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New Trends in Stochastic Analysis and Related Topics
The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random phenomena in physics, biology, finance, fluid, environment science, etc. This volume contains 12 comprehe...
On the Geometry of Diffusion Operators and Stochastic Flows
Stochastic differential equations, and Hoermander form representations of diffusion operators, can determine a linear connection associated to the underlying (sub)-Riemannian structure. This is systematically described, together with its invariants, and then exploited to discuss qualitative properties of stochastic flows, and analysis on path spaces of compact manifolds with diffusion measures. This should be useful to stochastic analysts, especially those with interests in stochastic flows, infinite dimensional analysis, or geometric analysis, and also to researchers in sub-Riemannian geometry. A basic background in differential geometry is assumed, but the construction of the connections is very direct and itself gives an intuitive and concrete introduction. Knowledge of stochastic analysis is also assumed for later chapters.
Teaching ESL in Canada
Teaching ESL in Canada is a valuable resource for anyone who teaches English as a Second Language (ESL) in academic or private language schools or to adult newcomers to Canada. The text can be used in TESL classrooms or as a resource for individual professional development. This book covers all the key topics that are important to anyone teaching ESL in Canada: cultural considerations, teaching methods, lesson planning, skills instruction, assessment, and using technology in the classroom. Teaching ESL in Canada guides the reader through numerous classroom scenarios that are common in our multicultural Canadian classrooms, giving them the opportunity to hone their teaching and problem-solving skills. Written by experts in the field of language learning and instruction; with a foreword by Jennifer Pearson Terell, former president of TESL Canada.
The Geometry of Filtering
Filtering is the science of nding the law of a process given a partial observation of it. The main objects we study here are di usion processes. These are naturally associated with second-order linear di erential operators which are semi-elliptic and so introduce a possibly degenerate Riemannian structure on the state space. In fact, much of what we discuss is simply about two such operators intertwined by a smooth map, the \projection from the state space to the observations space", and does not involve any stochastic analysis. From the point of view of stochastic processes, our purpose is to present and to study the underlying geometric structure which allows us to perform the ltering in a...
Identity and Second Language Learning
This collection of research has attempted to capture the essence and promise embodied in the concept of “identity” and built a bridge to the realm of second language studies. However, the reader will notice that we did not build just one link. This volume brings to light the diversity of research in identity and second language studies that are grounded the notions of community, instructors and students, language immersion and study abroad, pop culture and music, religion, code switching, and media. The chapters reflect the efforts of contributors from Canada, Japan, Norway, New Zealand, the United Arab Emirates, and the United States who performed their research in the countries just mentioned and in other regions around the world. Because of this, this volume truly offers an international perspective.
Lectures on Stochastic Analysis: Diffusion Theory
This book is based on a course given at Massachusetts Institute of Technology. It is intended to be a reasonably self-contained introduction to stochastic analytic techniques that can be used in the study of certain problems. The central theme is the theory of diffusions. In order to emphasize the intuitive aspects of probabilistic techniques, diffusion theory is presented as a natural generalization of the flow generated by a vector field. Essential to the development of this idea is the introduction of martingales and the formulation of diffusion theory in terms of martingales. The book will make valuable reading for advanced students in probability theory and analysis and will be welcomed as a concise account of the subject by research workers in these fields.
Patterns & Practice in Chinese Medicine
This book is a clinically oriented presentation of differential diagnosis and treatment in traditional Chinese medicine. This volume consists of eight series of case studies (40 in all), each focusing on a variety of patterns associated with a common clinical disorder: asthma, facial disorders, poor appetite, abdominal and epigastric pain, abnormal bowel movements, abnormal urination, constraint disorders, hypochondrial and intercostal pain. Each case provides a systematic analysis of the patient's presentation, from the cause and site of the disorder to the underlying theory of the case. The pathogenesis, pattern of disease, treatment principle, and modalities of treatment (including both h...
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Nematode-Trapping Fungi
These chapters provide up-to-date information on nematophagous fungi, particularly those of the Orbiliaceae in Ascomycota, whose asexual states produce nematode-trapping devices. The authors consider fungal-nematode interactions, fossil fungi, the biodiversity, ecology and geographical distribution of nematode-trapping fungi, and their potential use in biocontrol of nematodes, all in detail. Nematode-trapping fungi with adhesive or mechanical hyphal traps are the main focus of this book which begins with an overview of the data on nematode-trapping fungi, including their taxonomy, phylogeny and evolution. Subsequent chapters expand upon the methods and techniques used to study these fascinat...
Active Inference
The first comprehensive treatment of active inference, an integrative perspective on brain, cognition, and behavior used across multiple disciplines. Active inference is a way of understanding sentient behavior—a theory that characterizes perception, planning, and action in terms of probabilistic inference. Developed by theoretical neuroscientist Karl Friston over years of groundbreaking research, active inference provides an integrated perspective on brain, cognition, and behavior that is increasingly used across multiple disciplines including neuroscience, psychology, and philosophy. Active inference puts the action into perception. This book offers the first comprehensive treatment of a...
