Related papers: Sequences and dynamical systems associated with ca…
We prove the conjecture of Grosse-Kunstleve et al. that coordination sequences of periodic structures in n-dimensional Euclidean space are rational. This has been recently proven by Nakamura et al.; however, our proof is a straightforward…
We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…
The Nevanlinna matrix of a half-line Jacobi operator coincides, up to multiplication with a constant matrix, with the monodromy matrix of an associated canonical system. This canonical system is discrete in a certain sense, and is…
Morphic sequences form a natural class of infinite sequences, extending the well-studied class of automatic sequences. Where automatic sequences are known to have several equivalent characterizations and the class of automatic sequences is…
A theory of quantitative inference about the parameters of sampling distributions is constructed deductively by following very general rules, referred to as the Cox-Polya-Jaynes Desiderata. The inferences are made in terms of probability…
This is in some sense an addendum to the book Relational Mathematics by the first-named author. It originated from work on diverse other topics during which a lot of purely relational results with broad applicability have been produced.…
We show that, if an integer sequence is given by a linear recurrence of constant rational coefficients, then it can be represented as the difference of two arithmetic terms with exponentiation, which do not contain any irrational constant.…
In this note, we continue the investigation of the new version of characterized subgroups of the circle group $\mathbb{T}$, namely, "statistically characterized subgroups" (shortly, "s-characterized subgroups") recently introduced in…
Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of…
Consider a real matrix $\Theta$ consisting of rows $(\theta_{i,1},\ldots,\theta_{i,n})$, for $1\leq i\leq m$. The problem of making the system linear forms $x_{1}\theta_{i,1}+\cdots+x_{n}\theta_{i,n}-y_{i}$ for integers $x_{j},y_{i}$ small…
A novel type of approximants is introduced, being based on the ideas of self-similar approximation theory. The method is illustrated by the examples possessing the structure typical of many problems in applied mathematics. Good numerical…
A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…
Consider the representation of a rational number as a continued fraction, associated with "odd" Euclidean algorithm. In this paper we prove certain properties for the limit distribution function for sequences of rationals with bounded sum…
Continued fractions whose elements are polynomial sequences have been carefully studied mostly in the cases where the degree of the numerator polynomial is less than or equal to two and the degree of the denominator polynomial is less than…
This paper is a modified chapter of the author's Ph.D. thesis. We introduce the notions of sequentially approximated types and sequentially approximated Keisler measures. As the names imply, these are types which can be approximated by a…
In any setting in which observable properties have a quantitative flavour, it is natural to compare computational objects by way of \emph{metrics} rather than equivalences or partial orders. This holds, in particular, for probabilistic…
Assuming standard conjectures, we show that the canonical symmetrizing trace evaluated at powers of a Coxeter element produces rational Catalan numbers for irreducible spetsial complex reflection groups. This extends a technique used by…
The aim of this note is to show the existence of a correspondance between certain algebraic continued fractions in fields of power series over a finite field and automatic sequences in the same finite field. this connection is illustrated…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…