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5,494
Concentration Of Measure And Isoperimetric Inequalities In Product Spaces
, 1995
"... The concentration of measure phenomenon in product spaces roughly states that, if a set A in a product# N of probability spaces has measure at least one half, "most" of the points of# N are "close" to A. We proceed to a systematic exploration of this phenomenon. The meaning o ..."
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Cited by 376 (4 self)
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of the word "most" is made rigorous by isoperimetrictype inequalities that bound the measure of the exceptional sets. The meaning of the work "close" is defined in three main ways, each of them giving rise to related, but different inequalities. The inequalities are all proved through a
Strictly Proper Scoring Rules, Prediction, and Estimation
, 2007
"... Scoring rules assess the quality of probabilistic forecasts, by assigning a numerical score based on the predictive distribution and on the event or value that materializes. A scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distribution F if he ..."
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Cited by 373 (28 self)
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, the energy score admits a kernel representation in terms of negative definite functions, with links to inequalities of Hoeffding type, in both univariate and multivariate settings. Proper scoring rules for quantile and interval forecasts are also discussed. We relate proper scoring rules to Bayes factors
A Unified Framework for Hybrid Control: Model and Optimal Control Theory
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 1998
"... Complex natural and engineered systems typically possess a hierarchical structure, characterized by continuousvariable dynamics at the lowest level and logical decisionmaking at the highest. Virtually all control systems todayfrom flight control to the factory floorperform computercoded chec ..."
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Cited by 305 (9 self)
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coded checks and issue logical as well as continuousvariable control commands. The interaction of these different types of dynamics and information leads to a challenging set of "hybrid" control problems. We propose a very general framework that systematizes the notion of a hybrid system, combining
On the Decidability of Query Containment under Constraints
"... Query containment under constraints is the problem of checking whether for every database satisfying a given set of constraints, the result of one query is a subset of the result of another query. Recent research points out that this is a central problem in several database applications, and we addr ..."
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Cited by 256 (56 self)
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address it within a setting where constraints are specified in the form of special inclusion dependencies over complex expressions, built by using intersection and difference of relations, special forms of quantification, regular expressions over binary relations, and cardinality constraints. These types
An Efficient Constraint Handling Method for Genetic Algorithms
 Computer Methods in Applied Mechanics and Engineering
, 1998
"... Many realworld search and optimization problems involve inequality and/or equality constraints and are thus posed as constrained optimization problems. In trying to solve constrained optimization problems using genetic algorithms (GAs) or classical optimization methods, penalty function methods hav ..."
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Cited by 246 (19 self)
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Many realworld search and optimization problems involve inequality and/or equality constraints and are thus posed as constrained optimization problems. In trying to solve constrained optimization problems using genetic algorithms (GAs) or classical optimization methods, penalty function methods
A theory of urban growth,
 Journal of Political Economy
, 1999
"... In an economy experiencing endogenous economic growth and exogenous population growth, we explore two main themes: how urbanization affects efficiency of the growth process and how growth affects patterns of urbanization. Localized information spillovers promote agglomeration and human capital accu ..."
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Cited by 235 (12 self)
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externalities. In addition, we explore how growth involves real income differences across city types and how urbanization can foster income inequality. Most nonagricultural production in developed countries occurs in metropolitan areas. The underlying reasons why economic activity agglomerates into cities
On convex Sobolev inequalities and the rate of convergence to equilibrium for FokkerPlanck type equations
, 2000
"... It is well known that the analysis of the largetime asymptotics of FokkerPlanck type equations by the entropy method is closely related to proving the validity of convex Sobolev inequalities. Here we highlight this connection from an applied PDE point of view. In our unified presentation of the th ..."
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Cited by 163 (21 self)
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It is well known that the analysis of the largetime asymptotics of FokkerPlanck type equations by the entropy method is closely related to proving the validity of convex Sobolev inequalities. Here we highlight this connection from an applied PDE point of view. In our unified presentation
Type Inference with Polymorphic Recursion
 Transactions on Programming Languages and Systems
, 1991
"... The DamasMilner Calculus is the typed Acalculus underlying the type system for ML and several other strongly typed polymorphic functional languages such as Mirandal and Haskell. Mycroft has extended its problematic monomorphic typing rule for recursive definitions with a polymorphic typing rule. H ..."
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Cited by 145 (3 self)
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generally, in any language with (mutually) recursive definitions. In this paper we show that the type inference problem for the MilnerMycroft Calculus is logspace equivalent to semiunification, the problem of solving subsumption inequations between firstorder terms. This result has been proved
Sobolev inequalities in disguise
 Indiana Univ. Math. J
, 1995
"... We present a simple and direct proof of the equivalence of various functional inequalities such as Sobolev or Nash inequalities. This proof applies in the context of Riemannian or subelliptic geometry, as well as on graphs and to certain nonlocal Sobolev norms. It only uses elementary cutoff argu ..."
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Cited by 90 (14 self)
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off arguments. This method has interesting consequences concerning Trudinger type inequalities. 1. Introduction. On R n, the classical Sobolev inequality [27] indicates that, for every smooth enough function f with compact support,
Harnack Type Inequality: the Method of Moving Planes
 COMMUNICATIONS IN MATHEMATICAL PHYSICS
, 1999
"... A Harnack type inequality is established for solutions to some semilinear elliptic equations in dimension two. The result is motivated by our approach to the study of some semilinear elliptic equations on compact Riemannian manifolds, which originated from some Chernâ€“Simons Higgs model and have bee ..."
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Cited by 83 (3 self)
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A Harnack type inequality is established for solutions to some semilinear elliptic equations in dimension two. The result is motivated by our approach to the study of some semilinear elliptic equations on compact Riemannian manifolds, which originated from some Chernâ€“Simons Higgs model and have
Results 1  10
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5,494