Related papers: Reconstruction from Substrings with Partial Overla…
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…
Next-generation sequencing technologies generate millions of short sequence reads, which are usually aligned to a reference genome. In many applications, the key information required for downstream analysis is the number of reads mapping to…
In this paper, we propose a semi-supervised deep learning method for detecting the specific types of reads that impede the de novo genome assembly process. Instead of dealing directly with sequenced reads, we analyze their coverage graphs…
Sparse coding approximates the data sample as a sparse linear combination of some basic codewords and uses the sparse codes as new presentations. In this paper, we investigate learning discriminative sparse codes by sparse coding in a…
DNA emerges as a promising medium for the exponential growth of digital data due to its density and durability. This study extends recent research by addressing the \emph{coverage depth problem} in practical scenarios, exploring optimal…
In this paper, we study the Random Access Problem in DNA storage, which addresses the challenge of retrieving a specific information strand from a DNA-based storage system. In this framework, the data is represented by $k$ information…
In a DNA sequence, we have the celebrated Watson-Crick complement $\overline{T}=A$, $\overline{A}=T$, $\overline{C}=G$, and $\overline{G}=C$. Given an integer $m\ge 2$, a secondary structure in a DNA sequence refers to the existence of two…
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…
This paper studies the sequence reconstruction problem for a channel inspired by protein identification. We introduce a coloring channel, where a sequence is transmitted through a channel that deletes all symbols not belonging to a fixed…
The study of regenerating codes has advanced tremendously in recent years. However, most known constructions require large field size, and hence may be hard to implement in practice. By using notions from the theory of extension fields, we…
Large-scale deep learning models are known to memorize parts of the training set. In machine learning theory, memorization is often framed as interpolation or label fitting, and classical results show that this can be achieved when the…
We study an issue commonly seen with graph data analysis: many real-world complex systems involving high-order interactions are best encoded by hypergraphs; however, their datasets often end up being published or studied only in the form of…
Over the past two decades, a series of works have aimed at studying the problem of genome assembly: the process of reconstructing a genome from sequence reads. An early formulation of the genome assembly problem showed that genome…
Consider two or more strings $\mathbf{x}^1,\mathbf{x}^2,\ldots,$ that are concatenated to form $\mathbf{x}=\langle \mathbf{x}^1,\mathbf{x}^2,\ldots \rangle$. Suppose that up to $\delta$ deletions occur in each of the concatenated strings.…
Convolutional Neural Network (CNN) has gained state-of-the-art results in many pattern recognition and computer vision tasks. However, most of the CNN structures are manually designed by experienced researchers. Therefore, auto- matically…
Efficient continual learning in humans is enabled by a rich set of neurophysiological mechanisms and interactions between multiple memory systems. The brain efficiently encodes information in non-overlapping sparse codes, which facilitates…
Recent emergence of next-generation DNA sequencing technology has enabled acquisition of genetic information at unprecedented scales. In order to determine the genetic blueprint of an organism, sequencing platforms typically employ…
In the trace reconstruction problem, one seeks to reconstruct a binary string $s$ from a collection of traces, each of which is obtained by passing $s$ through a deletion channel. It is known that $\exp(\tilde O(n^{1/5}))$ traces suffice to…
In array-based DNA synthesis, multiple strands of DNA are synthesized in parallel to reduce the time cost from the sum of their lengths to the length their shortest common supersequences. To maximize the amount of information that can be…
We describe a strategy for constructing codes for DNA-based information storage by serial composition of weighted finite-state transducers. The resulting state machines can integrate correction of substitution errors; synchronization by…