Let K be a quadratic extension of Q, B a quaternion algebra over Q and A = B ⊗Q K. Let O be a maximal order in A extending an order in B. The projective norm one group PO1 is shown to be isomorphic to the spinorial kernel group O′(L), for an explicitly determined quadratic Z-lattice L of rank four, in several general situations. In other cases, only the local structures of O and L are given at ...

Hard problems for metaheuristic search can be a source of insight for developing better methods. We examine a challenging instance of such a problem that has exactly two local optima, with the novel property that these two solutions are separated by a maximum possible number of moves in the feasible space. Once a descent method based on flipping 0-1 variables reaches the first local optimum, al...

While the task of answering queries from an arbitrary propositional theory is intractable in general, it can typically be performed eeciently if the theory is Horn. This suggests that it may be more eecient to answer queries using a \Horn approximation"; i.e., a horn theory that is semantically similar to the original theory. The utility of any such approximation depends on how often it produce...

One of the issues in tuning an output probability of a Bayesian network by changing multiple parameters is the relative amount of the individual parameter changes. In an existing heuristic parameters are tied such that their changes induce locally a maximal change of the tuned probability. This heuristic, however, may reduce the attainable values of the tuned probability considerably. In anothe...

Most bus transit systems only offer direct service between a small fraction of the origin/destination pairs that they serve. As a consequence, many travelers must transfer between bus lines to complete their journey. In this paper schedule control policies are created to minimize transfer time under stochastic conditions. We determine how long a bus should be held at a transfer stop in anticipa...

This paper challenges common assumptions about convexity in forest rotation models which optimize timber &s nontimber benefits. If a local optimum occurs earlier than the globally optimal age, policy based on marginal incentives may achieve suboptimal results. Policy-relevant nonconvexities are more likely if (i) nontimber benefits dominate for young stands while the optimal age depends primari...

Finite loop spaces are a generalization of compact Lie groups. However, they do not enjoy all of the nice properties of compact Lie groups. For example, having a maximal torus is a quite distinguished property. Actually, an old conjecture, due to Wilkerson, says that every connected finite loop space with a maximal torus is equivalent to a compact connected Lie group. We give some more evidence...

We recall the basic idea of an algebraic approach to learning Bayesian network (BN) structures, namely to represent every BN structure by a certain (uniquely determined) vector, called a standard imset. The main result of the paper is that the set of standard imsets is the set of vertices (= extreme points) of a certain polytope. Motivated by the geometric view, we introduce the concept of the ...

We study a natural process for allocating m balls into n bins that are organized as the vertices of an undirected graph G. Balls arrive one at a time. When a ball arrives, it first chooses a vertex u in G uniformly at random. Then the ball performs a local search in G starting from u until it reaches a vertex with local minimum load, where the ball is finally placed on. Then the next ball arriv...

The paper investigates the problem of achieving globally optimal coverage for non-convex grid environments with a network of mobile sensor nodes. A distributed algorithm is proposed to solve the problem, which is locally implementable on individual sensor. That is, each mobile sensor only requires to update its current position to an adjacent location with certain probability relying on its cov...