Related papers: The DNA Coverage Depth Problem: Duality, Weight Di…
An exact-match overlap graph of $n$ given strings of length $\ell$ is an edge-weighted graph in which each vertex is associated with a string and there is an edge $(x,y)$ of weight $\omega = \ell - |ov_{max}(x,y)|$ if and only if $\omega…
Living in the age of the digital media explosion, the amount of data that is being stored increases dramatically. However, even if existing storage systems suggest efficiency in capacity, they are lacking in durability. Hard disks, flash,…
DNA computing, a nontraditional computing mechanism, provides a feasible and effective method for solving NP-hard problems because of the vast parallelism and high-density storage of DNA molecules. Although DNA computing has been exploited…
The seriation problem seeks to reorder a set of elements given pairwise similarity information, so that elements with higher similarity are closer in the resulting sequence. When a global ordering consistent with the similarity information…
DNA has immense potential as an emerging data storage medium. The principle of DNA storage is the conversion and flow of digital information between binary code stream, quaternary base, and actual DNA fragments. This process will inevitably…
The storage capacity of a graph measures the maximum amount of information that can be stored across its vertices, such that the information at any vertex can be recovered from the information stored at its neighborhood. The study of this…
We consider error-correcting coding for DNA-based storage. We model the DNA storage channel as a multi-draw IDS channel where the input data is chunked into $M$ short DNA strands, which are copied a random number of times, and the channel…
The hull of a linear code is defined as the intersection of the code and its dual. This concept was initially introduced to classify finite projective planes. The hull plays a crucial role in determining the complexity of algorithms used to…
We study how much a linear program (LP) can be compressed when solved repeatedly, given prior knowledge about its objective function. Existing data-driven projection methods learn low-dimensional surrogate LPs with approximate…
Linear codes can be employed to construct authentication codes, which is an interesting area of cryptography. The parameters of the authentication codes depend on the complete weight enumerator of the underlying linear codes. In order to…
Finding the minimum distance of linear codes is an NP-hard problem. Traditionally, this computation has been addressed by means of the design of algorithms that find, by a clever exhaustive search, a linear combination of some generating…
Neural Architecture Search (NAS), aiming at automatically designing neural architectures by machines, has been considered a key step toward automatic machine learning. One notable NAS branch is the weight-sharing NAS, which significantly…
In the context of classification problems, Deep Learning (DL) approaches represent state of art. Many DL approaches are based on variations of standard multi-layer feed-forward neural networks. These are also referred to as deep networks.…
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…
We present a generalization of Walsh-Hadamard transform that is suitable for applications in Coding Theory, especially for computation of the weight distribution and the covering radius of a linear code over a finite field. The transform…
Even though Deep Neural Networks (DNNs) are widely celebrated for their practical performance, they possess many intriguing properties related to depth that are difficult to explain both theoretically and intuitively. Understanding how…
In modern age, the increasing complexity of computation and communication technology is leading us towards the necessity of new paradigm. As a result, unconventional approach like DNA coding theory is gaining considerable attention. The…
Motivated by applications in DNA-based storage, we study explicit encoding and decoding schemes of binary strings satisfying locally balanced constraints, where the $(\ell,\delta)$-locally balanced constraint requires that the weight of any…
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 determination of the weight distribution of linear codes has been a fascinating problem since the very beginning of coding theory. There has been a lot of research on weight enumerators of special cases, such as self-dual codes and…