Random number generation combination generator

This is a technique developed during World War II for simulating stochastic physical processes, specifically, neutron transport in atomic bomb design. Its name comes from its resemblance to gambling. Each of the random variables in a relationship is represented by a distribution (Section 2.5). A random number generator picks a number from the distribution with a probability proportional to the pdf. After physical weighting the random numbers for each of the stochastic variables, the relationship is calculated to find the value of the independent variable (top event if a fault tree) for this particular combination of dependent variables (e.g.. components). 

To do the computations, we again use the random number generator of MATLAB to produce Normally-distributed random numbers with unity variance to represent the noise values of Er will then directly represent the S/N ratio of the data being evaluated. For the computations reported here, we use 100,000 synthetic values of the expression on the RHS of equation 44-76a to calculate the variance of, for each combination of conditions we investigate. 

The nine distinctly different factor combinations in Figure 13.13 were obtained from a random number generator. In this sense, the experimental design in Figure... 

P. L Ecuyer, Efficient and Portable Combined Random Number Generators, Common. ACM 31,742-774 (1988). 

The Marsaglia random number generator [Marsaglia et al. 1990] is known as a combination generator because it is constructed from two different generators. It has a period of about... 

We present results for two- and three-descriptor models addition of a fourth descriptor yielded no significant improvement in predictive accuracy. In the two-descriptor case there are only 276 possible input combinations, so we examine each explicitly, whereas, in the three-descriptor case there are 2024, so we use the genetic algorithm (GA) to optimize the descriptor selection. Use of the GA in the two-descriptor case gives models of comparable quality to the exhaustive search, but this test of the algorithm is not very stringent because the space of input combinations is small. Because both the GA and the NN depend on the random number generator seed, several trials were performed in each case (as detailed in Section IV.D.2). 

The Best (as Measured by r v) Five Two-Descriptor Models Obtained by Examining All Possible Combinations for Ten Different Random Number Generator Seeds ... 

The solution is obtained with the Monte Carlo method (cf. [31]). Using random numbers concrete values (realizations) of the random input parameters are generated. With this input the calculation is performed just as with the deterministic approach. This may lead to combinations of input parameters which result in the permissible stress for the bolts being exceeded and combinations where this does not occur. The calculation is repeated may times. The failure probability (support column failure) is assessed by dividing the number of failure cases by the total number of repetitions of the calculations. The latter are called trials. Figure 4.22 shows a schematic of the procedure. 

In a systematic search there is a defined endpoint to the procedure, which is reached whe all possible combinations of bond rotations have been considered. In a random search, ther is no natural endpoint one can never be absolutely sure that all of the minimum energ conformations have been found. The usual strategy is to generate conformations until n new structures can be obtained. This usually requires each structure to be generate many times and so the random methods inevitably explore each region of the conformc tional space a large number of times. 

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