Iterative localization

The practical approaches for protein geometry refinement rely on iterative local linearizations of the full nonlinear optimization problem. The procedure is to step along the potential surface in a direction that decreases the energy. Such iterative approaches in Cartesian coordinates may be symbolized by... 

In the other hand, We may distinguish between two categories [26] the first consists in designing a solver including components from a meta-heuristic into another one, while the second combines meta-heuristics with other techniques t q)ical of fields such as operations research and artificial intelligence. A prominent represent of the first category is the use of trajectory methods into population based techniques or the use of a specific local search method into a more general trajectory method such as iterated local search. 

Three dimensional localization requires the onset times from at least 4 sensors. The most common approach is to use an iterative localization algorithm, which requires the linearization of the problem. To do this, a first guess or trial h q)ocenter xo, yo, zo, to) is required. This first guess hypo-center must lie relatively close to the tme hypocenter, which is not known. The travel time residuals r, of the first guess h5qx)center are then a linear fimction of the correction in h q)ocentral distance (Havskov et al. 2002). 

Using the same theoretical example as mentioned above. Fig. 6.16 illustrates the effect of a systematically erroneous arrival time on the source localization. For an array of 40 by 40 AE-sources the theoretical arrival times at the four sensors were calculated. To introduce an error, 5 ps were added to the arrival times of Sensor 1. The iterative localization algorithm then yields AE-source locations that minimize the travel time residuals and thus distribute the error in arrival times over all sensors. Fig. 6.16 top depicts the difference between the actual and the calculated AE-source location, on the left side as error vectors and on the right side as a density function of the error value. Fig. 6.16 bottom left shows a density function of the minimized travel time residuals (mean value over all sensors) and bottom right the major axis of the error ellipsoid. In most cases the size and orientation of calculated location uncertainties (bottom right) corresponds well to the actual error vector (top left). 

Application and Practical Considerations of the Iterative Localization Method... 

Besides the iterative localization method, which is based on a linearization of the problem, and still most frequently used of the methods, several nonlinear approaches exist for 3-D localization. Three methods will be summarized in the following. The referenced papers contain further information about nonlinear source localization methods. 

Viswanathan N, Chu C (2005) FastPlace efficient analytical placement using cell shifting, iterative local refinement and a hybrid net model. IEEE Trans, on CAD 24(5) 722-733... 

P. E. Maslen and M. Head-Gordon, Chem. Phys. Lett., 283, 102 (1998). Non-Iterative Local... 

The basic structure of an iterative local optimization algorithm is one of greedy descent . It is based on one of the following two algorithmic frameworks line-search or trust-region methods. Both are found throughout the literature and in software packages and are essential components of effective... 

Programs to integrate first order differential equations require"nsolv" local atend odebl2 function(feqs,tvals,u,up,upp) local j, neq, t, h, h2,h2sq,hs,hx,hy,hz Local variables local sol,ynn,yn,jfirst, , , 0 local nit,nitt 0,0 Number of iterations local neq u... 

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