We will show that the Dirichlet-to-Neumann map Λ for the electrical conductivity equation on a simply connected plane region has an alternating property, which may be considered as a generalized maximum principle. Using this property, we will prove that the kernel, K, of Λ satisfies a set of inequalities of the form (−1) n(n+1) 2 detK(xi, yj) > 0. We will show that these inequalities imply Hopf...

The alternating and non-alternating harmonic sums and other algebraic objects of the same equivalence class are connected by algebraic relations which are induced by the product of these quantities and which depend on their index calss rather than on their value. We show how to find a basis of the associated algebra. The length of the basis l is found to be ≤ 1/d, where d is the depth of the su...

This paper introduces a novel statistical mixture model for probabilistic clustering of histogram data and, more generally, for the analysis of discrete co{occurrence data. Adopting the maximum likelihood framework, an alternating maximization algorithm is derived which is combined with annealing techniques to overcome the inherent locality of alternating optimization schemes. We demonstrate an...

Expectation propagation (EP), a family of methods for iterative approximate statistical inference closely related to belief propagation, is linked to a hybrid between Dykstra’s algorithm with cyclic Bregman projections and the method of alternating Bregman projections from convex analysis via the use of the information geometry of exponential families. Doing so justifies extrinsic information e...

We prove that, for a primitive permutation group G acting on a set X of size n, other than the alternating group, the probability that Aut(X, Y ) = G for a random subset Y of X, tends to 1 as n → ∞. So the property of the title holds for all primitive groups except the alternating groups and finitely many others. This answers a question of M. H. Klin. Moreover, we give an upper bound n for the ...

The automata-theoretic approach to model checking requires two basic ingredients: a translation from logic to automata, and an algorithm for checking language emptiness. LTL model checking has traditionally been based on (generalized) Büchi automata. Weak alternating automata provide an attractive alternative because there is an elegant and linear-time translation from LTL. However, due to thei...

The spectrum $\omega(G)$ is the set of orders elements $G$. We consider problem generating a finite nonabelian simple group $G$ given by degree if an alternating group, or Lie type, rank and order underlying field type.

This paper introduces a symmetric version of the generalized alternating direction method of multipliers for two-block separable convex programming with linear equality constraints, which inherits the superiorities of the classical alternating direction method of multipliers (ADMM), and which extends the feasible set of the relaxation factor α of the generalized ADMM to the infinite interval [F...