Related papers: Haplotype Assembly: An Information Theoretic View
A new approach to estimate the Shannon entropy of a long-range correlated sequence is proposed. The entropy is written as the sum of two terms corresponding respectively to power-law (\emph{ordered}) and exponentially (\emph{disordered})…
Haplotypes, the global patterns of DNA sequence variation, have important implications for identifying complex traits. Recently, blocks of limited haplotype diversity have been discovered in human chromosomes, intensifying the research on…
This paper studies two problems that are motivated by the novel recent approach of composite DNA that takes advantage of the DNA synthesis property which generates a huge number of copies for every synthesized strand. Under this paradigm,…
We consider the problem of assembling a sequence based on a collection of its substrings observed through a noisy channel. The mathematical basis of the problem is the construction and design of sequences that may be discriminated based on…
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…
In the past several years, the problem of genome assembly has received considerable attention from both biologists and computer scientists. An important component of current assembly methods is the scaffolding process. This process involves…
Short-read DNA sequencing instruments can yield over 1e+12 bases per run, typically composed of reads 150 bases long. Despite this high throughput, de novo assembly algorithms have difficulty reconstructing contiguous genome sequences using…
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…
Long reads produced by third-generation sequencing technologies are used to construct an assembly (i.e., the subject's genome), which is further used in downstream genome analysis. Unfortunately, long reads have high sequencing error rates…
Pedigrees, or family trees, are graphs of family relationships that are used to study inheritance. A fundamental problem in computational biology is to find, for a pedigree with $n$ individuals genotyped at every site, a set of…
This paper studies the problem of encoding messages into sequences which can be uniquely recovered from some noisy observations about their substrings. The observed reads comprise consecutive substrings with some given minimum overlap. This…
DNA has emerged as a promising alternative for long-term data storage due to its high capacity, durability, and low-energy potential. However, storing data in DNA presents several challenges. First, it requires complex and costly…
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…
The repeat content and heterozygosity rate of a target genome are important factors in determining the feasibility of achieving a complete telomere-to-telomere assembly. The mathematical relationship between the required coverage and read…
In shotgun sequencing, the input string (typically, a long DNA sequence composed of nucleotide bases) is sequenced as multiple overlapping fragments of much shorter lengths (called \textit{reads}). Modelling the shotgun sequencing pipeline…
Relation of genome sizes to organisms complexity is still described rather equivocally. Neither the number of genes (G-value), nor the total amount of DNA (C-value) correlates consistently with phenotype complexity. Using information theory…
In this paper, fundamental limits in sequencing of a set of closely related DNA molecules are addressed. This problem is called pooled-DNA sequencing which encompasses many interesting problems such as haplotype phasing, metageomics, and…
In this paper we present a collection of results pertaining to haplotyping. The first set of results concerns the combinatorial problem of reconstructing haplotypes from incomplete and/or imperfectly sequenced haplotype data. More…
Genome assembly, the process of reconstructing a long genetic sequence by aligning and merging short fragments, or reads, is known to be NP-hard, either as a version of the shortest common superstring problem or in a Hamiltonian-cycle…
Accurate identification of haplotypes in sequenced human genomes can provide invaluable information about population demography and fine-scale correlations along the genome, thus empowering both population genomic and medical association…