Related papers: On Counting Subsequences and Higher-Order Fibonacc…
The emerging field of DNA storage employs strands of DNA bases (A/T/C/G) as a storage medium for digital information to enable massive density and durability. The DNA storage pipeline includes: (1) encoding the raw data into sequences of…
Sequencing by synthesis is the underlying technology for many next-generation DNA sequencing platforms. We developed a new model, the fixed flow cycle model, to derive the distributions of sequence length for a given number of flow cycles…
Labeling of DNA molecules is a fundamental technique for DNA visualization and analysis. This process was mathematically modeled in [1], where the received sequence indicates the positions of the used labels. In this work, we develop error…
Composite DNA is a recent novel method to increase the information capacity of DNA-based data storage above the theoretical limit of 2 bits/symbol. In this method, every composite symbol does not store a single DNA nucleotide but a mixture…
A supersequence over a finite set is a sequence that contains as subsequence all permutations of the set. This paper defines an infinite array of methods to create supersequences of decreasing lengths. This yields the shortest known…
Periodic patterns play the important regulatory and structural roles in genomic DNA sequences. Commonly, the underlying periodicities should be understood in a broad statistical sense, since the corresponding periodic patterns have been…
DNA self-assembly is an important tool that has a wide range of applications such as building nanostructures, the transport of target virotherapies, and nano-circuitry. Tools from graph theory can be used to encode the biological process of…
Storing data in DNA is being explored as an efficient solution for archiving and in-object storage. Synthesis time and cost remain challenging, significantly limiting some applications at this stage. In this paper we investigate efficient…
In this paper, we show that the concatenation of the Fibonacci sequence is \textit{normal} in base $10$, meaning every string of a given length, $k$, occurs as frequently as every other string of length $k$ (there are as many $1$'s as $2$'s…
Motivation: Array Comparative Genomic Hybridization (aCGH) is used to scan the entire genome for variations in DNA copy number. A central task in the analysis of aCGH data is the segmentation into groups of probes sharing the same DNA copy…
We consider a novel approach of measuring the homology of DNA sequences based of the variety of optimal alignments in the longest common subsequence sense. The proposed approach is compared with BLAST in measuring the homology of four…
A method for encoding information in DNA sequences is described. The method is based on the precision-resolution framework, and is aimed to work in conjunction with a recently suggested terminator-free template independent DNA synthesis…
We look at a family of meta-Fibonacci sequences which arise in studying the number of leaves at the largest level in certain infinite sequences of binary trees, restricted compositions of an integer, and binary compact codes. For this…
Shannon information (SI) and its special case, divergence, are defined for a DNA sequence in terms of probabilities of chemical words in the sequence and are computed for a set of complete genomes highly diverse in length and composition.…
While most current high-throughput DNA sequencing technologies generate short reads with low error rates, emerging sequencing technologies generate long reads with high error rates. A basic question of interest is the tradeoff between read…
We provide an overview of current approaches to DNA-based storage system design and accompanying synthesis, sequencing and editing methods. We also introduce and analyze a suite of new constrained coding schemes for both archival and random…
Biological data mainly comprises of Deoxyribonucleic acid (DNA) and protein sequences. These are the biomolecules which are present in all cells of human beings. Due to the self-replicating property of DNA, it is a key constitute of genetic…
We study statistical properties of DNA chains of thirteen microbial complete genomes. We find that the power spectrum of several of the sequences studied flattens off in the low frequency limit. This implies that the correlation length in…
Topological and metric entropies of the DNA sequences from different organisms were calculated. Obtained results were compared each other and with ones of corresponding artificial sequences. For all envisaged DNA sequences there is a…
We consider the problem of storing and retrieving information from synthetic DNA media. The mathematical basis of the problem is the construction and design of sequences that may be discriminated based on their collection of substrings…