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Computing Linear Matrix Representations of HeltonVinnikov Curves
 MATHEMATICAL METHODS IN SYSTEMS, OPTIMIZATION AND CONTROL, (EDS. HARRY DYM, MAURICIO DE OLIVEIRA, MIHAI PUTINAR), "OPERATOR THEORY: ADVANCES AND APPLICATIONS", VOL 222, BIRKHAUSER
, 2012
"... Helton and Vinnikov showed that every rigidly convex curve in the real plane bounds a spectrahedron. This leads to the computational problem of explicitly producing a symmetric (positive definite) linear determinantal representation for a given curve. We study three approaches to this problem: an a ..."
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Cited by 10 (3 self)
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Helton and Vinnikov showed that every rigidly convex curve in the real plane bounds a spectrahedron. This leads to the computational problem of explicitly producing a symmetric (positive definite) linear determinantal representation for a given curve. We study three approaches to this problem
Tribble, Debbie Helton, A Comparison of Personality Types of
, 1997
"... The purpose of this study was to determine personality characteristics of students who are successful on traditional campuses and students who are successful on alternative campuses. With this knowledge, more students may be served on the traditional campus without the necessity for alternative educ ..."
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The purpose of this study was to determine personality characteristics of students who are successful on traditional campuses and students who are successful on alternative campuses. With this knowledge, more students may be served on the traditional campus without the necessity for alternative education. The targeted sample was 120 students who were 16 or 17 years of age. They were selected through a random sampling technique from students at a traditional high school and from an alternative education center. The instrument used to assess personality types was the MversBriggs Type Indicator (MBTI): some historical background and an overview of preferences and types were given. Applications of the MBTI were discussed, focusing on the educational uses concerning the study of learning styles. Each dichotomous preference scale was discussed as to what aspect of learning style it measured, each having a unique importance in the relation of the MBTI to learning style.
Bayesian Calibration of Computer Models
 Journal of the Royal Statistical Society, Series B, Methodological
, 2000
"... this paper a Bayesian approach to the calibration of computer models. We represent the unknown inputs as a parameter vector `. Using the observed data we derive the posterior distribution of `, which in particular quantifies the `residual uncertainty' about ..."
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Cited by 192 (3 self)
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this paper a Bayesian approach to the calibration of computer models. We represent the unknown inputs as a parameter vector `. Using the observed data we derive the posterior distribution of `, which in particular quantifies the `residual uncertainty' about
Linear Controller Design: Limits of Performance Via Convex Optimization
, 1990
"... this paper, we first give a very brief overview of control engineering. The goal of control engineering is to improve, or in some cases ena ble, the performance of a system by the addition of sensors, which measure various signals in the system and external command signals, control processors, whic ..."
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Cited by 190 (25 self)
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, Stanford University, Stanford, CA 94305, USA. IEEE Log Number 8933936. system to various excitations, a procedure known as s)zstem identification [3]. In some cases, several models are developed, varying in complexity and accu racy. 2. Control configuration: selection and placement of sensors an...
Probabilistic sensitivity analysis of complex models: a Bayesian approach
 Journal of the Royal Statistical Society, Series B
, 2004
"... Summary. In many areas of science and technology, mathematical models are built to simulate complex real world phenomena. Such models are typically implemented in large computer programs and are also very complex, such that the way that the model responds to changes in its inputs is not transparent ..."
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Cited by 121 (4 self)
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Summary. In many areas of science and technology, mathematical models are built to simulate complex real world phenomena. Such models are typically implemented in large computer programs and are also very complex, such that the way that the model responds to changes in its inputs is not transparent. Sensitivity analysis is concerned with understanding how changes in the model inputs influence the outputs.This may be motivated simply by a wish to understand the implications of a complex model but often arises because there is uncertainty about the true values of the inputs that should be used for a particular application. A broad range of measures have been advocated in the literature to quantify and describe the sensitivity of a model’s output to variation in its inputs. In practice the most commonly used measures are those that are based on formulating uncertainty in the model inputs by a joint probability distribution and then analysing the induced uncertainty in outputs, an approach which is known as probabilistic sensitivity analysis. We present a Bayesian framework which unifies the various tools of probabilistic sensitivity analysis. The Bayesian approach is computationally highly efficient. It allows effective sensitivity analysis to be achieved by using far smaller numbers of model runs than standard Monte Carlo methods. Furthermore, all measures of interest may be computed from a single set of runs.
Probability is perfect, but we can’t elicit it perfectly
 RELIABILITY ENGINEERING AND SYSTEM SAFETY
, 2004
"... The challenge problems set out in Oberkampf, Helton, Joslyn, Wojtkiewicz ..."
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Cited by 25 (0 self)
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The challenge problems set out in Oberkampf, Helton, Joslyn, Wojtkiewicz
The mathematics of eigenvalue optimization
 MATHEMATICAL PROGRAMMING
"... Optimization problems involving the eigenvalues of symmetric and nonsymmetric matrices present a fascinating mathematical challenge. Such problems arise often in theory and practice, particularly in engineering design, and are amenable to a rich blend of classical mathematical techniques and contemp ..."
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Cited by 117 (11 self)
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Optimization problems involving the eigenvalues of symmetric and nonsymmetric matrices present a fascinating mathematical challenge. Such problems arise often in theory and practice, particularly in engineering design, and are amenable to a rich blend of classical mathematical techniques and contemporary optimization theory. This essay presents a personal choice of some central mathematical ideas, outlined for the broad optimization community. I discuss the convex analysis of spectral functions and invariant matrix norms, touching briefly on semidefinite representability, and then outlining two broader algebraic viewpoints based on hyperbolic polynomials and Lie algebra. Analogous nonconvex notions lead into eigenvalue perturbation theory. The last third of the article concerns stability, for polynomials, matrices, and associated dynamical systems, ending with a section on robustness. The powerful and elegant language of nonsmooth analysis appears throughout, as a unifying narrative thread.
Combination of evidence in DempsterShafer theory
, 2002
"... DempsterShafer theory offers an alternative to traditional probabilistic theory for the mathematical representation of uncertainty. The significant innovation of this framework is that it allows for the allocation of a probability mass to sets or intervals. DempsterShafer theory does not require a ..."
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Cited by 79 (2 self)
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of these rules for discrete and intervalvalued data. 3 ACKNOWLEDGEMENTS The authors wish to thank Bill Oberkampf, Jon Helton, and Marty Pilch of Sandia
A review of techniques for parameter sensitivity analysis of environmental models
 ENVIRONMENTAL MONITORING AND ASSESSMENT
, 1994
"... Mathematical models are utilized to approximate various highly complex engineering, physical, environmental, social, and economic phenomena. Model parameters exerting the most influence on model results are identified through a 'sensitivity analysis'. A comprehensive review is presented o ..."
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Cited by 91 (1 self)
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Mathematical models are utilized to approximate various highly complex engineering, physical, environmental, social, and economic phenomena. Model parameters exerting the most influence on model results are identified through a 'sensitivity analysis'. A comprehensive review is presented of more than a dozen sensitivity analysis methods. This review is intended for those not intimately familiar with statistics or the techniques utilized for sensitivity analysis of computer models. The most fundamental of sensitivity techniques utilizes partial differentiation whereas the simplest approach requires varying parameter values oneatatime. Correlation analysis is used to determine relationships between independent and dependent variables. Regression analysis provides the most comprehensive sensitivity measure and is commonly utilized to build response surfaces that approximate complex models.
Results 1  10
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2,543