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We show h o w to nd a minimum weight loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the rst step in the method of conditioning for inference. Our randomized algorithm for nding a loop cutset outputs a minimum loop cutset after O(c 6 k kn) steps with probability at least 1 ; (1 ; 1 6 k ) c6 k , where c > 1 i s a constant speci ed by the user, k is the minimal size of a minimum weight loop cutset, and n is the number of vertices. We also show empirically that a variant of this algorithm often nds a loop cutset that is closer to the minimum weight loop cutset than the ones found by the best deterministic algorithms known.

We show how to find a minimum loop cut set in a Bayesian network with high proba bility. Finding such a loop cutset is the first step in Pearl's method of conditioning for in ference. Our random algorithm for finding a loop cutset, called REPEATEDWGUESSI, out puts a minimum loop cutset, after O(c · 6kk n) steps, with probability at least 1-(1--if. )cs•, where c > 1 is a constant specified by the user, k is the size of a minimum weight loop cutset, and n is the number of vertices. We also show empirically that a variant of this al gorithm, called WRA, often finds a loop cut set that is closer to the minimum loop cutset than the ones found by the best deterministic algorithms known.

An algorithm is developed for finding a close to optimal junction tree of a given graph G. The algorithm has a worst case complexity 0 ( c k n a) where a and c are constants, n is the number of vertices , and k is the size of the largest clique in a junction tree of Gi n which this size is minimized. The algorithm guaran tees that the logarithm of the size of the state space of the heaviest clique in the junction tree produced is less than a constant factor off tl ; e optimal value. When k = O(logn), our algorithm yields a polynomial inference algorithm fo r Bayesian networks.

Pedigree loops pose a difficult computational challenge in genetic linkage analysis. The most popular linkage analysis package, LINKAGE, uses an algorithm that converts a looped pedigree into a loopless pedigree, which is traversed many times. The conversion is controlled by user selection of individuals to act as loop breakers. The selection of loop breakers has significant impact on the running time of the subsequent linkage analysis. We have automated the process of selecting loop breakers, implemented a hybrid algorithm for it in the FASTLINK version of LINKAGE, and tested it on many real pedigrees with excellent performance. We point out that there is no need to break each loop by a distinct individual because, with minor modification to the algorithms in LINKAGE/FASTLINK, a single individual that participates in multiple marriages can serve as a loop breaker for several loops. Our algorithm for finding loop breakers, called LOOPBREAKER, is a combination of: (1) a new algorithm that is guaranteed to be optimal in the special case of pedigrees with no multiple marriages and (2) an adaptation of a known algorithm for breaking loops in general graphs. The contribution of this work is the adaptation of abstract methods from computer science to a challenging problem in genetics.

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The recent advance in hybrid imaging techniques enables offering simultaneous positron emission tomography (PET)/magnetic resonance imaging (MRI) in various clinical fields. 18F-fluorodeoxyglucose (FDG) PET has been widely used for diagnosis and evaluation of oncologic patients. The growing evidence from research and clinical experiences demonstrated that PET/MRI with FDG can provide comparable or superior diagnostic performance more than conventional radiological imaging such as computed tomography (CT), MRI or PET/CT in various cancers. Combined analysis using structural information and functional/molecular information of tumors can draw additional diagnostic information based on PET/MRI. Further studies including determination of the diagnostic efficacy, optimizing the examination protocol, and analysis of the hybrid imaging results is necessary for extending the FDG PET/MRI application in clinical oncology.

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