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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
The Economics of Inequality
, 1975
"... Measures of inequality are used by economists to answer a wide range of questions. Is the distribution of income more equal than it was in the past? Are underdeveloped countries characterised by greater inequality than advanced countries? Do taxes lead to greater equality in the distri ..."
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Cited by 1236 (4 self)
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Measures of inequality are used by economists to answer a wide range of questions. Is the distribution of income more equal than it was in the past? Are underdeveloped countries characterised by greater inequality than advanced countries? Do taxes lead to greater equality in the distri
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
Inequality and Growth in a Panel of Countries
 JOURNAL OF ECONOMIC GROWTH
, 1999
"... Evidence from a broad panel of countries shows little overall relation between income inequality and rates of growth and investment. However, for growth, higher inequality tends to retard growth in poor countries and encourage growth in richer places. The Kuznets curve—whereby inequality first incre ..."
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Cited by 487 (4 self)
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Evidence from a broad panel of countries shows little overall relation between income inequality and rates of growth and investment. However, for growth, higher inequality tends to retard growth in poor countries and encourage growth in richer places. The Kuznets curve—whereby inequality first
Pfam protein families database
 Nucleic Acids Research, 2008, 36(Database issue): D281–D288
"... Pfam is a comprehensive collection of protein domains and families, represented as multiple sequence alignments and as profile hidden Markov models. The current release of Pfam (22.0) contains 9318 protein families. Pfam is now based not only on the UniProtKB sequence database, but also on NCBI GenP ..."
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Cited by 748 (13 self)
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Pfam is a comprehensive collection of protein domains and families, represented as multiple sequence alignments and as profile hidden Markov models. The current release of Pfam (22.0) contains 9318 protein families. Pfam is now based not only on the UniProtKB sequence database, but also on NCBI Gen
A New Data Set Measuring Income Inequality
 World Bank Economic Review
, 1996
"... The following article is the first in an occasional series introducing new data bases. The series intends to make new development data bases more widely available and to contribute to discussion and further research on economic development issues. The data bases included in the series are selected f ..."
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Cited by 428 (1 self)
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The following article is the first in an occasional series introducing new data bases. The series intends to make new development data bases more widely available and to contribute to discussion and further research on economic development issues. The data bases included in the series are selected for their potential usefulness for research and policy analysis on critical issues in developing and transition economies. Some are drawn from microlevel firm or household surveys; others contain countrylevel data. The authors describe the data contents, criteria for inclusion or exclusion of values, sources, strengths and weaknesses, and any plans for maintenance or updating. Each data base is available
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