Nondeterministic

One can actually prove a stronger result all nondeterministic LG models that satisfy semi-detailed balance and possess no spurious conservation laws have universal equilibrium solutions whose mean populations are given by the Fermi-Dirac distribution (equation 9.93) [frishc87]. 

In this paper, t Hooft introduces several toy models that hint that typically nondeterministic quantum mechanical behavior can be achieved using local deterministic laws, in the sense that a basis can be found in terms of which the wave function does not spread. He shows how a CA-like formalism can be used to... 

All the models discussed above are based on a deterministic point of view. However, there is another type of model (i.e., a nondeterministic model) that includes the concept of nonequilibrium fluctuation. In the following section, we discuss such a model, i.e., the electrocapillarity breakdown model. 

Nucleation and growth of gas hydrate crystals have been investigated with optical methods under different pressures and temperatures. The particle sizes measured during gas hydrate nucleation ranged from 2 to 80 imi [1334,1335]. The nucleation process is nondeterministic, because of a probabilistic element within the nucleation mechanism [1393]. 

As in the application of any nondeterministic Artificial Intelligence method, it is not safe to assume that all that is needed for a successful GA calculation is to open the jaws of the algorithm, drop in the problem, and then wait. Various factors must be considered to determine whether the GA might be effective. 

This construction works because G is free and we are dealing with free interpretations. When we come to a test we can nondeterministically select either path - seme free interpretation will take either path. The final output under any free interpretation must be either f. -.f x for some input variable x or else for some constant o. In the first case, G guesses this will... 

Stochastic Model The stochastic model, on the other hand, designates and describes the nondeterministic or stochastic (probabilistic) properties of the variables involved, particularly those representing the measurements. 

Menger started with a probability distribution function rather than with random variables. This is related to the fact that the outcome of any series of measurements of the values of a nondeterministic quantity is a distribution function and the probability space is in principle unobservable. This point of view indicates a nonclassical behvior. 

It is one of the ironies of twentieth century science that, although his work on the photoelectric effect helped to advance quantum mechanics, Einstein came to be its chief critic. It was his antagonism toward the probabilistic and nondeterministic nature of quantum phenomena that prompted Einstein to make the often-quoted remark, I cannot believe that God would choose to play dice with the universe. ... 

Following the turbulent developments in classical chaos theory the natural question to ask is whether chaos can occur in quantum mechanics as well. If there is chaos in quantum mechanics, how does one look for it and how does it manifest itself In order to answer this question, we first have to realize that quantum mechanics comes in two layers. There is the statistical clicking of detectors, and there is Schrodinger s probability amplitude -0 whose absolute value squared gives the probability of occurrence of detector clicks. Prom all we know, the clicks occur in a purely random fashion. There simply is no dynamical theory according to which the occurrence of detector clicks can be predicted. This is the nondeterministic element of quantum mechanics so fiercely criticized by some of the most eminent physicists (see Section 1.3 above). The probability amplitude -0 is the deterministic element of quantum mechanics. Therefore it is on the level of the wave function ip and its time evolution that we have to search for quantum deterministic chaos which might be the analogue of classical deterministic chaos. 

Despite the similarity to the Gauss approach to classical mechanics, there is a key difference between the classical actions described above and the corresponding action of the stochastic difference equation. The classical actions are deterministic mechanical models the SDE is a nondeterministic approach that is based on stochastic modeling of the numerical errors introduced by the finite difference formula. 

Passivity breakdown appears to occur preferentially at local heterogeneities, such as inclusions, grain boundaries, dislocations, and flaws on the passive metal surface. In the case of stainless steels, the passivity breakdown and pit initiation occur almost exclusively at sites of MnS inclusions, and the pitting potential was observed to decrease linearly with the increasing size of MnS inclusions [44]. With metals containing no apparent defects, however, passivity breakdown is likely to occur in the presence of sufficient concentrations of film breaking ions. It is worth noting that any of the localized phenomena is nondeterministic but somehow stochastic. For stainless steels in chloride solution, the passivity breakdown was found to obey a stochastic distribution [45]. 

Genetic algorithms are nondeterministic optimizers due to the randomly acting genetic operators. Usually, several experiments are performed and the best solutions of each single experiment are presented as results. 

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