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891,771
On Closure Properties of GapP
 COMPUTATIONAL COMPLEXITY
, 1994
"... We study the closure properties of the function classes GapP and GapP+. We characterize the property of GapP+ being closed under decrement and of GapP being closed under maximum, minimum, median, or division by seemingly implausible collapses among complexity classes; thereby giving evidence tha ..."
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Cited by 3 (1 self)
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We study the closure properties of the function classes GapP and GapP+. We characterize the property of GapP+ being closed under decrement and of GapP being closed under maximum, minimum, median, or division by seemingly implausible collapses among complexity classes; thereby giving evidence
Closure Properties of GapP and #P
, 1995
"... We classify the univariate functions that are relativizable closure properties of GapP, solving a problem posed by Hertrampf, Vollmer, and Wagner (Structures '95). We also give a simple proof of their classification of univariate functions that are relativizable closure properties of #P. ..."
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Cited by 1 (0 self)
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We classify the univariate functions that are relativizable closure properties of GapP, solving a problem posed by Hertrampf, Vollmer, and Wagner (Structures '95). We also give a simple proof of their classification of univariate functions that are relativizable closure properties of #P.
Symmetry and Related Properties via the Maximum Principle
, 1979
"... We prove symmetry, and some related properties, of positive solutions of second order elliptic equations. Our methods employ various forms of the maximum principle, and a device of moving parallel planes to a critical position, and then showing that the solution is symmetric about the limiting plan ..."
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Cited by 539 (4 self)
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We prove symmetry, and some related properties, of positive solutions of second order elliptic equations. Our methods employ various forms of the maximum principle, and a device of moving parallel planes to a critical position, and then showing that the solution is symmetric about the limiting
Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to forecast error statistics
 J. Geophys. Res
, 1994
"... . A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The ..."
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Cited by 782 (22 self)
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. The unbounded error growth found in the extended Kalman filter, which is caused by an overly simplified closure in the error covariance equation, is completely eliminated. Open boundaries can be handled as long as the ocean model is well posed. Wellknown numerical instabilities associated with the error
Beyond Market Baskets: Generalizing Association Rules To Dependence Rules
, 1998
"... One of the more wellstudied problems in data mining is the search for association rules in market basket data. Association rules are intended to identify patterns of the type: “A customer purchasing item A often also purchases item B. Motivated partly by the goal of generalizing beyond market bask ..."
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Cited by 623 (6 self)
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squared test for independence from classical statistics. This leads to a measure that is upwardclosed in the itemset lattice, enabling us to reduce the mining problem to the search for a border between dependent and independent itemsets in the lattice. We develop pruning strategies based on the closure
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 919 (55 self)
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; the spi calculus enables us to consider cryptographic issues in more detail. We represent protocols as processes in the spi calculus and state their security properties in terms of coarsegrained notions of protocol equivalence.
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 778 (5 self)
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hard. We prove that (1 \Gamma o(1)) ln n is a threshold below which set cover cannot be approximated efficiently, unless NP has slightly superpolynomial time algorithms. This closes the gap (up to low order terms) between the ratio of approximation achievable by the greedy algorithm (which is (1 \Gamma
Nonmonotonic Reasoning, Preferential Models and Cumulative Logics
, 1990
"... Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns of ..."
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Cited by 624 (14 self)
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Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns
Coherent Measures of Risk
, 1998
"... In this paper we study both market risks and nonmarket risks, without complete markets assumption, and discuss methods of measurement of these risks. We present and justify a set of four desirable properties for measures of risk, and call the measures satisfying these properties "coherent" ..."
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Cited by 882 (4 self)
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In this paper we study both market risks and nonmarket risks, without complete markets assumption, and discuss methods of measurement of these risks. We present and justify a set of four desirable properties for measures of risk, and call the measures satisfying these properties "
Mining Sequential Patterns: Generalizations and Performance Improvements
 Research Report RJ 9994, IBM Almaden Research
, 1995
"... Abstract. The problem of mining sequential patterns was recently introduced in [3]. We are given a database of sequences, where each sequence is a list of transactions ordered by transactiontime, and each transaction is a set of items. The problem is to discover all sequential patterns with a user ..."
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Cited by 748 (5 self)
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these generalized sequential patterns. Empirical evaluation using synthetic and reallife data indicates that GSP is much faster than the AprioriAll algorithm presented in [3]. GSP scales linearly with the number of datasequences, and has very good scaleup properties with respect to the average datasequence size
Results 1  10
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891,771