Drawing on the author's extensive fieldwork in the Dong areas in southwest China, this book presents a detailed picture of the Dong's buildings and techniques, with new insights into the Dong's cosmology and rituals of everyday life meshed with the architecture, and the symbolic meanings. It examines how the buildings and techniques of the Dong are ordered and influenced by the local culture and context. The timber bridges and drum towers are the Dong's most prominent architectural monuments. Usually built elaborately with multiple roofs, these bridges and drum towers were designed and maintained by the local carpenters who also built the village suspended houses, in an oral tradition carried down from father to son or to apprentice. They were funded entirely by the local people, and the bridges tend to be built in places without great pressure of traffic or another bridge already existing close by. Why does such great expense go into the Dong's buildings with elaboration? How were they built? And what do they mean to their users and builders? This book is an anthropological study on the Dong's architecture and technique, and it aims to contribute a discourse on the interdisciplinary research area. It is suitable for graduate and postgraduate readers.

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.

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 Markovian framework with the resulting conditional law being that of a Markov process which is time inhomogeneous in general. This geometry is determined by the symbol of the operator on the state space which projects to a symbol on the observation space. The projectible symbol induces a (possibly non-linear and partially de ned) connection which lifts the observation process to the state space and gives a decomposition of the operator on the state space and of the noise. As is standard we can recover the classical ltering theory in which the observations are not usually Markovian by application of the Girsanov- Maruyama-Cameron-Martin Theorem. This structure we have is examined in relation to a number of geometrical topics.

Diabetic Nephropathy (DN) is the leading cause to end-stage renal disease all over the world. Unfortunately, no effective treatment is available to stop its progression. So far, many key issues remain unrevealed in relation to its pathogenesis, new forms of therapy, and complication intervention. In this book, the authors aim to provide updated medical knowledge and practical management strategies to medical professionals who are caring for DN patients based on their ample clinical experiences, strong bench and bedside research background, and tight collaboration with experts in other fields caring for common complications in DN. The authors also want to shed light on the work of bench researchers in fields of DN and its complications from a clinical perspective.