Free differential algebras and generic 2D dilatonic (super)gravities

The field equations for both generic bosonic and generic locally supersymmetric 2D dilatonic gravity theories in the absence of matter are written as free differential algebras. This constitutes a generalization of the gauge theoretic formulation. Moreover, it is shown that the condition of free differential algebra can be used to obtain the equations in the locally supersymmetric case. Using this formulation, the general solution of the field equations is found in the language of differential forms. The relation with the ordinary formulation and the coupling to supersymmetric conformal matter are also studied.Comment: 19 pages, Late

Reinforcement Learning Dynamics in Social Dilemmas

In this paper we replicate and advance Macy and Flache\'s (2002; Proc. Natl. Acad. Sci. USA, 99, 7229–7236) work on the dynamics of reinforcement learning in 2�2 (2-player 2-strategy) social dilemmas. In particular, we provide further insight into the solution concepts that they describe, illustrate some recent analytical results on the dynamics of their model, and discuss the robustness of such results to occasional mistakes made by players in choosing their actions (i.e. trembling hands). It is shown here that the dynamics of their model are strongly dependent on the speed at which players learn. With high learning rates the system quickly reaches its asymptotic behaviour; on the other hand, when learning rates are low, two distinctively different transient regimes can be clearly observed. It is shown that the inclusion of small quantities of randomness in players\' decisions can change the dynamics of the model dramatically.Reinforcement Learning; Replication; Game Theory; Social Dilemmas; Agent-Based; Slow Learning

Sources, lability and solubility of Pb in alluvial soils of the River Trent catchment, U.K.

Alluvial soils are reservoirs of metal contaminants such as Pb that originate from many different sources and are integrated temporally and spatially through erosional and depositional processes. In this study the source, lability and solubility of Pb was examined in a range of alluvial soils from the middle and lower River Trent and its tributary the River Dove using Pb isotope apportionment and isotopic dilution. All samples were collected within 10 m of the river bank to represent the soil that is most likely to be remobilised during bank erosion. Paired samples were taken from the topsoil (0-15 cm) and subsoil (35-50 cm) to assess differences with depth. Lead concentrations in soil ranged from 43 to 1282 mg/kg. The lability of soil Pb varied between 9-56% of total metal concentration whilst Pb concentrations in pore water varied between 0.2 and 6.5 µg/L. There was little difference in the % Pb lability between paired top and sub soils, possibly because soil characteristics such as pH, iron oxides and clay content were generally similar; a result of the recycling of eroded and deposited soils within the river system. Soil pH was found to be negatively correlated with % Pb lability. Source apportionment using 206Pb/207Pb and 208Pb/207Pb ratios showed that the isotopic ratios of Pb in the total, labile and solution pools fitted along a mixing line between Broken Hill Type (‘BHT’) Pb, used as an additive in UK petrol, and the local coal/Sourthern Pennine ore Pb. Various anomalies were found in the Pb isotopes of the bankside alluvial soils which were explained by point source pollution. Statistically significant differences were found between (i) the isotopic composition of Pb in the total soil pool and the labile/solution pools and (ii) the isotopic composition of Pb in the labile and solution pools, suggesting an enrichment of recent non-Pennine sources of Pb entering the soils in the labile and solution pools

Minimal D=4 supergravity from the superMaxwell algebra

We show that the first-order D=4, N=1 pure supergravity lagrangian four-form can be obtained geometrically as a quadratic expression in the curvatures of the Maxwell superalgebra. This is achieved by noticing that the relative coefficient between the two terms of the Lagrangian that makes the action locally supersymmetric also determines trivial field equations for the gauge fields associated with the extra generators of the Maxwell superalgebra. Along the way, a convenient geometric procedure to check the local supersymmetry of a class of lagrangians is developed.Comment: Plain latex, 14 pages. Two misprints corrected, one reference adde