McGill University

About: McGill University is a education organization based out in Montreal, Quebec, Canada. It is known for research contribution in the topics: Population & Poison control. The organization has 72688 authors who have published 162565 publications receiving 6966523 citations. The organization is also known as: Royal institution of advanced learning & University of McGill College.

Footprint prediction of scalar fluxes from analytical solutions of the diffusion equation

Abstract: The use of analytical solutions of the diffusion equation for ‘footprint prediction’ is explored. Quantitative information about the ‘footprint’, i.e., the upwind area most likely to affect a downwind flux measurement at a given height z, is essential when flux measurements from different platforms, particularly airborne ones, are compared. Analytical predictions are evaluated against numerical Lagrangian trajectory simulations which are detailed in a companion paper (Leclerc and Thurtell, 1990). For neutral stability, the structurally simple solutions proposed by Gash (1986) are shown to be capable of satisfactory approximation to numerical simulations over a wide range of heights, zero displacements and roughness lengths. Until more sophisticated practical solutions become available, it is suggested that apparent limitations in the validity of some assumptions underlying the Gash solutions for the case of very large surface roughness (forests) and tentative application of the solutions to cases of small thermal instability be dealt with by semi-empirical adjustment of the ratio of horizontal wind to friction velocity. An upper limit of validity of these solutions for z has yet to be established.

On black hole entropy

Abstract: Two techniques for computing black hole entropy in generally covariant gravity theories including arbitrary higher derivative interactions are studied. The techniques are Wald's Noether charge approach introduced recently, and a field redefinition method developed in this paper. Wald's results are extended by establishing that his local geometric expression for the black hole entropy gives the same result when evaluated on an arbitrary cross section of a Killing horizon (rather than just the bifurcation surface). Further, we show that his expression for the entropy is not affected by ambiguities which arise in the Noether construction. Using the Noether charge expression, the entropy is evaluated explicitly for black holes in a wide class of generally covariant theories. For a Lagrangian of the functional form L\ifmmode \tilde{}\else \~{}\fi{}=L\ifmmode \tilde{}\else \~{}\fi{}(${\mathrm{\ensuremath{\psi}}}_{\mathit{m}}$, ${\mathrm{\ensuremath{ abla}}}_{\mathit{a}}$${\mathrm{\ensuremath{\psi}}}_{\mathit{m}}$,${\mathit{g}}_{\mathit{a}\mathit{b}}$,${\mathit{R}}_{\mathit{a}\mathit{b}\mathit{c}\mathit{d}}$, ${\mathrm{\ensuremath{ abla}}}_{\mathit{e}}$${\mathit{R}}_{\mathit{a}\mathit{b}\mathit{c}\mathit{d}}$), it is found that the entropy is given by S=-2\ensuremath{\pi}\ensuremath{\oint}(${\mathit{Y}}^{\mathit{a}\mathit{b}\mathit{c}\mathit{d}}$-${\mathrm{\ensuremath{ abla}}}_{\mathit{e}}$${\mathit{Z}}^{\mathit{e}:\mathit{a}\mathit{b}\mathit{c}\mathit{d}}$) \ensuremath{\epsilon}${\mathrm{^}}_{\mathit{a}\mathit{b}}$\ensuremath{\epsilon}${\mathrm{^}}_{\mathit{c}\mathit{d}}$\ensuremath{\epsilon}\ifmmode\bar\else\textasciimacron\fi{}, where the integral is over an arbitrary cross section of the Killing horizon, \ensuremath{\epsilon}${\mathrm{^}}_{\mathit{a}\mathit{b}}$ is the binormal to the cross section, ${\mathit{Y}}^{\mathit{a}\mathit{b}\mathit{c}\mathit{d}}$=\ensuremath{\partial}L\ifmmode \tilde{}\else \~{}\fi{}/\ensuremath{\partial}${\mathit{R}}_{\mathit{a}\mathit{b}\mathit{c}\mathit{d}}$, and ${\mathit{Z}}^{\mathit{e}:\mathit{a}\mathit{b}\mathit{c}\mathit{d}}$=\ensuremath{\partial}L\ifmmode \tilde{}\else \~{}\fi{}/\ensuremath{\partial}${\mathrm{\ensuremath{ abla}}}_{\mathit{e}}$${\mathit{R}}_{\mathit{a}\mathit{b}\mathit{c}\mathit{d}}$.Further, it is shown that the Killing horizon and surface gravity of a stationary black hole metric are invariant under field redefinitions of the metric of the form g${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathit{a}\mathit{b}}$\ensuremath{\equiv}${\mathit{g}}_{\mathit{a}\mathit{b}}$+${\mathrm{\ensuremath{\Delta}}}_{\mathit{a}\mathit{b}}$, where ${\mathrm{\ensuremath{\Delta}}}_{\mathit{a}\mathit{b}}$ is a stationary tensor field that vanishes at infinity and is regular on the horizon (including the bifurcation surface). Using this result, a technique is developed for evaluating the black hole entropy in a given theory in terms of that of another theory related by field redefinitions. Remarkably, it is established that certain perturbative, first order, results obtained with this method are in fact exact. A particular result established in this fashion is that a scalar matter term of the form ${\mathrm{\ensuremath{ abla}}}^{2\mathit{p}}$\ensuremath{\varphi}${\mathrm{\ensuremath{ abla}}}^{2\mathit{q}}$\ensuremath{\varphi} in the Lagrangian makes no contribution to the black hole entropy. The possible significance of these results for the problem of finding the statistical origin of black hole entropy is discussed.

Evaluating Learning Algorithms: A Classification Perspective

Abstract: The field of machine learning has matured to the point where many sophisticated learning approaches can be applied to practical applications. Thus it is of critical importance that researchers have the proper tools to evaluate learning approaches and understand the underlying issues. This book examines various aspects of the evaluation process with an emphasis on classification algorithms. The authors describe several techniques for classifier performance assessment, error estimation and resampling, obtaining statistical significance as well as selecting appropriate domains for evaluation. They also present a unified evaluation framework and highlight how different components of evaluation are both significantly interrelated and interdependent. The techniques presented in the book are illustrated using R and WEKA facilitating better practical insight as well as implementation.Aimed at researchers in the theory and applications of machine learning, this book offers a solid basis for conducting performance evaluations of algorithms in practical settings.

Ion-Induced Morphological Changes in “Crew-Cut” Aggregates of Amphiphilic Block Copolymers

Abstract: The addition of ions in micromolar (CaCl2 or HCl) or millimolar (NaCl) concentrations can change the morphology of "crew-cut" aggregates of amphiphilic block copolymers in dilute solutions. In addition to spherical, rodlike, and univesicular or lamellar aggregates, an unusual large compound vesicle morphology can be obtained from a single block copolymer. Some features of the spontaneously formed large compound vesicles may make them especially useful as vehicles for delivering drugs and as models of biological cells. Gelation of a dilute spherical micelle solution can also be induced by ions as the result of the formation of a cross-linked "pearl necklace" morphology.