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The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
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Cited by 512 (2 self)
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Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k
SeibergWitten prepotential from instanton counting
, 2002
"... In my lecture I consider integrals over moduli spaces of supersymmetric gauge field configurations (instantons, Higgs bundles, torsion free sheaves). The applications are twofold: physical and mathematical; they involve supersymmetric quantum mechanics of Dparticles in various dimensions, direct co ..."
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Cited by 496 (9 self)
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In my lecture I consider integrals over moduli spaces of supersymmetric gauge field configurations (instantons, Higgs bundles, torsion free sheaves). The applications are twofold: physical and mathematical; they involve supersymmetric quantum mechanics of Dparticles in various dimensions, direct
Inducing Features of Random Fields
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1997
"... We present a technique for constructing random fields from a set of training samples. The learning paradigm builds increasingly complex fields by allowing potential functions, or features, that are supported by increasingly large subgraphs. Each feature has a weight that is trained by minimizing the ..."
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Cited by 664 (14 self)
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introduced in this paper differ from those common to much of the computer vision literature in that the underlying random fields are nonMarkovian and have a large number of parameters that must be estimated. Relations to other learning approaches, including decision trees, are given. As a demonstration
Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models
 Journal of Business and Economic Statistics
, 2002
"... Time varying correlations are often estimated with Multivariate Garch models that are linear in squares and cross products of the data. A new class of multivariate models called dynamic conditional correlation (DCC) models is proposed. These have the flexibility of univariate GARCH models coupled wi ..."
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Cited by 684 (17 self)
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Time varying correlations are often estimated with Multivariate Garch models that are linear in squares and cross products of the data. A new class of multivariate models called dynamic conditional correlation (DCC) models is proposed. These have the flexibility of univariate GARCH models coupled
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 545 (60 self)
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particular realization of the N = 2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira– Spencer theory, which may be viewed as the closed string analog of the Chern–Simon theory. Using the mirror map this leads to computation of the ‘number
Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics
, 1996
"... For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has ..."
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Cited by 548 (13 self)
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For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain
Boosting a Weak Learning Algorithm By Majority
, 1995
"... We present an algorithm for improving the accuracy of algorithms for learning binary concepts. The improvement is achieved by combining a large number of hypotheses, each of which is generated by training the given learning algorithm on a different set of examples. Our algorithm is based on ideas pr ..."
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Cited by 516 (15 self)
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presented by Schapire in his paper "The strength of weak learnability", and represents an improvement over his results. The analysis of our algorithm provides general upper bounds on the resources required for learning in Valiant's polynomial PAC learning framework, which are the best general
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical
From data mining to knowledge discovery in databases
 AI Magazine
, 1996
"... ■ Data mining and knowledge discovery in databases have been attracting a significant amount of research, industry, and media attention of late. What is all the excitement about? This article provides an overview of this emerging field, clarifying how data mining and knowledge discovery in databases ..."
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Cited by 510 (0 self)
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in databases are related both to each other and to related fields, such as machine learning, statistics, and databases. The article mentions particular realworld applications, specific datamining techniques, challenges involved in realworld applications of knowledge discovery, and current and future
Simulating Physics with Computers
 SIAM Journal on Computing
, 1982
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
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Cited by 601 (1 self)
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A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration
Results 1  10
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