Schemata as Building Blocks: Does Size Matter?

We analyze the schema theorem and the building block hypothesis using a recently derived, exact schemata evolution equation. We derive a new schema theorem based on the concept of effective fitness showing that schemata of higher than average effective fitness receive an exponentially increasing number of trials over time. The building block hypothesis is a natural consequence in that the equation shows how fit schemata are constructed from fit sub-schemata. However, we show that generically there is no preference for short, low-order schemata. In the case where schema reconstruction is favoured over schema destruction large schemata tend to be favoured. As a corollary of the evolution equation we prove Geiringer's theorem. We give supporting numerical evidence for our claims in both non-epsitatic and epistatic landscapes.Comment: 17 pages, 10 postscript figure

B^F Theory and Flat Spacetimes

We propose a reduced constrained Hamiltonian formalism for the exactly soluble $B \wedge F$ theory of flat connections and closed two-forms over manifolds with topology $\Sigma^3 \times (0,1)$. The reduced phase space variables are the holonomies of a flat connection for loops which form a basis of the first homotopy group $\pi_1(\Sigma^3)$, and elements of the second cohomology group of $\Sigma^3$ with value in the Lie algebra $L(G)$. When $G=SO(3,1)$, and if the two-form can be expressed as $B= e\wedge e$, for some vierbein field $e$, then the variables represent a flat spacetime. This is not always possible: We show that the solutions of the theory generally represent spacetimes with ``global torsion''. We describe the dynamical evolution of spacetimes with and without global torsion, and classify the flat spacetimes which admit a locally homogeneous foliation, following Thurston's classification of geometric structures.Comment: 21 pp., Mexico Preprint ICN-UNAM-93-1

Contribution of seasonal sub-Antarctic surface water variability to millennial-scale changes in atmospheric CO<inf>2</inf> over the last deglaciation and Marine Isotope Stage 3

The Southern Ocean is thought to have played a key role in past atmospheric carbon dioxide (CO2,atm) changes. Three main factors are understood to control the Southern Ocean's influence on CO2,atm, via their impact on surface ocean pCO2 and therefore regional ocean–atmosphere CO2 fluxes: 1) the efficiency of air–sea gas exchange, which may be attenuated by seasonal- or annual sea-ice coverage or the development of a shallow pycnocline; 2) the supply of CO2-rich water masses from the sub-surface and the deep ocean, which is associated with turbulent mixing and surface buoyancy- and/or wind forcing; and 3) biological carbon fixation, which depends on nutrient availability and is therefore influenced by dust deposition and/or upwelling. In order to investigate the possible contributions of these processes to millennial-scale CO2,atm variations during the last glacial and deglacial periods, we make use of planktonic foraminifer census counts and stable oxygen- and carbon isotope measurements in the planktonic foraminifera Globigerina bulloides and Neogloboquadrina pachyderma (sinistral) from marine sediment core MD07-3076Q in the sub-Antarctic Atlantic. These data are interpreted on the basis of a comparison of core-top and modern seawater isotope data, which permits an assessment of the seasonal biases and geochemical controls on the stable isotopic compositions of G. bulloides and N. pachyderma (s.). Based on a comparison of our down-core results with similar data from the Southeast Atlantic (Cape Basin) we infer past basin-wide changes in the surface hydrography of the sub-Antarctic Atlantic. We find that millennial-scale rises in CO2,atm over the last 70 ka are consistently linked with evidence for increased spring upwelling, and enhanced summer air–sea exchange in the sub-Antarctic Atlantic. Parallel evidence for increased summer export production would suggest that seasonal changes in upwelling and air–sea exchange exerted a dominant influence on surface pCO2 in the sub-Antarctic Atlantic. These results underline the role of Southern Ocean dynamics, in particular their seasonal variations, in driving millennial-scale variations in CO2,atm.This work was supported by the Gates Cambridge Trust, the Royal Society and NERC grant NE/J010545/1.This was originally published in Earth and Planetary Science Letters (J Gottschalk, LC Skinner, C Waelbroeck, Earth and Planetary Science Letters 2015, 411, 87-99

Homotopy Invariants and Time Evolution in (2+1)-Dimensional Gravity

We establish the relation between the ISO(2,1) homotopy invariants and the polygon representation of (2+1)-dimensional gravity. The polygon closure conditions, together with the SO(2,1) cycle conditions, are equivalent to the ISO(2,1) cycle conditions for the representa- tions of the fundamental group in ISO(2,1). Also, the symplectic structure on the space of invariants is closely related to that of the polygon representation. We choose one of the polygon variables as internal time and compute the Hamiltonian, then perform the Hamilton-Jacobi transformation explicitly. We make contact with other authors' results for g = 1 and g = 2 (N = 0).Comment: 34 pages, Mexico preprint ICN-UNAM-93-1

Radiocarbon evidence for enhanced respired carbon storage in the Atlantic at the Last Glacial Maximum

The influence of ocean circulation changes on atmospheric CO2 hinges primarily on the ability to alter the ocean interior's respired nutrient inventory. Here we investigate the Atlantic overturning circulation at the Last Glacial Maximum and its impact on respired carbon storage using radiocarbon and stable carbon isotope data from the Brazil and Iberian Margins. The data demonstrate the existence of a shallow well-ventilated northern-sourced cell overlying a poorly ventilated, predominantly southern-sourced cell at the Last Glacial Maximum. We also find that organic carbon remineralisation rates in the deep Atlantic remained broadly similar to modern, but that ventilation ages in the southern-sourced overturning cell were significantly increased. Respired carbon storage in the deep Atlantic was therefore enhanced during the last glacial period, primarily due to an increase in the residence time of carbon in the deep ocean, rather than an increase in biological carbon export