My Account
Digital Library
Bookstore
News
Archives
SIAM Engage
Contact
Donate
Become A Member
Society for Industrial and Applied Mathematics
Become a Member
Login
Get Involved
Society for Industrial and Applied Mathematics
Home
Publications
Journals
Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal (MMS)
SIAM Journal on Applied Algebra and Geometry (SIAGA)
SIAM Journal on Applied Dynamical Systems (SIADS)
SIAM Journal on Applied Mathematics (SIAP)
SIAM Journal on Computing (SICOMP)
SIAM Journal on Control and Optimization (SICON)
SIAM Journal on Discrete Mathematics (SIDMA)
SIAM Journal on Financial Mathematics (SIFIN)
SIAM Journal on Imaging Sciences (SIIMS)
SIAM Journal on Mathematical Analysis (SIMA)
SIAM Journal on Mathematics of Data Science (SIMODS)
SIAM Journal on Matrix Analysis and Applications (SIMAX)
SIAM Journal on Numerical Analysis (SINUM)
SIAM Journal on Optimization (SIOPT)
SIAM Journal on Scientific Computing (SISC)
SIAM / ASA Journal on Uncertainty Quantification (JUQ)
SIAM Review (SIREV)
Theory of Probability and Its Applications (TVP)
Related
Recent Articles
Information for Authors
Subscriptions and Ordering Information
Journal Policies
Open Access
Books
Book Series
For Authors
For Booksellers
For Librarians
For Educators
SIAM News
SIURO
Volume 15
Volume 14
Volume 13
Volume 12
Volume 11
Volume 10
Volume 9
Volume 8
Volume 7
Volume 6
Volume 5
Volume 4
Volume 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 2
Volume 1, Issue 1
Related
Editorial Information
Instructions for Undergraduate Authors
Reports
Digital Library
SIAM Unwrapped
Proceedings
Research Areas
Analysis and Partial Differential Equations
Applied Geometry
Applied Mathematics Education
Classical Applied Mathematics
Computational Science & Numerical Analysis
Control and Systems Theory
Data Science
Discrete Mathematics and Theoretical Computing
Dynamical Systems, Nonlinear Waves
Financial Mathematics and Engineering
Geosciences and Mathematics of Planet Earth
Imaging Science
Life Sciences
Linear Algebra
Mathematical Aspects of Materials Science
Optimization
Uncertainty Quantification
Conferences
Calendar
SIAM Conferences
Cooperating Conferences
Archives
Conference Support
SIAM Student Travel Awards
SIAM Early Career Travel Awards
About SIAM Conferences
Conference Guidelines
Navigating a SIAM Conference
Featured Lectures & Videos
Ways to Sponsor
Exhibitors and Sponsors
Propose a Conference or Workshop
FAQ
Proceedings
Careers
Job Board
Internships
Fellowships
Funding Opportunities
Resources
Companies and Industries
Careers in the Math Sciences
What is Applied Mathematics and Computational Science?
SIAM Career Fairs
Students & Education
Programs & Initiatives
BIG Math Network
Gene Golub SIAM Summer School
James Crowley Fund for Student Support
Mathematics and Statistics Awareness Month
MathWorks Math Modeling (M3) Challenge
MGB-SIAM Early-Career Fellowship
SIAM Prize Program
SIAM Science Policy Fellowship Program
SIAM Visiting Lecturer Program
Tondeur Initiatives
Thinking of a Career in Applied Mathematics?
Resources
For Undergraduate Students
For K-12 Students
For Educators
Student Chapters
Start a Chapter
Student Chapter Directory
Chapter Resources
Membership
Join SIAM
Individual Members
Institutional Members
Activity Groups
Algebraic Geometry SI(AG)2
Analysis of Partial Differential Equations
Applied and Computational Discrete Algorithms
Applied Mathematics Education
Computational Science and Engineering
Control and Systems Theory
Data Science
Discrete Mathematics
Dynamical Systems
Financial Mathematics and Engineering
Geometric Design
Geosciences
Imaging Science
Life Sciences
Linear Algebra
Mathematics of Planet Earth
Mathematical Aspects of Materials Science
Nonlinear Waves and Coherent Structures
Optimization
Orthogonal Polynomials and Special Functions
Supercomputing
Uncertainty Quantification
Related
Start an Activity Group
Information for Activity Group Officers
SIAM Activity Group Leadership Suggestion
Sections
SIAM Central States Section
Great Lakes Section of SIAM
Mexico Section of SIAM
SIAM Northern States Section
SIAM Pacific Northwest Section
SIAM Southeastern Atlantic Section
SIAM Southern California Section
SIAM Texas-Louisiana Section
SIAM Washington-Baltimore Section
Argentina Section of SIAM
Bulgaria Section of SIAM
Colombia Section of SIAM
East Asia Section of SIAM
United Kingdom and Republic of Ireland of SIAM
Related
Start a Section
Information for Section Officers
Policies & Guidelines
Prizes & Recognition
Deadline Calendar
View All Prizes
Major Prizes & Lectures
Activity Group Prizes
Student Prizes
Joint Prizes
Fellows Program
Nomination Procedures
Selection Criteria
Eligibility
All SIAM Fellows
FAQ
Policies & Guidelines
SIAM Prize Policy
For SIAM Activity Group Officers
Prizes & Recognition FAQ
For Selection Committees
For Prize Winners
For Nominators
Publications
SIURO
Volume 4
Text/HTML
SIAM Undergraduate Research Online
Volume 4
SIAM Undergraduate Research Online Volume 4
Spectral Clustering and Visualization: A Novel Clustering of Fisher's Iris Data Set
Published electronically February 23, 2011
DOI:
10.1137/10S010752
Authors:
David Benson-Putnins (University of Michigan), Margaret Bonfardin (Washington University), Meagan E. Magnoni (Rensselaer Polytechnic Institute), and Daniel Martin (Davidson College)
Sponsors:
Carl D. Meyer (North Carolina State University) and Charles D. Wessell (North Carolina State University)
Abstract
: Clustering is the act of partitioning a set of elements into subsets, or clusters, so that elements in the same cluster are, in some sense, similar. Determining an appropriate number of clusters in a particular data set is an important issue in data mining and cluster analysis. Another important issue is visualizing the strength, or connectivity, of clusters.
We begin by creating a consensus matrix using multiple runs of the clustering algorithm
k
-means. This consensus matrix can be interpreted as a graph, which we cluster using two spectral clustering methods: the Fiedler Method and the MinMaxCut Method. To determine if increasing the number of clusters from
k
to
k
+1 is appropriate, we check whether an existing cluster can be split. Finally, we visualize the strength of clusters by using the consensus matrix and the clustering obtained through one of the aforementioned spectral clustering techniques.
Using these methods, we then investigate Fisher's Iris data set. Our methods support the existence of four clusters, instead of the generally accepted three clusters in this data.
Parameter Estimation in Differential Equations: A Numerical Study of Shooting Methods
Published electronically February 23, 2011
DOI:
10.1137/10S010739
Author:
Franz Hamilton (George Mason University)
Sponsor:
Timothy Sauer (George Mason University)
Abstract
: Differential equation modeling is central to applications of mathematics to science and engineering. When a particular system of equations in used in an application, it is often important to determine unknown parameters. We compare the traditional shooting method to versions of multiple shooting methods in chaotic systems with noise added and conduct numerical experiments as to the reliability and accuracy of both methods.
On Numerical Methods for Elliptic Transmission Eigenvalue Problems
Published electronically March 4, 2011
DOI:
10.1137/10S010806
Author:
Anirban Roy (Pennsylvania State University)
Sponsors:
Anna L. Mazzucato (Pennsylvania State University) and Victor Nistor (Pennsylvania State University)
Abstract
: The use of numerical tools to solve challenging problems in mathematics has exploded in the past several decades. The purpose of this paper is to compare the results of two different types of numerical methods in finding solutions to the eigenvalue problem for a second order elliptic partial differential equations (PDE) with boundary and transmission conditions. Transmission properties result from jumps in the coefficients of the equation and require more complex numerical methods to solve the eigenvalue problem than when the coefficients are continuous. We present the setup of both the bisection method to solve the exact equation satisfied by the eigenvalues and an application of the power method on a Finite Element Method discretization to find the largest eigenvalues and eigenfunction. We also provide some numerical evidence as to which method is more efficient given the complexities of our problem.
Macroscopic Cross-Diffusion Models Derived from Spatially Discrete Continuous Time Microscopic Models
Published electronically May 12, 2011
DOI:
10.1137/10S010818
Author:
Stephen Ostrander (McMaster University)
Sponsor:
Hermann J. Eberl (University of Guelph)
Abstract
: We formulate a continuous time, discrete in space model for two spatially interacting species. The spatial interaction is described in terms of a measure for the desire or ability of a population to move from one location into a neighboring site. This can depend on local densities of both populations in the current and the target site. Refining the spatial resolution and passing to a continuous in space model, one obtains a system of partial differential equations with cross diffusion terms. We show that certain cross-diffusion models that have been used in the literature to describe interacting species can be derived as special cases with our approach.
Attractors: Nonstrange to Chaotic
Published electronically June 21, 2011
DOI:
10.1137/10S01079X
Author:
Robert L. V. Taylor (The College of Wooster)
Sponsor:
John David (The College of Wooster)
Abstract
: The theory of chaotic dynamical systems can be a tricky area of study for a non-expert to break into. Because the theory is relatively recent, the new student finds himself immersed in a subject with very few clear and intuitive definitions. This paper aims to carve out a small section of the theory of chaotic dynamical systems---that of attractors---and outline its fundamental concepts from a computational mathematics perspective. The motivation for this paper is primarily to define what an attractor is and to clarify what distinguishes its various types (nonstrange, strange nonchaotic, and strange chaotic). Furthermore, by providing some examples of attractors and explaining how and why they are classified, we hope to provide the reader with a good feel for the fundamental connection between fractal geometry and the existence of chaos.
Computational Methods for a One-Dimensional Plasma Model with Transport Field
Published electronically August 18, 2011
DOI:
10.1137/11S010906
Author:
Dustin W. Brewer (The University of Texas at Arlington)
Sponsor:
Stephen Pankavich (United States Naval Academy)
Abstract
: The electromagnetic behavior of a collisionless plasma is described by a system of partial differential equations known as the Vlasov-Maxwell system. From a mathematical standpoint, little is known about this physically accurate three-dimensional model, but a one-dimensional toy model of the equations can be studied much more easily. Knowledge of the dynamics of solutions to this reduced system, which computer simulation can help to determine, would be useful in predicting the behavior of solutions to the unabridged Vlasov-Maxwell system. Hence, we design, construct, and implement a novel algorithm that couples efficient finite-difference methods with a particle-in-cell code. Finally, we draw conclusions regarding their accuracy and efficiency, as well as, the behavior of solutions to the one-dimensional plasma model.
Moody's Mega Math Challenge 2011 Champion Paper-Colorado River Water: Good to the Last Acre-Foot
Published electronically November 11, 2011
DOI:
10.1137/11S011249
M3 Challenge Introduction
Authors:
Caroline Bowman, Patrick Braga, Anthony Grebe, Alex Kiefer, and Jason Oettinger (Pine View School, Osprey, FL)
Sponsor:
Ann Hankinson (Pine View School, Osprey, FL)
Summary:
The arid region of the Southwestern United States holds one of the most important bodies of water in the nation: the Colorado River, which provides water to nearly 30 million people. The Colorado River Basin has been divided into Upper and Lower Basin regions since the signing of an interstate compact in 1922, and further agreements have specified the amount of water allocated to each state. Lake Powell, the reservoir formed by the Glen Canyon Dam, facilitates the sharing of water between the two basins by providing longterm storage for the Upper Basin's water and water to be sent to the Lower Basin.
With our first model, we develop a simplified geometric model of the shape of Lake Powell to simulate the effects of drought on the volume of the water in the reservoir. We conclude that in the worst-case scenario, when inflow equals 39% of the historic average, then the lake would run dry in 3.2 years. If inflow equals the probable value of 83% of the average then the lake's volume would reach about four-fifths of its capacity, and the high inflow of 137% of the average would yield maximum capacity.
From the second model, we conclude that the Glen Canyon Dam produces more energy if the reservoir is full, and that there is a large difference in the power generated between the three provided scenarios. This is due in part to the height of the reservoir as a direct result of the inflow and also to the fact that the outflow through the dam is dependent on the inflow if the reservoir becomes empty or full.
In our third model, we analyze the agricultural data related to the economy of the states that make up the Basin, examining the correlation between each state's water allocation and its agricultural GSP (Gross State Product). We consider how much water is allocated to each state as a result of the 1922 Compact and how this affects each state's GSP. We finally make recommendations of potential reductions to the amount of water that might be removed from the Colorado River to maintain a minimum capacity in Lake Powell.
Analysis of a Co-Epidemic Model
Published electronically November 15, 2011
DOI:
10.1137/11S010852
Author:
Quinn A. Morris (Wake Forest University)
Sponsor:
Stephen Robinson (Wake Forest University)
Abstract
: Solutions to systems of differential equations which model disease transmission are of particular use and importance to epidemiologists who wish to study effective means to slow and prevent the spread of disease. In this paper, we examine a system that models two related diseases within a population, which is of particular importance to those studying co-infection and partial cross-immunity phenomena. Criteria for stability of equilibria are improved upon from previous research by Long, Vaidya, and Brandeau (2008).
Interval Estimates for Predictive Values in Diagnostic Testing with Three Outcomes
Published electronically November 17, 2011
DOI:
10.1137/11S010888
Authors:
Scott Clark, Lauren Mondin, Courtney Weber, and Jessica Winborn (Sam Houston State University)
Sponsor:
Melinda Miller Holt (Sam Houston State University)
Abstract
: In disease testing, patients and doctors are interested in estimates for positive predictive value (PPV) and negative predictive value (NPV). The PPV of a test is the probability that a patient actually has the disease, given a positive test result. The NPV is the probability that a patient actually does not have the disease, given a negative test result. Here we consider diagnostic tests in which the disease state remains uncertain, so the uncertain predictive value (UPV) is also of interest. UPV is the probability that, given an uncertain test result, follow-up testing will remain inconclusive. We derive classical Wald-type and Bayesian interval estimates of PPV, NPV, and UPV. Performance of these intervals is compared through simulation studies of interval coverage and width.
Understanding the Impact Of Boundary and Initial Condition Errors on the Solution to a Thermal Diffusivity Inverse Problem
Published electronically November 18, 2011
DOI:
10.1137/11S011237
Author:
Xiaojing Fu and Brian Leventhal (Clarkson University)
Sponsor:
Kathleen Fowler (Clarkson University)
Abstract
: In this work, we consider simulation of heat fl w in the shallow subsurface. As sunlight heats up the surface of soil, the thermal energy received dissipates downward into the ground. This process can be modeled using a partial differential equation known as the heat equation. The spatial distribution of soil thermal conductivities is a key factor in the modeling process. Prior to this study, temperature profile were recorded at different depths at various times. This work is motivated by trying to match these temperature profile using a simulation-based approach in the context of an inverse problem. Specificall we determine soil thermal conductivities using derivative-free optimization to minimize the nonlinear-least square errors between simulation and data profile We also study how errors in the initial and boundary conditions propagate overtime using numerical approach.
European Option Pricing Using a Combined Inverse Congruential Generator
Published electronically November 28, 2011
DOI:
10.1137/10S010776
Authors:
Yered Pita-Juarez and Steven Melanson (California State University, Sacramento)
Sponsor:
Coskun Cetin (California State University, Sacramento)
Abstract
: One of the main problems in mathematical finance is to find the fair price of various contracts that convey a right, known as options, which depend on the price of other financial assets like stocks, known as the underlying assets. A "fair" price for some of these contracts may not be obtained analytically. In this manner, Monte Carlo simulations offer a convenient way to compute the fair price numerically, relying on the approximation of an expected value by the average of the simulated values. We briefly discuss some common random number generators, including a combined inverse congruential random number generator, in Monte Carlo simulations to compute the fair price of a European call option and to analyze the sensitivity of the price with respect to the changes in the key model parameters.
Choosing Basis Functions and Shape Parameters for Radial Basis Function Methods
Published electronically December 2, 2011
DOI:
10.1137/11S010840
Author:
Michael Mongillo (Illinois Institute of Technology)
Sponsor:
Greg Fasshauer (Illinois Institute of Technology)
Abstract
: Radial basis function (RBF) methods have broad applications in numerical analysis and statistics. They have found uses in the numerical solution of PDEs, data mining, machine learning, and kriging methods in statistics. This work examines the use of radial basis functions in scattered data approximation. In particular, the experiments in this paper test the properties of shape parameters in RBF methods, as well as methods for finding an optimal shape parameter. Locating an optimal shape parameter is a difficult problem and a topic of current research. Some experiments also consider whether the same methods can be applied to the more general problem of selecting basis functions.