Given a finite set E, a subset D ✓ E (viewed as a function E ! F2) is orthogonal to a given subspace F of the F2-vector space of functions E ! F2 as soon as D is orthogonal to every ✓-minimal element of F . This fails in general when E is infinite. However, we prove the above statement for the six subspaces F of the edge space of any 3-connected locally finite graph that are relevant to its hom...

New types of designs called nested space-filling designs have been proposed for conducting multiple computer experiments with different levels of accuracy. In this article, we develop several approaches to constructing such designs. The development of these methods also leads to the introduction of several new discrete mathematics concepts, including nested orthogonal arrays and nested differen...

Measurement of the size of anatomic regions of interest in medical images is used to diagnose disease, track growth, and evaluate response to therapy. The discrete nature of medical images allows for both continuous and discrete definitions of region boundary. These definitions may, in turn, support several methods of area calculation that give substantially different quantitative values. This ...

We show that the topological cycle space of a locally finite graph is a canonical quotient of the first singular homology group of its Freudenthal compactification, and we characterize the graphs for which the two coincide. We construct a new singular-type homology for non-compact spaces with ends, which in dimension 1 captures precisely the topological cycle space of graphs but works in any di...

In [1] we defined symmetry classes, commutation symmetries and symmetry operators in the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites and investigated them by means of tools from the representation theory of symmetric groups SN such as decompositions of ideals of the group ring C[SN ], idempotents of C[SN ], discrete Fourier transforms of SN , Littlewood-Richardson p...