Biased sampling methods

As an illustration of the biased sampling method in application to the problems of polymer chain adsorption on a hard wall we shall recall here briefly the procedure used on a diamond lattice [35]. Starting the chain at the origin, the first bond is fixed at the plane and all the following bonds are determined at random apart from the non-reversal condition. Suppose, after a certain number i of steps, that the (/+l)st monomer reaches the plane at z = 0 again. With = 4 on the diamond lattice one has the probability p = /3 for each new possible choice of a bond. Thus in... 

Indirect Methods Test particle method Grand canonical ensemble method Biased sampling methods Thermodynamic integration... 

There are many variants of biased sampling methods for the SAW, for instance the idea of scanning future steps [28] but these techniques will remain outside of consideration here. 

A randomly collected sample makes no assumptions about the target population, making it the least biased approach to sampling. On the other hand, random sampling requires more time and expense than other sampling methods since a greater number of samples are needed to characterize the target population. 

An improvement of this method—the so-called biased sampling [55] (or inversely restrieted sampling)—suggests to look ahead at least one step in order to overcome the attrition. Consider a SAW of i steps on a -coordination number lattice. To add the / + 1st step one first checks which of the = q — neighboring sites are empty. If k qQ > k>0) sites are empty one takes one of these with equal probability 1 /A if A = 0 the walk is terminated and one starts from the beginning. This reduces the attrition dramatically. Now each A-step walk has a probability PAr( i ) = Ylf=i so that dense configurations are clearly more probable. To compensate for this bias, each chain does not count as 1 in the sample but with a weight... 

Oberhofer, H. Dellago, C. Geissler, P. L., Biased sampling of nonequilibrium trajectories. Can fast switching simulations outperform conventional free energy calculation methods, J. Phys. Chem. B 2005,109, 6902-6915... 

Tx and Tx are the kinetic energies of the atomic coordinates and X variables, respectively. The As are treated as volumeless particles with mass mx. Since the X variables are associated with the chemical reaction coordinates , the A-dynamics method can utilize the power of specific biasing potentials in the umbrella sampling method to overcome sampling problems that require conventional FEP calculations to be performed in multiple steps. 

Liikala et al. [146] compared different sampling methods in the determination of volatile organic compounds in soil. Large negative biases occurred for aromatic compounds when conventional sampling was used compared to placing the soil aliquot in methanol. 

MC is often used to sample the conformational space of biomolecules. Efficient biased MC methods make use of structural information (extracted either from simulation or from structural databases) to bias the generated conformations towards low energy structures [26-31]. 

Lately it was discovered by Pourdeyhimi et.al. [6] that the best way to simulate nonwovens of continuous fibers is through the second method. The aim is to obtain unbiased arrays and both of the first and third methods produce biased samples and are not appropriate for simulating continuous filaments. 

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