Stochastic sampling

In the MC/MD method, the stochastic sampling by MC steps permit one to restrict the sampling of chemical space, i.e., the space of A. For example, Kollman and co-workers6,7 limit their chemical sampling only to transitions between the end points in their CMC/MD simulations... 

Linear Models. Variable selection approaches can be applied in combination with both linear and nonlinear optimization algorithms. Exhaustive analysis of all possible combinations of descriptor subsets to find a specific subset of variables that affords the best correlation with the target property is practically impossible because of the combinatorial nature of this problem. Thus, stochastic sampling approaches such as genetic or evolutionary algorithms (GA or EA) or simulated annealing (SA) are employed. To illustrate one such application we shall consider the GA-PLS method, which was implemented as follows (136). 

Various deterministic and stochastic sampling techniques for path ensembles have been proposed [4-6]. Here we consider only Monte Carlo methods. It is important, however, to be aware that while the path ensemble is sampled with a Monte Carlo procedure each single pathway is a fully dynamical trajectory such as one generated by molecular dynamics. 

In (25) it is required that G contains Do among its members. The has the same meaning as before all vertices in G must be visited by the paths. Using (24) and (19) leads to an expression for Eq suitable for a stochastic sampling of graphs, analogous to (15) ... 

In the simulations tab the maximum number of molecular components in the complexes of the simulated reaction networks and the precision of the numerical integration of the dynamics of the biochemistry of the model (wNote 10) can be specified. The external update step defines the time between updates of the visualizations of the simulation (r eNote 11). The random generator seed can be varied for stochastic sampling see Note... 

The probabilistic model is solved by a numerical stochastic sampling experiment. 

It is important to note that in this approach, the computed partition coefficients of flexible solutes depend only on their conformational gas phase energy minima. Thus only one conformational analysis (i.e., in the gas phase) must be performed to predict the global, conformation-dependent log P. In principle, any method of conformational analysis can be selected that is able to determine a distribution of conformers in the gas phase. < " < To study linear, uncharged dipeptides, Richards and Williams used a stochastic sampling technique.Their results (Table 12) illustrate the accuracy of the method and demonstrate that stochastic sampling methods in combination with empirical solvation potentials provide fair estimates of experimental log P values of flexible compounds. 

MC technique, also called Metropolis method, [24] is a stochastic method that uses random munbers to generate a sample population of the system from which one can calculate the properties of interest. A MC simulation usually consists of three typical steps. In the first step, the physical problem under investigation is translated into an analogous probabilistic or statistical model. In the second step, the probabilistic model is solved by a munerical stochastic sampling experiment. In the third step, the obtained data are analyzed by using statistical methods. MC provides only the information on equilibrium properties (e.g., free energy, phase equilibrium), different from MD whieh gives nonequilibrium as well as equilibrium properties. In a NVT ensemble with N atoms, one hypoth-... 

Table 1 presents basic descriptive statistics of obtained data. Finally, the stochastic sample was consisting of 2838 cases and the total number of obtained cases of all considered variables was equal to 23,967. However, there are many missing data, so in further study the set of 333 cases was considered. This set consists of these sample points for which the chloroform concentration at network point and at water treatment plant were given (laboratory analyzes are made according to the monitoring plan which takes into account high costs of gas chromatography). 

The general idea behind all Monte Carlo methodologies is to provide an efficient stochastic sampling of the configurational or conformational phase space or parts of it with the... 

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