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Abstract. Consider Sk = ∑k
, 2008
"... j=1Xj, where Xk = j=0 cjξk−j, k ≥ 1, with ξj, − ∞ < j <∞, iid belonging to the domain attraction of a strictly stable law with index 0 < α ≤ 2. Under certain conditions on cj, it is known that for γn = n Hτn, 0 < H < 1, with τn slowly varying, γ−1n S[nt] converges in distribution to a ..."
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j=1Xj, where Xk = j=0 cjξk−j, k ≥ 1, with ξj, − ∞ < j <∞, iid belonging to the domain attraction of a strictly stable law with index 0 < α ≤ 2. Under certain conditions on cj, it is known that for γn = n Hτn, 0 < H < 1, with τn slowly varying, γ−1n S[nt] converges in distribution to a fractional stable motion. In addition, if f (y) is such that ∫ (f (y)+ f (y)2) dy < ∞, then for βn such that βn → ∞ and βnn → 0 (in particular βn = γn), βn n ∑n k=1 f βn γn
Abstract. Consider a semiclassical Hamiltonian
"... where h> 0 is a semiclassical parameter, ∆ is the positive Laplacian on R d, V ∈ C ∞ c (Rd), i.e. V is a smooth, compactly supported potential function which is central, that is, depends only on x  and E> 0 is an energy level. In this setting the scattering matrix Sh(E) can be defined at an ..."
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where h> 0 is a semiclassical parameter, ∆ is the positive Laplacian on R d, V ∈ C ∞ c (Rd), i.e. V is a smooth, compactly supported potential function which is central, that is, depends only on x  and E> 0 is an energy level. In this setting the scattering matrix Sh(E) can be defined at any positive energy E; it is a unitary operator on L 2 (S d−1), hence with spectrum lying on the unit circle; moreover, the spectrum is discrete except at 1. We show under certain additional assumptions on the potential that the eigenvalues of Sh(E) can be divided into two classes: a finite number ∼ cd(R √ E/h) d−1, as h → 0, where B(0, R) is the convex hull of the support of the potential, that equidistribute around the unit circle, and the remainder that are all very close to 1. Semiclassically, these are related to the rays that meet the support of, and hence are scattered by, the potential, and those that do not meet the support of the potential, respectively. A similar property is shown for the obstacle problem in the case that the obstacle is the ball of radius R. 1.
Construction of abstract state graphs with PVS
, 1997
"... We describe in this paper a method based on abstract interpretation which, from a theoretical point of view, is similar to the splitting methods proposed in [DGG93, Dam96] but the weaker abstract transition relation we use, allows us to construct automatically abstract state graphs paying a reasonab ..."
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Cited by 742 (10 self)
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reasonable price. We consider a particular set of abstract states: the set of the monomials on a set of state predicates ' 1 ; :::; ' ` . The successor of an abstract state m for a transition ø of the program is the least monomial satisfied by all successors via ø of concrete states satisfying m
Between MDPs and SemiMDPs: A Framework for Temporal Abstraction in Reinforcement Learning
, 1999
"... Learning, planning, and representing knowledge at multiple levels of temporal abstraction are key, longstanding challenges for AI. In this paper we consider how these challenges can be addressed within the mathematical framework of reinforcement learning and Markov decision processes (MDPs). We exte ..."
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Cited by 569 (38 self)
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Learning, planning, and representing knowledge at multiple levels of temporal abstraction are key, longstanding challenges for AI. In this paper we consider how these challenges can be addressed within the mathematical framework of reinforcement learning and Markov decision processes (MDPs). We
Abstraction Considered Harmful: Lazy Learning Of Language Processing
 IN PROC. OF 6TH BELGIANDUTCH CONFERENCE ON MACHINE LEARNING
, 1996
"... ..."
Abstract. Consider a Gaussian Entire Function
, 707
"... ∞ ∑ z f(z) = k k! k=0 where ζ0, ζ1,... are Gaussian i.i.d. complex random variables. The zero set of this function is distribution invariant with respect to the isometries of the complex plane. Let n(R) be the number of zeroes of f in the disk of radius R. It is easy to see that En(R) = R 2, and it ..."
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∞ ∑ z f(z) = k k! k=0 where ζ0, ζ1,... are Gaussian i.i.d. complex random variables. The zero set of this function is distribution invariant with respect to the isometries of the complex plane. Let n(R) be the number of zeroes of f in the disk of radius R. It is easy to see that En(R) = R 2, and it is known that the variance of n(R) grows linearly with R (Forrester and Honner). We prove that, for every α> 1/2, the tail probability P { n(R)−R 2 > R α} behaves as exp [ −R ϕ(α)] with some explicit piecewise linear function ϕ(α). For some special values of the parameter α, this law was found earlier by Sodin and Tsirelson, and by Krishnapur. In the context of charge fluctuations of a onecomponent Coulomb system of particles of one sign embedded into a uniform background of another sign, a similar law was discovered some time ago by Jancovici, Lebowitz and Manificat. ζk
Learning with local and global consistency.
 In NIPS,
, 2003
"... Abstract We consider the general problem of learning from labeled and unlabeled data, which is often called semisupervised learning or transductive inference. A principled approach to semisupervised learning is to design a classifying function which is sufficiently smooth with respect to the intr ..."
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Cited by 673 (21 self)
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Abstract We consider the general problem of learning from labeled and unlabeled data, which is often called semisupervised learning or transductive inference. A principled approach to semisupervised learning is to design a classifying function which is sufficiently smooth with respect
A calculus for cryptographic protocols: The spi calculus
 Information and Computation
, 1999
"... We introduce the spi calculus, an extension of the pi calculus designed for the description and analysis of cryptographic protocols. We show how to use the spi calculus, particularly for studying authentication protocols. The pi calculus (without extension) suffices for some abstract protocols; the ..."
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Cited by 898 (50 self)
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We introduce the spi calculus, an extension of the pi calculus designed for the description and analysis of cryptographic protocols. We show how to use the spi calculus, particularly for studying authentication protocols. The pi calculus (without extension) suffices for some abstract protocols
Improving generalization with active learning
 Machine Learning
, 1994
"... Abstract. Active learning differs from "learning from examples " in that the learning algorithm assumes at least some control over what part of the input domain it receives information about. In some situations, active learning is provably more powerful than learning from examples ..."
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Cited by 544 (1 self)
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Abstract. Active learning differs from "learning from examples " in that the learning algorithm assumes at least some control over what part of the input domain it receives information about. In some situations, active learning is provably more powerful than learning from examples
Near Shannon limit errorcorrecting coding and decoding
, 1993
"... Abstract This paper deals with a new class of convolutional codes called Turbocodes, whose performances in terms of Bit Error Rate (BER) are close to the SHANNON limit. The TurboCode encoder is built using a parallel concatenation of two Recursive Systematic Convolutional codes and the associated ..."
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Cited by 1776 (6 self)
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Abstract This paper deals with a new class of convolutional codes called Turbocodes, whose performances in terms of Bit Error Rate (BER) are close to the SHANNON limit. The TurboCode encoder is built using a parallel concatenation of two Recursive Systematic Convolutional codes
Results 1  10
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146,314