Probability model single events

Fig. 3.3. The probability of an event recorded by the flow cytometer as a single cell actually resulting from more than one cell coinciding in the laser beam. For this model, the laser beam was considered to be 30 pm high and the stream flowing at 10 m per second.

Once a scaling model has been found the scaled data should be examined carefully to ascertain that the variance is equal over the domain of the data. If not then a suitable transform must be found to equalize the variance. Otherwise, no single stochastic model will accurately reflect the probability of an occurrence of the "event" in question over the data domain, much less for an extrapolated prediction. For example, if the standard deviation is proportional to the mean, a very common situation in nature, the variance is equalized by taking the log of the model variable. This is the case for both of the above examples, where the probability model was fitting to In x rather than x itself. Suitable transformations for other common situations, as well as a general method for finding transforms is given by Johnson Leone (7). 

The traditional methods of CCF modeling when probability of CCF events is derived from the component failure probability by the means of specific factors (ALPHA, BETA, MGL, etc.) could hardly work as the biggest problem is to establish the basic software fault probability. Moreover values of parameters for particular combinations (couples, triples, etc.) would be significantly different from. .traditional" ones (Mosleh, A., 1993) as the portion of CCF prob-abihty on the single train software probability would be much higher. 

The patch-clamp data consist in records of single-channel current or on macroscopic current records. The single-channel data is obtained, and properties of current amplitude, duration distributions and probability of single channel events are studied. Macroscopic currents are fitted according to kinetic models, or the noise of current records is analyzed to obtain the microscopoic properties of single-channel events that underlie the macroscopic currents. The analysis methods will not be discussed here. Some criteria and methods are discussed in several articles and reviews, as for example [5, 8, 10, 17-23]. 

Within these two classes of models, there exist numerous subclasses. For example, within the empirical class, there are functional models, in which (discrete) data are represented by continuous mathematical functions or by approximations that sometimes follow a natural law. Within the broad class of deterministic models there can exist definite models that yield a single output for a given set of input values and probabilistic models, in which the inputs are distributed, resulting in a distributed output from which the probability of an event occurring can be estimated. Also, as mentioned above, there are other possible ways to classify models ... 

The mechanism of charge transfer that constitutes recombination in a DSC can be formulated as a product of three quantities the electron density, the concentration of the acceptor (the oxidized half of the redox electrolyte), Cqx, and the probability of single transfer event Vei, that is described by the electron transfer model of the previous section, as shown in Fig. 12a. Due to the disorder in the energy axis of the metal oxide, we have a variety of possible electronic channels that constitute parallel recombination mechanisms, as indicated in Fig. 12b. 

One major concern of both groups is the statistical analysis used in WASH-1400. One example is the estimation of the probabilities of common-cause failures, i.e., those where a single event produces a common failure in several pieces of equipment. Where the actual safety system is too complicated for a failure probability to be calculated directly, the analysis sets up a series of simple models, each simple enough to permit the calculation of the failure probability for the model, P(M). Next a subjective engineering judgement is made of the probability, Q M), that the particular model is in fact a correct description of the system. The overall... 

In the continuous-time random walk model, a random walker is pictured to execute jumps at time steps chosen from the waiting time pdf w(t). In the isotropic and homogeneous (that is, force-free) case, the distance covered in a single jump event can be drawn from the jump length pdf X x). Then, the probability t) (x, t) of just having arrived at position x is given through [49]... 

The above physical situation may be modelled by a modified Markov process, where the states represent the various ions attached at the catalytic sites, and the transition probabilities are the above-mentioned probabilities of an ion being replaced or modified within a period of time. This will not be an ordinary Markov process, because the transition probabilities are not all constant. In particular, those probabilities corresponding to the transition of single sites to double sites depend not only on the states in question, but also on the availability of other single sites. That probability in turn, changes, as sites are removed by irreversible decay events. 

Translation of cellular stress models needs to be linked to the cellular physiology that occurs in single cells. This will ensure that the probability of events in terms of modeling will play a prime role. These events include the amount of transcripts and, therefore, molecules of certain transcription factors regulating the onset of stress response routes (Brul et al., 2002a). 

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