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On crossintersecting families of sets
 Graphs Combin
"... Abstract. A family A of ‘element subsets and a family B of kelement subsets of an nelement set are crossintersecting if every set from A has a nonempty intersection with every set from B. We compare two previously established inequalities each related to the maximization of the product jAjjBj, a ..."
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Abstract. A family A of ‘element subsets and a family B of kelement subsets of an nelement set are crossintersecting if every set from A has a nonempty intersection with every set from B. We compare two previously established inequalities each related to the maximization of the product j
CrossIntersecting Families of Vectors
"... Abstract. Given a sequence of positive integers p = (p1,..., pn), let Sp denote the family of all sequences of positive integers x = (x1,..., xn) such that xi ≤ pi for all i. Two families of sequences (or vectors), A, B ⊆ Sp, are said to be rcrossintersecting if no matter how we select x ∈ A and ..."
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Abstract. Given a sequence of positive integers p = (p1,..., pn), let Sp denote the family of all sequences of positive integers x = (x1,..., xn) such that xi ≤ pi for all i. Two families of sequences (or vectors), A, B ⊆ Sp, are said to be rcrossintersecting if no matter how we select x ∈ A
CrossIntersecting Sets of Vectors
"... Given a sequence of positive integers p = (p1,..., pn), let Sp denote the set of all sequences of positive integers x = (x1,..., xn) such that xi ≤ pi for all i. Two families of sequences (or vectors), A,B ⊆ Sp, are said to be rcrossintersecting if no matter how we select x ∈ A and y ∈ B, there ar ..."
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, there are at least r distinct indices i such that xi = yi. We show that for any pair of 1crossintersecting families, A,B ⊆ Sp, we have A·B  ≤ Sp2/k2, where k = mini pi. We also determine the minimal value of A  · B  for any pair of rcrossintersecting families and characterize the extremal pairs for r
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
N Degrees of Separation: MultiDimensional Separation of Concerns
 IN PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON SOFTWARE ENGINEERING
, 1999
"... Done well, separation of concerns can provide many software engineering benefits, including reduced complexity, improved reusability, and simpler evolution. The choice of boundaries for separate concerns depends on both requirements on the system and on the kind(s) of decompositionand composition a ..."
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Cited by 514 (8 self)
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Done well, separation of concerns can provide many software engineering benefits, including reduced complexity, improved reusability, and simpler evolution. The choice of boundaries for separate concerns depends on both requirements on the system and on the kind(s) of decompositionand composition a
The Optimal Degree of Commitment to an Intermediate Monetary Target
 QUARTERLY JOURNAL OF ECONOMICS
, 1985
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A Critical Point For Random Graphs With A Given Degree Sequence
, 2000
"... Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 the ..."
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Cited by 511 (8 self)
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Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0
A LongMemory Property of Stock Market Returns and a New Model
 Journal of Empirical Finance
, 1993
"... A ‘long memory ’ property of stock market returns is investigated in this paper. It is found that not only there is substantially more correlation between absolute returns than returns themselves, but the power transformation of the absolute return lrfl ” also has quite high autocorrelation for lo ..."
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Cited by 606 (21 self)
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A ‘long memory ’ property of stock market returns is investigated in this paper. It is found that not only there is substantially more correlation between absolute returns than returns themselves, but the power transformation of the absolute return lrfl ” also has quite high autocorrelation
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 498 (68 self)
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We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query
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