Amenability of Groupoids Arising from Partial Semigroup Actions and Topological Higher Rank Graphs

We consider the amenability of groupoids $G$ equipped with a group valued cocycle $c:G\to Q$ with amenable kernel $c^{-1}(e)$. We prove a general result which implies, in particular, that $G$ is amenable whenever $Q$ is amenable and if there is countable set $D\subset G$ such that $c(G^{u})D=Q$ for all $u\in G^{(0)}$. We show that our result is applicable to groupoids arising from partial semigroup actions. We explore these actions in detail and show that these groupoids include those arising from directed graphs, higher rank graphs and even topological higher rank graphs. We believe our methods yield a nice alternative groupoid approach to these important constructions.Comment: Revised as suggested by a very helpful referee. In particular, a gap in the proof of Theorem 5.13 has been repaired resulting in a much improved version (with fewer hypotheses

State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy

We consider a connection-level model of Internet congestion control, introduced by Massouli\'{e} and Roberts [Telecommunication Systems 15 (2000) 185--201], that represents the randomly varying number of flows present in a network. Here, bandwidth is shared fairly among elastic document transfers according to a weighted $\alpha$-fair bandwidth sharing policy introduced by Mo and Walrand [IEEE/ACM Transactions on Networking 8 (2000) 556--567] [$\alpha\in (0,\infty)$]. Assuming Poisson arrivals and exponentially distributed document sizes, we focus on the heavy traffic regime in which the average load placed on each resource is approximately equal to its capacity. A fluid model (or functional law of large numbers approximation) for this stochastic model was derived and analyzed in a prior work [Ann. Appl. Probab. 14 (2004) 1055--1083] by two of the authors. Here, we use the long-time behavior of the solutions of the fluid model established in that paper to derive a property called multiplicative state space collapse, which, loosely speaking, shows that in diffusion scale, the flow count process for the stochastic model can be approximately recovered as a continuous lifting of the workload process.Comment: Published in at http://dx.doi.org/10.1214/08-AAP591 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Theory of Feshbach molecule formation in a dilute gas during a magnetic field ramp

Starting with coupled atom-molecule Boltzmann equations, we develop a simplified model to understand molecule formation observed in recent experiments. Our theory predicts several key features: (1) the effective adiabatic rate constant is proportional to density; (2) in an adiabatic ramp, the dependence of molecular fraction on magnetic field resembles an error function whose width and centroid are related to the temperature; (3) the molecular production efficiency is a universal function of the initial phase space density, the specific form of which we derive for a classical gas. Our predictions show qualitative agreement with the data from [Hodby et al, Phys. Rev. Lett. {\bf{94}}, 120402 (2005)] without the use of adjustable parameters

Mercury accumulation in fishes from tropical aquatic ecosystems in the Niger Delta, Nigeria

Fishes are important biomarkers of trace elements in aquatic ecosystems, and are used to evaluate the status of water pollution by mercury in tropical aquatic ecosystems in Nigeria. Common fishes, Chrysichthys nigrodigitatus,Brycinus nurse, Hemichromis fasciatus, Lutianus ava, Oreochromis nilotica, Pomadasys jubelini, Stellifer stellifer and Tilapia guineensis were analysed for Hg accumulation using the cold vapour atomic absorption spectrophotometry technique. The results showed that Hg concentration in P. jubelini was relatively the highest, with a mean concentration of 0.063 ± 0.03 mg kg–1. Other concentration values were 0.044 ± 0.031 mg kg–1 for O. nilotica, 0.026 ± 0.013 mg kg–1 for B. nurse, 0.034 ± 0.034 mg kg–1 for H. fasciatus, 0.023 ± 0.020 mg kg–1 for C. nigrodigitatus and 0.33 ± 0.016 mg kg–1 for L. ava. Concentrations of Hg accumulated by the fishes were low and within internationally accepted limit, not likely to cause mercury poisoning. Because of the high Hg accumulating potential of P. jubelini, it is recommended as a biomarker for assessment of Hg toxicity in a tropical aquatic environment

QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments

QUAGMIRE is a quasi-geostrophic numerical model for performing fast, high-resolution simulations of multi-layer rotating annulus laboratory experiments on a desktop personal computer. The model uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. Version 1.3 implements the special case of two fluid layers of equal resting depths. The flow is forced either by a differentially rotating lid, or by relaxation to specified streamfunction or potential vorticity fields, or both. Dissipation is achieved through Ekman layer pumping and suction at the horizontal boundaries, including the internal interface. The effects of weak interfacial tension are included, as well as the linear topographic beta-effect and the quadratic centripetal beta-effect. Stochastic forcing may optionally be activated, to represent approximately the effects of random unresolved features. A leapfrog time stepping scheme is used, with a Robert filter. Flows simulated by the model agree well with those observed in the corresponding laboratory experiments

Hot Electron Capture Dissociation Distinguishes Leucine from Isoleucine in a Novel Hemoglobin Variant, Hb Askew, β54(D5)Val→Ile

Population migration has led to the global dispersion of human hemoglobinopathies and has precipitated a need for their identification. An effective mass spectrometry-based procedure involves analysis of the intact α- and β-globin chains to determine their mass, followed by location of the variant amino acid residue by direct analysis of the enzymatically digested chains and low-energy collision induced dissociation of the variant peptide. Using this procedure, a variant was identified as either β54Val→Leu or β54Val→Ile, since the amino acids leucine and isoleucine cannot be distinguished using low-energy collisions. Here, we describe how hot electron capture dissociation on a Fourier transform-ion cyclotron resonance mass spectrometer was used to distinguish isoleucine from leucine and identify the mutation as β54(D5)Val→Ile. This is a novel variant, and we have named it Hb Askew