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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 507 (2 self)
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is to construct families of curves X, some singular, with pa(X)=g, over nonsingular parameter spaces, which in some sense contain enough singular curves to link together any two components that Mg might have. The essential thing that makes this method work now is a recent " stable reduction theorem "
Problem reduction to parameter space
 MATHEMATICS OF SURFACE IX (PROC. OF THE NINTH IMA CONFERENCE
, 2000
"... This paper presents a problem reduction scheme that converts geometric constraints in work space to a system of equations in parameter space. We demonstrate that this scheme can solve many interesting geometric problems that have been considered quite difficult to deal with using conventional tech ..."
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Cited by 7 (4 self)
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This paper presents a problem reduction scheme that converts geometric constraints in work space to a system of equations in parameter space. We demonstrate that this scheme can solve many interesting geometric problems that have been considered quite difficult to deal with using conventional
Estimation on Restricted Parameter Spaces
"... The problem of finding point estimates of parameters when the feasible parameter space is a proper and convex subset of Euclidean m~space was studied. The algorithms of maximum likelihood estimation for the parameters of linear models, restricted in such a manner, were reviewed for the case in which ..."
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The problem of finding point estimates of parameters when the feasible parameter space is a proper and convex subset of Euclidean m~space was studied. The algorithms of maximum likelihood estimation for the parameters of linear models, restricted in such a manner, were reviewed for the case
The Parameter Space of Galaxy Formation
 Mon.Not.Roy.Astron.Soc.l
, 2010
"... Semianalytic models are a powerful tool for studying the formation of galaxies. However, these models inevitably involve a significant number of poorly constrained parameters that must be adjusted to provide an acceptable match to the observed universe. In this paper, we set out to quantify the d ..."
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Cited by 4 (3 self)
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the degree to which observational datasets can constrain the model parameters. By revealing degeneracies in the parameter space we can hope to better understand the key physical processes probed by the data. We use novel mathematical techniques to explore the parameter space of the GALFORM semi
Mean shift: A robust approach toward feature space analysis
 In PAMI
, 2002
"... A general nonparametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure, the mean shift. We prove for discrete data the convergence ..."
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Cited by 2401 (37 self)
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A general nonparametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure, the mean shift. We prove for discrete data
Summation in Impact Parameter Space
, 2008
"... The BlochNordsieck model for the parton distribution of hadrons in impact parameter space, constructed using soft gluon summation, is investigated in detail. Its dependence upon the infrared structure of the strong coupling constant αs is discussed, both for finite as well as singular, but integrab ..."
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The BlochNordsieck model for the parton distribution of hadrons in impact parameter space, constructed using soft gluon summation, is investigated in detail. Its dependence upon the infrared structure of the strong coupling constant αs is discussed, both for finite as well as singular
Probabilistic Roadmaps for Path Planning in HighDimensional Configuration Spaces
 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION
, 1996
"... A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collisionfree configurations and whose edg ..."
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Cited by 1277 (120 self)
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nodes. The method is general and easy to implement. It can be applied to virtually any type of holonomic robot. It requires selecting certain parameters (e.g., the duration of the learning phase) whose values depend on the scene, that is the robot and its workspace. But these values turn out
Surveys and the Blazar Parameter Space
, 2000
"... The rareness of blazars, combined with the previous history of relatively shallow, singleband surveys, has dramatically colored our perception of these objects. Despite a quartercentury of research, it is not at all clear whether current samples can be combined to give us a relatively unbiased vie ..."
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needed in depth and coverage of parameter space to give us a less biased view of blazars. These surveys have drastically increased our knowledge of blazars ’ properties. We will specifically review the discovery of “blue ” blazars, objects with broad emission lines but broadband spectral characteristics
Julia Sets in Parameter Spaces
"... Given a complex number of modulus 1, we show that the bifurcation locus of the one parameter family ff b (z) = z + bz 2 + z 3 g b2C contains quasiconformal copies of the quadratic Julia set J(z + z 2 ). As a corollary, we show that when the Julia set J(z + z 2 ) is not locally connected ( ..."
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Cited by 7 (0 self)
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(for example when z 7! z + z 2 has a Cremer point at 0), the bifurcation locus is not locally connected. To our knowledge, this is the rst example of complex analytic parameter space of dimension 1, with connected but nonlocally connected bifurcation locus. We also show that the set of complex
Greedy Function Approximation: A Gradient Boosting Machine
 Annals of Statistics
, 2000
"... Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed for additi ..."
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Cited by 997 (12 self)
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Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed
Results 1  10
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