20 papers · ranked by Valyu relevance
Guillaume J. Filion
Seeding heuristics are the most widely used strategies to speed up sequence alignment in bioinformatics. Such strategies are most successful if they are calibrated, so that the speed-versus-accuracy trade-off can be properly tuned. In the widely used case of read mapping, it has been so far impossible to predict the…
Nikolaos Konstantinides
The RNA pseudoknot is a conserved secondary structure encountered in a number of ribozymes, which assume a central role in the RNA world hypothesis. However, RNA folding algorithms could not predict pseudoknots until recently. Analytic combinatorics – a newly arisen mathematical field – has introduced a way of…
Stephen Melczer, Bruno Salvy
Analytic combinatorics studies the asymptotic behavior of sequences through the analytic properties of their generating functions. This article provides effective algorithms required for the study of analytic combinatorics in several variables, together with their complexity analyses. Given a multivariate rational…
Stephen Melczer
The field of analytic combinatorics, which studies the asymptotic behaviour of sequences through analytic properties of their generating functions, has led to the development of deep and powerful tools with applications across mathematics and the natural sciences. In addition to the now classical univariate theory…
Guillaume J. Filion, Ruggero Cortini, Eduard Zorita
The increasing throughput of DNA sequencing technologies creates a need for faster algorithms. The fate of most reads is to be mapped to a reference sequence, typically a genome. Modern mappers rely on heuristics to gain speed at a reasonable cost for accuracy. In the seeding heuristic, short matches between the reads…
Maciej Bendkowski, Katarzyna Grygiel, Marek Zaionc
We present a quantitative basis-independent analysis of combinatory logic. Using a general argument regarding plane binary trees with labelled leaves, we generalise the results of David et al. (see [9]) and Bendkowski et al. (see [6]) to all Turing-complete combinator bases proving, inter alia, that asymptotically…
David Bevan, Josep Conde
of irrational size Authors: ['David Bevan' 'Josep Conde'] We extend the scope of analytic combinatorics to classes containing objects that have irrational sizes. The generating function for such a class is a power series that admits irrational exponents (which we call a Ribenboim series). A transformation then yields a…
Andrew MacFie
We survey some general-purpose symbolic software packages that implement algorithms from enumerative and analytic combinatorics. Software for the following areas is covered: basic combinatorial objects, symbolic combinatorics, Pólya theory, combinatorial species, and asymptotics. We describe the capabilities that the…
Tanay Wakhare
We introduce new refinements of the Bell, factorial, and unsigned Stirling numbers of the first and second kind that unite the derangement, involution, associated factorial, associated Bell, incomplete Stirling, restricted factorial, restricted Bell, and r-derangement numbers (and probably more!). By combining methods…
Runqiao Li, Ali K. Uncu
We study cylindric partitions with two-element profiles using MacMahon’s partition analysis. We find explicit formulas for the generating functions of the number of cylindric partitions by first finding the recurrences using partition analysis and then solving them. We also note some q-series identities related to…
Cristian Lenart
This is a survey of recent developments in combinatorics. The goal is to give a big picture of (and related references for) its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including algebraic geometry), topology, probability theory, and…
Eduardo S. Zeron, Paul M. Gauthier
We show that the analytic content $\lambda \cdot $ is neither subadditive nor semiadditive. To be precise, for compact sets K in the complex plane, $\lambda K$ is the K-uniform distance from the complex conjugation to the algebra of all rational functions with poles outside K. Thus, given any integer $n\ge 1$, it is…
Authors not listed
The Polytope Formalism provides a rigorous and unifying mathematical framework for representing all possible molecular configurations and their interrelationships. Extending its application from stereoisomerism to molecular constitution reveals that both arise from a common structural foundation linking discrete and…
Mohammad Faisal Khan, Mohammed Abaoud, Naeem Ahmad, Muqrin A. Almuqrin + 1 more
'Muqrin A. Almuqrin' 'Mohamed Kamel Riahi'] Function theory research has long struggled with the challenge of deriving sharp estimates for the coefficients of analytic and univalent functions. Researchers have advanced the field by developing and applying a variety of approaches to get these bounds. In the current…
David Ozonoff, Alex Pogel
Identifying patterns of disease distribution in a population is the task of descriptive epidemiology, where the patterns are descriptions of how the disease is distributed in the population. In everyday public health practice it is descriptive epidemiology that is hard at work when we inform the public about health…
Dustin Broderick, John Herbert
The many-body expansion lies at the heart of numerous fragment-based methods that are intended to sidestep the nonlinear scaling of ab initio quantum chemistry, making electronic structure calculations feasible in large systems. In principle, inclusion of higher-order n-body terms ought to improve the accuracy in a…
Rineau Valentin, Prin Stéphane
Triplets, as minimal informative rooted trees, are fundamental units of information in phylogenetics. Their importance for phylogenetic reconstruction, cladistic biogeography, or supertree methods relies on the fact that any rooted tree can be decomposed into a set of triplets. In order to formalize the tree building…
Dan Siegal-Gaskins, Elisa Franco, Tiffany Zhou, Richard M. Murray
Small biomolecular circuits with two distinct and stable steady states have been identified as essential components in a wide range of biological networks, with a variety of mechanisms and topologies giving rise to their important bistable property. Understanding the differences between circuit implementations is an…
Wolfgang Hornfeck, Kamil Červený, M. I. Aroyo
The number of Wyckoff sequences of a given subdivision complexity is calculated by means of a generating polynomial approach and a dynamic programming approach. The result depends on the choice of space-group symmetry (which is obligatory) and Wyckoff sequence length (which is optional). It also takes into account…
Bjorn K. Berntson, Christoph Sünderhauf
Quantum signal processing is a framework for implementing polynomial functions on quantum computers. To implement a given polynomial P, one must first construct a corresponding complementary polynomial*Q. Existing approaches to this problem employ numerical methods that are not amenable to explicit error analysis. We…