Difference between canonical and grand canonical ensembles in discrete lattice gas models

We calculate the site occupation probabilities of one-dimensional lattice gas models within the canonical and grand canonical ensembles. The appearing differences do not vanish if we increase the system size keeping the site energies discrete. In this way one can explain the surprising numerical results of Barszczak and Kutner. This effect in the single-site occupation number disappears in higher dimensions.     

A Maximum Entropy Method for Particle Filtering

Standard ensemble or particle filtering schemes do not properly represent states of low priori probability when the number of available samples is too small, as is often the case in practical applications. We introduce here a set of parametric resampling methods to solve this problem. Motivated by a general H-theorem for relative entropy, we construct parametric models for the filter distributions as maximum-entropy/minimum-information models consistent with moments of the particle ensemble. When the prior distributions are modeled as mixtures of Gaussians, our method naturally generalizes the ensemble Kalman filter to systems with highly non-Gaussian statistics. We apply the new particle filters presented here to two simple test cases: a one-dimensional diffusion process in a double-well potential and the three-dimensional chaotic dynamical system of Lorenz.     

Berezin quantization of gauged WZW and coset models

Gauged WZW and coset models are known to be useful to prove holomorphic factorization of the partition function of WZW and coset models. In this note we show that these gauged models can be also important to quantize the theory in the context of the Berezin formalism. For gauged coset models Berezin quantization procedure also admits a further holomorphic factorization in the complex structure of the moduli space.This work is dedicated to Professor Michel Ryan on the occasion of his 60th birthday.     

The physical role of gravitational and gauge degrees of freedom in general relativity — I: Dynamical synchronization and generalized inertial effects

This is the first of a couple of papers in which the peculiar capabilities of the Hamiltonian approach to general relativity are exploited to get both new results concerning specific technical issues, and new insights about old foundational problems of the theory. The first paper includes: (1) a critical analysis of the various concepts of symmetry related to the Einstein-Hilbert Lagrangian viewpoint on the one hand, and to the Hamiltonian viewpoint, on the other. This analysis leads, in particular, to a re-interpretation of active diffeomorphisms as passive and metric-dependent dynamical symmetries of Einstein's equations, a re-interpretation which enables to disclose the (not widely known)) connection of a subgroup of them to Hamiltonian gauge transformations on-shell; (2) a re-visitation of the canonical reduction of the ADM formulation of general relativity, with particular emphasis on the geometro-dynamical effects of the gauge-fixing procedure, which amounts to the definition of a global non-inertial, space-time laboratory. This analysis discloses the peculiar dynamical nature that the traditional definition of distant simultaneity and clock-synchronization assume in general relativity, as well as the gauge relatedness of the “conventions” which generalize the classical Einstein's convention. (3) a clarification of the physical role of Dirac and gauge variables, as their being related to tidal-like and generalized inertial effects, respectively. This clarification is mainly due to the fact that, unlike the standard formulations of the equivalence principle, the Hamiltonian formalism allows to define a generalized notion of “force” in general relativity in a natural way.     

Measuring efficiency and productivity in professional football teams: evidence from the English Premier League

Professional football clubs are unusual businesses, their performance judged on and off the field of play. This study is concerned with measuring the efficiency of clubs in the English Premier League. Information from clubs’ financial statements is used as a measure of corporate performance. To measure changes in efficiency and productivity the Malmquist non-parametric technique has been used. This is derived from the Data Envelopment Analysis (DEA) linear programming approach, with Canonical Correlation Analysis (CCA) being used to ensure the cohesion of the input–output variables. The study concludes that while clubs operate close to efficient levels for the assessed models, there is limited technological advance in their performance in terms of the displacement of the technological frontier. The research was supported by the Investigation Program of the Technical University of Cartagena (Spain) and by the Department of Sports Studies at the University of Stirling (Scotland, UK).     

Bubble point pressure estimates from Gibbs ensemble simulations

Bubble pressure points of ethanol–1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea refrigerant) mixtures from the third Industrial Fluid Properties Simulation Challenge are computed using publicly available molecular simulation software. Several published force fields are compared against the known answers provided in the contest guidelines and the best force fields are used to make predictions for the unknown results.     

An efficient distributed algorithm for canonical labeling on directed split-stars

We consider the problem of canonical labeling in anonymous directed split-stars. This paper proposes a distributed algorithm for finding the vertex sets with specified leading symbols in directed split-stars and which has a linear message and constant time complexity. The algorithm runs on an asynchronous timing model without shared memory. In addition, our algorithm generalizes the previous distributed algorithms on directed split-stars that we know.     

Schur Q-polynomials, multiple hypergeometric series and enumeration of marked shifted tableaux

We study Schur Q-polynomials evaluated on a geometric progression, or equivalently q-enumeration of marked shifted tableaux, seeking explicit formulas that remain regular at q=1. We obtain several such expressions as multiple basic hypergeometric series, and as determinants and pfaffians of continuous q-ultraspherical or continuous q-Jacobi polynomials. As special cases, we obtain simple closed formulas for staircase-type partitions.     

Canonical correlation analysis based on information theory

In this article, we propose a new canonical correlation method based on information theory. This method examines potential nonlinear relationships between p×1 vector Y-set and q×1 vector X-set. It finds canonical coefficient vectors a and b by maximizing a more general measure, the mutual information, between a^TX and b^TY. We use a permutation test to determine the pairs of the new canonical correlation variates, which requires no specific distributions for X and Y as long as one can estimate the densities of a^TX and b^TY nonparametrically. Examples illustrating the new method are presented.