Results 1  10
of
1,833
Effective Hilbert Irreducibility
, 1985
"... n this paper we prove by entirely elementary means a very effective version of the Hilbert Irreducibility  n Theorem. We then apply our theorem to construct a probabilistic irreducibility test for sparse multivariate poly omials over arbitrary perfect fields. For the usual coefficient fields the te ..."
Abstract

Cited by 11 (6 self)
 Add to MetaCart
n this paper we prove by entirely elementary means a very effective version of the Hilbert Irreducibility  n Theorem. We then apply our theorem to construct a probabilistic irreducibility test for sparse multivariate poly omials over arbitrary perfect fields. For the usual coefficient fields
Manifold regularization: A geometric framework for learning from labeled and unlabeled examples
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2006
"... We propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution. We focus on a semisupervised framework that incorporates labeled and unlabeled data in a generalpurpose learner. Some transductive graph learning al ..."
Abstract

Cited by 578 (16 self)
 Add to MetaCart
algorithms and standard methods including Support Vector Machines and Regularized Least Squares can be obtained as special cases. We utilize properties of Reproducing Kernel Hilbert spaces to prove new Representer theorems that provide theoretical basis for the algorithms. As a result (in contrast to purely
On the Hilbert Irreducibility Theorem
, 2009
"... We discuss the Hilbert Irreducibility Theorem, presenting briefly a new approach which leads to novel conclusions, especially in the context of algebraic groups. After a short survey of the issues and of the known theory, we shall illustrate the main principles and mention some new results; in par ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
We discuss the Hilbert Irreducibility Theorem, presenting briefly a new approach which leads to novel conclusions, especially in the context of algebraic groups. After a short survey of the issues and of the known theory, we shall illustrate the main principles and mention some new results
Dimensionality reduction for supervised learning with reproducing kernel Hilbert spaces
 Journal of Machine Learning Research
, 2004
"... We propose a novel method of dimensionality reduction for supervised learning problems. Given a regression or classification problem in which we wish to predict a response variable Y from an explanatory variable X, we treat the problem of dimensionality reduction as that of finding a lowdimensional ..."
Abstract

Cited by 162 (34 self)
 Add to MetaCart
using covariance operators on reproducing kernel Hilbert spaces. This characterization allows us to derive a contrast function for estimation of the effective subspace. Unlike many conventional methods for dimensionality reduction in supervised learning, the proposed method requires neither assumptions
SMOOTH AND IRREDUCIBLE MULTIGRADED HILBERT SCHEMES
, 2009
"... The multigraded Hilbert scheme parametrizes all homogeneous ideals in a polynomial ring graded by an abelian group with a fixed Hilbert function. We prove that any multigraded Hilbert scheme is smooth and irreducible when the polynomial ring is Z[x, y], which establishes a conjecture of Haiman and ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
The multigraded Hilbert scheme parametrizes all homogeneous ideals in a polynomial ring graded by an abelian group with a fixed Hilbert function. We prove that any multigraded Hilbert scheme is smooth and irreducible when the polynomial ring is Z[x, y], which establishes a conjecture of Haiman
Factoring Multivariate Polynomials via Partial Differential Equations
 Math. Comput
, 2000
"... A new method is presented for factorization of bivariate polynomials over any field of characteristic zero or of relatively large characteristic. It is based on a simple partial differential equation that gives a system of linear equations. Like Berlekamp's and Niederreiter's algorithms fo ..."
Abstract

Cited by 56 (10 self)
 Add to MetaCart
polynomials over the ground field. The new method finds absolute and rational factorizations simultaneously and is easy to implement for finite fields, local fields, number fields, and the complex number field. The theory of the new method allows an effective Hilbert irreducibility theorem, thus an efficient
Irreducible components of the equivariant punctual Hilbert schemes.
 Adv. Math.,
, 2004
"... Abstract Let H ab be the equivariant Hilbert scheme parameterizing the zerodimensional subschemes of the affine plane invariant under the natural action of the onedimensional torus T ab :¼ fðt Àb ; t a ÞtAk Ã g: We compute the irreducible components of H ab : they are in onetoone correspondence ..."
Abstract

Cited by 19 (6 self)
 Add to MetaCart
Abstract Let H ab be the equivariant Hilbert scheme parameterizing the zerodimensional subschemes of the affine plane invariant under the natural action of the onedimensional torus T ab :¼ fðt Àb ; t a ÞtAk Ã g: We compute the irreducible components of H ab : they are in one
The moral problem
, 1994
"... Even with the considerable progress in atmospheric science during the twentieth century, there remains considerable room for improvement in the accuracy of the public warnings of tornadoes, flash floods, large hail and damaging thunderstorm winds. But even if we had perfect knowledge of the process ..."
Abstract

Cited by 204 (9 self)
 Add to MetaCart
of tornadogenesis, for example, inadequate atmospheric sampling and measurements would still prevent warning accuracy from ever reaching 100 percent. Stewart (2000) states the problem succinctly: Every prediction contains an element of irreducible uncertainty … actions that are based on predictions lead to two
Finiteness results for Hilbert’s irreducibility theorem
 Ann. Inst. Fourier
, 2002
"... Let k be a number field, Ok its ring of integers, and f(t,X) ∈ k(t)[X] be an irreducible polynomial. Hilbert’s irreducibility theorem gives infinitely many integral specializations t ↦ → ¯t ∈ Ok such that f(¯t,X) is still irreducible. In this paper we study the set Redf(Ok) of those ¯t ∈ Ok with f(¯ ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
Let k be a number field, Ok its ring of integers, and f(t,X) ∈ k(t)[X] be an irreducible polynomial. Hilbert’s irreducibility theorem gives infinitely many integral specializations t ↦ → ¯t ∈ Ok such that f(¯t,X) is still irreducible. In this paper we study the set Redf(Ok) of those ¯t ∈ Ok with f
Results 1  10
of
1,833