A Direct Reduction from k-Player to 2-Player Approximate Nash Equilibrium

We present a direct reduction from k-player games to 2-player games that preserves approximate Nash equilibrium. Previously, the computational equivalence of computing approximate Nash equilibrium in k-player and 2-player games was established via an indirect reduction. This included a sequence of works defining the complexity class PPAD, identifying complete problems for this class, showing that computing approximate Nash equilibrium for k-player games is in PPAD, and reducing a PPAD-complete problem to computing approximate Nash equilibrium for 2-player games. Our direct reduction makes no use of the concept of PPAD, thus eliminating some of the difficulties involved in following the known indirect reduction.Comment: 21 page

Transmission Through Carbon Nanotubes With Polyhedral Caps

We study electron transport between capped carbon nanotubes and a substrate, and relate the transmission probability to the local density of states in the cap. Our results show that the transmission probability mimics the behavior of the density of states at all energies except those that correspond to localized states in the cap. Close proximity of a substrate causes hybridization of the localized state. As a result, new transmission paths open from the substrate to nanotube continuum states via the localized states in the cap. Interference between various transmission paths gives rise to antiresonances in the transmission probability, with the minimum transmission equal to zero at energies of the localized states. Defects in the nanotube that are placed close to the cap cause resonances in the transmission probability, instead of antiresonances, near the localized energy levels. Depending on the spatial position of defects, these resonant states are capable of carrying a large current. These results are relevant to carbon nanotube based studies of molecular electronics and probe tip applications

Phen­yl(1-phenyl­sulfonyl-1H-indol-2-yl)methanone

The asymmetric unit of the title compound, C21H15NO3S, contains two crystallographically independent mol­ecules. As a result of the electron-withdrawing character of the phenyl­sulfonyl groups, the N—Csp 2 bond lengths are slightly longer than the anti­cipated value of approximately 1.35 Å for N atoms with planar configurations. Both unique S atoms have a distorted tetra­hedral configuration. In each mol­ecule, the indole ring system is essentially planar (r.m.s. deviations for all non-H atoms of 0.020 and 0.023 Å). In one mol­ecule, the indole ring system makes dihedral angles of 65.7 (8) and 73.4 (8)°, respectively, with the benzene and phenyl rings [62.2 (7) and 72.1 (7)°, respectively, in the other mol­ecule]

Understanding edge-connectivity in the Internet through core-decomposition

Internet is a complex network composed by several networks: the Autonomous Systems, each one designed to transport information efficiently. Routing protocols aim to find paths between nodes whenever it is possible (i.e., the network is not partitioned), or to find paths verifying specific constraints (e.g., a certain QoS is required). As connectivity is a measure related to both of them (partitions and selected paths) this work provides a formal lower bound to it based on core-decomposition, under certain conditions, and low complexity algorithms to find it. We apply them to analyze maps obtained from the prominent Internet mapping projects, using the LaNet-vi open-source software for its visualization

Global climate models violate scaling of the observed atmospheric variability

We test the scaling performance of seven leading global climate models by using detrended fluctuation analysis. We analyse temperature records of six representative sites around the globe simulated by the models, for two different scenarios: (i) with greenhouse gas forcing only and (ii) with greenhouse gas plus aerosol forcing. We find that the simulated records for both scenarios fail to reproduce the universal scaling behavior of the observed records, and display wide performance differences. The deviations from the scaling behavior are more pronounced in the first scenario, where also the trends are clearly overestimated.Comment: Accepted for publishing in Physical Review Letter