Probability Definition A.6 If(\Omega ; A; ¯) is a measure space, and ¯(\Omega\Gamma = 1, then(\Omega ; A;<F64.19

:) : 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.

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

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. 87-97.) 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. 1-15). The proof uses Ramsey-theoretic and combinatorial arguments. The result implies a separation between the powers of some variants of the PRAM model of parallel computation.

Given a sequence of non-negative 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

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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

We present an unsupervised technique for visual learning which is based on density estimation in high-dimensional 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 Mixture-of-Gaussians model (for multimodal distributions). These probability densities are then used to formulate a maximum-likelihood 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 non-rigid objects such as hands.

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

Least fixpoints as meanings of recursive definitions.