Algorithmic randomness

In RMC, random moves, i.e., changes in the configuration of the system, are performed as in the metropolis MC algorithm. Random moves are accepted or rejected so that the difference between the calculated and target S q) or g r) is minimized. If g(r) is used as the target function, the parameter to be minimized is ... 

Propp, J. G., and Wilson, D. B. (1996), Exact sampling with coupled Markov chains and applications to statistical mechanics. Proceedings of Seventh International Conference on Random Structures and Algorithms, Random Structures Algorithms 9, pp. 223-252. 

A configurational Monte Carlo algorithm based on uniform random trial moves and the acceptance probability... 

A related algorithm can be written also for the Brownian trajectory [10]. However, the essential difference between an algorithm for a Brownian trajectory and equation (4) is that the Brownian algorithm is not deterministic. Due to the existence of the random force, we cannot be satisfied with a single trajectory, even with pre-specified coordinates (and velocities, if relevant). It is necessary to generate an ensemble of trajectories (sampled with different values of the random force) to obtain a complete picture. Instead of working with an ensemble of trajectories we prefer to work with the conditional probability. I.e., we ask what is the probability that a trajectory being at... 

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. 

A molecular dynamics simulation samples the phase space of a molecule (defined by the position of the atoms and their velocities) by integrating Newton s equations of motion. Because MD accounts for thermal motion, the molecules simulated may possess enough thermal energy to overcome potential barriers, which makes the technique suitable in principle for conformational analysis of especially large molecules. In the case of small molecules, other techniques such as systematic, random. Genetic Algorithm-based, or Monte Carlo searches may be better suited for effectively sampling conformational space. 

The maximum dissimilarity algorithm works in an iterative manner at each step one compormd is selected from the database and added to the subset [Kennard and Stone 1969]. The compound selected is chosen to be the one most dissimilar to the current subset. There are many variants on this basic algorithm which differ in the way in which the first compound is chosen and how the dissimilarity is measured. Three possible choices for fhe initial compormd are (a) select it at random, (b) choose the molecule which is most representative (e.g. has the largest sum of similarities to the other molecules) or (c) choose the molecule which is most dissimilar (e.g. has the smallest sum of similarities to the other molecules). 

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