Discussion of: Brownian distance covariance

Discussion on "Brownian distance covariance" by G\'{a}bor J. Sz\'{e}kely and Maria L. Rizzo [arXiv:1010.0297]Comment: Published in at http://dx.doi.org/10.1214/09-AOAS312E the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Detecting Generalized Synchronization Between Chaotic Signals: A Kernel-based Approach

A unified framework for analyzing generalized synchronization in coupled chaotic systems from data is proposed. The key of the proposed approach is the use of the kernel methods recently developed in the field of machine learning. Several successful applications are presented, which show the capability of the kernel-based approach for detecting generalized synchronization. It is also shown that the dynamical change of the coupling coefficient between two chaotic systems can be captured by the proposed approach.Comment: 20 pages, 15 figures. massively revised as a full paper; issues on the choice of parameters by cross validation, tests by surrogated data, etc. are added as well as additional examples and figure

Comment on "Support Vector Machines with Applications"

Comment on "Support Vector Machines with Applications" [math.ST/0612817]Comment: Published at http://dx.doi.org/10.1214/088342306000000475 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Molecular Dynamics in a Grand Ensemble: Bergmann-Lebowitz model and Adaptive Resolution Simulation

This article deals with the molecular dynamics simulation of open systems that can exchange energy and matter with a reservoir; the physics of the reservoir and its interactions with the system are described by the model introduced by Bergmann and Lebowitz.Despite its conceptual appeal, the model did not gain popularity in the field of molecular simulation and, as a consequence, did not play a role in the development of open system molecular simulation techniques, even though it can provide the conceptual legitimation of simulation techniques that mimic open systems. We shall demonstrate that the model can serve as a tool to devise both numerical procedures and conceptual definitions of physical quantities that cannot be defined in a straightforward way by systems with a fixed number of molecules. In particular, we discuss the utility of the Bergmann-Lebowitz (BL) model for the calculation of equilibrium time correlation functions within the Grand Canonical Adaptive Resolution method (GC-AdResS) and report numerical results for the case of liquid water.Comment: 31 pages, 6 figure