Functional Representations for Fock Superalgebras

The Fock space of bosons and fermions and its underlying superalgebra are represented by algebras of functions on a superspace. We define Gaussian integration on infinite dimensional superspaces, and construct superanalogs of the classical function spaces with a reproducing kernel -- including the Bargmann-Fock representation -- and of the Wiener-Segal representation. The latter representation requires the investigation of Wick ordering on Z2-graded algebras. As application we derive a Mehler formula for the Ornstein-Uhlenbeck semigroup on the Fock space.Comment: 33 pages, Late

The GENGA Code: Gravitational Encounters in N-body simulations with GPU Acceleration

We describe an open source GPU implementation of a hybrid symplectic N-body integrator, GENGA (Gravitational ENcounters with Gpu Acceleration), designed to integrate planet and planetesimal dynamics in the late stage of planet formation and stability analyses of planetary systems. GENGA uses a hybrid symplectic integrator to handle close encounters with very good energy conservation, which is essential in long-term planetary system integration. We extended the second order hybrid integration scheme to higher orders. The GENGA code supports three simulation modes: Integration of up to 2048 massive bodies, integration with up to a million test particles, or parallel integration of a large number of individual planetary systems. We compare the results of GENGA to Mercury and pkdgrav2 in respect of energy conservation and performance, and find that the energy conservation of GENGA is comparable to Mercury and around two orders of magnitude better than pkdgrav2. GENGA runs up to 30 times faster than Mercury and up to eight times faster than pkdgrav2. GENGA is written in CUDA C and runs on all NVIDIA GPUs with compute capability of at least 2.0.Comment: Accepted by ApJ. 18 pages, 17 figures, 4 table

International price discovery in the presence of microstructure noise

This paper addresses and resolves the issue of microstructure noise when measuring the relative importance of home and U.S. market in the price discovery process of Canadian interlisted stocks. In order to avoid large bounds for information shares, previous studies applying the Cholesky decomposition within the Hasbrouck (1995) framework had to rely on high frequency data. However, due to the considerable amount of microstructure noise inherent in return data at very high frequencies, these estimators are distorted. We offer a modified approach that identifies unique information shares based on distributional assumptions and thereby enables us to control for microstructure noise. Our results indicate that the role of the U.S. market in the price discovery process of Canadian interlisted stocks has been underestimated so far. Moreover, we suggest that rather than stock specific factors, market characteristics determine information shares

Endogenous Environmental Policy when Pollution is Transboundary

We analyze the formation of environmental policy to regulate transboundary pollution if governments are self-interested. In a common agency framework, we portray the environmental policy calculus of two political supportmaximizing governments that are in a situation of strategic interaction with respect to their environmental policies, but too small to affect world market prices. We show how governments systematically deviate from socially optimal environmental policies. Taxes may be too high if environmental interests and pollution-intensity of production are very strong; under different constellations they may be too low. Governments may actually subsidize the production of a polluting good. Politically motivated environmental policy thus may be more harmful to the environment as compared to the benevolent dictators’ solution. In other cases it may enhance environmental quality and welfare beyond what a benevolent government would achieve.Political economy, environmental policy, transboundary pollution, common agency, strategic interaction

Endogenous Environmental Policy when Pollution is Transboundary

We analyze the formation of environmental policy to regulate transboundary pollution if governments are self-interested. In a common agency framework, we portray the environmental policy calculus of two political supportmaximizing governments that are in a situation of strategic interaction with respect to their environmental policies, but too small to affect world market prices. We show how governments systematically deviate from socially optimal environmental policies. Taxes may be too high if environmental interests and pollution-intensity of production are very strong; under different constellations they may be too low. Governments may actually subsidize the production of a polluting good. Politically motivated environmental policy thus may be more harmful to the environment as compared to the benevolent dictators’ solution. In other cases it may enhance environmental quality and welfare beyond what a benevolent government would achieve.Political economy, environmental policy, transboundary pollution, common agency, strategic interaction

Adaptation in tunably rugged fitness landscapes: The Rough Mount Fuji Model

Much of the current theory of adaptation is based on Gillespie's mutational landscape model (MLM), which assumes that the fitness values of genotypes linked by single mutational steps are independent random variables. On the other hand, a growing body of empirical evidence shows that real fitness landscapes, while possessing a considerable amount of ruggedness, are smoother than predicted by the MLM. In the present article we propose and analyse a simple fitness landscape model with tunable ruggedness based on the Rough Mount Fuji (RMF) model originally introduced by Aita et al. [Biopolymers 54:64-79 (2000)] in the context of protein evolution. We provide a comprehensive collection of results pertaining to the topographical structure of RMF landscapes, including explicit formulae for the expected number of local fitness maxima, the location of the global peak, and the fitness correlation function. The statistics of single and multiple adaptive steps on the RMF landscape are explored mainly through simulations, and the results are compared to the known behavior in the MLM model. Finally, we show that the RMF model can explain the large number of second-step mutations observed on a highly-fit first step backgound in a recent evolution experiment with a microvirid bacteriophage [Miller et al., Genetics 187:185-202 (2011)].Comment: 43 pages, 12 figures; revised version with new results on the number of fitness maxim