A sequence is called perfect if its autocorrelation function is a delta function. In this paper, we give a new definition of autocorrelation function: generalized even and odd periodic autocorrelation, and generalized even and odd periodic cyclically conjugated autocorrelation. In particular, we study a special case of autocorrelation function called cyclically conjugated autocorrelation functi...

Correspondence: homidan@kfupm. edu.sa Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, P. O. Box 119, Saudi Arabia Abstract Hankel operators and Hankel transforms are required in a number of applications. This article proves a number of theorems that efficiently and accurately approximates a function using Hankel transforms and Hankel sum....

jpHMM is a very accurate and widely used tool for recombination detection in genomic sequences of HIV-1. Here, we present an extension of jpHMM to analyze recombinations in viruses with circular genomes such as the hepatitis B virus (HBV). Sequence analysis of circular genomes is usually performed on linearized sequences using linear models. Since linear models are unable to model dependencies ...

In 1996 Arquès and Michel [1996. A complementary circular code in the protein coding genes. J. Theor. Biol. 182, 45-58] discovered the existence of a common circular code in eukaryote and prokaryote genomes. Since then, circular code theory has provoked great interest and underwent a rapid development. In this paper we discuss some theoretical issues related to the synchronization properties of...

In this paper, homogeneous, wavelength shift biosensor is designed for sensing the protein concentration using two dimensional Photonic Crystal Ring Resonator (PCRR). The sensor is designed to monitor the protein concentration from 0% to 100%. The proposed sensor is composed of periodic Si rods embedded in an air host with a circular PCRR that is placed between the inline quasi waveguides. It i...

We report the use of an engineered ribozyme to produce a circular human exon in vitro. Specifically, we have designed a derivative of a yeast self-splicing group II intron that is able to catalyze the formation of a circular exon encoding the first kringle domain (K1) of the human tissue plasminogen activator protein. We show that the circular K1 exon is formed with high fidelity in vitro. Furt...

Many proteins with unusual structural properties are comprised of multiple repeating amino acid sequences and are often fractious to expression in recombinant systems. To facilitate recombinant production of such proteins for structural and engineering studies, we have produced circular messenger RNAs with infinite open reading frames. We show that a circular mRNA containing a simple green fluo...

De Bruijn sequences are circular strings of length 2 whose substrings are the binary strings of length n. Our focus is on de Bruijn sequences for binary strings that have the same density (number of 1s). We construct circular strings of length ( n−1 d )

The linear complexity of sequences is an important measure of the cryptographic strength of key streams used in stream ciphers. The instability of linear complexity caused by changing a few symbols of sequences can be measured using k-error linear complexity. In their SETA 2006 paper, Fu, Niederreiter, and Su [3] studied linear complexity and 1-error linear complexity of 2-periodic binary seque...