Related papers: On Algebraic Approaches for DNA Codes with Multipl…
Modern biological science produces vast amounts of genomic sequence data. This is fuelling the need for efficient algorithms for sequence compression and analysis. Data compression and the associated techniques coming from information…
Constrained coding is a fundamental field in coding theory that tackles efficient communication through constrained channels. While channels with fixed constraints have a general optimal solution, there is increasing demand for parametric…
An example of a nonspecific molecular bond is the affinity of any positive charge for any negative charge (like-unlike), or of nonpolar material for itself when in aqueous solution (like-like). This contrasts specific bonds such as the…
Motivated by applications in DNA-based data storage, constrained codes have attracted a considerable amount of attention from both academia and industry. We study the maximum cardinality of constrained codes for which the constraints can be…
A new construction is proposed for low density parity check (LDPC) codes using quadratic permutation polynomials over finite integer rings. The associated graphs for the new codes have both algebraic and pseudo-random nature, and the new…
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…
The problem of RNA secondary structure design (also called inverse folding) is the following: given a target secondary structure, one aims to create a sequence that folds into, or is compatible with, a given structure. In several practical…
The genetic code is the function from the set of codons to the set of amino acids by which a DNA sequence encodes proteins. Since the codons also influence the shape of the DNA molecule itself, the same sequence that encodes a protein also…
The design of crystal materials plays a critical role in areas such as new energy development, biomedical engineering, and semiconductors. Recent advances in data-driven methods have enabled the generation of diverse crystal structures.…
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…
Specific binding of proteins to DNA is one of the most common ways in which gene expression is controlled. Although general rules for the DNA-protein recognition can be derived, the ambiguous and complex nature of this mechanism precludes a…
The yearly global production of data is growing exponentially, outpacing the capacity of existing storage media, such as tape and disk, and surpassing our ability to store it. DNA storage - the representation of arbitrary information as…
The problem of reconstructing strings from their substring spectra has a long history and in its most simple incarnation asks for determining under which conditions the spectrum uniquely determines the string. We study the problem of coded…
The problem of string reconstruction based on its substrings spectrum has received significant attention recently due to its applicability to DNA data storage and sequencing. In contrast to previous works, we consider in this paper a setup…
Based on the theoretical neuroscience, G. Cotardo and A. Ravagnavi in \cite{CR} introduced a kind of asymmetric binary codes called combinatorial neural codes (CN codes for short), with a "matched metric" $\delta_{r}$ called asymmetric…
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 propose coding techniques that limit the length of homopolymers runs, ensure the GC-content constraint, and are capable of correcting a single edit error in strands of nucleotides in DNA-based data storage systems. In particular, for…
In many applications of shape analysis, lengths between some landmarks are constrained. For instance, biomolecules often have some bond lengths and some bond angles constrained, and variation occurs only along unconstrained bonds and…
The de Bruijn graph, its sequences, and their various generalizations, have found many applications in information theory, including many new ones in the last decade. In this paper, motivated by a coding problem for emerging memory…
DNA code design aims to generate a set of DNA sequences (codewords) with minimum likelihood of undesired hybridizations among sequences and their reverse-complement (RC) pairs (cross-hybridization). Inspired by the distinct hybridization…