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644
The primes contain arbitrarily long polynomial progressions
- ACTA MATH
, 2006
"... We establish the existence of infinitely many polynomial progressions in the primes; more precisely, given any integer-valued polynomials P1,..., Pk ∈ Z[m] in one unknown m with P1(0) =... = Pk(0) = 0 and any ε> 0, we show that there are infinitely many integers x, m with 1 ≤ m ≤ x ε such tha ..."
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Cited by 48 (7 self)
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We establish the existence of infinitely many polynomial progressions in the primes; more precisely, given any integer-valued polynomials P1,..., Pk ∈ Z[m] in one unknown m with P1(0) =... = Pk(0) = 0 and any ε> 0, we show that there are infinitely many integers x, m with 1 ≤ m ≤ x ε
Large margin methods for structured and interdependent output variables
- JOURNAL OF MACHINE LEARNING RESEARCH
, 2005
"... Learning general functional dependencies between arbitrary input and output spaces is one of the key challenges in computational intelligence. While recent progress in machine learning has mainly focused on designing flexible and powerful input representations, this paper addresses the complementary ..."
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Cited by 624 (12 self)
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Learning general functional dependencies between arbitrary input and output spaces is one of the key challenges in computational intelligence. While recent progress in machine learning has mainly focused on designing flexible and powerful input representations, this paper addresses
GSAT and Dynamic Backtracking
- Journal of Artificial Intelligence Research
, 1994
"... There has been substantial recent interest in two new families of search techniques. One family consists of nonsystematic methods such as gsat; the other contains systematic approaches that use a polynomial amount of justification information to prune the search space. This paper introduces a new te ..."
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Cited by 386 (15 self)
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that guarantee that this database will be polynomial in the size of the problem in question. 1 INTRODUCTION The past few years have seen rapid progress in the development of algorithms for solving constraintsatisfaction problems, or csps. Csps arise naturally in subfields of AI from planning to vision
Progress on Polynomial Identity Testing
"... Polynomial identity testing (PIT) is the problem of checking whether a given arithmetic circuit is the zero circuit. PIT ranks as one of the most important open problems in the intersection of algebra and computational complexity. In the last few years, there has been an impressive progress on this ..."
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Cited by 16 (3 self)
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Polynomial identity testing (PIT) is the problem of checking whether a given arithmetic circuit is the zero circuit. PIT ranks as one of the most important open problems in the intersection of algebra and computational complexity. In the last few years, there has been an impressive progress
Intersective polynomials and polynomial Szemerédi theorem
, 2008
"... Let P = {p1,..., pr} ⊂ Q[n1,..., nm] be a family of polynomials such that pi(Zm) ⊆ Z, i = 1,..., r. We say that the family P has the PSZ property if for any set E ⊆ Z with d ∗ |E∩[M,N−1]| (E) = lim supN−M→ ∞ N−M> 0 there exist infinitely many n ∈ Zm such that E contains a polynomial progressio ..."
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Cited by 22 (4 self)
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progression of the form {a, a + p1(n),..., a + pr(n)}. We prove that a polynomial family P = {p1,..., pr} has the PSZ property if and only if the polynomials p1,..., pr are jointly intersective, meaning that for any k ∈ N there exists n ∈ Zm such that the integers p1(n),..., pr(n) are all divisible by k
Vertex Cover: Further Observations and Further Improvements
- Journal of Algorithms
, 1999
"... Recently, there have been increasing interests and progresses in lowering the worst case time complexity for well-known NP-hard problems, in particular for the Vertex Cover problem. In this paper, new properties for the Vertex Cover problem are indicated and several simple and new techniques are int ..."
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Cited by 186 (19 self)
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Recently, there have been increasing interests and progresses in lowering the worst case time complexity for well-known NP-hard problems, in particular for the Vertex Cover problem. In this paper, new properties for the Vertex Cover problem are indicated and several simple and new techniques
Progress on Polynomial Identity Testing -- II
, 2013
"... We survey the area of algebraic complexity theory; with the focus being on the problem of polynomial identity testing (PIT). We discuss the key ideas that have gone into the results of the last few years. ..."
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Cited by 1 (0 self)
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We survey the area of algebraic complexity theory; with the focus being on the problem of polynomial identity testing (PIT). We discuss the key ideas that have gone into the results of the last few years.
Polynomial Learning of Distribution Families
"... Abstract—The question of polynomial learnability of probability distributions, particularly Gaussian mixture distributions, has recently received significant attention in theoretical computer science and machine learning. However, despite major progress, the general question of polynomial learnabili ..."
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Cited by 49 (0 self)
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Abstract—The question of polynomial learnability of probability distributions, particularly Gaussian mixture distributions, has recently received significant attention in theoretical computer science and machine learning. However, despite major progress, the general question of polynomial
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