Extracting Information from Simulations

Here the prime notation indicates the data set at a given compression level. Eq. (14.33) clearly illustrates that the estimate of the variance becomes increasingly uncertain as the number of data blocks decreases, i.e. when the data has been compressed into only two blocks, the (relative) standard deviation is In order to determine whether it is actually possible to obtain uncorrelated data from the simulation, a plot of c l N -1) against compression level should therefore include the associated statistical error from eq. (14.33). If the statistical errors impinge on a conclusion as to whether a constant plateau has been reached, this is an indication that the simulation length is insufficient for obtaining valid estimates of the given quantity. 

Ensembles generated by MC techniques are naturally of the constant NVT type, while MD methods naturally generate a constant NVE ensemble. Both MC and MD methods, however, may be modified to simulate other ensembles, as described in Sections 14.1.1 and 14.2.2. Of special importance is the constant NPT condition, which directly relates to most experimental conditions. The primary advantage of MD methods is that time appears explicitly, i.e. such methods are natural for simulating time-dependent properties, such as correlation functions, and for calculating properties that depend on particle velocities. Furthermore, if the relaxation time for a given process is (approximately) known, the required simulation time can be estimated beforehand (i.e. it must be at least several multiples of the relaxation time). 

The expressions derived from statistical mechanics (Section 13.4) are often rewritten into computationally more suitable forms that may be evaluated from the basic descriptors positions r, velocities v or momenta p and energies E. The temperature is related to the average kinetic energy. 

In a standard MC simulation the temperature is fixed NVT conditions), while it is a derived quantity in a standard MD simulation NVE conditions). 

The pressure is related to the product of positions and forces (for pairwise potentials). 

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The statistical degree of overlapping (SDO) and 2D autocovariance function (ACVF) methods have been applied to 2D-PAGE maps (Marchetti et al., 2004 Pietrogrande et al., 2002, 2003, 2005, 2006a Campostrini et al., 2005) the means for extracting information from the experimental data and their relevance to proteomics are discussed in the following. The procedures were validated on computer-simulated maps. Their applicability to real samples was tested on reference maps obtained from literature sources. Application to experimental maps is also discussed. 

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]. 

This will be done by the theoretical simulation techniques described in Section II.B by extracting information from molecular ab initio all-electron calculations. 

In order to extract information from these curves we performed simulations using the Surface Evolver software, which allows to compute the equilibrium shape of a liquid body in many different situations, even nonaxisymmetric geometry. We considered a liquid bridging a flat plane (the surface) and a conical surface (the tip), as represented in Fig. 9.1a. We used as boundary conditions on the surface a circular CL with a fixed Rsurf radius corresponding to the molecules deposit observed in the experiment and measured... 

In a different context, conformational analysis is essential for the analysis of molecular dynamics simulations. As discussed in Chapter 3, the direct output of a molecular dynamics simulation is a set of confonnations ( snapshots ) that were saved along the trajectory. These conformations are subsequently analyzed in order to extract information about the system. However, if, during a long simulation, the molecule moves from one... 

One of the problems to extract structural information from EPR lies in the correct simulation of the experimental spectra. Misra536 reviewed spin Hamiltonians applicable to exchange-coupled Mn complexes, and described techniques for simulation of EPR spectra. Various structural models for the Mm-cluster in PS II were presented. 

The main task considered in the book is that of extracting useful information from measurements via modelling, simulation, and statistical data evaluations. Efficient and robust... 

The definition of epigenesis as a reconstruction from incomplete information suggests that embryonic development can be simulated (in a very abstract way) by the reconstruction of a super matrix made of a growing number of individual matrices, each of which would represent a cell. In this case, however, the reconstruction could be performed with two different strategies one where the memory information is extracted only from individual memory matrices, and a second one where it is also extracted from a collective memory. 

Data mining to extract information on dynamics from time series data from experiments and simulations of molecular dynamics. 

For a long time the main topic of research in the area of sensitivity analysis was to find an accurate and effective method for the calculation of local concentration sensitivities. This question now seems to be settled, and the decoupled direct method (ddm) is generally considered the best numerical method. All the main combustion simulation packages such as CHEMKIN, LSENS, RUNIDL and FACSIMILE calculate sensitivities as well as the simulation results and, therefore, many publications contain sensitivity calculations. However, usually very little information is actually deduced from the sensitivity results. It is surprising that the application of principal component analysis is not widespread, since it is a simple postprocessing method which can be used to extract a lot of information from the sensitivities about the structure of the kinetic mechanism. Also, methods for parameter estimation should always be preceded by the principal component analysis of the concentration sensitivity matrix. 

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