Method bias

The main difference between the force-bias and the smart Monte Carlo methods is that the latter does not impose any limit on the displacement that m atom may undergo. The displacement in the force-bias method is limited to a cube of the appropriate size centred on the atom. However, in practice the two methods are very similar and there is often little to choose between them. In suitable cases they can be much more efficient at covering phase space and are better able to avoid bottlenecks in phase space than the conventional Metropolis Monte Carlo algorithm. The methods significantly enhance the acceptance rate of trial moves, thereby enabling Icirger moves to be made as well as simultaneous moves of more than one particle. However, the need to calculate the forces makes the methods much more elaborate, and comparable in complexity to molecular dynamics. 

The essence of the configurational bias Monte Cculo method is that a growing molecuh preferentially directed (i.e. biased) towards acceptable structures. The effects of th biases can then be removed by modifying the acceptance rules. The configuratio bias methods are based upon work published in 1955 by Rosenbluth and Rosenbli... 

The distribution of estimated biases for these methods is shown in Figure 3. Except for a bias of zero, the methods tend to be distributed evenly in the -10% to 10% bias region. The high proportion of zero-bias methods may be explained by the number of filter collection methods which have 100% collection efficiency many of these methods use low-biased analysis techniques, particularly atomic absorption spectroscopy. 

Different sources of systematic errors contribute to the overall bias (Figure 8). Thompson and Wood [8] describe persistant bias as the bias affecting all data of the analytical system over longer periods of time and being relatively small but continuously present. Different components contribute to the persistant bias, such as laboratory bias, method bias, and the matrix variation effect. Next to persistant bias, the larger run effect is the bias of the analytical system during a particular run... 

One or more of these bias components are encountered when analyzing RMs. In general, RMs are divided into certified RMs (CRMs, either pure substances/solu-tions or matrix CRMs) and (noncertified) laboratory RMs (LRMs), also called QC samples [89]. CRMs can address all aspects of bias (method, laboratory, and run bias) they are defined with a statement of uncertainty and traceable to international standards. Therefore, CRMs are considered useful tools to achieve traceability in analytical measurements, to calibrat equipment and methods (in certain cases), to monitor laboratory performance, to validate methods, and to allow comparison of methods [4, 15, 30]. However, the use of CRMs does not necessarely guarantee trueness of the results. The best way to assess bias practically is by replicate analysis of samples with known concentrations such as reference materials (see also Section 8.2.2). The ideal reference material is a matrix CRM, as this is very similar to the samples of interest (the latter is called matrix matching). A correct result obtained with a matrix CRM, however, does not guarantee that the results of unknown samples with other matrix compositions will be correct [4, 89]. 

Snurr et al. (192) used biased GC-MC simulations to predict isotherms, isosteric heats of adsorption, and locations of benzene and p-xylene at various concentrations. The suitability of a bias method is clear, at low coverages to prevent trial insertions overlapping with the zeolite walls and at high coverages to prevent overlap with other sorbate molecules. (Slightly different bias schemes were used for the two extremes of concentrations.) Interactions between sorbates and zeolites—both of which were considered to be rigid—were modeled with parameters from the literature (79, 87). Electrostatic interactions were included to account for the quadrupole moment of the sorbates. Sorbate-sorbate interaction parameters were taken from Shi and Bartell (194) for benzene and from Jorgensen et al. (195) for p-xylene. 

Site Method Bias. Method bias, defined as derived weekly minus measured weekly values, and relative mean bias, the bias per mean derived weekly value, were calculated for each site. The average of the collocated pair results for each daily and weekly sample was used. Figure 2 shows the distribution of the method bias for hydrogen ion and sulfate for each site. The median, mean, and... 

Depending on the biological compounds, the number of screenings required, and the accuracy of the physical parameter needed, one or a combination of several BIA methods should be chosen. The price per assay depends not only on the costs of chemicals and hardware for the respective assay but also on the availability of receptor and ligand. 

Selection bias = random selection of controls failed orthechosen control population is biased, information bias = methods used to obtain information about analgesic consumption were doubtful, indication (protopathic) bias = failure to control for analgesic intake preceding the development of renal failure,... 

Evaluation, characterization, and testing of a particular analytical method is necessary to ensure the intended use of the method is met. In general, this process requires the determination of intra-and interlaboratory studies for precision and bias, method detection limits, matrix effects, interferences, limits of reliable measurements and ruggedness of the method. Before the EPA commits time and resources for an in-depth evaluation study, the developer must meet certain developmental criteria or justify why they were not met. The developer must also clearly define all necessary reagents as well as the underlying basis of the immunoassay. 

The bismuth active substances (BiAS) method for the determination of nonionic surfactants with barium tetraiodobismuthate (BaBil4, modified Dragendorff reagent) is used in the standardized (DIN-Norm) procedure in Germany, as well as in other countries. Ba as a hard Lewis acid forms cationic coordination complexes with the polyethoxylate chain of the nonionic surfactants, which are precipitated by [Bim in the presence of acetic acid. The orange precipitate is then dissolved with ammonium tartrate solution, and the released bismuth ions are determined by potentiometric titration with pyrrolidinedithiocarbamate solution. Waters et al. optimized the BiAS procedure by introduction of a cation/anion exchange clean-up of the sublation extracts. The BiAS procedure fails to determine ethoxylates with less than five ethoxy units because these compounds are not precipitated by barium tetraiodobismuthate. Thus, this procedure is not suitable for determination of APEO metabolites, i.e., the shorter APEO and AP. ... 

Recently, recursive sampling has been combined with configurational bias methods (see Section III.D). In the Pruned-enriched Rosenbluth method of Grassberger [11], the number of copies of a growing chain is either reduced (pruning) or increased (enrichment) based on the chain s... 

Frenkel [3,7] has recently given a review of configurational bias methods for simulation of polymers. An account of these methods and their application to phase equilibria calculations is also described in the first chapter in this volume (by I. Siepmann). Here we merely outline the main ideas behind them (see also Fig. 1). In a configurational bias Monte Carlo move... 

Grand canonical ensemble Monte Carlo simulations of the adsorption properties of several model faujasite zeolites were performed using the statistical bias method. The results enable a better understanding of the effect of cation exchange in the selective adsorption of binary mixtures of para and meta xylene isomers. We predict that adding a small amount of water molecules could enhance the adsorption selectivity in favour ofp-xylene. 

In the course of the research into the synthesis of diamond under metastable conditions, a new class of materials, diamond-hke carbon and hydrocarbon phases, have been discovered. The diamond-like hydrocarbons (aC H) are generated by the RF self-bias method, a technique derived from RF sputtering, developed by L. Holland [61,62]. The molecular ions, derived from the particular hydrocarbon used in the plasma, disintegrate upon colliding with the substrate surface resulting in the formation of diamond-like hydrocarbon films [63]. The main structural feature of diamond-like hydrocarbons is the presence of both sp - and sp -carbon. Solid-state NMR-investigations revealed that the material contains sp -carbon atoms of the form -C-H or H-C-H [6]. 

A core management code system has been developed to predict the core parameters for operation and refueling plans within the design limitations. The nuclear calculation is based on diffusion theory and corrected with a bias method. Results from core physics tests and Post Irradiation Examinations (PIE) have been used to confirm the accuracy of these predictions. These verifications are also important to conduct various irradiation tests accurately. This section describes the method and verification for core and fuel management used with the JOYO MK-II core. 

By using this bias method, it was found that the excess reactivity after refueling can be well predicted within an error of 0.1%Ak/kk . The bumup reactivity was determined by measuring the reactivity change during rated power operation. Measured values were compared with the MAGI burnup calculation and both agreed within 5% as shown in Table 3. 

For example, in Figure 5.11-left-down a bias method is graphically illustrated the real stmcture factor is F, the one calculated from the model is (the sub-index C indicates the calculated nature)- which, despite indexed, provides the calculated phase exp(/a ) which by combining with the observed (measured) amplitude F generates the bias model (calculation + experiment) of the bias structure factor F exp(/a ) this should be closer to the real one than the one F provided by applying of theoretical model alone. Thus, properties of the stmcture will be identified, as close to the real ones, namely if inside the calculated model there were not certain atoms, they will appear in the bias electronic map, built on the bias stmcture factor. 

The reverse bias method was applied successfully to both bulk aluminum and thin aluminum layers deposited on Ti/Si O/Si wafers (20). 

In principle, this method can also be applied to multichain systems, but the problem of correcting for the bias becomes even more severe. In practice, one therefore has to resort to the configurational bias method which is an extension of the Rosenbluth sampling (see Chapter 7). But, inversely restricted sampling is still one of the possible options for not too large... 

Once the bounds for 9 have been established, several orientations of the bond vector b,-, i are sampled according to the usual configurational bias method, and one is selected from the probability distribution given by Eq. (14). 

Configurational Bias methods have now also been used to simulate molecules with strong intramolecular potentials [37,38] in that case, it is necessary to incorporate such potentials in the biasing factors used to generate trial orientations. If the trial orientations are proposed at random, the efficiency of the trial move is low, due to high intramolecular energies... 

In some cases, in particular lattice and polymeric systems, volume change moves may be hard to perform, but particle insertions and deletions may be relatively easy, especially when using configurational-bias methods. Escobedo and de Pablo [46,47] proposed a modification of the Gibbs-Duhem approach that is based on the expression... 

Configurational-bias methods trace their ancestry to biased sampling for lattice polymer configurations proposed by Rosenbluth and Rosenbluth [85]. Development of configurational-bias methods for canonical and grand canonical simulations and for continuous-space models took place in the early 1990s [86-90] and dramatically expanded the range of intermolecular potential models that can be studied by the methods described in the previous sections. 

Jaffrin MYl, Morel H. Body fluid volumes measurement gy impedance A review of bioimpedance spectroscopy (BIS) and Bioimpedance analysis (BIA) methods. Med Eng Phys. 2008 Dec 30(10) 1257-69. 

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