Related papers: Formal series and numerical integrators: some hist…
Iteration is a programming operation that traditionally refers to visiting the elements of a data structure in sequence. However, modern programming systems such as Rust, Java, and C# generalise iteration far beyond the traditional use…
A systematic study of holomorphic gauge invariant operators in general $\mathcal{N}=1$ quiver gauge theories, with unitary gauge groups and bifundamental matter fields, was recently presented in [1]. For large ranks a simple counting…
The B-series composition theorem has been an important topic in numerical analysis of ordinary differential equations for the past-half century. Traditional proofs of this theorem rely on labelled trees, whereas recent developments in…
In their work on `Coxeter-like complexes', Babson and Reiner introduced a simplicial complex $\Delta_T$ associated to each tree $T$ on $n$ nodes, generalizing chessboard complexes and type A Coxeter complexes. They conjectured that…
The Burrows-Wheeler-Transform (BWT), a reversible string transformation, is one of the fundamental components of many current data structures in string processing. It is central in data compression, as well as in efficient query algorithms…
An involution in a Coxeter group has an associated set of involution words, a variation on reduced words. These words are saturated chains in a partial order first considered by Richardson and Springer in their study of symmetric varieties.…
We provide a unified framework for the treatment of special integrable systems which we propose to call "generalized mean field systems". Thereby previous results on integrable classical and quantum systems are generalized. Following…
Evolutionary deep neural networks have emerged as a rapidly growing field of research. This paper studies numerical integrators for such and other classes of nonlinear parametrizations $ u(t) = \Phi(\theta(t)) $, where the evolving…
In this paper, we extend the Paired-Explicit Runge-Kutta schemes by Vermeire et. al. to fourth-order of consistency. Based on the order conditions for partitioned Runge-Kutta methods we motivate a specific form of the Butcher arrays which…
Motivated by numerical integration on manifolds, we relate the algebraic properties of invariant connections to their geometric properties. Using this perspective, we generalize some classical results of Cartan and Nomizu to invariant…
By using meromorphic "characters" and "logarithms" built up from Euler's Gamma function, and by using convergent factorial series, we will give, in a first pat, a "normal form" to the solutions of a singular regular system. It will enable…
We introduce two new binary operations with combinatorial species; the arithmetic product and the modified arithmetic product. The arithmetic product gives combinatorial meaning to the product of Dirichlet series and to the Lambert series…
The $n$th term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of $n$ in a suitable numeration system. In this paper, instead of considering automatic sequences built on a numeration…
We present BSeries.jl, a Julia package for the computation and manipulation of B-series, which are a versatile theoretical tool for understanding and designing discretizations of differential equations. We give a short introduction to the…
Burrows-Wheeler transform (BWT) is an invertible text transformation that, given a text $T$ of length $n$, permutes its symbols according to the lexicographic order of suffixes of $T$. BWT is one of the most heavily studied algorithms in…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
The notion of transducer integer sequences is considered through a series of examples. By definition, transducer integer sequences are integer sequences produced, under a suitable interpretation, by finite automata encoding tree morphisms…
It is generally well agreed that developing a unifying theory is one of the most important issues in Data Mining research. In the last two decades, a great deal of work has been devoted to the algorithmic aspects of the Frequent Itemset…
Time-series classification has attracted considerable research attention due to the various domains where time-series data are observed, ranging from medicine to econometrics. Traditionally, the focus of time-series classification has been…
In this paper we examine a number of term rewriting system for integer number representations, building further upon the datatype defining systems described in [2]. In particular, we look at automated methods for proving confluence and…