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Let {Xti t ~ O} be a Markov process in Rl, and break up the path X t into (random) component pieces consisting of the zero set ({ tlX = O}) and t the "excursions away from 0," that is pieces of path X. : T ::5 s ::5 t, with Xr- = X = 0, but X. 1= 0 for T < s < t. When one measures the time in t the zero set appropriately (in terms of the local time) the excursions acquire a measure theoretic structure practically identical to that of processes with stationary independent increments, except the values of the process are paths rather than real numbers. And there is a measure on path space that helps describe the measure theoretic properties of the excursions in the same way that the Levy measure describes the jumps of a process with independent increments. The entire circle of ideas is called excursion theory. There are many attractive things about the subject: it is an area where one can use to advantage general probabilistic potential theory to make quite specific calculations, it provides a natural setting for apply ing esoteric things like David Williams' path decomposition, it provides a method for constructing processes whose description in terms of an in finitesimal generator or some such analytic object would be complicated. And the ideas seem to be closely related to a good deal of current research in probability.
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This invaluable volume, written by an international group of scientists, presents an overview of the AdoMet-dependent methyltransferases, with special emphasis on structure-function relationships.S-adenosyl-L-methionine (AdoMet) is the second most commonly used enzyme cofactor after ATP. The AdoMet-dependent methyltransferases act on a wide variety of target molecules, including DNA, RNA, protein, polysaccharides, lipids and a range of small molecules.The well-conserved architecture of these enzymes, and the implications of this conservation for their evolutionary history, are major themes of this book. The thirteen chapters describe in detail the structures, enzyme kinetics and biological roles of the AdoMet-dependent methyltransferases from a wide range of cell types: plant, animal, bacterial and archaeal.