16 papers · ranked by Valyu relevance
Biswajyoti Sahu, Tuomo Hartonen, Päivi Pihlajamaa, Bei Wei + 9 more
DNA can determine where and when genes are expressed, but the full set of sequence determinants that control gene expression is unknown. Here, we measured the transcriptional activity of DNA sequences that represent an ~100 times larger sequence space than the human genome using massively parallel reporter assays…
Guo-Niu Han
For a sequence $\mathbf a=(a_0,a_1,\dots)$ we define its dilated Hankel determinant $\ddot{H}_n(\mathbf a)=\det(a_{2i+j})_{0\le i,j\le n-1}$, the minor of the infinite Hankel matrix $(a_{i+j})$ formed from the even-indexed rows and the first $n$ columns. We prove that, for a broad class of sequences, $\ddot{H}_n$…
Inbal Zigdon, Miri Carmi, Sagie Brodsky, Zohar Rosenwaser + 2 more
'Naama Barkai' 'Felix Jonas'] RNA-binding proteins (RBPs) are composed of RNA-binding domains (RBDs) often linked via intrinsically disordered regions (IDRs). Structural and biochemical analyses have shown that disordered linkers contribute to RNA binding by orienting the adjacent RBDs and also characterized certain…
Christophe Reutenauer, Jeffrey Shallit
| 1. | Introduction | 2 | | --- | --- | --- | | Part 1. | Group of Christoffel matrices | 3 | | 2. | Burrows-Wheeler matrix of a Christoffel word | 3 | | 3. | Group of Christoffel matrices | 5 | | 4. | Consequences | 7 | | Part 2. | Sturmian determinants | 9 | | 5. | Determinants of Sturmian factors | 9 | | | 6.…
İbrahim GÖKCAN, Ali Hikmet Değer
and Special Number Sequences Authors: ['İbrahim GÖKCAN' 'Ali Hikmet Değer'] The research aims to construct a new type of matrix called the Fibonacci-Hessenberg-Lorentz matrix by multiplying Fibonacci-Hessenberg matrices with Lorentz matrix multiplication. The study will start by examining the properties of Hessenberg…
Karl Dilcher, Lin Jiu
Hankel determinants of sequences related to Bernoulli and Euler numbers have been studied before, and numerous identities are known. However, when a sequence is shifted by one unit, the situation often changes significantly. In this paper we use classical orthogonal polynomials and related methods to prove a general…
Hsu-Lin Chien, Sen‐Peng Eu, Tung-Shan Fu
For any integer m ≥ 2 and a set V ⊂ {1, . . . , m}, let (m, V ) denote the union of congruence classes of the elements in V modulo m. We study the Hankel determinants for the number of Dyck paths with peaks avoiding the heights in the set (m, V ). For any set V of even elements of an even modulo m, we give an explicit…
Paweł J. Szabłowski
We recall the definition and the properties of a moment sequence and recall that all real sequences that have a finite rank of its Hankel matrix (see definition in the sequel) satisfy a homogeneous linear equation with constant coefficients. Then we analyze cases when a difference equation with constant coefficients…
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…
Vitaly Kuryavyi
The universe of possible nucleotide sequences expands combinatorially with sequence length, vastly exceeding the fraction sampled by real genomes. Yet genomic sequences exhibit reproducible compositional symmetries and recurrent structural motifs, indicating that biological sequence space is shaped by strong organizing…
Jessica K. Bonnie, Omar Ahmed, Ben Langmead
Genome assembly databases are growing rapidly. The sequence content in each new assembly can be largely redundant with previous ones, but this is neither conceptually nor algorithmically easy to measure. We propose new methods and a new tool called DandD that addresses the question of how much new sequence is gained…
Authors not listed
A framework for catalysis based on categorical aperture selection rather than temporal acceleration is presented. Traditional catalysis theory describes catalysts as agents that accelerate reactions by lowering activation energies, implicitly treating time as the fundamental variable and reaction rate enhancement as…
Maciej Zakarczemny, Małgorzata Zajęcka, Stefano Lonardi
The paper contains a discussion on mathematical modifying and redesigning DNA with the use of Markov chains. We give a simple mathematical technique for overwriting missing parts of DNA. With a certain probability (without even knowing the function of the missing codon) we can find a synonymous codon, so that there is…
Clemens Heuberger, Daniel Krenn, Gabriel F. Lipnik
For an integer $q\ge 2$, a q-recursive sequence is defined by recurrence relations on subsequences of indices modulo some powers of q. In this article, q-recursive sequences are studied and the asymptotic behavior of their summatory functions is analyzed. It is shown that every q-recursive sequence is q-regular in the…
Hao-Che Peng, Shrijaa Mohan, Muhammad T. Huq, Julie A. Bull + 7 more
Experimental methods to determine transition temperatures for individual base pair melting events in DNA duplexes are lacking despite intense interest in these thermodynamic parameters. Here, we determine the dimensions of the thymine (T) C2=O stretching vibration when it is within the DNA duplex via iso-topic…
Ke Chen, Vinamratha Pattar, Mingfu Shao
Sequence similarity estimation is essential for many bioinformatics tasks, including functional annotation, phylogenetic analysis, and overlap graph construction. Alignment-free methods aim to solve large-scale sequence similarity estimation by mapping sequences to more easily comparable features that can approximate…