Related papers: Levenshtein's Sequence Reconstruction Problem and …

DNA codes have garnered significant interest due to their utilization in digital media storage, cryptography, and DNA computing. In this paper, we first extend the results of constructing reversible group codes \cite{Cengellenmis} and…

Labeling of DNA molecules is a fundamental technique for DNA visualization and analysis. This process was mathematically modeled in [1], where the received sequence indicates the positions of the used labels. In this work, we develop error…

Levenshtein distance is a commonly used edit distance metric, typically applied in language processing, and to a lesser extent, in molecular biology analysis. Biological nucleic acid sequences are often embedded in longer sequences and are…

Earlier formulations of the DNA assembly problem were all in the context of perfect assembly; i.e., given a set of reads from a long genome sequence, is it possible to perfectly reconstruct the original sequence? In practice, however, it is…

The problem of reconstructing a sequence from the set of its length-$k$ substrings has received considerable attention due to its various applications in genomics. We study an uncoded version of this problem where multiple random sources…

The term Big Data is usually used to describe huge amount of data that is generated by humans from digital media such as cameras, internet, phones, sensors etc. By building advanced analytics on the top of big data, one can predict many…

The double digest problem is a common NP-hard approach to constructing physical maps of DNA sequences. This paper presents a new approach called the enhanced double digest problem. Although this new problem is also NP-hard, it can be solved…

Why do even the most powerful 7B-parameter embedding models struggle with simple retrieval tasks that the decades old BM25 handles with ease? Recent theory suggests that this happens because of a dimensionality bottleneck. This occurs when…

Analysis of molecular scale interactions and chemical structure offers an enormous opportunity to tune material properties for targeted applications. However, designing materials from molecular scale is a grand challenge owing to the…

Deep learning networks have shown state-of-the-art performance in many image reconstruction problems. However, it is not well understood what properties of representation and learning may improve the generalization ability of the network.…

In the information explosion era, the demand for high-density stable storage technologies is soaring. Multi-dimensional optical storage with femtosecond laser writing offers a potential solution for massive data storage. However, equipment…

Motivation: Next Generation Sequencing technologies revolutionized many fields in biology by enabling the fast and cheap sequencing of large amounts of genomic data. The ever increasing sequencing capacities enabled by current sequencing…

We investigate the structure and reconstruction complexity of Manacher arrays. First, we establish a combinatorial lower bound, proving that the number of rooted tandem repeat trees with $n+1$ genes exceeds the number of distinct Manacher…

Due to the redundant nature of DNA synthesis and sequencing technologies, a basic model for a DNA storage system is a multi-draw "shuffling-sampling" channel. In this model, a random number of noisy copies of each sequence is observed at…

Advances in DNA sequencing mean databases of thousands of human genomes will soon be commonplace. In this paper we introduce a simple technique for reducing the size of conventional indexes on such highly repetitive texts. Given upper…

We consider deletion correcting codes over a q-ary alphabet. It is well known that any code capable of correcting s deletions can also correct any combination of s total insertions and deletions. To obtain asymptotic upper bounds on code…

The paper describes an algorithm to compute a consensus sequence from a set of DNA sequences of approximatively identical length generated by 3rd sequencing generation technologies. Its purpose targets DNA storage and is guided by specific…

Sequencing a DNA strand, as part of the read process in DNA storage, produces multiple noisy copies which can be combined to produce better estimates of the original strand; this is called trace reconstruction. One can reduce the error rate…

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…

Neural machine learning methods, such as deep neural networks (DNN), have achieved remarkable success in a number of complex data processing tasks. These methods have arguably had their strongest impact on tasks such as image and audio…