Apparent randomness

Figure C3.6.10 Defect-mediated turbulence in tire complex Ginzburg-Landau equation, (a) The phase, arg( ), as grey shades, (b) The amplitude [A], witli a similar color coding. In tire left panel topological defects can be identified as points around which one finds all shades of grey. Note tire apparently random spatial pattern of amplitudes.

The irregular part of the motion comes from the apparently random bombardment of the particle by surrounding fluid molecules i.e. Brownian motion. The systematic part derives from the action of various external influences -mechanical, electrical and gravitational for example - the strength of which change in time and place. 

All of the structures shown in Figures 7.2 and 7.3 are D-configurations, and the D-forms of monosaccharides predominate in nature, just as L-amino acids do. These preferences, established in apparently random choices early in evolution, persist uniformly in nature because of the stereospecificity of the enzymes that synthesize and metabolize these small molecules. 

Today we work confidently with the rows and columns of the periodic table. Yet less than 150 years ago, only about half of all elements known today had been discovered, and these presented a bewildering collection of chemical and physical properties. The discoveiy of the patterns that underlie this apparent randomness is a tale of inspired chemical detective work. 

Quite early on (p. 361) in this discussion of linear free energy relationships consideration was restricted to the side-chain reactions of m- and p-substituted benzene derivatives. The reactions of o-substituted benzene derivatives, and indeed of aliphatic compounds, were excluded because of the operation of steric and other effects, which led to non-linear, or even to apparently random, plots. 

In order to assess how the bulk of the arene influences the structure of such stacked assemblies, the adducts of 137 with toluene, o-, m-, and -xylenes, and mesitylene have been synthesized and structurally characterized.236 These adducts tend to form extended binary stacks similar to those found in [137-benzene], The substituted benzene molecules adopt an apparently random orientation with respect to the trinuclear core of 137, thus suggesting that the binding might be... 

The bunching pattern in T plots differ from cycles in two respects in bunching, the changes are precipitous, and they do not have a characteristic repetition frequency. The sudden systematic error shifts are due to apparently random events. These events are most commonly associated with calibration errors and/or operator technique. Rotation of laboratory personnel can produce this pattern if the individuals follow different procedures. Operator related systematic errors can be detected by plotting points with separate ssrmbols for different operators. Bunching may also appear when reagent lots are changed. 

The puzzle we had to solve consists in deep analyses of the possible direct relationships which must exist between the 8 apparently random sets of aziridinyl conformations within Figs. 50 to 56. In other words, we had to attempt a reduction of the 5-, 6 and... 

This continual replacement of liquid is readily visible with talc particles sprinkled on to the interface though stationary on the average (if the stirrers in phases 1 and 2 are contra-rotated at appropriate relative speeds), they make occasional sudden, apparently random, local movements, which indicate that considerable replacement of the interface is occurring by liquid impelled into the interface from the bulk. Spontaneous interfacial turbulence, associated with such processes as the transfer of acetone from solvent to water, may further increase the rate of transfer by a factor of two or three times (44, 48, 51). Other systems (48), such as benzoic acid transferring (in either direction) between water and toluene, give transfer rates only about 50% of those calculated by Eq. (26), suggesting either that this equation is not valid or that there is an interfacial resistance. This point is discussed in detail below. 

Finally, on a still larger scale, about the scale of a small town, there will be isopleths (lines of constant concentration) of our tracer that look something like those given in the last illustration of Figure 6.15. If enough particle and lense effects have occurred with an apparent randomness to our tracer cloud, then the cloud disperses in a manner similar to that illustrated. 

In a record obtained by the patch clamp technique, the channel is closed for much of the time (i.e. no current flows across the patch of membrane that contains it), but at irregular intervals the channel opens for a short time, producing a pulse of current. Successive current pulses are always of much the same size in any one experiment, suggesting that the channel is either open or closed, and not half open (there are exceptions to this rule). The durations of the pulses, however, and the intervals between them, vary in an apparently random fashion from one pulse to the next. Hence the openings and closings of channels are stochastic events. This means that, as with many other molecular processes, we can predict when they will occur only in terms of statistical probabilities. But one of the most useful features of the patch clamp method is that it allows observation of these stochastic changes in single ion channels as they actually happen individual protein molecules can be observed in action. 

These experiments had been performed in my laboratory but the literature is full of such examples. Why do others not see the same phenomenon and acknowledge the problem Perhaps they were primed to look at their results from the platform of the old prejudices. Frank Plumpton Ramsey20 and his theory tells us in brief that any large enough, apparently random, collection of items will contain an orderly substructure, and that the complexity of possible substructures depends upon the number of members of a basic set. 

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