Ensemble approach for generalized network dismantling

Finding a set of nodes in a network, whose removal fragments the network below some target size at minimal cost is called network dismantling problem and it belongs to the NP-hard computational class. In this paper, we explore the (generalized) network dismantling problem by exploring the spectral approximation with the variant of the power-iteration method. In particular, we explore the network dismantling solution landscape by creating the ensemble of possible solutions from different initial conditions and a different number of iterations of the spectral approximation.Comment: 11 Pages, 4 Figures, 4 Table

Resonance Raman studies of the primary photochemical event in visual pigments.

Resonance Raman multicomponent spectra of bovine rhodopsin, isorhodopsin, and bathorhodopsin have been obtained at low temperature. Application of the double beam "pump-probe" technique allows us to extract a complete bathorhodopsin spectrum from the mixture in both protonated and deuterated media. Our results show that the Schiff base of bathorhodopsin is fully protonated and that the extent of protonation is unaffected by its photochemical formation from either rhodopsin or isorhodopsin. The Raman spectrum of bathorhodopsin is significantly different than that of either parent pigment, thus supporting the notion that a geometric change in the chromophore is an important component of the primary photochemical event in vision. A normal mode analysis is carried out with particular attention devoted to the factors that determine the frequency of the C=N stretching vibration. We find that the increased frequency of this mode in protonated relative to unprotonated Schiff bases is due to coupling between C=N stretching and C=N-H bending motions, and the shift observed upon deuteration of the Schiff base can also be understood in these terms. Various models for the primary event are discussed in light of our experimental and theoretical results

Inapproximability of hypergraph vertex cover and applications to scheduling problems

Assuming the Unique Games Conjecture (UGC), we show optimal inapproximability results for two classic scheduling problems. We obtain a hardness of 2¿-¿e for the problem of minimizing the total weighted completion time in concurrent open shops. We also obtain a hardness of 2¿-¿e for minimizing the makespan in the assembly line problem. These results follow from a new inapproximability result for the Vertex Cover problem on k-uniform hypergraphs that is stronger and simpler than previous results. We show that assuming the UGC, for every k¿=¿2, the problem is inapproximable within k¿-¿e even when the hypergraph is almost k -partite