Quantum Weakly Nondeterministic Communication Complexity

We study the weakest model of quantum nondeterminism in which a classical proof has to be checked with probability one by a quantum protocol. We show the first separation between classical nondeterministic communication complexity and this model of quantum nondeterministic communication complexity for a total function. This separation is quadratic.Comment: 12 pages. v3: minor correction

Modulation of internuclear communication in multinuclear Ruthenium(II) polypyridyl complexes

The syntheses and characterisation of a series of mononuclear and dinuclear ruthenium polypyridyl complexes based on the bridging ligands 1,3-bis-[5-(2-pyridyl)-1H-1,2,4-triazol-3-yl]benzene, 1,4-bis-[5-(2-pyridyl)-1H-1,2,4-triazol-3-yl]benzene, 2,5-bis-[5-(2-pyridyl)-1H-1,2,4-triazol-3-yl]thiophene, 2,5-bis-[5-pyrazinyl-1H-1,2,4-triazol-3-yl]thiophene are reported. Electrochemical studies indicate that in these systems, the ground state interaction is critically dependent on the nature of the bridging ligand and its protonation state, with strong and weak interactions being observed for thiophene- and phenylene-bridged complexes, respectively

Constructing monotone homotopies and sweepouts

This article investigates when homotopies can be converted to monotone homotopies without increasing the lengths of curves. A monotone homotopy is one which consists of curves which are simple or constant, and in which curves are pairwise disjoint. We show that, if the boundary of a Riemannian disc can be contracted through curves of length less than $L$, then it can also be contracted monotonously through curves of length less than $L$. This proves a conjecture of Chambers and Rotman. Additionally, any sweepout of a Riemannian $2$-sphere through curves of length less than $L$ can be replaced with a monotone sweepout through curves of length less than $L$. Applications of these results are also discussed.Comment: 16 pages, 6 figure

Maps of zeroes of the grand canonical partition function in a statistical model of high energy collisions

Theorems on zeroes of the truncated generating function in the complex plane are reviewed. When examined in the framework of a statistical model of high energy collisions based on the negative binomial (Pascal) multiplicity distribution, these results lead to maps of zeroes of the grand canonical partition function which allow to interpret in a novel way different classes of events in pp collisions at LHC c.m. energies.Comment: 17 pages, figures (ps included); added references, some figures enlarged. To appear in J. Phys.

Restricted Power - Computational Complexity Results for Strategic Defense Games

We study the game Greedy Spiders, a two-player strategic defense game, on planar graphs and show PSPACE-completeness for the problem of deciding whether one player has a winning strategy for a given instance of the game. We also generalize our results in metatheorems, which consider a large set of strategic defense games. We achieve more detailed complexity results by restricting the possible strategies of one of the players, which leads us to Sigma^p_2- and Pi^p_2-hardness results