressed Sensing Guarantees For Total Variation Minimization,
2013
Claremont McKenna College
Near-Optimal Compressed Sensing Guarantees For Total Variation Minimization, Deanna Needell, R. Ward
CMC Faculty Publications and Research
Consider the problem of reconstructing a multidimensional signal from an underdetermined set of measurements, as in the setting of compressed sensing. Without any additional assumptions, this problem is ill-posed. However, for signals such as natural images or movies, the minimal total variation estimate consistent with the measurements often produces a good approximation to the underlying signal, even if the number of measurements is far smaller than the ambient dimensionality. This paper extends recent reconstruction guarantees for two-dimensional images x ∈ ℂN2 to signals x ∈ ℂNd of arbitrary dimension d ≥ 2 and to isotropic total variation problems. In this …
The Neural Ring: An Algebraic Tool For Analyzing
The Intrinsic Structure Of Neural Codes,
2013
University of Nebraska - Lincoln
The Neural Ring: An Algebraic Tool For Analyzing The Intrinsic Structure Of Neural Codes, Carina Curto, Vladimir Itskov, Alan Veliz-Cuba, Nora Youngs
Department of Mathematics: Faculty Publications
Neurons in the brain represent external stimuli via neural codes. These codes often arise from stereotyped 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, …
Gp Representation Space Reduction Using A Tiered Search Scheme,
2013
University of Missouri-St. Louis
Gp Representation Space Reduction Using A Tiered Search Scheme, John Joseph Aleshunas
Dissertations
The size and complexity of a GP representation space is defined by the set of functions and terminals used, the arity of those functions, and the maximal depth of candidate solution trees in the space. Practice has shown that some means to reduce the size or bias the search must be provided. Adaptable Constrained Genetic Programming (ACGP) can discover beneficial substructures and probabilistically bias the search to promote the use of these substructures. ACGP has two operating modes: a more efficient low granularity mode (1st order heuristics) and a less efficient higher granularity mode (2nd order heuristics). Both of these …
Nguyen ’15 Places In Putnam Competition,
2013
Illinois Wesleyan University
Nguyen ’15 Places In Putnam Competition, Natalya Grabavoy
News and Events (Discontinued Series)
No abstract provided.
A Discrete Approach To The Poincare-Miranda Theorem,
2013
Harvey Mudd College
A Discrete Approach To The Poincare-Miranda Theorem, Connor Thomas Ahlbach
HMC Senior Theses
The Poincare-Miranda Theorem is a topological result about the existence of a zero of a function under particular boundary conditions. In this thesis, we explore proofs of the Poincare-Miranda Theorem that are discrete in nature - that is, they prove a continuous result using an intermediate lemma about discrete objects. We explain a proof by Tkacz and Turzanski that proves the Poincare-Miranda theorem via the Steinhaus Chessboard Theorem, involving colorings of partitions of n-dimensional cubes. Then, we develop a new proof of the Poincare-Miranda Theorem that relies on a polytopal generalization of Sperner's Lemma of Deloera - Peterson - Su. …
Using Partial Differential Equations To Model And Analyze The Treatment Of A Chronic Wound With Oxygen Therapy Techniques,
2013
Western Kentucky University
Using Partial Differential Equations To Model And Analyze The Treatment Of A Chronic Wound With Oxygen Therapy Techniques, Brandon C. Russell
Mahurin Honors College Capstone Experience/Thesis Projects
Chronic wounds plague approximately 1.3-3 million Americans. The treatment of these wounds requires knowledge of the complex healing process of typical wounds. With a system of partial differential equations, this project attempts to model the intricate biological process and to describe oxygen levels, neutrophil and bacteria concentrations, and other biological parameters with respect to time and space. Analytical solutions for the model will be derived for various frames of time in the wound-healing process. The system of equations will be numerically solved using Matlab. Numerical simulations are performed to determine optimal treatment strategies for a chronic wound.
Time Scales Integral Inequalities For Superquadratic Functions,
2013
Missouri University of Science and Technology
Time Scales Integral Inequalities For Superquadratic Functions, Josipa Barić, Rabia Bibi, Martin Bohner, Josip Pečarić
Mathematics and Statistics Faculty Research & Creative Works
In this paper, two different methods of proving Jensen's inequality on time scales for superquadratic functions are demonstrated. Some refinements of classical inequalities on time scales are obtained using properties of superquadratic functions and some known results for isotonic linear functionals. © 2013 The Korean Mathematical Society.
Generalized Local Test For Local Extrema In Single-Variable Functions,
2013
The University of Texas Rio Grande Valley
Generalized Local Test For Local Extrema In Single-Variable Functions, Eleftherios Gkioulekas
School of Mathematical & Statistical Sciences Faculty Publications
We give a detailed derivation of a generalization of the second derivative test of single-variable calculus which can classify critical points as local minima or local maxima (or neither), whenever the traditional second derivative test fails, by considering the values of higher-order derivatives evaluated at the critical points. The enhanced test is local, in the sense that it is only necessary to evaluate all relevant derivatives at the critical point itself, and it is reasonably robust. We illustrate an application of the generalized test on a trigonometric function where the second derivative test fails to classify some of the critical …
Algebro-Geometric Solutions For The Degasperis--Procesi Hierarchy,
2013
The University of Texas Rio Grande Valley
Algebro-Geometric Solutions For The Degasperis--Procesi Hierarchy, Yu Hou, Peng Zhao, Engui Fan, Zhijun Qiao
School of Mathematical & Statistical Sciences Faculty Publications
Though the completely integrable Camassa--Holm (CH) equation and Degasperis--Procesi (DP) equation are cast in the same peakon family, they possess the second- and third-order Lax operators, respectively. From the viewpoint of algebro-geometrical study, this difference lies in hyper-elliptic and non-hyper-elliptic curves. The non-hyper-elliptic curves lead to great difficulty in the construction of algebro-geometric solutions of the DP equation. In this paper, we derive the DP hierarchy with the help of Lenard recursion operators. Based on the characteristic polynomial of a Lax matrix for the DP hierarchy, we introduce a third order algebraic curve $\mathcal{K}_{r-2}$ with genus $r-2$, from which the …
Chebyshev Polynomial Approximation To Solutions Of Ordinary Differential Equations,
2013
University of Southern Mississippi
Chebyshev Polynomial Approximation To Solutions Of Ordinary Differential Equations, Amber Sumner Robertson
Undergraduate Theses
In this thesis, we develop a method for finding approximate particular solutions for second order ordinary differential equations. We use Chebyshev polynomials to approximate the source function and the particular solution of an ordinary differential equation. The derivatives of each Chebyshev polynomial will be represented by linear combinations of Chebyshev polynomials, and hence the derivatives will be reduced and differential equations will become algebraic equations. Another advantage of the method is that it does not need the expansion of Chebyshev polynomials. This method is also compared with an alternative approach for particular solutions. Examples including approximation, particular solution, a class …
Effects In The Anomalistic Period Of Celestial Bodies Due To A Logarithmic Correction To The Newtonian Gravitational Potential,
2013
University of Patras
Effects In The Anomalistic Period Of Celestial Bodies Due To A Logarithmic Correction To The Newtonian Gravitational Potential, Omiros Ragos, Ioannis Haranas, Ioannis Gkigkitzis
Physics and Computer Science Faculty Publications
We study the motion of a secondary celestial body under the influence of the logarithmic corrected gravitational force of a primary one. This kind of correction was introduced by Fabris et al. (2009). We derive two equations to compute the rate of change of the periastron w.r.t. the eccentric anomaly and its total variation over one revolution, In a kinematical sense, this influence produces an apsidal motion. We perform numerical estimations for Mercury and for the companion star of the pulsar PSR 1913+16. We also consider the case of the artificial Earth satellite GRACE-A, but the results present a low …
