. Introduction The task of calculating posterior marginals on nodes in an arbitrary Bayesian network is known to be NP hard In this paper we investigate the approximation performance of "loopy belief propagation". This refers to using the well-known Pearl polytree algorithm [12] on a Bayesian network

to the language L. It was previously suspected (and proved in a relativized sense) that coNP-complete languages do not admit such proof systems. In sharp contrast, we show that the class of languages having two-prover interactive proof systems is nondeterministic exponential time. After the recent results

carcinoma derived from mucosal epithelium of the naso- genes among NPC and nasopharyngeal tissues (NP) and

First, here is some notation for binomial probabilities. Let X be the number of successes in n independent trials with probability p of success on each trial. Let q ≡ 1−p. Then we know that EX = np, the variance of X is npq where q = 1 − p, and so the

Problem 1: (20 points) Suppose we have random variables δ1,..., δn, independent and each either 0 or 1 with E δi = p. Write X = ∑n i=1 δi and µ = EX = np. The Chernoff bound states that for any ε> 0

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assignments. We first show that whereas an ex post efficient assignment can be computed easily, checking whether a given random assignment is ex post efficient is NP-complete. Hence implementing a given random assignment via deterministic Pareto opti-mal assignments is NP-hard. We then formalize another

hard. This ap-proach has had some limited success, exhibiting rules under which the problem of finding a beneficial manipulation is NP-hard, #P-hard, or even PSPACE-hard. Thus, under these rules, it is unlikely that a computationally efficient algorithm can be constructed that always finds a beneficial

Study Design: We performed an ex vivo study to observe cell morphology and viability of human nucleus pulposus (NP) chondrocytes isolated from degenerated intervertebral discs (IVD). Purpose: To better understand the biological behavior of NP chondrocytes in monolayer cultures. Overview

PURPOSE. To evaluate the effect of phorbol 12-myristate 13-acetate (PMA) on the expression of ⌬Np63 in human limbal epithelial cells (HLECs) during ex vivo expansion on amniotic membrane (AM). METHODS. Primary HLECs were cultured either on AM or plastic surfaces and were treated with 1 g/mL PMA