Space as a low-temperature regime of graphs

I define a statistical model of graphs in which 2-dimensional spaces arise at low temperature. The configurations are given by graphs with a fixed number of edges and the Hamiltonian is a simple, local function of the graphs. Simulations show that there is a transition between a low-temperature regime in which the graphs form triangulations of 2-dimensional surfaces and a high-temperature regime, where the surfaces disappear. I use data for the specific heat and other observables to discuss whether this is a phase transition. The surface states are analyzed with regard to topology and defects.Comment: 22 pages, 12 figures; v3: published version; J.Stat.Phys. 201

Rigid upper bounds for the angular momentum and centre of mass of non-singular asymptotically anti-de Sitter space-times

We prove upper bounds on angular momentum and centre of mass in terms of the Hamiltonian mass and cosmological constant for non-singular asymptotically anti-de Sitter initial data sets satisfying the dominant energy condition. We work in all space-dimensions larger than or equal to three, and allow a large class of asymptotic backgrounds, with spherical and non-spherical conformal infinities; in the latter case, a spin-structure compatibility condition is imposed. We give a large class of non-trivial examples saturating the inequality. We analyse exhaustively the borderline case in space-time dimension four: for spherical cross-sections of Scri, equality together with completeness occurs only in anti-de Sitter space-time. On the other hand, in the toroidal case, regular non-trivial initial data sets saturating the bound exist.Comment: improvements in the presentation; some statements correcte

Twistors and Black Holes

Motivated by black hole physics in N=2, D=4 supergravity, we study the geometry of quaternionic-Kahler manifolds M obtained by the c-map construction from projective special Kahler manifolds M_s. Improving on earlier treatments, we compute the Kahler potentials on the twistor space Z and Swann space S in the complex coordinates adapted to the Heisenberg symmetries. The results bear a simple relation to the Hesse potential \Sigma of the special Kahler manifold M_s, and hence to the Bekenstein-Hawking entropy for BPS black holes. We explicitly construct the ``covariant c-map'' and the ``twistor map'', which relate real coordinates on M x CP^1 (resp. M x R^4/Z_2) to complex coordinates on Z (resp. S). As applications, we solve for the general BPS geodesic motion on M, and provide explicit integral formulae for the quaternionic Penrose transform relating elements of H^1(Z,O(-k)) to massless fields on M annihilated by first or second order differential operators. Finally, we compute the exact radial wave function (in the supergravity approximation) for BPS black holes with fixed electric and magnetic charges.Comment: 47 pages, v2: typos corrected, reference added, v3: minor change

What the egg can tell about its hen: embryo development on the basis of Dynamic Energy Budgets.

The energy cost of offspring is important in the conversion of resources allocated to reproduction to numbers of offspring, and in obtaining energy budget parameters from quantities that are easy to measure. An efficient numerical procedure is presented to obtain this cost for eggs and foetusses in the context of the dynamic energy budget theory, which specifies that birth occurs when maturity exceeds a threshold value and maternal effects determine the reserve density at birth. This paper extends previous work to arbitrary values of the ratio of the maturity and somatic maintenance costs. I discuss the body size scaling implications for the relative size and age at birth and conclude that the size at birth, contrary to the age at birth, covaries with the maintenance ratio. Apart from evolutionary adaptation of the maturity at birth, this covariation might explain some of the observed scatter in the relative length at birth. The theory can be used to evaluate the effects of the separation of cells in e.g. the two-cell stage of embryonic development, and of the removal of initial egg mass. If cell separation hardly affects energy parameters, body size scaling relationships imply that cell separation can only occur successfully in species with sufficiently large maximum body length (as adult); i.e. some two times that of Daphnia magna. Toxic compounds that increase the cost of synthesis of structure, decrease the allocation to reproduction indirectly via the life cycle, because food uptake is linked to size. They can also decrease the egg size, however, such that the reproduction rate is stimulated at low concentrations. The present theory offers a possible explanation for this well-known phenomenon. © 2008 Springer-Verlag