Related papers: On Counting Subsequences and Higher-Order Fibonacc…
The synthesis of DNA strands remains the most costly part of the DNA storage system. Thus, to make DNA storage system more practical, the time and materials used in the synthesis process have to be optimized. We consider the most common…
DNA synthesis is considered as one of the most expensive components in current DNA storage systems. In this paper, focusing on a common synthesis machine, which generates multiple DNA strands in parallel following a fixed supersequence,we…
In the recent years, DNA has emerged as a potentially viable storage technology. DNA synthesis, which refers to the task of writing the data into DNA, is perhaps the most costly part of existing storage systems. Accordingly, this high cost…
Fibonacci sequence, generated by summing the preceding two terms, is a classical sequence renowned for its elegant properties. In this paper, leveraging properties of generalized Fibonacci sequences and formulas for consecutive sums of…
Motivated by DNA based data storage system, we investigate the errors that occur when synthesizing DNA strands in parallel, where each strand is appended one nucleotide at a time by the machine according to a template supersequence. If…
This paper presents a probabilistic approach for DNA sequence analysis. A DNA sequence consists of an arrangement of the four nucleotides A, C, T and G and different representation schemes are presented according to a probability measure…
This paper introduces a new family of reconstruction codes which is motivated by applications in DNA data storage and sequencing. In such applications, DNA strands are sequenced by reading some subset of their substrings. While previous…
DNA-based storage offers unprecedented density and durability, but its scalability is fundamentally limited by the efficiency of parallel strand synthesis. Existing methods either allow unconstrained nucleotide additions to individual…
We dedicate this paper to investigate the most generalized form of Fibonacci Sequence, one of the most studied sections of the mathematical literature. One can notice that, we have discussed even a more general form of the conventional one.…
DNA sequences are prone to creating secondary structures by folding back on themselves by non-specific hybridization among its nucleotides. The formation of secondary structures makes the sequences chemically inactive towards synthesis and…
This paper introduces a new family of reconstruction codes which is motivated by applications in DNA data storage and sequencing. In such applications, DNA strands are sequenced by reading some subset of their substrings. While previous…
Consider two independent random strings having same length and taking values uniformly in a common finite alphabet. We study the order of the variance of the length of the longest common subsequences (LCS) of these strings when long blocks,…
DNA sequencing is the basic workhorse of modern day biology and medicine. Shotgun sequencing is the dominant technique used: many randomly located short fragments called reads are extracted from the DNA sequence, and these reads are…
We study the theoretical problem of synthesizing multiple DNA strands under spatial constraints, motivated by large-scale DNA synthesis technologies. In this setting, strands are arranged in an array and synthesized according to a fixed…
Let (F_n^{(k)})_{n\geq -(k-2)} be the k-generalized Fibonacci sequence, defined as the linear recurrence sequence whose first k terms are \(0, 0, \ldots, 0, 1\), and whose subsequent terms are determined by the sum of the preceding k terms.…
Large pools of synthetic DNA molecules have been recently used to reliably store significant volumes of digital data. While DNA as a storage medium has enormous potential because of its high storage density, its practical use is currently…
Composite DNA is a recent method to increase the base alphabet size in DNA-based data storage.This paper models synthesizing and sequencing of composite DNA and introduces coding techniques to correct substitutions, losses of entire…
The prevalent technique for DNA sequencing consists of two main steps: shotgun sequencing, where many randomly located fragments, called reads, are extracted from the overall sequence, followed by an assembly algorithm that aims to…
With recent high-throughput technology we can synthesize large heterogeneous collections of DNA structures, and also read them all out precisely in a single procedure. Can we use these tools, not only to do things faster, but also to devise…
Traditionally, we usually utilize the method of shotgun to cut a DNA sequence into pieces and we have to reconstruct the original DNA sequence from the pieces, those are widely used method for DNA assembly. Emerging DNA sequence…