Random effect of noise

The presence of a non-zero dark reading, E0, will, of course, cause an error in the value of r computed. However, this is a systematic error and therefore is of no interest to us here we are interested only in the behavior of random variables. Therefore we set E0s and Eqj. equal to zero and note, if T as described in equation 41-1 represents the true value of the transmittance, then the value we obtain for a given reading, including the instantaneous random effect of noise, is... 

Response Of course we used noise-free data. Otherwise we could not be sure that the effects we see are due to the characteristics we impose on the data, rather than the random effects of the noise. When anyone does an actual, physical experiment and takes real readings, the noise level or the signal-to-noise ratio is a consideration of paramount importance, and any experimenter normally takes great pains to reduce the noise as much as possible, for just that reason. Why shouldn t we do the same in a computer experiment ... 

There is, however, something unexpected about Figure 44-1 la-1. That is the decrease in absorbance noise at the very lowest values of S/N, i.e., those lower than approximately Er = 1. This decrease is not a glitch or an artifact or a result of the random effects of divergence of the integral of the data such as we saw when performing a similar computation on the simulated transmission values. The effect is consistent and reproducible. In fact, it appears to be somewhat similar in character to the decrease in computed transmittance we observed at very low values of S/N for the low-noise case, e.g., that shown in Figure 43-6. 

Stochastic simulations confirm the existence of bifurcation values of the control parameters bounding a domain in which sustained oscillations occur. The effect of noise diminishes as the number of molecules increases. Only when the maximum numbers of molecules of mRNA and protein become smaller than a few tens does noise begin to obliterate the circadian rhythm. The robustness of circadian rhythms with respect to molecular noise is enhanced when the rate of binding of the repressor molecule to the gene promoter increases [128]. Conditions that enhance the resistance of genetic oscillators to random fluctuations have been investigated [130]. 

It should be emphasized that this way of including fluctuations has no other justification than that it is convenient and bypasses a description of the noise sources, compare IX.4. It may provide some qualitative insight into the effect of noise, but does not describe its actual mechanism. For instance, fluctuations in the pumping should give rise to randomness in the coefficient a, rather than to an additive term. Yet the equation (7.6) has been the subject of extensive study and it is famous in statistical mechanics under the name of generalized Ginzburg-Landau equation. It may well serve us as an illustration for a stochastic process.510... 

Averaging is a least-squares process that reduces the effects of noise, if the noise is zero-mean and fairly random [10], and the moving-average filter removes high-frequency noise well. It is less successful at removing low-frequency noise, since these nonzero-mean variations are less likely to be affected by the averaging. It also... 

A second facility that is sometimes useful is the random number generator function. There are several possible distributions, but the most usual is the normal distribution. It is necessary to specify a mean and standard deviation. If one wants to be able to return to the distribution later, also specify a seed, which must be an integer number. Figure A. 15 illustrates the generation of 10 random numbers coming from a distribution of mean 0 and standard deviation 2.5 placed in cells A1 -A10 (note that the standard deviation is of the parent population and will not be exactly the same for a sample). This facility is very helpful in simulations and can be employed to study die effect of noise on a dataset. 

Noise The random fluctuation in an electrical signal which can be further categorized as thermal noise, shot noise, flicker noise, burst noise, and avalanche noise, based on the effect of noise generation ... 

Noise is a random phenomenon its instantaneous value cannot be known. Thus, statistical concepts are employed to determine the effects of noise on a circuit. If e (t) is a noise voltage, then its root-mean-square (rms) value E is given by... 

There was a logical progression of technology development from continuous to piezoelecttic ink jet. Designers of continuous ink-jet systems ensure that the ink stream breaks into drops of constant size and frequency by applying vibrational energy with piezoelecttic crystals at the natural frequency of drop formation. This overcomes the effects of any random forces from noise, vibrations, or air currents. 

Figure 44-9a-l shows what happens to the noise level, for the same condition of constant sample transmittance as a function of S/N, for different values of sample transmittance. As we see, in the low noise regime the noise has the behavior we have derived for it. However, the effect of the exaggeration of the random variations very quickly takes over, and in the high noise regime there is virtually no difference in the... 

Fig. 30(b) are better resolved than those of Fig. 29(b), yet the artifacts are no worse. The major effect of the noise for all cases seems to be the introduction of randomly located low-amplitude artifacts (over and above those obtained for the noise-free case). Note also that the degradation and restoration operations affect each spectral line the same way, regardless of its wavelength. 

Protection of quantum states from the influence of noise is important. It has been shown that the alternating transport of a EEC generated by the fast-forward driving field suppresses the influence of a fluctuating random potential on the EEC [47], The EEC is kept undisturbed for a longer time than is characteristic of the simple trapping with a stationary potential because the effective potential, which the quanmm state feels, becomes uniform when the transport velocity is sufficiently large. 

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