Random sequence generator seeded

A random sequence generator starts from a seed and produces a new Sequence of output bits whenever it receives a clock pulse. It is only a pseudorandom sequence however, as the same seed will always produce the same following sequence. 

Figure 7.19 Random sequence generator with external seed.

The random sequence generator has particularly demonstrated die use of the procedure as bodi a concurrent and sequential statement. The function itself is quite simple. A loadable seed value has enabled the use of three-state buffers plus the effect of a bidirectional signal to be demonstrated. The optimization statistics clearly hig ighted the effect that these buffers have on the performance of the circuit. 

In modern software packages random number generators should work satisfactorily. However, if seeds are set manually, procedures should ensure that repetition of sequences is avoided. 

The above search was conducted with the seed value of the MATLAB random number generator set to zero, its default value when MATLAB is invoked. To repeat the search with a different random step sequence, enter the command rand( seed ,z) where z is the desired seed value. Although the length of the search will vary somewhat with different random number sequences, convergence to a region very close to the global optimum should occur provided the initial parameters, particularly j8 and o, are appropriate for the problem at hand. 

In many circumstances, we desired to change the random sequence of retention times and amplitudes produced by the random number generator. This was accomplished by allocating two unique numbers at the start of a program run as the random number seeds. The random sequence is unique for each different Initial seed Input. The random number generation of noise Is programmed to be Independent of the generation of retention times and peak amplitudes. 

Cycle Parameterization. Another scheme makes use of the fact that some PRNGs have more than one cycle. If we choose the seeds carefully, then we can ensure that each random sequence starts out in a different cycle, and so two sequences will not overlap. Thus the seeds are parameterized (i.e., sequence i gets a seed from cycle i, the sequence number being the parameter that determines its cycle). This is the case for the lagged fibonacci generator described in the next section. 

The random generator seed completely determines the sequence of the pseudorandom numbers that will be used for random events in simulations. Depending on the platform the sofiware is used on, the random generator seed may be set globally. This has to be taken into account when running simulation simultaneously. 

The difficulty with any random number generator is that there is often some rhythm or pattern to the numbers that will start to be significant if the numbering sequence is maintained for long enough. Such a pattern may be difficult to spot, but it will always be present because, once a number is repeated, the cycle restarts. One method of addressing this problem is to restart the sequence occasionally with a new seed value, and possibly with a new algorithm. 

Random numbers are defined as a sequence of numbers which lack any pattern, unlike pseudorandom numbers which starting from an arbitrary seed state, wiU tend to repeat after a certain period. In simulations, random numbers are constantly generated to model stochastic processes and other events any correlation between random numbers will have the effect of biasing the results with an unphysical correlation. In the Appendices (Sect. B.I) statistical tests were first carried out to ensure that no bias was detected in the algorithm adopted for this work. The analysis of the statistical tests showed that the random number generator was capable of producing the required level of randoumess required for this work. 

The nature of the inherent statistical variation is most easily examined for separate stochastic realizations of additional virtuaP network sections (using the same parameters, but varying the value of the seed initiation for generation of sequences of random numbers). Three results are presented in Table 2, using nominal seed values of 1, 2, and 3. Seed 1 was already used for the theoretical sections in Table 1. The results for the additional seeds, 2 and 3, are consistent with the expected degree of variation amongst the repeat stochastic realizations. 

A statistical analysis of the peak counts obtained from the simulated chromatograms was made as follows. We changed the random number sequence, by means of the seed change previously described, to generate random changes In component retention times and amplitudes while holding constant component number, zone width, and peak capacity. This procedure. In essence, mimicked the Injection of different samples with the same component number and zone width onto a column. A mean peak count and standard deviation at each of the different peak capacities were calculated. The means and standard deviations of the peak counts were fit by a least squares analysis to Equation 11 with a proper transformation of the standard deviations from an exponential to a linear function (5). From the value of the least squares slope and Intercept, an estimated component number was calculated. 

The c sequence requires one initial seed value and the x sequence requires 97 initial seeds (which should themselves be reasonably random). These can be supplied by the user but in the published algorithm these 97 values were obtained from another combination generator comprising a lagged Fibonacci generator and a congruential algorithm. 

A pseudorandom number generator is a function that takes a short random seed and outputs a longer bit sequence that appears random. To be cryptographically secure, the output of a pseudorandom number generator should be computationally indistinguishable from a random string. In particular, given a short prefix of the sequence, it should be computationally infeasible to predict the rest of the se-... 

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