Vortex configurations in the electroweak gauge theory are investigated. Two gauge-inequivalent solutions of the field equations, the Z and W vortices, have previously been found. They correspond to embeddings of the abelian Nielsen-Olesen vortex solution into a U(1) subgroup of SU(2)×U(1). It is shown here that any electroweak vortex solution can be mapped into a solution of the same energy wit...

Given an n-node undirected simple graph G and a positive integer k, the k-connectivity labeling problem for G seeks short labels for the nodes of G such that whether any two nodes are k-connected in G can be determined merely by their labels. For k = 1, an optimal solution to the problem is to give each node in the same connected component of G a common log2 n -bit label, uniquely chosen for th...

The equation solving problem is to derive the behavior of the unknown component X knowing the joint behavior of the other components (or the context) C and the specification of the overall system S. The component X can be derived by solving the Finite State Machine (FSM) equation C ◊ X ∼ S, where ◊ is the parallel composition operator and ∼ is the trace equivalence or the trace reduction relati...

A method that uses the abundances of large clusters formed in electrospray ionization to determine the solution-phase molar fractions of amino acids in multi-component mixtures is demonstrated. For solutions containing either four or 10 amino acids, the relative abundances of protonated molecules differed from their solution-phase molar fractions by up to 30-fold and 100-fold, respectively. For...