The lexicographic flow problem is a flow problem in which the edges are assigned priorities, and we wish to find a flow that is lexicographically maximum with respect to the priority assignment. The problem is reducible to a weighted flow problem, but we show that exponentially large weights are necessary in general. We then give an efficient direct algorithm that does not use weights.

Although every terminating loop has a ranking function, not every loop has a ranking function of a restricted form, such as a lexicographic tuple of polynomials over program variables. The polyranking principle is proposed as a generalization of polynomial ranking for analyzing termination of loops. We define lexicographic polyranking functions in the context of loops with parallel transitions ...

The Hall-ratio ρ(G) of a graph G is the ratio of the number of vertices and the independence number maximized over all subgraphs of G. The ultimate lexicographic Hall-ratio of a graph G is defined as limn→∞ n √ ρ(G◦n), where G◦n denotes the nth lexicographic power of G (that is, n times repeated substitution of G into itself). Here we prove the conjecture of Simonyi stating that the ultimate le...

This work incorporates Selectional Preferences (SP) into a Semantic Role (SR) Classification system. We learn separate selectional preferences for noun phrases and prepositional phrases and we integrate them in a state-of-the-art SR classification system both in the form of features and individual class predictors. We show that the inclusion of the refined SPs yields statistically significant i...

Each month many women experience an ovulatory cycle that regulates fertility. Whereas research finds that this cycle influences women’s mating preferences, we propose that it might also change women’s political and religious views. Building on theory suggesting that political and religious orientation are linked to reproductive goals, we tested how fertility influenced women’s politics, religio...

Many preference aggregation problems are not, by nature, one-shot. In these settings, voter preferences need to be repeatedly aggregated as a function of the underlying pool of options that are being voted over. For example, imagine that a firm votes an offer to a candidate. If the offer is declined, then the pool of options shrinks, votes are aggregated once more, and a subsequent offer is mad...

Consider two graphs G and H. Let H[G] be the lexicographic product of H and G, where H is the lexicographic product of the graph H by itself k times. In this paper, we determine the spectrum of H[G] and H whenG andH are regular and the Laplacian spectrum ofH[G] andH for G and H arbitrary. Particular emphasis is given to the least eigenvalue of the adjacency matrix in the case of lexicographic p...