Hamiltonian mappings and circle packing phase spaces

We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of three different phase space geometries (planar, hyperbolic or spherical) and exhibits an infinite number of coexisting stable periodic orbits which appear to `pack' the phase space with circular resonances.Comment: 23 pages including 12 figures, REVTEX

Game Refinement Relations and Metrics

We consider two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose probability distributions over moves, rather than single moves. Given a goal, for example, reach a target state, the question of winning is thus a probabilistic one: what is the maximal probability of winning from a given state? On these game structures, two fundamental notions are those of equivalences and metrics. Given a set of winning conditions, two states are equivalent if the players can win the same games with the same probability from both states. Metrics provide a bound on the difference in the probabilities of winning across states, capturing a quantitative notion of state similarity. We introduce equivalences and metrics for two-player game structures, and we show that they characterize the difference in probability of winning games whose goals are expressed in the quantitative mu-calculus. The quantitative mu-calculus can express a large set of goals, including reachability, safety, and omega-regular properties. Thus, we claim that our relations and metrics provide the canonical extensions to games, of the classical notion of bisimulation for transition systems. We develop our results both for equivalences and metrics, which generalize bisimulation, and for asymmetrical versions, which generalize simulation

The structure of Phocaeicola vulgatus sialic acid acetylesterase

Sialic acids terminate many N- and O-glycans and are widely distributed on cell surfaces. There are a diverse range of enzymes which interact with these sugars throughout the tree of life. They can act as receptors for influenza and specific betacoronaviruses in viral binding and their cleavage is important in virion release. Sialic acids are also exploited by both commensal and pathogenic bacteria for nutrient acquisition. A common modification of sialic acid is 9-O-acetylation, which can limit the action of sialidases. Some bacteria, including human endosymbionts, employ esterases to overcome this modification. However, few bacterial sialic acid 9-O-acetylesterases (9-O-SAEs) have been structurally characterized. Here, the crystal structure of a 9-O-SAE from Phocaeicola vulgatus (PvSAE) is reported. The structure of PvSAE was determined to resolutions of 1.44 and 2.06 Å using crystals from two different crystallization conditions. Structural characterization revealed PvSAE to be a dimer with an SGNH fold, named after the conserved sequence motif of this family, and a Ser-His-Asp catalytic triad. These structures also reveal flexibility in the most N-terminal α-helix, which provides a barrier to active-site accessibility. Biochemical assays also show that PvSAE deacetylates both mucin and the acetylated chromophore para-nitrophenyl acetate. This structural and biochemical characterization of PvSAE furthers the understanding of 9-O-SAEs and may aid in the discovery of small molecules targeting this class of enzyme.Bio-organic Synthesi

Further restrictions on the topology of stationary black holes in five dimensions

We place further restriction on the possible topology of stationary asymptotically flat vacuum black holes in 5 spacetime dimensions. We prove that the horizon manifold can be either a connected sum of Lens spaces and "handles" $S^1 \times S^2$, or the quotient of $S^3$ by certain finite groups of isometries (with no "handles"). The resulting horizon topologies include Prism manifolds and quotients of the Poincare homology sphere. We also show that the topology of the domain of outer communication is a cartesian product of the time direction with a finite connected sum of $\mathbb R^4,S^2 \times S^2$'s and $CP^2$'s, minus the black hole itself. We do not assume the existence of any Killing vector beside the asymptotically timelike one required by definition for stationarity.Comment: LaTex, 22 pages, 9 figure

Continuous Quantum Measurement and the Quantum to Classical Transition

While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the trajectories of the correct classical motion must emerge from quantum mechanics, a process referred to as the quantum to classical transition. Extending previous work [Bhattacharya, Habib, and Jacobs, Phys. Rev. Lett. {\bf 85}, 4852 (2000)], here we elucidate this transition in some detail, showing that once the measurement processes which affect all macroscopic systems are taken into account, quantum mechanics indeed predicts the emergence of classical motion. We derive inequalities that describe the parameter regime in which classical motion is obtained, and provide numerical examples. We also demonstrate two further important properties of the classical limit. First, that multiple observers all agree on the motion of an object, and second, that classical statistical inference may be used to correctly track the classical motion.Comment: 12 pages, 4 figures, Revtex

Nonclassical statistics of intracavity coupled χ(2)\chi^{(2)} waveguides: the quantum optical dimer

A model is proposed where two $\chi^{(2)}$ nonlinear waveguides are contained in a cavity suited for second-harmonic generation. The evanescent wave coupling between the waveguides is considered as weak, and the interplay between this coupling and the nonlinear interaction within the waveguides gives rise to quantum violations of the classical limit. These violations are particularly strong when two instabilities are competing, where twin-beam behavior is found as almost complete noise suppression in the difference of the fundamental intensities. Moreover, close to bistable transitions perfect twin-beam correlations are seen in the sum of the fundamental intensities, and also the self-pulsing instability as well as the transition from symmetric to asymmetric states display nonclassical twin-beam correlations of both fundamental and second-harmonic intensities. The results are based on the full quantum Langevin equations derived from the Hamiltonian and including cavity damping effects. The intensity correlations of the output fields are calculated semi-analytically using a linearized version of the Langevin equations derived through the positive-P representation. Confirmation of the analytical results are obtained by numerical simulations of the nonlinear Langevin equations derived using the truncated Wigner representation.Comment: 15 pages, 8 figures, submitted to Phys. Rev.

On the variability of simulated source-receptor relationships for sulfur deposition

The use of Lagrangian models to estimate source-receptor relationships for ambient SO 4 = concentrations and S deposition has become fairly widespread over the past several years. This paper addresses the sensitivity of long-term simulations of a Lagrangian S transport and deposition model to actual variations in SO 2 emissions and meteorological conditions. The variations of predicted source-receptor relationships due to (1) the inclusion of day to day variations in emissions strength as opposed to the use of the annual average daily emission rate and (2) year-to-year variations in meteorological conditions were studied to identify causes of uncertainty in a Lagrangian model. The results suggested that adding information on day to day emission variations for a specific point source resulted in variations in estimated S wet deposition of the order of only 20% within 500 km of the source.Year-to-year variations in meteorological conditions, on the other hand, resulted in variations in predicted S wet deposition of the order of 50% for some receptors. The variation in estimated source-receptor relationships for a given source/receptor combination was found to range as high as 70% over a 5-yr modeling period.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43900/1/11270_2004_Article_BF00303346.pd