D sequences [1-15] are perhaps the simplest family of random sequences that subsumes other families such as shift register sequences [16]. In their ordinary form, d sequences are not computationally complex [2], but they can be used in a recursive form [8] that is much stronger from a complexity point of view. The basic method of the generating the binary d-sequences is given in [1]. The autoco...

The correlation between a random sequence and its transformed sequences is studied. In the case of a permutation operation or, in other word, the shuffling operation, it is shown that the correlation can be so small that the sequences can be regarded as independent random sequences. The applications to the Monte Carlo simulations are also given. This method is especially useful in the Ising Mon...

We consider evidence relevant to whether a (possibly idealized) physical process is producing its output randomly. For definiteness, we’ll consider a coinflipper C which reports “H” for a heads and “T” for a tails. By C producing its output “randomly,” we mean H and T have equal probability and trials are independent. If C produces its output randomly (in the above sense), then we’ll say that C...

We study the random Fibonacci tree, which is an infinite binary tree with non-negative numbers at each node defined as follows. The root consists of the number 1 with a single child also the number 1. Then we define the tree recursively in the following way: if x is the parent of y, then y has two children, namely |x−y| and x+y. This tree was studied by Benoit Rittaud [?] who proved that any pa...

Background: RNA plays key role in many aspects of biological processes and its tertiary structure is critical for its biological function. RNA secondary structure represents various significant portions of RNA tertiary structure. Since the biological function of RNA is concluded indirectly from its primary structure, it would be important to analyze the relations between the RNA sequences and t...

A subset A of the set [n] = f1; 2; : : : ; ng, jAj = k, is said to form a Sidon (or Bh) sequence, h 2, if each of the sums a1 + a2 + : : : + ah; a1 a2 : : : ah; ai 2 A, are distinct. We investigate threshold phenomena for the Sidon property, showing that if An is a random subset of [n], then the probability that An is a Bh sequence tends to unity as n ! 1 if kn = jAnj n1=2h, and that P(An is Si...

in this article we consider the sequences of sample and population covariance operators for a sequence of arrays of hilbertian random elements. then under the assumptions that sequences of the covariance operators norm are uniformly bounded and the sequences of the principal component scores are uniformly sumable, we prove that the convergence of the sequences of covariance operators would impl...