Bayesiannetworks provide a languagefor qualitatively representing the conditional independence properties of a distribution. This allows a natural and compact representation of the distribution, eases knowledge acquisition, and supports effective inference algorithms.

Local conditioning (LC) is an exact algorithm for computing probability in Bayesian networks, developed as an extension of Kim and Pearl's algorithm for singly-connected networks. A list of variables associated to each node guarantees that only the nodes inside a loop are conditioned on the variable which breaks it. The main advantage of this algorithm is that it computes the probability directly on the original network instead of building a cluster tree, and this can save time when debugging a model and when the sparsity of evidence allows a pruning of the network. The algorithm is also advantageous when some families in the network interact through AND/OR gates. A parallel implementation of the algorithm with a processor for each node is possible even in the case of multiply-connected networks. 1 Introduction A Bayesian network is an acyclic directed graph in which every node represents a random variable, together with a probability distribution such that P (x 1 ; : : : ; x n ) = ...

A feedback vertex set of an undirected graph is a subset of vertices that intersects with the vertex set of each cycle in the graph. Given an undirected graph G with n vertices and weights on its vertices, polynomial-time algorithms are provided for approximating the problem of finding a feedback vertex set of G with a smallest weight. When the weights of all vertices in G are equal, the performance ratio attained by these algorithms is 4 \Gamma (2=n). This improves a previous algorithm which achieved an approximation factor of O( p log n) for this case. For general vertex weights, the performance ratio becomes minf2\Delta 2 ; 4 log 2 ng where \Delta denotes the maximum degree in G. For the special case of planar graphs this ratio is reduced to 10. An interesting special case of weighted graphs where a performance ratio of 4 \Gamma (2=n) is achieved is the one where a prescribed subset of the vertices, so called blackout vertices, is not allowed to participate in any feedback verte...

We show how to find a small loop cutset in a Bayesian network.

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One critical, yet seldom measured, factor to the mission success is the leadership preferences of those in positions of authority. While project and program management methods are assessed and correlated to mission success, the leadership factor has been neglected. This work uses existing personality and leadership preference measuring instruments (MBTI and MLQ) to give a general quantification to this leadership factor and phenotypes to define systems by their complexity and precedented/unprecedented nature. By examining that system in a current context, leaders can generate a risk profile of how their actual style of leadership may not be well-matched to the challenges that tend to be experienced by systems of that phenotype. By identifying these leadership style/system phenotype mismatchs, the leader can create a leadership development plan that targets developing specific styles in priority order.