Dataset of Edmonds' bi-vectors and tri-vectors with realizations.

In 1965, Jack Edmonds characterized pairs of graphs and with a bijection between their edge sets that form a pair of dual graphs realizing the vertices and countries of a map embedded in a surface. A necessary condition is that, if = (d, …, d) and = (t,…, t) denote the degree sequences of two such graphs, then , where is the number of edges in each of the two graphs and is the Euler characteristic of the surface. However, this condition is not sufficient, and it is an open question to characterize bi-vectors () that are , that is, that can be realized as the degree sequences of pairs and of surface-embedded graphs.

A Hypergraph-Based Reduction for Higher-Order Binary Markov Random Fields.

Higher-order Markov Random Fields, which can capture important properties of natural images, have become increasingly important in computer vision. While graph cuts work well for first-order MRF's, until recently they have rarely been effective for higher-order MRF's. Ishikawa's graph cut technique [1], [2] shows great promise for many higher-order MRF's.

Deceptive detection methods for effective security with inadequate budgets: the testing power index.

Detection of contraband depends on countermeasures, some of which involve examining cargo containers and/or their associated documents. Document screening is the least expensive, physical methods, such as gamma ray detection are more expensive, and definitive manual unpacking is most expensive. We cannot apply the full array of methods to all incoming cargoes, for budgetary reasons.