Sequential parameterization

The parameterization process may be done sequentially or in a combined fashion. In the sequential method a certain class of compound, such as hydrocarbons, is parameterized first. These parameters are held fixed, and a new class of compound, for example alcohols and ethers, is then parameterized. Tins method is in line with the basic assumption of force fields parameters are transferable. The advantage is that only a fairly small number of parameters are fitted at a time. The ErrF is therefore a relatively low-dimensional function, and one can be reasonably certain that a good minimum has been found (although it may not be the global minimum). The disadvantage is that the final set of parameters necessarily provides a poorer fit (as defined from the value of the ErrF) than if all the parameters are fitted simultaneously. 

In the sequential strategy, a control (manipulated) variable profile is discretized over a time interval. The discretized control profile can be represented as a piecewise constant, a piecewise linear, or a piecewise polynomial function. The parameters in such functions and the length of time subinterval become decision variables in optimization problem. This strategy is also referred to a control vector parameterization (CVP). 

We now give some test results for the LCG with (parameterized) prime addend and a modified version of the LFG. Both of these generators performed acceptably in the sequential tests with 1011 random numbers. Preliminary results from other tests of PPRNG can also be found in the paper by Coddington [37]. 

These conclusions are also supported by the presented examples, but some additional trends should be pointed out. Effective virtual screening today includes a multitude of approaches, often applied in a sequential manner or integrated within a flexible workflow. There is no unique protocol for every virtual screening task -every problem is unique and requires careful validation, filtering, and parameterization in the beginning to result in a protocol with the potential to yield valuable hit lists after productive application to large databases. Extensive validation based on sample databases of known actives and decoy molecules is essential. 

OC/DO-problems can be solved very efficiently and reliably by combining the above problem discretization (piecewise control parameterization and multiple shooting state discretization) with a specifically tailored sequential quadratic programming (SQP) algorithm for the solution of the large, but structured NLP problem (2.3). Such a strategy has been implemented in the optimal control code MUSCOD [6, 13]. 

Process. An LNT process, whose the definition is included in listing 1.1, is an object that describe a behaviom, it can be parameterized by a list of formal gates, a list of formal variables and a list of formal exceptions. LNT allows to describe several behavioms such as sequential composition, non-deterministic assignment, conditional behaviom, non-deterministic choice and parallel composition. 

The first term accounts for bond stretching and compression (the term here is quadratic but could be a Morse function), the second accounts for angle bends, the third is a truncated Fourier expansion for torsions involving four sequentially connected atoms, the fourth term accounts for space exclusion and dispersion attraction and the final term approximately accounts for Coulomb interactions. A force field of this kind is a function of the positions of the atoms. It serves as an approximation to the quantum mechanical Bom-Oppenheimer potential energy surface (PES). It is parameterized by a combination of spectroscopic and calorimetric measurements, and by accurate quantum mechanical calculations. 

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