A model for cleaning a graph with brushes was recently introduced. Let α = (v1, v2, . . . , vn) be a permutation of the vertices of G; for each vertex vi let N (vi) = {j : vjvi ∈ E and j > i} and N−(vi) = {j : vjvi ∈ E and j < i}; finally let bα(G) = ∑n i=1 max{|N+(vi)|−|N−(vi)|, 0}. The Broom number is given by B(G) = maxα bα(G). We consider the Broom number of d-regular graphs, focusing on th...

We propose a network of generalized Toffoli gates with multiple EXORs for the realization of reversible functions. If implemented as a quantum circuit, the cost of such gates is shown to be only marginally higher than the cost of a Toffoli gate with a single EXOR and the same number of controls. The main result is a regular synthesis procedure which allows for the creation of asymptotically opt...

I present further analytic time symmetric initial data for five dimensions describing “bubbles of nothing” which have no Kaluza-Klein circle asymptotically. The new solutions consist of a large family of single bubbles in both asymptotically flat and asymptotically AdS space. I also numerically construct gravitational solitons in AdS where the usual boundary conditions are modified geometricall...

We study nearly equal and nearly convex sets, ranges of maximally monotone operators, and ranges and fixed points of convex combinations of firmly nonexpansive mappings. The main result states that the range of an average of firmly nonexpansive mappings is nearly equal to the average of the ranges of the mappings. A striking application of this result yields that the average of asymptotically r...

The problem of existence of spacelike hypersurfaces with constant mean curvature in asymptotically flat spacetimes is considered for a class of asymptotically Schwarzschild spacetimes satisfying an interior condition. Using a barrier construction, a proof is given of the existence of complete hypersurfaces with constant mean cuvature which intersect null infinity in a regular cut. 1991 Mathemat...

decomposability of an algebraic structure into the :union: of its sub-structures goes back to g. scorza&apos;s theorem of 1926 for groups. an analogue of this theorem for rings has been recently studied by a. lucchini in 2012. on the study of this problem for non-group semigroups, the first attempt is due to clifford&apos;s work of 1961 for the regular semigroups. since then, n.p. mukherjee in ...

In the maximum scatter traveling salesman problem the objective is to find a tour that maximizes the shortest distance between any two consecutive nodes. This model can be applied to manufacturing processes, particularly laser melting processes. We extend an algorithm by Arkin et al. that yields optimal solutions for nodes on a line to a regular m×n-grid. The new algorithm Weave(m,n) takes line...

We give a new bound on the parameter λ (number of common neighbors of a pair of adjacent vertices) in a distance-regular graph G, improving and generalizing bounds for strongly regular graphs by Spielman (1996) and Pyber (2014). The new bound is one of the ingredients of recent progress on the complexity of testing isomorphism of strongly regular graphs (Babai, Chen, Sun, Teng, Wilmes 2013). Th...