Neurally Implementable Semantic Networks

We propose general principles for semantic networks allowing them to be implemented as dynamical neural networks. Major features of our scheme include: (a) the interpretation that each node in a network stands for a bound integration of the meanings of all nodes and external events the node links with; (b) the systematic use of nodes that stand for categories or types, with separate nodes for instances of these types; (c) an implementation of relationships that does not use intrinsically typed links between nodes.Comment: 32 pages, 12 figure

The core size of the Fornax dwarf Spheroidal

We exploit the detection of three distinct stellar subpopulations in the red giant branch of the Fornax dwarf Spheroidal to probe its density distribution. This allows us to resolve directly the evolution with radius of the dark matter mass profile. We find that a cored dark matter halo provides a perfect fit to the data, being consistent with all three stellar populations well within 1-sigma, and for the first time we are able to put constraints on the core size of such a halo. With respect to previous work, we do not strengthen the statistical exclusion of a dark matter cusp in Fornax, but we find that Navarro-Frenk-White haloes would be required to have unrealistically large scale radii in order to be compatible with the data, hence low values of the concentration parameter. We are then forced to conclude that the Fornax dwarf Spheroidal sits within a dark matter halo having a constant density core, with a core size of between 0.6 and 1.8 kpc.Comment: MNRAS Letters, submitte

Lensing Properties of Cored Galaxy Models

A method is developed to evaluate the magnifications of the images of galaxies with lensing potentials stratified on similar concentric ellipses. A simple contour integral is provided which enables the sums of the magnifications of even parity or odd parity or the central image to be easily calculated. The sums for pairs of images vary considerably with source position, while the signed sums can be remarkably uniform inside the tangential caustic in the absence of naked cusps. For a family of models in which the potential is a power-law of the elliptic radius, the number of visible images is found as a function of flattening, external shear and core radius. The magnification of the central image depends on the core radius and the slope of the potential. For typical source and lens redshifts, the missing central image leads to strong constraints; the mass distribution in the lensing galaxy must be nearly cusped, and the cusp must be isothermal or stronger. This is in accord with the cuspy cores seen in high resolution photometry of nearby, massive, early-type galaxies, which typically have the surface density falling like distance^{-1.3} outside a break radius of a few hundred parsecs. Cuspy cores by themselves can provide an explanation of the missing central images. Dark matter at large radii may alter the slope of the projected density; provided the slope remains isothermal or steeper and the break radius remains small, then the central image remains unobservable. The sensitivity of the radio maps must be increased fifty-fold to find the central images in abundance.Comment: 42 pages, 11 figures, ApJ in pres

Axisymmetric Self-Similar Equilibria of Self-Gravitating Isothermal Systems

All axisymmetric self-similar equilibria of self-gravitating, rotating, isothermal systems are identified by solving the nonlinear Poisson equation analytically. There are two families of equilibria: (1) Cylindrically symmetric solutions in which the density varies with cylindrical radius as R^(-alpha), with 0 <= alpha <= 2. (2) Axially symmetric solutions in which the density varies as f(theta)/r^2, where `r' is the spherical radius and `theta' is the co-latitude. The singular isothermal sphere is a special case of the latter class with f(theta)=constant. The axially symmetric equilibrium configurations form a two-parameter family of solutions and include equilibria which are surprisingly asymmetric with respect to the equatorial plane. The asymmetric equilibria are, however, not force-free at the singular points r=0, infinity, and their relevance to real systems is unclear. For each hydrodynamic equilibrium, we determine the phase-space distribution of the collisionless analog.Comment: 13 pages, 7 figures, uses emulateapj.sty. Submitted to Ap

Layering Transitions and Solvation Forces in an Asymmetrically Confined Fluid

We consider a simple fluid confined between two parallel walls (substrates), separated by a distance L. The walls exert competing surface fields so that one wall is attractive and may be completely wet by liquid (it is solvophilic) while the other is solvophobic. Such asymmetric confinement is sometimes termed a `Janus Interface'. The second wall is: (i) purely repulsive and therefore completely dry (contact angle 180 degrees) or (ii) weakly attractive and partially dry (the contact angle is typically in the range 160-170 degrees). At low temperatures, but above the bulk triple point, we find using classical density functional theory (DFT) that the fluid is highly structured in the liquid part of the density profile. In case (i) a sequence of layering transitions occurs: as L is increased at fixed chemical potential (mu) close to bulk gas--liquid coexistence, new layers of liquid-like density develop discontinuously. In contrast to confinement between identical walls, the solvation force is repulsive for all wall separations and jumps discontinuously at each layering transition and the excess grand potential exhibits many metastable minima as a function of the adsorption. For a fixed temperature T=0.56Tc, where Tc is the bulk critical temperature, we determine the transition lines in the L, mu plane. In case (ii) we do not find layering transitions and the solvation force oscillates about zero. We discuss how our mean-field DFT results might be altered by including effects of fluctuations and comment on how the phenomenology we have revealed might be relevant for experimental and simulation studies of water confined between hydrophilic and hydrophobic substrates, emphasizing it is important to distinguish between cases (i) and (ii).Comment: 16 pages, 13 figure

Resonant Orbits and the High Velocity Peaks Towards the Bulge

We extract the resonant orbits from an N-body bar that is a good representation of the Milky Way, using the method recently introduced by Molloy et al. (2015). By decomposing the bar into its constituent orbit families, we show that they are intimately connected to the boxy-peanut shape of the density. We highlight the imprint due solely to resonant orbits on the kinematic landscape towards the Galactic centre. The resonant orbits are shown to have distinct kinematic features and may be used to explain the cold velocity peak seen in the APOGEE commissioning data (Nidever at al., 2012). We show that high velocity peaks are a natural consequence of the motions of stars in the 2:1 orbit family and that stars on other higher order resonances can contribute to the peaks. The locations of the peaks vary with bar angle and, with the tacit assumption that the observed peaks are due to the 2:1 family, we find that the locations of the high velocity peaks correspond to bar angles in the range 10 < theta_bar < 25 (deg). However, some important questions about the nature of the peaks remain, such as their apparent absence in other surveys of the Bulge and the deviations from symmetry between equivalent fields in the north and south. We show that the absence of a peak in surveys at higher latitudes is likely due to the combination of a less prominent peak and a lower number density of bar supporting orbits at these latitudes.Comment: 7 Figures, 1 Table, Now includes figures & discussion of higher order resonances, Minor revisions to text throughout, Conclusions unchange

Chemodynamic subpopulations of the Carina dwarf galaxy

We study the chemodynamical properties of the Carina dwarf spheroidal by combining an intermediate spectroscopic resolution dataset of more than 900 red giant and red clump stars, with high-precision photometry to derive the atmospheric parameters, metallicities and age estimates for our targets. Within the red giant branch population, we find evidence for the presence of three distinct stellar sub-populations with different metallicities, spatial distributions, kinematics and ages. As in the Fornax and Sculptor dwarf spheroidals, the subpopulation with the lowest average metallicity is more extended and kinematically hotter than all other populations. However, we identify an inversion in the parallel ordering of metallicity, kinematics and characteristic length scale in the two most metal rich subpopulations, which therefore do not contribute to a global negative chemical gradient. Contrary to common trends in the chemical properties with radius, the metal richest population is more extended and mildly kinematically hotter than the main component of intermediate metallicity. More investigations are required to ascertain the nature of this inversion, but we comment on the mechanisms that might have caused it.Comment: 9 pages, 9 figures, accepted for publication in MNRA

A sub-regional management framework for South Pacific longline fisheries

The principal objective of this study was to determine if additional net benefits can be derived from the sub-regional longline fishery by the introduction of a new management agreement that would centre on the provision of licensing arrangements that would allow access by eligible longline vessels to multiple Exclusive Economic Zones, i.e. Multi-zone Access. [90pp.

Resonant Clumping and Substructure in Galactic Discs

We describe a method to extract resonant orbits from N-body simulations exploiting the fact that they close in a frame rotating with a constant pattern speed. Our method is applied to the N-body simulation of the Milky Way by Shen et al. (2010). This simulation hosts a massive bar, which drives strong resonances and persistent angular momentum exchange. Resonant orbits are found throughout the disc, both close to the bar itself and out to the very edges of the disc. Using Fourier spectrograms, we demonstrate that the bar is driving kinematic substructure even in the very outer parts of the disc. We identify two major orbit families in the outskirts of the disc that make significant contributions to the kinematic landscape, namely the m:l = 3:-2 and 1:-1 families resonating with the pattern speed of the bar. A mechanism is described that produces bimodal distributions of Galactocentric radial velocities at selected azimuths in the outer disc. It occurs as a result of the temporal coherence of particles on the 3:-2 resonant orbits, which causes them to arrive simultaneously at pericentre or apocentre. This resonant clumping, due to the in-phase motion of the particles through their epicycle, leads to both inward and outward moving groups which belong to the same orbital family and consequently produce bimodal radial velocity distributions. This is a possible explanation of the bimodal velocity distributions observed towards the Galactic anti-Centre by Liu et al. (2012). Another consequence is that transient overdensities appear and dissipate (in a symmetric fashion) on timescales equal to the their epicyclic period resulting in a periodic pulsing of the disc's surface density.Comment: 11 Figures, 1 Table. Accepted for publication in ApJ. Version 2 reflects minor changes to the text. Animation referenced in Figure 7 is available at http://hubble.shao.ac.cn/~shen/resonantclumping/DensMovie.mp