Exploration algorithm

Our research is to determine the existence of certain states without having to explore the entire SSp. This is done with a reachability analysis, by using a partial exploration algorithm. 

The output of any partial exploration can be seen as a probabilistic sample. Upon unsuccessful search, a hypothesis test can be conducted for completeness using the sample. In general, random walk is used in the partial exploration algorithm, but random walk cannot be used as a sampling method because the probability that a given state is visited is far from being uniform [13]. Therefore, the sample is biased and any posterior hypothesis test will be incorrect. 

This chapter presents a partial exploration algorithm guided by a quota sampling. It is basically a table of quotas to fill in during the exploration. The sampling method is neither totally unbiased nor valid variance estimate, but it goes in the direction toward obtaining a representative sample. Then, we show a proper treatment to the sample by means of a hypothesis test [10] to provide conclusiveness to the analysis. 

Non-probabilistic sampling methods appeal more to notions of representativity [14]. In this section we explain how to get a representative sample of the SSp according to the variable Y which is assumed to be normally distributed. The sample is obtained with a partial exploration algorithm guided by a quota sampling [14]. 

In our reachability analysis, in searching a target marking m, with cardinality of c, the partial exploration algorithm fills in the quota of samples for a table of n markings from the SSp. 

This chapter has described a set of behavioral and structural transformations that can be applied to the Value Trace. Lower-level transformations can be used to improve the efficiency of the design, and to facilitate higher-level transformations. Higher-level transformations can be used to explore Algorithmic Level design alternatives, including multiple processes and pipelines. Examples of this exploration are presented in Chapter 8. 

Other methods which are applied to conformational analysis and to generating multiple conformations and which can be regarded as random or stochastic techniques, since they explore the conformational space in a non-deterministic fashion, arc genetic algorithms (GA) [137, 1381 simulation methods, such as molecular dynamics (MD) and Monte Carlo (MC) simulations 1139], as well as simulated annealing [140], All of those approaches and their application to generate ensembles of conformations arc discussed in Chapter II, Section 7.2 in the Handbook. 

Alternative algorithms employ global optimization methods such as simulated annealing that can explore the set of all possible reaction pathways [35]. In the MaxFlux method it is helpful to vary the value of [3 (temperamre) that appears in the differential cost function from an initially low [3 (high temperature), where the effective surface is smooth, to a high [3 (the reaction temperature of interest), where the reaction surface is more rugged. 

Clearly, the extent of exotherm-generated temperature overshoot predicted by the Chiao and finite element models differs substantially. The finite element results were not markedly changed by refining the mesh size or the time increments, so the difference appears to be inherent in the numerical algorithms used. Such comparison is useful in further development of the codes, as it provides a means of pinpointing those model parameters or algorithms which underlie the numerical predictions. These points will be explored more fully in future work. 

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