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A Partial Solution to Last Issue's Homework Assignment: Beetles, Cannibalism, and Chaos--Analyzing a Dynamical System Model
Found in: Computing in Science and Engineering
By Dianne P. O'Leary
Issue Date:May 2007
pp. 80-83
The last issue's installment of Your Homework Assignment featured the final problem in Dianne O'Leary's popular long-running department. In this issue, she offers a partial solution to it.
 
Light a Single Candle: Studying Supernovae
Found in: Computing in Science and Engineering
By Dianne P. O'Leary,Bert W. Rust
Issue Date:March 2012
pp. 90-96
This case study investigates how well an acceleration hypothesis formulated in 1976—stipulating that the decay rates for supernovae seem to be accelerated by a common factor—fits data accumulated since then. The first Web extra (mcs20...
 
Computational Software: Writing Your Legacy
Found in: Computing in Science and Engineering
By Dianne P. O'Leary
Issue Date:January 2006
pp. 78-83
In scientific computing, we sometimes begin with a clean slate; we're given a new problem to solve, and we write software to accomplish the task. In this situation, we?re the inventors. Other times, we work on a problem for which considerable software deve...
 
Beetles, Cannibalism, and Chaos: Analyzing a Dynamical System Model
Found in: Computing in Science and Engineering
By Dianne P. O'Leary
Issue Date:March 2007
pp. 96-103
A system's evolution over time can be described with a set of equations called a dynamical system. In this installment, we use a dynamical system to model the life cycle of flour beetles to estimate key parameters that describe their behavior.
 
Blind Deconvolution: A Matter of Norm
Found in: Computing in Science and Engineering
By Dianne P. O'Leary
Issue Date:March 2005
pp. 60-66
We continue the spectroscopy problem from the last issue, trying to reconstruct a true spectrum from an observed one. Again, we'll use blind deconvolution, but this time we'll impose some constraints on the error matrix E, leading to a more difficult probl...
 
Iterative Methods for Linear Systems: Following the Meandering Way
Found in: Computing in Science and Engineering
By Dianne P. O'Leary
Issue Date:July 2006
pp. 74-80
Solving a linear system of equations is one of the easiest computational tasks imaginable, but when the matrix is very large, the algorithms we learned in linear algebra class take too long, and we need to use a different type of method. In this homework a...
 
Classified Information: The Data Clustering Problem
Found in: Computing in Science and Engineering
By Nargess Memarsadeghi, Dianne P. O'Leary, Yalin E. Sagduyu
Issue Date:September 2003
pp. 54-60
<p>Many projects in engineering and science require data classification based on different heuristics. Designers, for example, classify automobile engine performance as acceptable or unacceptable based on a combination of efficiency, emissions, noise...
 
Monte Carlo Minimization and Counting: One, Two, ., Too Many
Found in: Computing in Science and Engineering
By Isabel Beichl, Dianne P. O'Leary, Francis Sullivan
Issue Date:January 2007
pp. 72-80
Monte Carlo methods use sampling to produce approximate solutions to problems for which other methods aren't practical. In this homework assignment, we study three uses of Monte Carlo methods: for function minimization, discrete optimization, and counting.
 
Sensitivity Analysis: When a Little Means a Lot
Found in: Computing in Science and Engineering
By Dianne P. O'Leary
Issue Date:November 2006
pp. 70-75
In this homework assignment, we use some simple problems to investigate the use of several tools for sensitivity analysis.
 
Multigrid Methods: Managing Massive Meshes
Found in: Computing in Science and Engineering
By Dianne P. O'Leary
Issue Date:September 2006
pp. 96-103
In our last homework assignment, we investigated iterative methods for solving large, sparse, linear systems of equations. We saw that the Gauss-Seidel (GS) method was intolerably slow, but various forms of preconditioned conjugate gradient (CG) algorithms...
 
Computer Memory and Arithmetic: A Look under the Hood
Found in: Computing in Science and Engineering
By Dianne P. O'Leary
Issue Date:May 2006
pp. 54-59
In this homework assignment, we'll consider a model of computer memory organization. We'll hide some detail but give enough information to let us make decisions about how to organize our computations for efficiency. We'll use mathematical modeling to estim...
 
Updating and Downdating Matrix Factorizations: A Change in Plans
Found in: Computing in Science and Engineering
By Dianne P. O'Leary
Issue Date:March 2006
pp. 66-71
We seldom get it right the first time. Whether we're composing an email, seasoning a stew, painting a picture, or planning an experiment, we almost always make improvements on our original thought. The same is true of engineering design; we draft a plan, b...
 
Fast Solvers and Sylvester Equations: Both Sides Now
Found in: Computing in Science and Engineering
By Dianne P. O'Leary
Issue Date:November 2005
pp. 74-80
In our last homework, we solved large sparse systems of linear equations and learned that to keep storage and computational costs low, it's very important to exploit structure in our matrix. We also exploited sparsity; in this homework, we'll consider a se...
 
Solving Sparse Linear Systems: Taking the Direct Approach
Found in: Computing in Science and Engineering
By Dianne P. O'Leary
Issue Date:September 2005
pp. 62-70
Our startup company, PoissonIsUs.com, has hired you as a consultant to advise us on solving linear systems of equations. Our business is to solve elliptic partial differential equations in two and three dimensions, but we have limited venture capital fundi...
 
George Dantzig: A Remembrance
Found in: Computing in Science and Engineering
By Dianne P. O'Leary
Issue Date:September 2005
pp. 96
George Dantzig was one of my heroes. In my junior year of high school, I happened upon his book <em>Linear Programming and Extensions</em> while working on a science fair project. The text was clear and comprehensive, yet managed to communicate...
 
Eigenvalues: Valuable Principles
Found in: Computing in Science and Engineering
By Dianne P. O'Leary
Issue Date:July 2005
pp. 68-75
In this homework assignment, we'll study eigenvalue problems arising from partial differential equations. Eigenvalues help us solve differential equations analytically, but they also provide valuable information about a physical system's behavior. Specific...
 
Finite Differences and Finite Elements: Getting to Know You
Found in: Computing in Science and Engineering
By Dianne P. O'Leary
Issue Date:May 2005
pp. 72-79
Numerical solution of differential equations relies on two main methods: finite differences and finite elements. In this homework assignment, we explore the nuts and bolts of the two methods for a simple two-point boundary value problem.
 
Multidimensional Integration: Partition and Conquer
Found in: Computing in Science and Engineering
By Dianne P. O'Leary
Issue Date:November 2004
pp. 58-66
Understanding the behavior of particles subjected to forces is a basic theme in physics. The simplest system is a set of particles confined to motion along a line, but even this system presents computational challenges. One method of obtaining approximatio...
 
Achieving a Common Viewpoint: Yaw, Pitch, and Roll
Found in: Computing in Science and Engineering
By Dianne P. O'Leary, David A. Schug
Issue Date:September 2004
pp. 60-65
Life is about change; nothing ever stays the same. In particular, objects move, and tracking them is an essential ingredient in applications such as navigation and robot motion. Surprisingly, the same mathematical tools used in tracking are also used in th...
 
Elastoplastic Torsion: Twist and Stress
Found in: Computing in Science and Engineering
By Dianne P. O'Leary
Issue Date:July 2004
pp. 74-83
Consider a long rod made of metal, plastic, rubber, or some other homogeneous material. Hold the rod at the ends and twist one end clockwise and the other end counterclockwise. This torsion (twisting) causes stresses in the rod. If the force we apply is sm...
 
Fitting Exponentials: An Interest in Rates
Found in: Computing in Science and Engineering
By Dianne P. O'Leary
Issue Date:May 2004
pp. 66-72
In this project, we study efficient algorithms for solving problems with exponentials, but we'll see that for many data sets, the solution is not well determined.
 
More Models of Infection: It's Epidemic
Found in: Computing in Science and Engineering
By Dianne P. O'Leary
Issue Date:March 2004
pp. 50-56
<p>In the last issue, we used Monte Carlo simulations and Markov models to gain insight into a simple model of an infection's spread. We discuss this further in the solution section of this column, but first we develop some alternate models of epidem...
 
Models of Infection: Person to Person
Found in: Computing in Science and Engineering
By Dianne P. O'Leary
Issue Date:January 2004
pp. 68-73
<p>When faced with a spreading infection, public health workers want to predict its path and severity to make decisions about vaccination strategies, quarantine policy, and the use of public health resources. This is true whether the pathogen?s dispe...
 
The Direction-of-Arrival Problem: Coming at You
Found in: Computing in Science and Engineering
By Dianne P. O'Leary, Nargess Memarsadeghi
Issue Date:November 2003
pp. 60-70
<p>In this month's problem, we use linear algebra and matrix-updating techniques to track a set of moving signals. The solution to last month's problem on clustering data, which appears at the end of this article, illustrates the complications of det...
 
Image Deblurring: I Can See Clearly Now
Found in: Computing in Science and Engineering
By James G. Nagy, Dianne P. O'Leary
Issue Date:May 2003
pp. 82-84
<p>Inverse problems are among the most challenging computations in science and engineering because they involve determining the parameters of a system that is only observed indirectly. For example, we might have a spectrum and want to determine the s...
 
Hidden Markov Models for Chromosome Identification
Found in: Computer-Based Medical Systems, IEEE Symposium on
By John M. Conroy, Robert L. Becker Jr, William Lefkowitz, Kewi L. Christopher, Rawatmal B. Surana, Timothy J. O'Leary, Dianne P. O'Leary, Tamara G. Kolda
Issue Date:March 2001
pp. 0473
Abstract: In this talk we present a Hidden Markov Markov for automatic karyotyping. Previously, we demonstrated that this method is robust in the presence of different types of metaphase spreads, truncation of chromosomes, and minor chromosome abnormalitie...
 
Blind Deconvolution: Errors, Errors Everywhere
Found in: Computing in Science and Engineering
By Dianne P. O'Leary
Issue Date:January 2005
pp. 56-63
This homework assignment focuses on a class of methods that accounts for uncertainty in the model as well as the data. <p>Our example concerns spectroscopy--the attempt to reconstruct a true spectrum from an observed one. The problem we're considerin...
 
Machine and Human Performance for Single and Multidocument Summarization
Found in: IEEE Intelligent Systems
By Judith D. Schlesinger, John M. Conroy, Mary Ellen Okurowski, Dianne P. O'Leary
Issue Date:January 2003
pp. 46-54
<p>Automatic multidocument summarization holds great promise and commercial potential in the Information Age. The Document Understanding Conference II evaluation revealed several language processing challenges that impact text summarization. This art...
 
Phantom Measurements
Found in: Computing in Science & Engineering
By Dianne P. O'Leary
Issue Date:July 2013
pp. 57-59
In measurement, what you don't know can be much more important than what you do! This Web extra is a zip file that contains some of the data needed to help solve the challenges listed in this article.
 
The Interface between Computer Science and the Mathematical Sciences
Found in: Computing in Science and Engineering
By Dianne P. O'Leary, Scott T. Weidman
Issue Date:May 2001
pp. 60-65
On 28-29 April 2000, the Board on Mathematical Sciences and the Computer Science and Telecommunications Board of the National Research Council cosponsored a workshop on the interface between the mathematical sciences and three areas of computer science: ne...
 
Teamwork: Computational Science and Applied Mathematics
Found in: Computing in Science and Engineering
By Dianne P. O'Leary
Issue Date:April 1997
pp. 13-18
<p>Few people have the breadth of a genius like Gauss, so successful work in computational science and engineering often requires an interdisciplinary team. Applied mathematics is one critical component of many CSE projects. </p>
 
Text summarization via hidden Markov models
Found in: Proceedings of the 24th annual international ACM SIGIR conference on Research and development in information retrieval (SIGIR '01)
By Dianne P. O'leary, John M. Conroy
Issue Date:September 2001
pp. 406-407
A sentence extract summary of a document is a subset of the document's sentences that contains the main ideas in the document. We present an approach to generating such summaries, a hidden Markov model that judges the likelihood that each sentence should b...
     
Preconditioning parallel multisplittings for solving linear systems of equations
Found in: Proceedings of the 6th international conference on Supercomputing (ICS '92)
By Chiou-Ming Huang, Dianne P. O'Leary
Issue Date:July 1992
pp. 478-484
We consider the practical implementation of Krylov subspace methods (conjugate gradients, GMRES, etc.) for parallel computers in the case where the preconditioning matrix is a multisplitting. The algorithm can be efficiently implemented by dividing the wor...
     
A semidiscrete matrix decomposition for latent semantic indexing information retrieval
Found in: ACM Transactions on Information Systems (TOIS)
By Dianne P. O'Leary, Tamara G. Kolda
Issue Date:January 1992
pp. 322-346
The vast amount of textual information available today is useless unless it can be effectively and efficiently searched. The goal in information retrieval is to find documents that are relevant to a given user query. We can represent and document collectio...
     
Algorithm 805: computation and uses of the semidiscrete matrix decomposition
Found in: ACM Transactions on Mathematical Software (TOMS)
By Dianne P. O'Leary, Tamara G. Kolda
Issue Date:March 1988
pp. 415-435
We present algorithms for computing a semidiscrete approximation to a matrix in a weighted norm, with the Frobenius norm as a special case. The approximation is formed as a weighted sum of outer products of vectors whose elements are ±1 or 0, so the s...
     
Data-flow algorithms for parallel matrix computation
Found in: Communications of the ACM
By Dianne P. O'Leary, G. W. Stewart
Issue Date:August 1985
pp. 840-853
In this article we develop some algorithms and tools for solving matrix problems on parallel processing computers. Operations are synchronized through data-flow alone, which makes global synchronization unnecessary and enables the algorithms to be implemen...
     
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