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Inverse Rendering for Computer Graphics
, 1998
"... Creating realistic images has been a major focus in the study of computer graphics for much of its history. This effort has led to mathematical models and algorithms that can compute predictive, or physically realistic, images from known camera positions and scene descriptions that include the geome ..."
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Cited by 99 (4 self)
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Creating realistic images has been a major focus in the study of computer graphics for much of its history. This effort has led to mathematical models and algorithms that can compute predictive, or physically realistic, images from known camera positions and scene descriptions that include the geometry of objects, the reflectance of surfaces, and the lighting used to illuminate the scene. These images accurately describe the physical quantities that would be measured from a real scene. Because these algorithms can predict real images, they can also be used in inverse problems to work backward from photographs to attributes of the scene. Work on three such inverse rendering problems is described. The first, inverse lighting, assumes knowledge of geometry, reflectance, and the recorded photograph and solves for the lighting in the scene. A technique using a linear leastsquares system is proposed and demonstrated. Also demonstrated is an application of inverse lighting, called relighting, which modi es lighting in photographs. The second two inverse rendering problems solve for unknown reflectance, given images with known geometry, lighting, and camera positions. Photographic texture measurement
Symbolic model checking for probabilistic processes
 IN PROCEEDINGS OF ICALP '97
, 1997
"... We introduce a symbolic model checking procedure for Probabilistic Computation Tree Logic PCTL over labelled Markov chains as models. Model checking for probabilistic logics typically involves solving linear equation systems in order to ascertain the probability of a given formula holding in a stat ..."
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Cited by 97 (29 self)
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We introduce a symbolic model checking procedure for Probabilistic Computation Tree Logic PCTL over labelled Markov chains as models. Model checking for probabilistic logics typically involves solving linear equation systems in order to ascertain the probability of a given formula holding in a state. Our algorithm is based on the idea of representing the matrices used in the linear equation systems by MultiTerminal Binary Decision Diagrams (MTBDDs) introduced in Clarke et al [14]. Our procedure, based on the algorithm used by Hansson and Jonsson [24], uses BDDs to represent formulas and MTBDDs to represent Markov chains, and is efficient because it avoids explicit state space construction. A PCTL model checker is being implemented in Verus [9].
The quantitative structure of exponential time
 Complexity Theory Retrospective II
, 1997
"... ..."
Equivalence of Measures of Complexity Classes
"... The resourcebounded measures of complexity classes are shown to be robust with respect to certain changes in the underlying probability measure. Specifically, for any real number ffi ? 0, any uniformly polynomialtime computable sequence ~ fi = (fi 0 ; fi 1 ; fi 2 ; : : : ) of real numbers (biases ..."
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Cited by 73 (22 self)
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The resourcebounded measures of complexity classes are shown to be robust with respect to certain changes in the underlying probability measure. Specifically, for any real number ffi ? 0, any uniformly polynomialtime computable sequence ~ fi = (fi 0 ; fi 1 ; fi 2 ; : : : ) of real numbers (biases) fi i 2 [ffi; 1 \Gamma ffi], and any complexity class C (such as P, NP, BPP, P/Poly, PH, PSPACE, etc.) that is closed under positive, polynomialtime, truthtable reductions with queries of at most linear length, it is shown that the following two conditions are equivalent. (1) C has pmeasure 0 (respectively, measure 0 in E, measure 0 in E 2 ) relative to the cointoss probability measure given by the sequence ~ fi. (2) C has pmeasure 0 (respectively, measure 0 in E, measure 0 in E 2 ) relative to the uniform probability measure. The proof introduces three techniques that may be useful in other contexts, namely, (i) the transformation of an efficient martingale for one probability measu...
The price impact and survival of irrational traders
 Journal of Finance
, 2006
"... Milton Friedman argued that irrational traders will consistently lose money, won’t survive and, therefore, cannot influence long run equilibrium asset prices. Since his work, survival and price influence have been assumed to be the same. Often partial equilibrium analysis has been relied upon to exa ..."
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Cited by 66 (4 self)
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Milton Friedman argued that irrational traders will consistently lose money, won’t survive and, therefore, cannot influence long run equilibrium asset prices. Since his work, survival and price influence have been assumed to be the same. Often partial equilibrium analysis has been relied upon to examine the survival of irrational traders and to make inferences on their influence on prices. In this paper, we demonstrate that survival and influence on prices are two independent concepts. The price impact of irrational traders does not rely on their longrun survival and they can have a significant impact on asset prices even when their wealth becomes negligible. In addition, in contrast to a partial equilibrium analysis, general equilibrium considerations matter since the ability of irrational traders to impact prices even when their wealth is diminishing can significantly affect their chances for longrun survival. In sum, in a longrun equilibrium, we explicitly show that price impact can occur whether or not the irrational traders survive. In related work, we show that even if the irrational
Learning Simple Concepts Under Simple Distributions
 SIAM JOURNAL OF COMPUTING
, 1991
"... We aim at developing a learning theory where `simple' concepts are easily learnable. In Valiant's learning model, many concepts turn out to be too hard (like NP hard) to learn. Relatively few concept classes were shown to be learnable polynomially. In daily life, it seems that things we ..."
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Cited by 57 (3 self)
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We aim at developing a learning theory where `simple' concepts are easily learnable. In Valiant's learning model, many concepts turn out to be too hard (like NP hard) to learn. Relatively few concept classes were shown to be learnable polynomially. In daily life, it seems that things we care to learn are usually learnable. To model the intuitive notion of learning more closely, we do not require that the learning algorithm learns (polynomially) under all distributions, but only under all simple distributions. A distribution is simple if it is dominated by an enumerable distrib...
THE THEORY OF THE UNIVERSAL WAVE FUNCTION
 THE MANYWORLDS INTERPRETATION OF QUANTUM MECHANICS
, 1973
"... We begin, as a way of entering our subject, by characterizing a particular interpretation of quantum theory which, although not representative of the more careful formulations of some writers, is the most common form encountered in textbooks and university lectures on the subject. ..."
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Cited by 49 (0 self)
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We begin, as a way of entering our subject, by characterizing a particular interpretation of quantum theory which, although not representative of the more careful formulations of some writers, is the most common form encountered in textbooks and university lectures on the subject.
An Extension Result for Continuous Valuations
, 1998
"... We show, by a simple and direct proof, that if a bounded valuation on a directed complete partial order (dcpo) is the supremum of a directed family of simple valuations then it has a unique extension to a measure on the Borel oealgebra of the dcpo with the Scott topology. It follows that every boun ..."
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Cited by 45 (6 self)
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We show, by a simple and direct proof, that if a bounded valuation on a directed complete partial order (dcpo) is the supremum of a directed family of simple valuations then it has a unique extension to a measure on the Borel oealgebra of the dcpo with the Scott topology. It follows that every bounded and continuous valuation on a continuous domain can be extended uniquely to a Borel measure. The result also holds for oefinite valuations, but fails for dcpo's in general. 1