Related papers: On Counting Subsequences and Higher-Order Fibonacc…
It is shown that metric representation of DNA sequences is one-to-one. By using the metric representation method, suppression of nucleotide strings in the DNA sequences is determined. For a DNA sequence, an optimal string length to display…
Parts of DNA sequences known as exons and introns play very different role in coding and storage of genetic information. Here we show that their conducting properties are also very different. Taking into account long-range correlations…
DNA storage has emerged as an important area of research. The reliability of DNA storage system depends on designing the DNA strings (called DNA codes) that are sufficiently dissimilar. In this work, we introduce DNA codes that satisfy a…
The so called long range correlation properties of DNA sequences are studied using the variance analyses of the density distribution of a single or a group of nucleotides in a model independent way. This new method which was suggested…
A new set of DNA base-nucleic acid codes and their hypercomplex number representation have been introduced for taking the probability of each nucleotide into full account. A new scoring system has been proposed to suit the hypercomplex…
One of the central problems in the classification of individual test sequences (e.g. genetic analysis), is that of checking for the similarity of sample test sequences as compared with a set of much longer training sequences. This is done…
When considering binary strings, it's natural to wonder how many distinct subsequences might exist in a given string. Given that there is an existing algorithm which provides a straightforward way to compute the number of distinct…
The dominant approach to sequence generation is to produce a sequence in some predefined order, e.g. left to right. In contrast, we propose a more general model that can generate the output sequence by inserting tokens in any arbitrary…
Although the expenses associated with DNA sequencing have been rapidly decreasing, the current cost of sequencing information stands at roughly $120/GB, which is dramatically more expensive than reading from existing archival storage…
Fabrication of DNA nanostructures primarily follows two fundamental rules. First, DNA oligonucleotides mutually combine by Watson-Crick base pairing rules between complementary base sequences. Second, the geometrical compatibility of the…
As DNA data storage moves closer to practical deployment, minimizing sequencing coverage depth is essential to reduce both operational costs and retrieval latency. This paper addresses the recently studied Random Access Problem, which…
The sequence a_1,...,a_m is a common subsequence in the set of permutations S = {p_1,...,p_k} on [n] if it is a subsequence of p_i(1),...,p_i(n) and p_j(1),...,p_j(n) for some distinct p_i, p_j in S. Recently, Beame and Huynh-Ngoc (2008)…
Let $(F_n)_{n\ge 1}$ be the Fibonacci sequence. Define $P(F_n): = (\sum_{i=1}^n F_i)_{n\ge 1}$; that is, the function $P$ gives the sequence of partial sums of $(F_n)$. In this paper, we first give an identity involving $P^k(F_n)$, which is…
In the classic sequential testing problem, we are given a system with several components each of which fails with some independent probability. The goal is to identify whether or not some component has failed. When the test costs are…
Motivation: Low-complexity (LC) DNA sequences are compositionally repetitive sequences that are often associated with spurious homologous matches and variant calling artifacts. While algorithms for identifying LC sequences exist, they…
In DNA-based data storage, DNA codes with biochemical constraints and error correction are designed to protect data reliability. Single-stranded DNA sequences with secondary structure avoidance (SSA) help to avoid undesirable secondary…
Most DNA sequencing technologies are based on the shotgun paradigm: many short reads are obtained from random unknown locations in the DNA sequence. A fundamental question, studied in arXiv:1203.6233, is what read length and coverage depth…
A tandem duplication denotes the process of inserting a copy of a segment of DNA adjacent to its original position. More formally, a tandem duplication can be thought of as an operation that converts a string $S = AXB$ into a string $T =…
The prevalent approach to sequence to sequence learning maps an input sequence to a variable length output sequence via recurrent neural networks. We introduce an architecture based entirely on convolutional neural networks. Compared to…
The Stern diatomic sequence is closely linked to continued fractions via the Gauss map on the unit interval, which in turn can be understood via systematic subdivisions of the unit interval. Higher dimensional analogues of continued…