20 papers · ranked by Valyu relevance
Iksoo Huh, Isabel Mendizabal, Taesung Park, Soojin V. Yi + 1 more
'Ilya Ioshikhes'] Recent advances in epigenomics have made it possible to map genome-wide regulatory regions using empirical methods. Subsequent comparative epigenomic studies have revealed that regulatory regions diverge rapidly between genome of different species, and that the divergence is more pronounced in…
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, $\ddot{H}_n$…
Durmuş Bozkurt
The generalized sequence of numbers is defined by Wn = pWn−1 + qWn−2 with initial conditions W0 = a and W1 = b for a, b, p, q ∈ Z and n ≥ 2, respectively. Let Wn = circ(W1, W2, . . . , Wn). The aim of this paper is to establish some useful formulas for the determinants and inverses of Wn using the nice properties of…
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…
T. C. Dorlas
We prove an interesting identity for the sum of determinants, which is a generalization of the sum of a geometric progression. The proof is quite long and a number of other identities are proved along the way. Some of the more elementary ones are deferred to another section at the end.
Sudip Bera
In this article we provide with combinatorial proofs of some recent identities due to Sury and McLaughlin. We show that, the solution of a general linear recurrence with constant coefficients can be interpreted as a determinant of a matrix. Also, we derive a determinantal expression of Fibonacci and Lucas numbers. We…
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…
Soichi Okada
Determinant and Pfaffian formulas for general matrices are a powerful tool in proving relations among special functions and in evaluating specific determinants and Pfaffians. For example, in [6], we applied the Cauchy–Sylvester formula for compound determinants to give a transparent proof of the evaluation of the…
Henryk A. Witek, Teobald Kupka, Luis R. Domingo
Multiple zigzag chains $Zm,n$ of length n and width m constitute an important class of regular graphene flakes of rectangular shape. The physical and chemical properties of these basic pericondensed benzenoids can be related to their various topological invariants, conveniently encoded as the coefficients of a…
Yann Garniron, Thomas Applencourt, Kevin Gasperich, Anouar Benali + 15 more
Quantum Package is an open-source programming environment for quantum chemistry specially designed for wave function methods. Its main goal is the development of determinant-driven selected configuration interaction (sCI) methods and multi-reference second-order perturbation theory (PT2). The determinant-driven…
Hoai Nguyen Huynh, Andri Pradana, Lock Yue Chew, Alejandro Raul Hernandez Montoya
We study properties of the symbolic sequences extracted from the fractals generated by the arc-fractal system introduced earlier by Huynh and Chew. The sequences consist of only a few symbols yet possess several nontrivial properties. First using an operator approach, we show that the sequences are not periodic, even…
V.M. Efimov, K.V. Efimov, V.Y. Kovaleva
In the 40s of the last century, Karhunen and Loève proposed a method for processing of one-dimensional numeric time series by converting it into a multidimensional by shifts. In fact, a one-dimensional number series was decomposed into several orthogonal time series. This method has many times been independently…
Sterling Sawaya, James Boocock, Michael A. Black, Neil Gemmell
Pausing of DNA polymerase can indicate the presence of a DNA structure that differs from the canonical double-helix. Here we detail a method to investigate how polymerase pausing in the Pacific Biosciences sequencer reads can be related to DNA structure. The Pacific Biosciences sequencer uses optics to view a…
Mehmet Ali Tibatan, Mustafa Sarisaman
We investigate the quantum behavior encountered in palindromes within DNA structure. In particular, we reveal the unitary structure of usual palindromic sequences found in genomic DNAs of all living organisms, using the Schwinger’s approach. We clearly demonstrate the role played by palindromic configurations with…
Robert M. Hanson, John Mayfield, Mikko J. Vainio, Andrey Yerin + 2 more
The most recent version of the Cahn-Ingold-Prelog rules for the determination of stereodescriptors as described in Nomenclature of Organic Chemistry: IUPAC Recommendations and Preferred Names 2013 (the “Blue Book”) were analyzed by an international team of cheminformatics software developers. Algorithms for machine…
Brian Cloteaux
We give a sufficient condition for a nonnegative integer list to be graphic based on its largest and smallest elements, length, and sum. This bound generalizes a result of Zverovich and Zverovich.
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…
Shanhe Wu, Gabriel Bercu
In this paper, we introduce new sequences, which generalize the celebrated DeTemple sequence, having enhanced speed of convergence. We also give a new representation for Euler’s constant in terms of the Riemann zeta function evaluated at positive odd integers.
Authors not listed
Building on prior mathematical formulations of the periodic law, this paper demonstrates that the algebraic formula S(k) = 2 * (floor(k/2) + 1)^2 accurately predicts the period lengths (2, 8, 8, 18, 18, 32, ...) of the periodic table. This pattern is not a numerical coincidence but a direct consequence of the…