Random number generation reproducibility

Figure 8.7 Fictitious results of replicate measurements of a quantity x, generated using an appropriate random number generator. The histograms show the fractions of measured values of x that fall within each bin. The bin width is chosen in each case so that several of the central bins contain some measured values, (a) results of 100 simulated experiments, (b) results of 1000 simulated experiments (the dashed curve represents the theoretical normal distribution o-(x) that was used to generate the plotted data by using it as a weighting function for a random number generator). Reproduced from Taylor, An Introduction to Error Analysis, University Science Books (1982), with permission.

The MCD-Program corresponds to the method described in Chap.6 The random number generator used here is ALEAT, of the mathematical library of the IRIS-50 computer. The MCD-program is described below and the complete listing is reproduced. The subroutine for computation of cartesian coordinates was realized by adaptation of the program written by Ray. ... 

A special kind of random noise, pseudo random noise, has the special property of not being really random. After a certain time interval, a sequence, the same pattern is repeated. The most suitable random input function used in CC is the Pseudo Random Binary Sequence (PRBS). The PRBS is a logical function, that has the combined properties of a true binary random signal and those of a reproducible deterministic signal. The PRBS generator is controlled by an internal clock a PRBS is considered with a sequence length N and a clock period t. It is very important to note that the estimation of the ACF, if computed over an integral number of sequences, is exactly equal to the ACF determined over an infinite time. 

Figure 5.30. Illustration of a poly(amidoamine-organosilicon) (PAMAMOS) dendrimer, with two generations of each PAMAM and organosihcon units. Although the PAMAMOS represents a block copolymer, an unhmited number of other variations that contain a random copolymer array, or varying dendron subunits, may also be synthesized. Reproduced with permission from Dvornic, P. R. Owen, M. J. Synthesis and Properties of Silicones and Silicone-Modified Materials, ACS Symposium Series 838,2002,236.

Figure 15. (Reproduced from http //astro.princeton.edu/ cen). Distribution of neutral gas at z = 3 from hydrodynamic cosmological simulation in a spatially flat, COBE-normalized, cold dark matter model with the cosmological parameters adopted in this article ( 1.1). The box size is 25Mpc/h (comoving) on the side, and the number of particles used in the simulation is 7683. The structure seen in this (and other similar simulations) reproduces very well the spectral properties of the Lya forest when artificial spectra are generated along random sightlines through the box.

In this step, recombination (crossover) and mutation operators are applied to the individuals selected for reproduction in the previous step. The number of chromosomes, which will be reproduced by crossover operation, as well as, crossover points, can be determined either deterministically by the user or randomly. For example, in case of one-point crossover (see for example in Fig. 11.4) the chromosomes of the parents are cut at some randomly chosen point and the resulting subchromosomes are swapped. As far as the mutation operator is concerned, the user gives the number of genes to be changed per generation. The points to be mutated are chosen either randomly or deterministically according to the accident scenario considered (see for example in Fig. 11.4). 

Figure 5 Reversed phase HPLC (linear gradient of 10-90% isopropanol in acetonitrile at 25°C) of natural (top) and rearranged (bottom) butterfat triacylglycerols as obtained with light-scattering detector. Peak identification by carbon and double bond number. (Reproduced with permission from Marai L, Kuksis A, and Myher JJ (1994) Reversed-phase liquid chromatography-mass spectrometry of the uncommon triacylglycerol structures generated by randomization of butteroil. Journal of Chromatography A 672 87-99.)...

The numbers in the last column of Table 19.3 show the probabilities of reproduction. Therefore, most likely members number 3 and 8 will not be reproduced, and members 1 and 6 may have two or more copies. Using a random reproduction process, the following population, arranged in pairs, could be generated... 

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