Multiple soft modeling

Stored in a table where columns are descriptors, and rows are compounds (or conformers), QSAR data sets contain separate columns for the measured target property (Y), attributed to the training set, as well as computed descriptors for (external) reference compounds on which the QSAR model is tested—the test set. Statistical procedures, e.g., multiple linear regression (MLR), projection to latent structures (PLS), or neural networks (NN) [38], are then used to establish a mathematical soft model relating the observed measurement(s) in the Y column(s) with some combination of the properties represented in the subsequent columns. PLS, NN, and AI (artificial intelligence) techniques have been explored by Green and Marshall in the context of 3D-QSAR models [39], and were shown to extract similar information. A problem that may lead to spurious (chance) correlations when using MLR techniques, the colinearity between various descriptors, or cross-correlation, is usually dealt with in PLS [40],... 

Factor analysis, like in spectrophotometry, can help here to get estimate of the number of species involved in extraction without any a priori suggestions. The ESI method leads to multiple minima problem, but it can speed up the search of chanical model or to prove if the model found is correct. Soft modeling methods like PLS or ANN enable fast determination of stability constants without solving mass balance... 

Frequency-selective REDOR (fsREDOR) is a very powerful technique developed for the study of 13C and 15N uniformly labeled peptides or proteins [92]. The basic idea of this technique is to combine REDOR and soft n pulses to recouple a selected 13C-15N dipole-dipole interaction in a multiple-spin system. Usually one could use Gaussian shaped pulses to achieve the required selective n inversions. Other band selective shaped pulses have been developed for a more uniform excitation profile [93]. In its original implementation, fsREDOR was used to extract the intemuclear distances of several model crystalline compounds [92], In the past few years, this technique has proven to be very useful for the study of amyloid fibrils as well. For the Ure2p10 39 fibril samples containing 13C and 15N uniformly... 

In a hard-sphere system, the trajectories of particles are determined by momentum conserving binary collisions. The interactions between particles are assumed to be pair-wise additive and instantaneous. In the simulation, the collisions are processed one by one according to the order in which the events occur. For not too dense systems, the hard-sphere models are considerably faster than the soft-sphere models. Note that the occurrence of multiple collisions at the same instant cannot be taken into account. 

In the following, we focus on the soft-sphere method since this really is the workhorse of the DPMs. The reason is that it can in principle handle any situation (dense regimes, multiple contacts), and also additional interaction forces—such as van der Waals or electrostatic forces—are easily incorporated. The main drawback is that it can be less efficient than the hard-sphere model. 

It was at that time that Franck and Seitz proposed mechanisms for the multiplication and generation of vacancies by intersection of dislocations88 explaining the observed softness of crystals and providing models that were subsequently verified by the technique of decoration of dislocations.89... 

Figure 38. Multiple scattering calculation of the soft X-ray spectrum of different sizes of pherical InAs nanoparticles and InAs bulk (solid lines). The Feff 7 calculations reproduce major features and broadening, but do not model the details well. After Hamad etal. (1999).

SIMCA is an acronym for Statistical Isolinear Multiple Components Analysis, or Soft Independent Modelling of Class Analogy, or SIMilarographic Computer Analysis, or SIMple Classification Algorithm, or... 

Other workers [112, 113] have shown that a chemical equilibrium model of hydrocarbons based on an exponential-6 fluid model using Ross s soft-sphere perturbation theory is successful in reproducing the behavior of shocked hydrocarbons. Our model of the supercritical phase includes the species H2, CH4, C2H6, and C2H4. We have chosen model parameters to match both static compression isotherms and shock measurements wherever possible. The ability to match multiple types of experiments well increases confidence in the general applicability of our high-pressure equation of state model. 

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