Imagine a sequence in which the first letter comes from a binary alphabet, the second letter can be chosen on an alphabet with 10 elements, the third letter can be chosen on an alphabet with 3 elements and so on. When such a sequence can be called random? In this paper we offer a solution to the above question using the approach to randomness proposed by Algorithmic Information Theory. 1 Varyin...

Allosteric nucleic acid ligases have been used previously to transform analyte-binding into the formation of oligonucleotide templates that can be amplified and detected. We have engineered binary deoxyribozyme ligases whose two components are brought together by bridging oligonucleotide effectors. The engineered ligases can 'read' one sequence and then 'write' (by ligation) a separate, distinc...

We investigate some attractive features of the 1-D sequence of pixels produced by the peano traversal of an image. We introduce two new hardware operations called bit-spreaded-meshing and its inverse bit-collation to produce and invert the sequence in real-time. A compact binary tree built using this sequence at its base implicitly contains the well known quadtree of the image also. The binary ...

A non-decreasing sequence of positive integer weights P = {p1, . . . , p2, pn} is called k-ordered if an intermediate sequence of weights produced by Huffman algorithm for initial sequence P on i-th step satisfies the following conditions: p (i) 2 = p (i) 3 , i = 0, k; p (i) 2 < p (i) 3 , i = k + 1, n − 3. Let T be a binary tree of size n and M = M(T ) be a set of such sequences of positive int...

An efficient algorithm is presented for computing the kerror linear complexity of a binary sequence with period 2p, where 2 is a primitive root modulo p. The new algorithm is a generalization of an algorithm for computing the k-error linear complexity of a binary sequence with period p presented by Wei, Chen, and Xiao.

The number of binary strings of length n containing no substrings consisting of r consecutive ones is examined and shown to be given in terms of a well known integer sequence namely, the r-Fibonacci sequence. In addition, difference equations for the number of zeros and the total number of runs within these binary strings are derived. Mathematics Subject Classification: Primary 11B39, Secondary...

The constant modulus algorithm (CMA) can misconverge when the received two-dimensional (2-D) signal is derived from encoding a binary PN sequence. The distortion of the probabilistic symmetry of the transmitted constellation can be controlled by careful selection of the underlying binary PN sequence, thereby influencing the convergence behavior of CMA.

This paper discusses the linear complexity property of binary sequences generated using matrix recurrence relation defined over Z4. Generally algorithm to generate random number is based on recursion with seed value/values. In this paper a linear recursion sequence of matrices or vectors over Z4 is generated from which random binary sequence is obtained. It is shown that such sequences have lar...

ABSTRACT The impact of stellar rotation on the morphology star cluster colour–magnitude diagrams is widely acknowledged. However, physics driving distribution equatorial velocities main-sequence turn-off stars as yet poorly understood. Using Gaia Data Release 2 photometry and new Southern African Large Telescope medium-resolution spectroscopy, we analyse intermediate-age ($\sim 1\text{-}{\rm Gy...

The sequence counting the number of unique tournaments with n people is the same as the sequence counting non-tracking binary strings corresponding to n − 2 radar observations with the tracking rule “3 out of 5 with loss 2.” This fact allows us to build a bijection between unique tournaments and non-tracking binary strings.