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Related papers: Substring Density Estimation from Traces

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Motivated by studies of data retrieval in polymer-based storage systems, we consider the problem of reconstructing a multiset of binary strings that have the same length and the same weight from the compositions of their prefixes and…

Discrete Mathematics · Computer Science 2024-11-07 Yaoyu Yang , Zitan Chen

Learning from data in the presence of outliers is a fundamental problem in statistics. In this work, we study robust statistics in the presence of overwhelming outliers for the fundamental problem of subspace recovery. Given a dataset where…

Data Structures and Algorithms · Computer Science 2020-02-11 Prasad Raghavendra , Morris Yau

This work studies problems in data reconstruction, an important area with numerous applications. In particular, we examine the reconstruction of binary and non-binary sequences from synchronization (insertion/deletion-correcting) codes.…

Information Theory · Computer Science 2017-03-09 Frederic Sala , Ryan Gabrys , Clayton Schoeny , Lara Dolecek

In this paper we study the reconstruction of binary sparse signals from partial random circulant measurements. We show that the reconstruction via the least-squares algorithm is as good as the reconstruction via the usually used program…

Information Theory · Computer Science 2020-06-29 Sandra Keiper

The Shortest Common Superstring problem (SCS) consists, for a set of strings S = {s_1,...,s_n}, in finding a minimum length string that contains all s_i, 1<= i <= n, as substrings. While a 2+11/30 approximation ratio algorithm has recently…

Data Structures and Algorithms · Computer Science 2018-05-02 Tristan Braquelaire , Marie Gasparoux , Mathieu Raffinot , Raluca Uricaru

In this paper we study a variant of string pattern matching which deals with tuples of strings known as \textit{multi-track strings}. Multi-track strings are a generalisation of strings (or \textit{single-track strings}) that have primarily…

Data Structures and Algorithms · Computer Science 2019-12-02 Carl Barton , Ewan Birney , Tomas Fitzgerald

In the paper, the Levenshtein's sequence reconstruction problem is considered in the case where at most $t$ substitution errors occur in each of the $N$ channels and the decoder outputs a list of length $\mathcal{L}$. Moreover, it is…

Information Theory · Computer Science 2022-11-17 Ville Junnila , Tero Laihonen , Tuomo Lehtilä

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…

Information Theory · Computer Science 2023-04-21 Yonatan Yehezkeally , Daniella Bar-Lev , Sagi Marcovich , Eitan Yaakobi

Mean-based reconstruction is a fundamental, natural approach to worst-case trace reconstruction over channels with synchronization errors. It is known that $\exp(O(n^{1/3}))$ traces are necessary and sufficient for mean-based worst-case…

Information Theory · Computer Science 2021-10-14 Mahdi Cheraghchi , Joseph Downs , João Ribeiro , Alexandra Veliche

The sequence reconstruction problem was proposed by Levenshtein in 2001. In this model, a sequence from a code is transmitted over several channels, and the decoder receives the distinct outputs from each channel. The main problem is to…

Information Theory · Computer Science 2025-10-16 Xiang Wang , Han Li , Fang-Wei Fu

We propose a list-decoding scheme for reconstruction codes in the context of uniform-tandem-duplication noise, which can be viewed as an application of the associative memory model to this setting. We find the uncertainty associated with…

Information Theory · Computer Science 2021-06-30 Yonatan Yehezkeally , Moshe Schwartz

Reconstructing weighted networks from partial information is necessary in many important circumstances, e.g. for a correct estimation of systemic risk. It has been shown that, in order to achieve an accurate reconstruction, it is crucial to…

Physics and Society · Physics 2017-03-07 Tiziano Squartini , Giulio Cimini , Andrea Gabrielli , Diego Garlaschelli

Given a random binary picture $P_n$ of size $n$, i.e., an $n\times n$ grid filled with zeros and ones uniformly at random, when is it possible to reconstruct $P_n$ from its $k$-deck, i.e., the multiset of all its $k\times k$ subgrids? We…

Combinatorics · Mathematics 2025-01-29 Bhargav Narayanan , Corrine Yap

The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a communication scenario where the sender transmits a codeword from some codebook and the receiver obtains multiple noisy reads of the codeword. Motivated by…

Information Theory · Computer Science 2020-04-14 Johan Chrisnata , Han Mao Kiah , Eitan Yaakobi

In this paper, we consider the Levenshtein's sequence reconstruction problem in the case where the transmitted codeword is chosen from $\{0,1\}^n$ and the channel can delete up to $t$ symbols from the transmitted codeword. We determine the…

Information Theory · Computer Science 2025-11-05 Fengxing Zhu

We explore whether medium-resolution stellar spectra can be reconstructed from photometric observations, taking advantage of the highly compressible nature of the spectra. We formulate the spectral reconstruction as a least-squares problem…

Solar and Stellar Astrophysics · Physics 2015-05-19 A. Asensio Ramos , C. Allende Prieto

In this paper, we consider the problem of reconstructing trees from traces in the tree edit distance model. Previous work by Davies et al. (2019) analyzed special cases of reconstructing labeled trees. In this work, we significantly expand…

Computational Complexity · Computer Science 2022-01-14 Thomas Maranzatto

We generalize the problem of reconstructing strings from their substring compositions first introduced by Acharya et al. in 2015 motivated by polymer-based advanced data storage systems utilizing mass spectrometry. Namely, we see strings as…

Combinatorics · Mathematics 2025-04-02 Antoine Dailly , Tuomo Lehtilä

Graphs are a powerful tool for analyzing large data sets, but many real-world phenomena involve interactions that go beyond the simple pairwise relationships captured by a graph. In this paper we introduce and study a simple combinatorial…

Data Structures and Algorithms · Computer Science 2025-11-25 Elise Tate , Joshua A. Grochow

Recent development in the reconstruction of the large-scale structure (LSS) has seen significant improvement in restoring the linear baryonic acoustic oscillation (BAO) from at least the non-linear matter field. This outstanding performance…

Cosmology and Nongalactic Astrophysics · Physics 2019-01-23 Xin Wang , Ue-Li Pen