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  • Book
    Martin T. Barlow, University of British Columbia, Canada.
    Summary: This introduction to random walks on infinite graphs gives particular emphasis to graphs with polynomial volume growth. It offers an overview of analytic methods, starting with the connection between random walks and electrical resistance, and then proceeding to study the use of isoperimetric and Poincar inequalities. The book presents rough isometries and looks at the properties of a graph that are stable under these transformations. Applications include the 'type problem': determining whether a graph is transient or recurrent. The final chapters show how geometric properties of the graph can be used to establish heat kernel bounds, that is, bounds on the transition probabilities of the random walk, and it is proved that Gaussian bounds hold for graphs that are roughly isometric to Euclidean space. Aimed at graduate students in mathematics, the book is also useful for researchers as a reference for results that are hard to find elsewhere.

    Contents:
    Random walks and electrical resistance
    Isoperimetric inequalities and applications
    Discrete time heat kernel
    Continuous time random walks
    Heat kernel bounds
    Potential Theory and harnack inequalities
    Digital Access Cambridge 2017
  • Article
    Hauge A, Bo G, Aarseth P.
    Acta Anaesthesiol Scand. 1977;21(5):413-22.
    The effect on lung compliance of changes in intra- and extravascular volumes has been studied. Such changes were induced by inflation and deflation of a balloon placed in the left atrium in open-chest cats. Blood constituents were labeled with isotopes, and tissue water content was found from the wet/dry labeled with isotopes, and tissue water content was found from the wet/dry weight ratio. When left atrial pressure (PLA) was elevated to a value not exceeding 32 mmHg (4.256 kPa), there was only a minute increase in tissue water volume, and we observed a reversible reduction in lung compliance related to the rise in lung blood volume. At higher PLA, a rapid rise occurred in extravascular fluid volume, with evidence of alveolar flooding. Earlier experiemtns have shown that, in isolated perfused lung, a situation of slow, steady increase in interstitial fluid can be created. This does not seem to be the case with lungs in situ: once the lymphatic drainage is unable to cope with transvascular fluid flow, an unstable situation is created. This rapidly leads to alveolar flooding and a fall in compliance in addition to that caused by a rise in blood volume. From our fluid and pressure determinations, we calculated a filtration coefficient (Kf) of 0.45 ml/100 g wet lung X cmH2O X h. This is within the range reported for sheep lungs. Observation of dynamic lung compliance cannot be used for detection of interstitial fluid accumulation. It appears, however, that in contrast to isolated lungs, this phase of edema-formation rapidly leads to alveolar flooding.
    Digital Access Access Options