First cummulant

It is convenient to describe the average decay rate of g " t) by its first cummulant r which is correlated to the cooperative diffusion coefficient D oop of the network chains ... 

Another method that has enjoyed a great deal of success is the method of cumulants. In 1972 Koppel (3) showed that the logarithm of the first order AC function was identical to the cummulant generating function for the distribution of decay constants. The coefficients of the cummulant expansion can be related to the moments of the distribution. From the complete set of moments it is theoretically possible to regenerate the exact distribution function. In practice however, even small amounts of noise in the AC data can cause large amounts of error in all but the first two or three moments. For narrow unimodal distributions the first two moments basically define the distribution. However, for multimodal, highly skewed, or very broad distributions, the cumulant expansion is inadequate. 

In a double blind controlled trial using Intramuscular iodinated oil in an iodine deficient population, the infant and childhood cummulative mortality over the first 15 years of life was significantly greater in the control than in the test group. 

All three methods presented in the previous section are based on a rather rough notion of events and their relationships. An important issue is mutual influence of events. Should we treat events as atomic, instantaneous entities or shoidd we allow that an event has a duration in time. In the first case, the consequence is that events can be totally ordered in time if events are atomic (i.e. they can not coincide in time) then they must have h pened in some order (which may be unknown at present). Note that the word time is used here to represent evolution (cummulation of changes) of the world under consideration, not the physical time. In other words, an event can be treated as being instantaneous even if it has a duration in physical time. However, in this case the change of state represented by the event must be properly isolated from the other changes. The assunqition about atomicity underlies most of the approaches to formalization of the event concept. Then, those events for which this assumption can not be justified are iq>resented as structures of more primitive, atomic events. Usually, the words action, transaction, operation, composed action, process, etc. are reserved to denote such events. Another important issue is the relation between events and the real time. Real time... 

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