On operad structures of moduli spaces and string theory

Recent algebraic structures of string theory, including homotopy Lie algebras, gravity algebras and Batalin-Vilkovisky algebras, are deduced from the topology of the moduli spaces of punctured Riemann spheres. The principal reason for these structures to appear is as simple as the following. A conformal field theory is an algebra over the operad of punctured Riemann surfaces, this operad gives rise to certain standard operads governing the three kinds of algebras, and that yields the structures of such algebras on the (physical) state space naturally.Comment: 33 pages (An elaboration of minimal area metrics and new references are added

Statistics of extinction and survival in Lotka-Volterra systems

We analyze purely competitive many-species Lotka-Volterra systems with random interaction matrices, focusing the attention on statistical properties of their asymptotic states. Generic features of the evolution are outlined from a semiquantitative analysis of the phase-space structure, and extensive numerical simulations are performed to study the statistics of the extinctions. We find that the number of surviving species depends strongly on the statistical properties of the interaction matrix, and that the probability of survival is weakly correlated to specific initial conditions.Comment: Previous version had error in authors. 11 pages, including 5 figure

Lowland river responses to intraplate tectonism and climate forcing quantified with luminescence and cosmogenic 10Be

Intraplate tectonism has produced large-scale folding that steers regional drainage systems, such as the 1600 km-long Cooper Ck, en route to Australia’s continental depocentre at Lake Eyre. We apply cosmogenic 10Be exposure dating in bedrock, and luminescence dating in sediment, to quantify the erosional and depositional response of Cooper Ck where it incises the rising Innamincka Dome. The detachment of bedrock joint-blocks during extreme floods governs the minimum rate of incision (17.4±6.5 mm/ky) estimated using a numerical model of episodic erosion calibrated with our 10Be measurements. The last big-flood phase occurred no earlier than ~112–121ka. Upstream of the Innamincka Dome long-term rates of alluvial deposition, partly reflecting synclinal-basin subsidence, are estimated from 47 luminescence dates in sediments accumulated since ~270 ka. Sequestration of sediment in subsiding basins such as these may account for the lack of Quaternary accumulation in Lake Eyre, and moreover suggests that notions of a single primary depocentre at base-level may poorly represent lowland, arid-zone rivers. Over the period ~75–55 ka Cooper Ck changed from a bedload- dominant, laterally-active meandering river to a muddy anabranching channel network up to 60 km wide. We propose that this shift in river pattern was a product of base-level rise linked with the slowly deforming syncline–anticline structure, coupled with a climate-forced reduction in discharge. The uniform valley slope along this subsiding alluvial and rising bedrock system represents an adjustment between the relative rates of deformation and the ability of greatly enhanced flows at times during the Quaternary to incise the rising anticline. Hence, tectonic and climate controls are balanced in the long term

Eroding market stability by proliferation of financial instruments

We contrast Arbitrage Pricing Theory (APT), the theoretical basis for the development of financial instruments, with a dynamical picture of an interacting market, in a simple setting. The proliferation of financial instruments apparently provides more means for risk diversification, making the market more efficient and complete. In the simple market of interacting traders discussed here, the proliferation of financial instruments erodes systemic stability and it drives the market to a critical state characterized by large susceptibility, strong fluctuations and enhanced correlations among risks. This suggests that the hypothesis of APT may not be compatible with a stable market dynamics. In this perspective, market stability acquires the properties of a common good, which suggests that appropriate measures should be introduced in derivative markets, to preserve stability.Comment: 26 pages, 8 figure

Operadic formulation of topological vertex algebras and Gerstenhaber or Batalin-Vilkovisky algebras

We give the operadic formulation of (weak, strong) topological vertex algebras, which are variants of topological vertex operator algebras studied recently by Lian and Zuckerman. As an application, we obtain a conceptual and geometric construction of the Batalin-Vilkovisky algebraic structure (or the Gerstenhaber algebra structure) on the cohomology of a topological vertex algebra (or of a weak topological vertex algebra) by combining this operadic formulation with a theorem of Getzler (or of Cohen) which formulates Batalin-Vilkovisky algebras (or Gerstenhaber algebras) in terms of the homology of the framed little disk operad (or of the little disk operad).Comment: 42 page

Comparison maps for relatively free resolutions

Let Λ be a commutative ring, A an augmented differential graded algebra over Λ (briefly, DGA-algebra) and X be a relatively free resolution of Λ over A. The standard bar resolution of Λ over A, denoted by B(A), provides an example of a resolution of this kind. The comparison theorem gives inductive formulae f : B(A)→X and g : X→B(A) termed comparison maps. In case that fg=1 X and A is connected, we show that X is endowed a A  ∞ -tensor product structure. In case that A is in addition commutative then (X,μ X ) is shown to be a commutative DGA-algebra with the product μ X =f*(g⊗g) (* is the shuffle product in B(A)). Furthermore, f and g are algebra maps. We give an example in order to illustrate the main results of this paper

The value of carbon sequestration and storage in coastal habitats

Coastal margin habitats are globally significant in terms of their capacity to sequester and store carbon, but their continuing decline, due to environmental change and human land use decisions, is reducing their capacity to provide this ecosystem service. In this paper the UK is used as a case study area to develop methodologies to quantify and value the ecosystem service of blue carbon sequestration and storage in coastal margin habitats. Changes in UK coastal habitat area between 1900 and 2060 are documented, the long term stocks of carbon stored by these habitats are calculated, and the capacity of these habitats to sequester CO2 is detailed. Changes in value of the carbon sequestration service of coastal habitats are then projected for 2000–2060 under two scenarios, the maintenance of the current state of the habitat and the continuation of current trends of habitat loss. If coastal habitats are maintained at their current extent, their sequestration capacity over the period 2000–2060 is valued to be in the region of £1 billion UK sterling (3.5% discount rate). However, if current trends of habitat loss continue, the capacity of the coastal habitats both to sequester and store CO2 will be significantly reduced, with a reduction in value of around £0.25 billion UK sterling (2000–2060; 3.5% discount rate). If loss-trends due to sea level rise or land reclamation worsen, this loss in value will be greater. This case study provides valuable site specific information, but also highlights global issues regarding the quantification and valuation of carbon sequestration and storage. Whilst our ability to value ecosystem services is improving, considerable uncertainty remains. If such ecosystem valuations are to be incorporated with confidence into national and global policy and legislative frameworks, it is necessary to address this uncertainty. Recommendations to achieve this are outlined

Effects of rapid prey evolution on predator-prey cycles

We study the qualitative properties of population cycles in a predator-prey system where genetic variability allows contemporary rapid evolution of the prey. Previous numerical studies have found that prey evolution in response to changing predation risk can have major quantitative and qualitative effects on predator-prey cycles, including: (i) large increases in cycle period, (ii) changes in phase relations (so that predator and prey are cycling exactly out of phase, rather than the classical quarter-period phase lag), and (iii) "cryptic" cycles in which total prey density remains nearly constant while predator density and prey traits cycle. Here we focus on a chemostat model motivated by our experimental system [Fussmann et al. 2000,Yoshida et al. 2003] with algae (prey) and rotifers (predators), in which the prey exhibit rapid evolution in their level of defense against predation. We show that the effects of rapid prey evolution are robust and general, and furthermore that they occur in a specific but biologically relevant region of parameter space: when traits that greatly reduce predation risk are relatively cheap (in terms of reductions in other fitness components), when there is coexistence between the two prey types and the predator, and when the interaction between predators and undefended prey alone would produce cycles. Because defense has been shown to be inexpensive, even cost-free, in a number of systems [Andersson and Levin 1999, Gagneux et al. 2006,Yoshida et al. 2004], our discoveries may well be reproduced in other model systems, and in nature. Finally, some of our key results are extended to a general model in which functional forms for the predation rate and prey birth rate are not specified.Comment: 35 pages, 8 figure