Series: Progress in Mathematics , Vol. 282
2010, X, 312 p. 47 illus., Hardcover
ISBN: 978-0-8176-4933-3
Due: November 2009
Includes papers written by leading experts in the field
Contains a selection of articles exploring rationality problems in algebraic geometry
Gives a representative sample of problems and most recent results in algebraic geometry
May serve as an intense introduction for graduate students and those wishing to pursue research in algebraic geometry, more specifically, rationality problems
Rationality problems link algebra to geometry. The difficulties involved depend on the transcendence degree over the ground field, or geometrically, on the dimension of the variety. A major success in 19th century algebraic geometry was a complete solution of the rationality problem in dimensions one and two over algebraically closed ground fields of characteristic zero. These advances have led to many interdisciplinary applications of algebraic geometry.
This comprehensive text consists of surveys and research papers by leading specialists in the field. Topics discussed include the rationality of quotient spaces, cohomological invariants of finite groups of Lie type, rationality of moduli spaces of curves, and rational points on algebraic varieties.
Preface.- Unremified cohomology of finite groups of Lie type.- The rationality of the moduli space of curves of genus 3 after P. Katsylo.- The rationality of certain moduli spaces of curves of genus 3.- on sextic double solids.- moduli stacks of vector bundles on curves and the King--Schofield rationality proof.- Noether's problem for some p-groups.-generalitzed homological mirror symmetry and rationality questions.- The Bogomolov multiplier of finite simple groups.- The rationality problem and birational rigidity
Series: Springer Series in Statistics
2010, XIV, 302 p., Hardcover
ISBN: 978-0-387-92256-0
Due: January 2010
Clear and precise presentation of the most important spatial models, including their probabilistic properties and related statistical methods
Implements these models and studies their statistics on a wide variety of real spatial data coming from real-world applications
Each chapter has numerous exercises to test the reader, and R scripts are provided (see the book’s web page) to help students and researchers deepen their understanding of the subject
Spatial statistics are useful in subjects as diverse as climatology, ecology, economics, environmental and earth sciences, epidemiology, image analysis and more. This book covers the best-known spatial models for three types of spatial data: geostatistical data (stationarity, intrinsic models, variograms, spatial regression and space-time models), areal data (Gibbs-Markov fields and spatial auto-regression) and point pattern data (Poisson, Cox, Gibbs and Markov point processes). The level is relatively advanced, and the presentation concise but complete.
The most important statistical methods and their asymptotic properties are described, including estimation in geostatistics, autocorrelation and second-order statistics, maximum likelihood methods, approximate inference using the pseudo-likelihood or Monte-Carlo simulations, statistics for point processes and Bayesian hierarchical models. A chapter is devoted to Markov Chain Monte Carlo simulation (Gibbs sampler, Metropolis-Hastings algorithms and exact simulation).
A large number of real examples are studied with R, and each chapter ends with a set of theoretical and applied exercises. While a foundation in probability and mathematical statistics is assumed, three appendices introduce some necessary background. The book is accessible to senior undergraduate students with a solid math background and Ph.D. students in statistics. Furthermore, experienced statisticians and researchers in the above-mentioned fields will find the book valuable as a mathematically sound reference.
This book is the English translation of Modelisation et Statistique Spatiales published by Springer in the series Mathematiques & Applications, a series established by Societe de Mathematiques Appliquees et Industrielles (SMAI).
Second order spatial models and geostatistics.- Gibbs-Markov random fields on networks.- Spatial point processes.- Simulation of spatial models.- Statistics for spatial models.
Series: Springer Series in Statistics
2010, Approx. 400 p., Hardcover
ISBN: 978-1-4419-1212-1
Due: January 2010
The concepts of causal inference in experiments and observational studies are introduced using the elementary mathematics of independent coin flips to determine treatment assignment
The basic tools of multivariate matching ? such as propensity scores, optimal matching, full matching, fine balance, risk set matching ? are introduced with many examples and with reference to implementation in R
The key source of uncertainty in an observational study is possible bias from covariates that were not measured. The ability of competing designs to separate treatment effects from unmeasured biases ? that is, the design sensitivity ? is discussed in detail for the first time in book form
An observational study is an empiric investigation of effects caused by treatments when randomized experimentation is unethical or infeasible. Observational studies are common in most fields that study the effects of treatments on people, including medicine, economics, epidemiology, education, psychology, political science and sociology. The quality and strength of evidence provided by an observational study is determined largely by its design. Design of Observational Studies is both an introduction to statistical inference in observational studies and a detailed discussion of the principles that guide the design of observational studies.
Design of Observational Studies is divided into four parts. Chapters 2, 3, and 5 of Part I cover concisely, in about one hundred pages, many of the ideas discussed in Rosenbaum’s Observational Studies (also published by Springer) but in a less technical fashion. Part II discusses the practical aspects of using propensity scores and other tools to create a matched comparison that balances many covariates. Part II includes a chapter on matching in R. In Part III, the concept of design sensitivity is used to appraise the relative ability of competing designs to distinguish treatment effects from biases due to unmeasured covariates. Part IV discusses planning the analysis of an observational study, with particular reference to Sir Ronald Fisher’s striking advice for observational studies, "make your theories elaborate."
Introduction.- Matching to control bias from measured covariates.- Addressing bias from covariates that were not measured.
Series: Frontiers in Mathematics
2010, Approx. 170 p., Softcover
ISBN: 978-3-0346-0175-7
Due: February 2010
The geometry which is the topic of this book is that determined by a map of one space N onto another, M, mapping a diffusion process, or operator, on N to one on M.
Filtering theory is the science of obtaining or estimating information about a system from partial and possibly flawed observations of it. The system itself may be random, and the flaws in the observations can be caused by additional noise. In this volume the randomness and noises will be of Gaussian white noise type so that the system can be modelled by a diffusion process; that is it evolves continuously in time in a Markovian way, the future evolution depending only on the present situation.
This is the standard situation of systems governed by Ito type stochastic differential equations. The state space will be the smooth manifold, N, possibly infinite dimensional, and the "observations" will be obtained by a smooth map onto another manifold, N, say. We emphasise that the geometry is important even when both manifolds are Euclidean spaces. This can also be viewed from a purely partial differential equations viewpoint as one smooth second order elliptic partial differential operator lying above another, both with no zero order term.
We consider the geometry of this situation with special emphasis on situations of geometric, stochastic analytic, or filtering interest. The most well studied case is of one Brownian motion being mapped to another with a consequent skew product decomposition (or equivalently the case of Riemannian submersions). This sort of decomposition is generalised and a key to the rest of the book. It is used to study in particular, classical filtering, (semi-)connections determined by stochastic flows, and generalised Weitzenbock formulae.
1 Diffusion Operators.- Representations of Diffusion Operators .- The Associated First Order Operator.- Diffusion Operators Along a Distribution.- Lifts of Diffusion Operators .- Notes.- 2 Decomposition of Diffusion Operators.- The Horizontal Lift Map.- Example: The Horizontal Lift Map of SDEs .- Lifts of Cohesive Operators and The Decomposition Theorem.- Diffusion Operators with Projectible Symbols.- Horizontal lifts of paths and completeness of semi-connections.- Topological Implications.- 3 Equivariant Diffusions on Principal Bundles.- Invariant Semi-connections on Principal Bundles.- Decompositions of Equivariant Operators.- Derivative Flows and Adjoint Connections.- Vector Bundles and Generalised Weitzenbock Formulae.- 4 Projectible Diffusion Processes.- Integration of predictable processes.- Horizontality and filtrations.- The Filtering Equation.- A family of Markovian kernels.- The filtering equation.- Approximations.- Krylov-Veretennikov Expansion.- Conditional Laws.- Equivariant case: skew product decomposition.- Conditional expectations of induced processes on vector bundles.- 5 Filtering with non-Markovian Observations.- Signals with Projectible Symbol.- Innovations and innovations processes.- Classical Filtering.- Examples.- 6 The Commutation Property.- Commutativity of Diffusion Semigroups.- Consequences for the Horizontal Flow.- 7 Example: Riemannian Submersions and Symmetric Spaces.- Riemannian Submersions.- Riemannian Symmetric Spaces.- 8 Example: Stochastic Flows.- Semi-connections on the Bundle of Diffeomorphisms.- Semi-connections Induced by Stochastic Flows.- Semi-connections on Natural Bundles.- 9 Appendices.- Girsanov-Maruyama-Cameron-Martin Theorem.-Stochastic differential equations for degenerate diffusions.- Semi-martingales and G-martingales along a Sub-bundle.
Series: Operator Theory: Advances and Applications , Preliminary entry 301
2010, Approx. 200 p., Hardcover
ISBN: 978-3-0346-0194-8
Due: February 2010
The asymptotic behaviour, in particular "stability" in some sense, is studied systematically for discrete and for continuous linear dynamical systems on Banach spaces. Of particular concern is convergence to an equilibrium with respect to various topologies. Parallels and differences between the discrete and the continuous situation are emphasised.
Introduction.- Chapter I. Functional analytic tools.- 1. Structure of compact semigroups.- 2. Mean ergodicity.- 3. Tools from semigroup theory.- Chapter II. Stability of linear operators.- 1. Power boundedness.- 2. Strong stability.- 3. Weak stability.- 4. Almost weak stability.- 5. Abstract examples.- 6. Stability via Lyapunov equation.- Chapter III. Stability of C0-semigroups.- 1. Boundedness.- 2. Uniform exponential stability.- 3. Strong stability.- 4. Weak stability.- 5. Almost weak stability.- 6. Abstract examples.- 7. Stability via Lyapunov equation.- Chapter IV. Discrete vs. continuous.- 1. Embedding operators into C0-semigroups.- 2. Cogenerators.- Bibliography.