23 research outputs found
Universal fluctuations in subdiffusive transport
Subdiffusive transport in tilted washboard potentials is studied within the
fractional Fokker-Planck equation approach, using the associated continuous
time random walk (CTRW) framework. The scaled subvelocity is shown to obey a
universal law, assuming the form of a stationary Levy-stable distribution. The
latter is defined by the index of subdiffusion alpha and the mean subvelocity
only, but interestingly depends neither on the bias strength nor on the
specific form of the potential. These scaled, universal subvelocity
fluctuations emerge due to the weak ergodicity breaking and are vanishing in
the limit of normal diffusion. The results of the analytical heuristic theory
are corroborated by Monte Carlo simulations of the underlying CTRW
Using Information Theory Approach to Randomness Testing
We address the problem of detecting deviations of binary sequence from randomness,which is very important for random number (RNG) and pseudorandom number generators (PRNG). Namely, we consider a null hypothesis H 0 that a given bit sequence is generated by Bernoulli source with equal probabilities of 0 and 1 and the alternative hypothesis H 1 that the sequence is generated by a stationary and ergodic source which di#ers from the source under H 0 . We show that data compression methods can be used as a basis for such testing and describe two new tests for randomness, which are based on ideas of universal coding. Known statistical tests and suggested ones are applied for testing PRNGs, which are practically used. Those experiments show that the power of the new tests is greater than of many known algorithms
Synthesis method of optimal substitution constructions based on the criterion of zero correlation between the output and input data vectors
How Much Can You Win When Your Adversary is Handicapped?
We consider infinite games where a gambler plays a coin-tossing game against an adversary. The gambler puts stakes on heads or tails, and the adversary tosses a fair coin, but has to choose his outcome according to a previously given law known to the gambler. In other words, the adversary is not allowed to play all infinite heads-tails-sequences, but only a certain subset F of them. We present an algorithm for the player which, depending on the structure of the set F , guarantees an optimal exponent of increase of the player's capital, independently on which one of the allowed heads-tails-sequences the adversary chooses. Using the known upper bound on the exponent provided by the maximum Kolmogorov complexity of sequences in F we show the optimality of our result