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Dogan and Yildiz introduce analyze the pro-con model that is inspired by Franklin’s prudential algebra. Consider an agent who endowed with two sets of orderings: pro- con-orderings. For each choice set, if alternative top-ranked a pro-ordering (con-ordering), then this pro (con) for choosing alternative. The more pros than cons chosen from set. Each ordering may have weight reflecting its salie...

In our study of the extremities of a graph, we define a moplex as a maximal clique module the neighborhood of which is a minimal separator of the graph. This notion enables us to strengthen Dirac’s theorem (Dirac, 1961): ‘‘Every non-clique triangulated graph has at least two non-adjacent simplicial vertices’’, restricting the definition of a simplicial vertex; this also enables us to strengthen...

The RAND Corporation in the early 1950s contained “what may have been the most remarkable group of mathematicians working on optimization ever assembled” [6]: Arrow, Bellman, Dantzig, Flood, Ford, Fulkerson, Gale, Johnson, Nash, Orchard-Hays, Robinson, Shapley, Simon, Wagner, and other household names. Groups like this need their challenges. One of them appears to have been the traveling salesm...

We develop an experimental algorithm of exact solving for the maximum independent set problem. The algorithm consecutively finds the maximal independent sets of vertices in an arbitrary undirected graph such that the next such set contains more elements than preceding one. For this purpose, we use a technique, developed by Ford and Fulkerson for the finite partially ordered sets, in particular,...

We introduce 2-partitionable clutters as the simplest case of the class of kpartitionable clutters and study some of their combinatorial properties. In particular, we study properties of the rank of the incidence matrix of these clutters and properties of their minors. A well known conjecture of Conforti and Cornuéjols [1, 2] states: That all the clutters with the packing property have the max-...

Ice-core records show that climate changes in the past have been large, rapid, and synchronous over broad areas extending into low latitudes, with less variability over historical times. These ice-core records come from high mountain glaciers and the polar regions, including small ice caps and the large ice sheets of Greenland and Antarctica.

[1] We use 22 monthly GRACE (Gravity Recovery and Climate Experiment) gravity fields to estimate the linear trend in Greenland ice mass during 2002–2004. We recover a decrease in total ice mass of 82 ± 28 km of ice per year, consistent with estimates from other techniques. Our uncertainty estimate is dominated by the effects of GRACE measurement errors and errors in our post glacial rebound (PG...

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