20 papers · ranked by Valyu relevance
Noam Teyssier, Alexander Dobin
Modern genomics produces billions of sequencing records per run, which are typically stored as gzip-compressed FASTQ files. While this format is widely used, it is not optimal for high-throughput processing due to its reliance on single-threaded decompression and sequential parsing of irregularly sized records. This…
Jean-Marc Girault, Sébastien Ménigot, Alessandro Giuliani
Today, the palindromic analysis of biological sequences, based exclusively on the study of “mirror” symmetry properties, is almost unavoidable. However, other types of symmetry, such as those present in friezes, could allow us to analyze binary sequences from another point of view. New tools, such as symmetropy and…
Chunlei Fan, Qun Ding, Boris Ryabko
Due to the influence of finite calculation accuracy and binary quantization method, the performance of chaotic binary sequences has been degraded in varying degrees, and some sequences emerge as multi-period phenomena. Aiming at the problem that it is difficult to accurately detect this phenomenon, this paper proposes…
Enrique Canessa
A comprehensive study of the properties of finite (0,1) binary systems from the mathematical viewpoint of quantum theory is presented. This is a quantum-inspired extension of the GenomeBits model to characterize observed genome sequences, where a complex wavefunction $\psi _{n}$ is considered as an analogous…
Maria F. Dal Martello, Keiji Ota, Dana E. Pietralla, Laurence T. Maloney
'Laurence T. Maloney'] We measured human ability to detect texture patterns in a signal detection task. Observers viewed sequences of 20 blue or yellow tokens placed horizontally in a row. They attempted to discriminate sequences generated by a random generator (“a fair coin”) from sequences produced by a disrupted…
Tuvi Etzion
—Binary self-dual sequences have been considered and analyzed throughout the years, and they have been used for various applications. Motivated by a construction for single-track Gray codes, we examine the structure and recursive constructions for binary and non-binary self-dual sequences. The feedback shift registers…
Christoph Lange, Andreas Ahrens, Yadu Krishnan Krishnakumar, Olaf Grote + 1 more
'Olaf Grote' 'Hyoungshick Kim'] Randomness plays an important role in data communication as well as in cybersecurity. In the simulation of communication systems, randomized bit sequences are often used to model a digital source information stream. Cryptographic outputs should look more random than deterministic in…
Г. В. Еремин
Dyck paths are among the most heavily studied Catalan families. In the paper we are dealing with the minimal numbering of Dyck paths, with the resulting numbers, the terms of the OEIS sequence A036991, which we have called Dyck numbers. We consider the successor function on the Dyck numbers, closed formulas are…
Bernard Costa, Marcus V. C. Baldo, Carolina Feher da Silva
Adaptive human behaviour depends on the ability to detect regularities and probabilistic structures within a noisy environment. Repeated binary choice tasks, in which individuals predict one of two possible outcomes, have long served as a fundamental tool for investigating learning, reward processing, and…
Eric Chen, Adam Ge, Andrew Kalashnikov, Tanya Khovanova + 7 more
'Evin Liang' 'Mira Lubashev' 'Matthew Qian' 'Rohith Raghavan' 'Benjamin Taycher' 'Samuel J. Wang'] In this paper, we generalize a lot of facts from John Conway and Alex Ryba's paper, The extra Fibonacci series and the Empire State Building, where we replace the Fibonacci sequence with the Tribonacci sequence. We study…
Authors not listed
Sequence is the critical determinant of macromolecular function, yet current polymer design approaches often optimize monomer composition and ratios while ignoring sequence. This creates poorly defined design spaces for active learning that miss the vast combinatorial landscape of sequence possibilities. We introduce…
Miguel Beltrá, Sara D. Cardell, Verónica Requena
The binary binomial sequences correspond to the diagonals of the Pascal's triangle modulo 2. They have interesting properties such as they form a basis of the linear space of all binary sequences with period a power of 2. Other properties of these sequences (period, linear complexity, construction rules or relations…
Seongjun Seo, Thi Hong Nhung Vu, Anshula Tandon, Suyoun Park + 3 more
DNA is emerging as a promising medium for ultra-dense, long-term digital data storage, yet sequence design remains hindered by homopolymer formation and compositional bias, which compromise synthesis, sequencing, and decoding accuracy. Here, the study introduces a quantitative framework to evaluate and optimize…
Xuncai Zhang, Baonan Qi, Ying Niu, Lenore Cowen
In nature, the DNA molecule consists of two complementary polymer chains, and the complementary nature of the DNA double-stranded structure enables it to form a stable double-helix structure, which can ensure the accuracy and stability of the genetic information in the transmission process. Inspired by the…
Bartosz Sobolewski, Maciej Ulas
In this note we investigate the solutions of certain meta-Fibonacci recurrences of the form f(n) = f(n − f(n − 1)) + f(n − 2) for various sets of initial conditions. In the case when f(n) = 1 for n ≤ 1, we prove that the resulting integer sequence is closely related to the function counting binary partitions of a…
Daniel B. Shapiro
Set h0i! = 1, and note that n 0 f = n n f = 1. Also, n k f is undefined when k > n and when n or k is negative. (Some authors set n k f = 0 when k > n.) That factorial formula helps explain the symmetry:
Humberto Pereira, Paulo César Silva, M. Wayne Davis, Louis Abraham + 3 more
Synthetic biology involves combining different DNA fragments, each containing functional biological parts, to address specific problems. Fundamental gene-function research often requires cloning and propagating DNA fragments, such as those from the iGEM Parts Registry or Addgene, typically distributed as circular…
Babu Bassa
In this communication the author describes a software tool named "ChameleonSort". The software program, developed by the present author is useful in the sorting of biological sequence variants like those accumulating mutations while diverging from the common ancestors. Examples include viral protein variants, protein…
Roland Wittler
To index or compare sequences efficiently, often k-mers, i.e., substrings of fixed length k, are used. For efficient indexing or storage, k-mers are often encoded as integers, e.g., applying some bijective mapping between all possible σ^k^ k-mers and the interval [0, σ^k^ −1], where σ is the alphabet size. In many…
N. J. A. Sloane
Until 1973 there was no database of integer sequences. Someone coming across the sequence 1, 2, 4, 9, 21, 51, 127, . . . would have had no way of discovering that it had been studied since 1870 (today these are called the Motzkin numbers, and form entry A001006 in the database). Everything changed in 1973 with the…