Random binary sequences are required in many applications of modern communication systems and in designing reliable circuits. However, truly random sequences are often associated with extremely high costs, and are therefore infeasible to use. Deterministically generated sequences that pass certain statistical tests suggested by random sequences are often used instead and are referred to as pseu...

Generalized Fibonacci-like sequences appear in finite difference approximations of the Partial Differential Equations based upon replacing partial differential equations by finite difference equations. This paper studies properties of the generalized Fibonacci-like sequence . It is shown that this sequence is periodic with the period ( ) if | | .

MOTIVATION Algorithm development for finding typical patterns in sequences, especially multiple pseudo-repeats (pseudo-periodic regions), is at the core of many problems arising in biological sequence and structure analysis. In fact, one of the most significant features of biological sequences is their high quasi-repetitiveness. Variation in the quasi-repetitiveness of genomic and proteomic tex...

Binary (periodic) aperiodic complementary sequences have been studied extensively due to their wide range of applications in engineering, for example in optics, radar and communications. They are also linked to topics in coding theory, combinatorics and Boolean functions. Complementary sequences have been generalized either by being defined over larger alphabets or by being defined from one dim...

When humans are presented with information, they tend to search for structure in the information-to encode it, to organize it, to look for regularities. The existence of this structure-seeking behavior can be seen in the behavior of subjects predicting a random sequence of binary events and in the behavior of subjects predicting more highly structured sequences. (A random sequence is a colloqui...

For each positive integer n ≥ 2, a new approach to expressing real numbers as sequences of nonnegative integers is given. The n = 2 case is equivalent to the standard continued fraction algorithm. For n = 3, it reduces to a new iteration of the triangle. Cubic irrationals that are roots of x3 +kx2 +x−1 are shown to be precisely those numbers with purely periodic expansions of period length one....