Generational distance

The performance of any multi-objective optimization algorithm can be qualitatively deduced from looking at the non-dominated front. To compare two algorithms one needs a quantitative measure. One such measure is Inverted Generational Distance (IGD) introduced by Veldhuizen and Lament (2000). IGD is defined by... 

Inverted Generational Distances for problems ZDTl, ZDT2 and ZDT3 are given in Table 5.1 for a better understanding. The true Pareto sets for ZDT test problems are represented by 100 solutions on the Pareto front. It is seen that IGD for the non-dominated solutions obtained by SAEA is smaller than that of NSGA-II. Other metrics can also be used to determine and compare results between different optimization algorithms. 

Table 5.1 Inverted Generational Distance for problems ZDTl, ZDT2, and ZDT3...

We recommend that experimental uncertainties in the coordinates be assessed by Eq. (10) and the vibration/rotation contributions be assessed by the Costain rule [Eq. (14)1 or by first moment or product of inertia relations. Then, either the procedure introduced by Tobiason and Schwendeman20 should be used to propagate the uncertainties into distances or angles, or the two contributions should be added together and used with Eq. (18) to generate distance and angle uncertainties. 

With this expression, 99% of the generated distances lie in the interval [do - 3a, do + 3o]. Figure 1.1.13 shows that, as expected, the mobility is reduced when the standard deviation increases, whatever the magnitude of electric field might be. However, this reduction is very moderate and points to the weak impact of such... 

A measurement procedure has been developed that allows to determine the mass of the inclusions as well as their locations with respect to radius, angle, and depth (2). For the depth determination use is made of the approximate 1/R dependence of the magnetic field strength from the distance R to the inclusion When in a first measurement at a small lift off an inclusion is detected, the measurement is repeated at an increased lift off From the signal ratio the depth can be calculated or seen from a diagram like fig. 5a which was generated experimentally. After that, from calibration curves like fig. 5b the absolute value of the signal leads to the mass of the inclusion. 

The signal comparison function has been impieinented and tested during a steam generator tube inspection. A formal test in the real-life context was successfully done with a simple rule (parameters phase and amplitude) based on the central frequency for the distance signal. 

The electrostatic potential generated by a molecule A at a distant point B can be expanded m inverse powers of the distance r between B and the centre of mass (CM) of A. This series is called the multipole expansion because the coefficients can be expressed in temis of the multipole moments of the molecule. With this expansion in hand, it is... 

This method relies on the simple principle that the flow of ions into an electrolyte-filled micropipette as it nears a surface is dependent on the distance between the sample and the mouth of the pipette [211] (figure B 1.19.40). The probe height can then be used to maintain a constant current flow (of ions) into the micropipette, and the technique fiinctions as a non-contact imaging method. Alternatively, the height can be held constant and the measured ion current used to generate the image. This latter approach has, for example, been used to probe ion flows tlirough chaimels in membranes. The lateral resolution obtainable by this method depends on the diameter of the micropipette. Values of 200 nm have been reported. 

Metzler W J, Hare D R and Pardi A 1989 Limited sampling of conformational space by the distance geometry algorithm implications for structures generated from NMR data Bioohemistry 2S 7045-52... 

The greatest value of molecular dynamic simulations is that they complement and help to explain existing data for designing new experim en ts. Th e sun ulation s are in creasin gly n sefn I for stnictural relinemcnt of models generated from XMR, distance geometry, an d X-ray data. 

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