Maekawa considered a simple but suboptimal grid-based quorum generation scheme in which N sites in the network are logically organized in the form of a p N p N grid, and the quorum sets are row-column pairs. Even though the quorum size 2 p N of the grid scheme is twice as large as nite projective plane with optimal sized quorums, it has the advantage of being simple and geometrically evident. A...

The individual on the cover is Endel Tulving, Professor Emeritus at the University of Toronto and one of the most influential memory researchers in experimental psychology. Our Neuron findings contradicted a prominent theory of memory lateralization put forth by Dr. Tulving and colleagues that argued for a left-hemisphere bias when encoding information into memory and a right-hemisphere bias wh...

For an arbitrary graph G = (V,E), let X be a graphical property that can be possessed, or satisfied by the subsets of V . For example, being a clique (maximal complete subgraph), a maximal independent set, an edge, a closed neighborhood, a minimal dominating set, etc. Let CX ={A|A ⊆ V , |A| > 1, and A possesses or satisfies property X}. A set S is an X cover (or X free) if A ∩ S (or A ∩ (V − S)...

Given graphs G and H, a mapping f : V (G) → V (H) is a homomorphism if (f(u), f(v)) is an edge of H for every edge (u, v) of G. In this paper, we initiate the study of computational complexity of locally injective homomorphisms called partial covers of graphs. We motivate the study of partial covers by showing a correspondence to generalized (2,1)-colorings of graphs, the notion stemming from a...

In this paper we calculate the number of equivariant diffeomorphism classes of small covers over a prism.

The biclique cover number (resp. biclique partition number) of a graph G, bc(G) (resp. bp(G)), is the least number of bicliques—complete bipartite subgraphs—that are needed to cover (resp. partition) the edges of G. The local biclique cover number (resp. local biclique partition number) of a graph G, lbc(G) (resp. lbp(G)), is the least r such that there is a cover (resp. partition) of the edges...

We initially consider an example of Flynn and Redmond, which gives an infinite family of curves to which Chabauty’s Theorem is not applicable, and which even resist solution by one application of a certain bielliptic covering technique. In this article, we shall consider a general context, of which this family is a special case, and in this general situation we shall prove that repeated applica...

Meteorological variables are essential inputs to many models in agriculture and hydrology. In particular, crop models need them because crop growth is substantially affected by weather. Frequently though, weather data will not be available in the required form. For instance, the available data may not be for exactly the right location, for the right time period or at the right scale, or simply ...

We analyze flat S3-covers, attempting to create structures parallel to those found in the abelian theory. We use an initial local analysis as a guide in finding a global description.

A monoid M is an extension of a submonoid T by a group G if there is a morphism from M onto G such that T is the inverse image of the identity of G. Our first main theorem gives descriptions of such extensions in terms of groups acting on categories. The theory developed is also used to obtain a second main theorem which answers the following question. Given a monoid M and a submonoid T , under...