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of \Omega\Gamma
"... 13> ffl 8 fA i g 1 i=1 mutually disjoint; ¯ ( S 1 i=1 A i ) = P +1 i=1 ¯ (A i ). Definition A.4 If\Omega is a set and A a oefield, (\Omega ; A) is a measurable space. Definition A.5 If(\Omega ; A) is a measurable space and ¯ a measure,(\Omega ; A; ¯) is a measure space. 112 Probab ..."
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Probability Definition A.6 If(\Omega ; A; ¯) is a measure space, and ¯(\Omega\Gamma = 1, then(\Omega ; A;<F64.19
Production of \Sigma 0 and \Omega \Gamma in Z Decays DELPHI Collaboration
, 1996
"... Abstract Reconstructed \Lambda baryon decays and photon conversions in DELPHI are used to measure the \Sigma 0 production rate from hadronic Z0 decays at LEP. The number of \Sigma 0 decays per hadronic Z decay is found to be:! \Sigma 0 + \Sigma 0? = 0:070 \Sigma 0:010 (stat:) \Sigma 0:010 (syst:) : ..."
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:) : The \Omega \Gamma production rate is similarly measured to be:! \Omega \Gamma + \Omega +? = 0:0014 \Sigma 0:0002 (stat:) \Sigma 0:0004 (syst:) by a combination of methods using constrained fits to the whole decay chain and particle identification.
An \Omega\Gamma D log(N=D)) Lower Bound for Broadcast in Radio Networks
 12th ACM Symp. on Principles of Distributed Computing
, 1993
"... We show that for any randomized broadcast protocol for radio networks, there exists a network in which the expected time to broadcast a message is \Omega\Gamma D log(N=D)), where D is the diameter of the network and N is the number of nodes. This implies a tight upper bound of \Omega\Gamma D log N) ..."
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Cited by 3 (2 self)
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We show that for any randomized broadcast protocol for radio networks, there exists a network in which the expected time to broadcast a message is \Omega\Gamma D log(N=D)), where D is the diameter of the network and N is the number of nodes. This implies a tight upper bound of \Omega\Gamma D log N
The parallel complexity of element distinctness is \Omega\Gamma p log n
 SIAM J. Disc. Math
, 1988
"... Abstract. We consider the problem of element distinctness. Here n synchronized processors, each given an integer input, must decide whether these integers are pairwise distinct, while communicating via an infinitely large shared memory. If simultaneous write access to a memory cell is forbidden, the ..."
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Cited by 6 (0 self)
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Abstract. We consider the problem of element distinctness. Here n synchronized processors, each given an integer input, must decide whether these integers are pairwise distinct, while communicating via an infinitely large shared memory. If simultaneous write access to a memory cell is forbidden, then a lower bound of f(log n) on the number of steps easily follows (from S. Cook, C. Dwork, and R. Reischuk, SIAM J. Comput., 15 (1986), pp. 8797.) When several (different) values can be written simultaneously to any cell, then there is an simple algorithm requiring O(1) steps. We consider the intermediate model, in which simultaneous writes to a single cell are allowed only if all values written are equal. We prove a lower bound of f((logn) 1/2) steps, improving the previous lower bound of f(log log log n) steps (F.E. Fich, F. Meyer auf der Heide, and A. Wigderson, Adv. in Comput., 4 (1987), pp. 115). The proof uses Ramseytheoretic and combinatorial arguments. The result implies a separation between the powers of some variants of the PRAM model of parallel computation.
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 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
Probabilistic Visual Learning for Object Representation
, 1996
"... We present an unsupervised technique for visual learning which is based on density estimation in highdimensional spaces using an eigenspace decomposition. Two types of density estimates are derived for modeling the training data: a multivariate Gaussian (for unimodal distributions) and a Mixtureof ..."
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Cited by 705 (15 self)
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We present an unsupervised technique for visual learning which is based on density estimation in highdimensional spaces using an eigenspace decomposition. Two types of density estimates are derived for modeling the training data: a multivariate Gaussian (for unimodal distributions) and a MixtureofGaussians model (for multimodal distributions). These probability densities are then used to formulate a maximumlikelihood estimation framework for visual search and target detection for automatic object recognition and coding. Our learning technique is applied to the probabilistic visual modeling, detection, recognition, and coding of human faces and nonrigid objects such as hands.
Term Rewriting Systems
, 1992
"... Term Rewriting Systems play an important role in various areas, such as abstract data type specifications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic comcepts and facts for TRS's. Specifically, we discuss Abstra ..."
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Cited by 613 (18 self)
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Term Rewriting Systems play an important role in various areas, such as abstract data type specifications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic comcepts and facts for TRS's. Specifically, we discuss Abstract Reduction Systems
Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 546 (25 self)
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Least fixpoints as meanings of recursive definitions.
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