Stochastic algorithms

The Boltzmaim weight appears implicitly in the way the states are chosen. The fomi of the above equation is like a time average as calculated in MD. The MC method involves designing a stochastic algorithm for stepping from one state of the system to the next, generating a trajectory. This will take the fomi of a Markov chain, specified by transition probabilities which are independent of the prior history of the system. 

Agrafiotis DK. Stochastic algorithms for maximising molecular diversity. J Chem Inf Comput Sci 1997 37 841-51. 

Most drug-like molecules adopt a number of conformations through rotations about bonds and/or inversions about atomic centers, giving the molecules a number of different three-dimensional (3D) shapes. To obtain different energy minimized structures using a force field, a conformational search technique must be combined with the local geometry optimization described in the previous section. Many such methods have been formulated, and they can be broadly classified as either systematic or stochastic algorithms. 

Till, J Engell, S. and Sand, G. (2005) Rigorous vs stochastic algorithms for two-stage stochastic integer programming applications. Inti. J. Inf. Technol., 11, 106-115. 

Combining the steps described above, a simple stochastic algorithm for a trajectory-based propagation of the QCL equation can be constructed as follows ... 

Agrafiotis, D. K. (1997) Stochastic algorithms for maximizing molecular diversity. 

This quantity has fluctuations of 1), and a nonvanishing mean value of the same order. The use of this filtered expression is essential to the construction of a practical stochastic algorithm for the stress. 

Monte Carlo (MC) methods can address the time gap problem of MD. The basis of MC methods is that the deterministic equations of the MD method are replaced by stochastic transitions for the slow processes in the system.3 MC methods are stochastic algorithms for exploring the system phase space although their implementation for equilibrium and non-equilibrium calculations presents some differences. 

Agrafiotis, D.K. Stochastic Algorithms for Maximizing Molecular Diversity. J. Chem. 

Agrafiotis. D.K. Stochastic Algorithms for Maximizing Molecular Diversity. J. Chem. Inf. Comput. Sci., 1997,37, 841-851. 

In recent times, stochastic methods have become frequently used for solving different types of optimization problems [4.54—4.59]. If we consider here, for a steady state process analysis, the optimization problem given schematically in Fig. 4.14, we can wonder where the place of stochastic methods is in such a process. The answer to this question is limited to each particular case where we identify a normal type distribution for a fraction or for all the independent variables of the process pc = pCj]). When we use a stochastic algorithm to solve an optimization problem, we note that stochastic involvement can be considered in [4.59] ... 

Alternatively, the number of desired compounds can be predefined and a stochastic algorithm used to maximize the diversity of the selected set, although these methods are even slower than addition methods. Sphere-exclusion methods, which Pearlman calls "elimination" algorithms because the diverse subset is created by eliminating compounds from the superset, have been implemented in Diverse-Solutions (31) (see Section 2.2.1.1), providing a rapid distance-based diverse subset selection method. The minimum distance between nearest neighbors within the diverse subset is first defined a compound is chosen at... 

Now that we know how to evolve the dynamics within a small time segment, we can decide to construct a Monte-Carlo-style stochastic algorithm to account for the quantum transitions that arise from the action of J. At the end of each time segment, the system either may remain in the same pair of adiabatic states or make a transition to a new pair of states. More specifically, for an initial pair of quantum states, (ckockq), the phase point R, P) is evolved for a time At to a new value RAt, PaO (here we use a simplified notation for the time-evolved phase points in the interval At) using the classical propagator and the phase factor is computed. With probability 1/2,... 

In [1] we provide an algorithm to sample graphs generated according to a stochastic algorithm, and we will not elaborate further on this aspect. 

We shall see in Chapter 7 that stochastic algorithms can be used to simulate the evolution of a population of particles represented by the NDF. However, the NDF is not a random quantity rather it is the ensemble average of an infinite number of realizations of the stochastic algorithm (assuming that the latter is unbiased). 

Neurock, M., Nigam, A., Trauth, D., and Klein, M. T., Molecular representation of complex hydrocarbon feedstocks through efficient characterization and stochastic algorithms, Chem. Eng. Sci. 49(24A), 4153-4177 (1994). 

Agrahotis D K 1997 Stochastic Algorithms for Maximising Molecular Diversity. Journal of Chemical Information and Computer Science 37 841-851. 

Some recent approaches to solve these problems are to use stochastic algorithms including nature inspired algorithms that are known to have delivered good results for this class of problems. Ant Colony Optimisation (ACO), as one such algorithm is inspired by the way in which ants in the wild find a short path from the nest to food using pheromones. Ant colony optimisation... 

Pitts [1943] proposed neuron models in the form of binary threshold devices and stochastic algorithms involving sudden 0-1 and 1-0 changes of states in neurons as the bases for modeling neural system. Subsequent work by Hebb [1949] was based on mathematical models that attempted to capture the concept of learning by reinforcement or association. 

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