Memoires de la SMF 122 (2010), ii+98 pages
Entropie des applications meromorphes et dynamique des applications birationnelles
On etudie la dynamique des applications meromorphes sur les varietes Kahleriennes compactes. Plus precisement, on donne un critere simple qui permet de produire des mesures d'entropie maximale. On peut appliquer ce resultat pour borner les exposants de Lyapounov. Ensuite, on etudie le cas particulier d'une famille generique d'applications birationnelles de pour laquelle on construit les courants de Green et la mesure d'equilibre. On utilise pour cela la theorie des super-potentiels. On montre que la mesure est melangeante et qu'elle n'a pas de masse sur les ensemble pluripolaires. En utilisant le critere on obtient que la mesure est d'entropie maximale. Cela implique finalement que la mesure est hyperbolique.
We study the dynamics of meromorphic maps for a compact Kahler manifold . More precisely, we give a simple criterion that allows us to produce a measure of maximal entropy. We can apply this result to bound the Lyapunov exponents. Then, we study the particular case of a family of generic birational maps of for which we construct the Green currents and the equilibrium measure. We use for that the theory of super-potentials. We show that the measure is mixing and gives no mass to pluripolar sets. Using the criterion we get that the measure is of maximal entropy. It implies finally that the measure is hyperbolic.
Keywords: Complex dynamics, meromorphic maps, super-potentials, currents, entropy, hyperbolic measure
ISBN : 978-85629-302-7
Memoires de la SMF 123 (2010), viii+136 pages
Projecteurs en plusieurs variables complexes
Ce travail comporte deux parties. Dans la premiere, nous appliquons la methode de Menikoff-Sjostrand au laplacien de Kohn, defini sur une variete CR compacte orientee connexe et nous obtenons un developpement asymptotique complet du projecteur de Szeg? pour les formes quand la forme de Levi est non-degeneree. Cela generalise un resultat de Boutet de Monvel et Sjostrand pour les formes. Nous utilisons des operateurs integraux de Fourier a phases complexes de Melin et Sjostrand. Dans la deuxieme partie, nous obtenons un developpement asymptotique de la singularite du noyau de Bergman pour les formes quand la forme de Levi est non-degeneree. Cela generalise un resultat de Boutet de Monvel et Sjostrand pour les formes. Nous introduisons un nouvel operateur analogue au laplacien de Kohn defini sur le bord du domaine, et nous y appliquons la methode de Menikoff-Sjostrand. Cela donne une description modulo les operateurs regularisants d'un nouvel projecteur de Szeg?. Enfin, nous obtenons notre resultat principal en utilisant l'operateur de Poisson.
This work consists two parts. In the first part, we completely study the heat equation method of Menikoff-Sjostrand and apply it to the Kohn Laplacian defined on a compact orientable connected CR manifold. We then get the full asymptotic expansion of the Szeg? projection for forms when the Levi form is non-degenerate. This generalizes a result of Boutet de Monvel and Sjostrand for forms. Our main tools are Fourier integral operators with complex valued phase Melin and Sjostrand functions. In the second part, we obtain the full asymptotic expansion of the Bergman projection for forms when the Levi form is non-degenerate. This also generalizes a result of Boutet de Monvel and Sjostrand for forms. We introduce a new operator analogous to the Kohn Laplacian defined on the boundary of a domain and we apply the heat equation method of Menikoff and Sjostrand to this operator. We obtain a description of a new Szeg? projection up to smoothing operators. Finally, we get our main result by using the Poisson operator.
Keywords: CR manifold, Szeg kernel, Bergman kernel, heat equation, microlocal analysis
ISBN : 978-85629-304-1
ISBN: 978-0-470-66095-9
Hardcover
320 pages
May 2011
It is quite common in a randomized clinical trial (RCT) to encounter patients who do not comply with their assigned treatment. Since noncompliance often occurs non-randomly, the commonly-used approaches, including both the as-treated (AT) and as-protocol (AP) analysis, and the intent-to-treat (ITT) (or as-randomized) analysis, are all well known to possibly produce a biased inference of the treatment efficacy.
This book provides a systematic and organized approach to analyzing data for RCTs with noncompliance under the most frequently-encountered situations. These include parallel sampling, stratified sampling, cluster sampling, parallel sampling with subsequent missing outcomes, and a series of dependent Bernoulli sampling for repeated measurements. The author provides a comprehensive approach by using contingency tables to illustrate the latent probability structure of observed data. Using real-life examples, computer-simulated data and exercises in each chapter, the book illustrates the underlying theory in an accessible, and easy to understand way.
*Consort-flow diagrams and numerical examples are used to illustrate the
bias of commonly used approaches, such as, AT analysis, AP analysis and
ITT analysis for a RCT with noncompliance.
*Real-life examples are used throughout the book to explain the practical
usefulness of test procedures and estimators.
?Each chapter is self-contained, allowing the book to be used as a reference source.
*Includes SAS programs which can be easily modified in calculating the
required sample size.
Biostatisticians, clinicians, researchers and data analysts working in pharmaceutical industries will benefit from this book. This text can also be used as supplemental material for a course focusing on clinical statistics or experimental trials in epidemiology, psychology and sociology.
ISBN: 978-0-470-68819-9
Hardcover
336 pages
June 2011
This book provides a comprehensive review on the Dirichlet distribution including its basic properties, marginal and conditional distributions, cumulative distribution and survival functions.
The authors provide insight into new materials such as survival function, characteristic functions for two uniform distributions over the hyper-plane and simplex distribution for linear function of Dirichlet components estimation via the expectation-maximization gradient algorithm and application. Two new families of distributions (GDD and NDD) are explored, with emphasis on applications in incomplete categorical data and survey data with non-response.
Theoretical results on inverted Dirichlet distribution and its applications are featured along with new results that deal with truncated Dirichlet distribution, Dirichlet process and smoothed Dirichlet distribution. The final chapters look at results gathered for Dirichlet-multinomial distribution, Generalized Dirichlet distribution, Liouville distribution, generalized Liouville distribution and matrix-variate Dirichlet distribution.
ISBN: 978-1-1199-9389-6
Hardcover
328 pages
June 2011
This book uses the EM (expectation maximization) algorithm to simultaneously estimate the missing data and unknown parameter(s) associated with a data set. The parameters describe the component distributions of the mixture; the distributions may be continuous or discrete.
The editors provide a complete account of the applications, mathematical structure and statistical analysis of finite mixture distributions along with MCMC computational methods, together with a range of detailed discussions covering the applications of the methods and features chapters from the leading experts on the subject. The applications are drawn from scientific discipline, including biostatistics, computer science, ecology and finance. This area of statistics is important to a range of disciplines, and its methodology attracts interest from researchers in the fields in which it can be applied.