Abstract:
We present a model for evolution and extinction in large ecosystems. The model incorporates the effects of interactions between species and the influences of abiotic environmental factors. We study the properties of the model by approximate analytic solution and also by numerical simulation, and use it to make predictions about the distribution of extinctions and species lifetimes that we would expect to see in real ecosystems. It should be possible to test these predictions against the fossil record. The model indicates that a possible mechanism for mass extinction is the coincidence of a large coevolutionary avalanche in the ecosystem with a severe environmental disturbance.

Abstract:
We present a new model for extinction in which species evolve in bursts or `avalanches', during which they become on average more susceptible to environmental stresses such as harsh climates and so are more easily rendered extinct. Results of simulations and analytic calculations using our model show a power-law distribution of extinction sizes which is in reasonable agreement with fossil data. e also see a number of features qualitatively similar to those seen in the fossil record. For example, we see frequent smaller extinctions in the wake of a large mass extinction, which arise because there is reduced competition for resources in the aftermath of a large extinction event, so that species which would not normally be able to compete can get a foothold, but only until the next cold winter or bad attack of the flu comes along to wipe them out.

Abstract:
Let $X$ be $k$-regular graph on $v$ vertices and let $\tau$ denote the least eigenvalue of its adjacency matrix $A(X)$. If $\alpha(X)$ denotes the maximum size of an independent set in $X$, we have the following well known bound: \[ \alpha(X) \le\frac{v}{1-\frac{k}{\tau}}. \] It is less well known that if equality holds here and $S$ is a maximum independent set in $X$ with characteristic vector $x$, then the vector \[ x-\frac{|S|}{v}\one \] is an eigenvector for $A(X)$ with eigenvalue $\tau$. In this paper we show how this can be used to characterise the maximal independent sets in certain classes of graphs. As a corollary we show that a graph defined on the partitions of $\{1,...,9\}$ with three cells of size three is a core.

Abstract:
We deal with a graph colouring problem that arises in quantum information theory. Alice and Bob are each given a $\pm1$-vector of length $k$, and are to respond with $k$ bits. Their responses must be equal if they are given equal inputs, and distinct if they are given orthogonal inputs; however, they are not allowed to communicate any information about their inputs. They can always succeed using quantum entanglement, but their ability to succeed using only classical physics is equivalent to a graph colouring problem. We resolve the graph colouring problem, thus determining that they can succeed without entanglement exactly when $k\leq3$.

Abstract:
We derive bounds on the size of an independent set based on eigenvalues. This generalizes a result due to Delsarte and Hoffman. We use this to obtain new bounds on the independence number of the Erd\H{o}s-R\'{e}nyi graphs. We investigate further properties of our bounds, and show how our results on the Erd\H{o}s-R\'{e}nyi graphs can be extended to other polarity graphs.

Abstract:
This work investigates the short wavelength stability of the magnetopause between a rapidly-rotating, supersonic, dense accretion disc and a slowly-rotating low-density magnetosphere of a magnetized star. The magnetopause is a strong shear layer with rapid changes in the azimuthal velocity, the density, and the magnetic field over a short radial distance and thus the Kelvin-Helmholtz (KH) instability may be important. The plasma dynamics is treated using non-relativistic, compressible (isentropic) magnetohydrodynamics. It is necessary to include the displacement current in order that plasma wave velocities remain less than the speed of light. We focus mainly on the case of a star with an aligned dipole magnetic field so that the magnetic field is axial in the disc midplane and perpendicular to the disc flow velocity. However, we also give results for cases where the magnetic field is at an arbitrary angle to the flow velocity. For the aligned dipole case the magnetopause is most unstable for KH waves propagating in the azimuthal direction perpendicular to the magnetic field which tends to stabilize waves propagating parallel to it. The wave phase velocity is that of the disc matter. A quasi-linear theory of the saturation of the instability leads to a wavenumber ($k$) power spectrum $\propto k^{-1}$ of the density and temperature fluctuations of the magnetopause, and it gives the mass accretion and angular momentum inflow rates across the magnetopause. For self-consistent conditions this mass accretion rate will be equal to the disc accretion rate at large distances from the magnetopause.

Abstract:
It is shown that narrow channels of high electric field are an effective mechanism for injecting plasma into the inner magnetosphere. Analytical expressions for the electric field cannot produce these channels of intense plasma flow, and thus, result in less entry and adiabatic energization of the plasma sheet into near-Earth space. For the ions, omission of these channels leads to an underprediction of the strength of the stormtime ring current and therefore, an underestimation of the geoeffectiveness of the storm event. For the electrons, omission of these channels leads to the inability to create a seed population of 10-100 keV electrons deep in the inner magnetosphere. These electrons can eventually be accelerated into MeV radiation belt particles. To examine this, the 1-7 May 1998 magnetic storm is studied with a plasma transport model by using three different convection electric field models: Volland-Stern, Weimer, and AMIE. It is found that the AMIE model can produce particle fluxes that are several orders of magnitude higher in the L = 2 – 4 range of the inner magnetosphere, even for a similar total cross-tail potential difference. Key words. Space plasma physics (charged particle motion and acceleration) – Magnetospheric physics (electric fields, storms and substorms)

Abstract:
In the crystal structure of the title compound, C9H8O3, essentially planar molecules [the carboxyl group makes a dihedral angle of 4.53 (7)° with the plane of the ring, while the acid group forms a dihedral angle of 3.45 (8)° to the ring] aggregate by centrosymmetric hydrogen-bond pairing of ordered carboxyl groups. This yields dimers which have two orientations in a unit cell, creating a herringbone pattern. In addition, two close C—H...O intermolecular contacts exist: one is between a methyl H atom and the ketone of a symmetry-related molecule and the other involves a benzene H atom and the carboxyl group O atom of another molecule. The crystal studied was a non-merohedral twin with twin law [100, 0overline10, overline10overline1] and a domain ratio of 0.8104(14): 0.1896(14).

Abstract:
The organization of lipids within biological membranes is poorly understood. Some studies have suggested lipids group into microdomains within cells, but the evidence remains controversial due to non-native imaging techniques. A recently developed NanoSIMS technique indicated that sphingolipids group into microdomains within membranes of human fibroblast cells. We extended this NanoSIMS approach to study the localization of hopanoid lipids in bacterial cells by developing a stable isotope labeling method to directly detect subcellular localization of specific lipids in bacteria with ca. 60 nm resolution. Because of the relatively small size of bacterial cells and the relative abundance of hopanoid lipids in membranes, we employed a primary 2H-label to maximize our limit of detection. This approach permitted the analysis of multiple stable isotope labels within the same sample, enabling visualization of subcellular lipid microdomains within different cell types using a secondary label to mark the growing end of the cell. Using this technique, we demonstrate subcellular localization of hopanoid lipids within alpha-proteobacterial and cyanobacterial cells. Further, we provide evidence of hopanoid lipid domains in between cells of the filamentous cyanobacterium Nostoc punctiforme. More broadly, our method provides a means to image lipid microdomains in a wide range of cell types and test hypotheses for their functions in membranes.

Abstract:
We present real--space renormalization group (RG) calculations of the critical properties of the random--field Ising model on a cubic lattice in three dimensions. We calculate the RG flows in a two--parameter truncation of the Hamiltonian space. As predicted, the transition at finite randomness is controlled by a zero temperature, disordered critical fixed point, and we exhibit the universal crossover trajectory from the pure Ising critical point. We extract scaling fields and critical exponents, and study the distribution of barrier heights between states as a function of length scale.