Random-selection

If two variables are dependent, the value chosen in the simulation for the dependent variable can be linked to the randomly selected value of the first variable using the defined correlation. 

The extent and manner of NDE applied in different shipyards has been the subject of a recently completed exercise within LR. The exercise involved randomly selected shipyards building ship types which included oil tankers, bulk carriers, gas carriers, container ships, ro-ro and general cargo ships. The variation in extent of applied NDE that was observed is summarised in Table 1. 

This ensemble is a weighted superposition of NVT ensembles with different values, of N. As a rule of tiuiinb, a typical MC sweep consists of N attempted moves, each of which is chosen randomly to be (i) a displacement (liandled exactly as in constant-AfTMC) (ii) the creation of a new particle at a randomly selected position (iii) the destruction of a randomly selected particle from the system. The probabilities for attempting creation and destniction must be equal (for consistency with what follows), but they need not be equal to the probability for attempting displacement (although they often are). 

As an alternative to the random selection of particles it is possible to move the atom sequentially (this requires one fewer call to the random number generator per iteration) Alternatively, several atoms can be moved at once if an appropriate value for the maximun displacement is chosen then this may enable phase space to he covered more efficiently. 

Lonally, the templates were chosen by trial and error or exhaustive enumeration. A itafional method named ZEBEDDE (ZEolites By Evolutionary De novo DEsign) en developed to try to introduce some rationale into the selection of templates et al. 1996 Willock et al. 1997]. The templates are grown within the zeolite by an iterative inside-out approach, starting from a seed molecule. At each jn an action is randomly selected from a list that includes the addition of new (from a library of fragments), random translation or rotation, random bond rota-ing formation or energy minimisation of the template. A cost function based on erlap of van der Waals spheres is used to control the growth of the template ale ... 

Compute the probability of finding a randomly selected experimental measurement between the limits of 0.5 standard deviations from the mean. 

If we randomly select a single member from a population, what will be its most likely value This is an important question, and, in one form or another, it is the fundamental problem for any analysis. One of the most important features of a population s probability distribution is that it provides a way to answer this question. 

The population standard deviation for the amount of aspirin in a batch of analgesic tablets is known to be 7 mg of aspirin. A single tablet is randomly selected, analyzed, and found to contain 245 mg of aspirin. What is the 95% confidence interval for the population mean ... 

The second complication is that the values of z shown in Table 4.11 are derived for a normal distribution curve that is a function of O, not s. Although is an unbiased estimator of O, the value of for any randomly selected sample may differ significantly from O. To account for the uncertainty in estimating O, the term z in equation 4.11 is replaced with the variable f, where f is defined such that f > z at all confidence levels. Thus, equation 4.11 becomes... 

A second example is also informative. When samples are obtained from a normally distributed population, their values must be random. If results for several samples show a regular pattern or trend, then the samples cannot be normally distributed. This may reflect the fact that the underlying population is not normally distributed, or it may indicate the presence of a time-dependent determinate error. For example, if we randomly select 20 pennies and find that the mass of each penny exceeds that of the preceding penny, we might suspect that the balance on which the pennies are being weighed is drifting out of calibration. 

Example What is the prohahihty that an appointed special committee of 4 has no female members when the members are randomly selected from a candidate group of 10 males and 7 females ... 

Count data, based on a random selection of individuals or items which are classified according to two different criteria, can be statistically analyzed through the distribution. The purpose of this analysis is to determine whether the respective criteria are dependent. That is, is the product preferred because of a particular characteristic ... 

If X is a continuous variable and the interval ranges are made smaller and smaller, a smooth cui ve will eventually result. The area under such a cui ve between X and Xo represents the probabihty that a randomly selected item will have a value of x lying in the range X to Xo-This is the information that is desired. 

The opinions of the experts, however obtained, provide a basis for plotting a frequency or probability distribution curve. If the relative Frequency is plotted as ordinate, the total area under the cui ve is unity. The area under the cui ve between two values of the quantity is the probability that a randomly selected value will fall in the range between the two values of the quantity. These probabilities are mere estimates, and their reliability depends on the skill of the forecasters. 

The area under the cui ve of f z) is unity if the abscissa extends from minus infinity to plus infinity. The area under the cui ve between Z and Zo is the probability that a randomly selected value of x will lie in the range Z and r2, since this is the relative frequency with which that range of values would be represented in an infinite number of trials. 

An alternative method, proposed by Andersen [23], shows that the coupling to the heat bath is represented by stochastic impulsive forces that act occasionally on randomly selected particles. Between stochastic collisions, the system evolves at constant energy according to the normal Newtonian laws of motion. The stochastic collisions ensure that all accessible constant-energy shells are visited according to their Boltzmann weight and therefore yield a canonical ensemble. 

In the basic metric matrix implementation of the distance constraint technique [16] one starts by generating a distance bounds matrix. This is an A X y square matrix (N the number of atoms) in which the upper bounds occupy the upper diagonal and the lower bounds are placed in the lower diagonal. The matrix is Ailed by information based on the bond structure, experimental data, or a hypothesis. After smoothing the distance bounds matrix, a new distance matrix is generated by random selection of distances between the bounds. The distance matrix is converted back into a 3D confonnation after the distance matrix has been converted into a metric matrix and diagonalized. A new distance matrix... 

Successful measurement of machine vibration requires more than a transducer randomly selected, installed, and a piece of wire to carry the signal to the analyzer. When the decision to monitor vibration is made, three choices of measurement are available (1) displacement, (2) velocity, and... 

We examined the role of vector percolation in the fracture of model nets at constant strain and subjected to random bond scission, as shown in Fig. 11 [1,2]. In this experiment, a metal net of modulus Eo containing No = 10" bonds was stressed and held at constant strain (ca. 2%) on a tensile tester. A computer randomly selected a bond, which was manually cut, and the relaxation of the net modulus was measured. The initial relaxation process as a function of the number of bonds cut N, could be well described by the effective medium theory (EMT) via... 

If an assembly is destructively inspected, the verification film is used to identify potential problem areas for particular attention. These areas and others randomly selected are cross-sectioned to determine bondline thickness (Fig. 22), bond details are peeled apart to inspect for voids and honeycomb core bonds are... 

The MC method can be implemented by a modification of the classic Metropolis scheme [25,67]. The Markov chain is generated by a three-step sequence. The first step is identical to the classic Metropolis algorithm a randomly selected molecule i is displaced within a small cube of side length 26r centered on its original position... 

A standard Metropolis algorithm is used, whereby an attempted move of a randomly selected particle in a random direction Ax e [-1/2,1/2], Ay e [-1/2,1/2], Az G [-1/2,1/2] is accepted according to the standard Metropolis procedure [57] described above. The above displacement widths ensure a reasonably high acceptance rate A of the moves, of the order of... 

A reaction is simulated by making random selections from the grid. From a table of random numbers, a two-digit random number is selected. If the cell corresponding to this number is occupied by an A, the A is crossed off (it reacts ) and a B is written in the corresponding space in the B grid. If the random number identifies a cell that does not contain an A or that contains a crossed-off A, no reaction occurs and no action is taken. 

Any combination of first-order reactions can be simulated by extension of this procedure. Reversible reactions add only the feature that reacted species can be regenerated from their products. Second-order reactions introduce a new factor, for now two molecules must each be independently selected in order that reaction occur in the real situation the two molecules are in independent motion, and their collision must take place to cause reaction. We load the appropriate numbers of molecules into each of two grids. Now randomly select from the first grid, and then, separately, randomly select from the second grid. If in both selections a molecule exists at the respective selected sites, then reaction occurs and both are crossed out if only one of the two selections results in selection of a molecule, no reaction occurs. (Of course, if pseudo-first-order conditions apply, a second-order reaction can be handled just as is a first-order reaction.)... 

---