Related papers: Symbolic recurrence plot for uniform binary substi…

A survey is given of the work on strong regularity for uniform algebras over the last thirty years, and some new results are proved, including the following. Let A be a uniform algebra on a compact space X and let E be the set of all those…

The classical concept of bounded completeness and its relation to sufficiency and ancillarity play a fundamental role in unbiased estimation, unbiased testing, and the validity of inference in the presence of nuisance parameters. In this…

Let $T$ be an $n\times n$ random matrix, such that each diagonal entry $T_{i,i}$ is a continuous random variable, independent from all the other entries of $T$. Then for every $n\times n$ matrix $A$ and every $t\ge0$ $$…

The concept of "lost positions" is a recently introduced tool for counting the number of runs in words. We investigate the frequency of lost positions in prefixes of words. This leads to an algorithm that allows to show, using an extensive…

By Zeckendorf's Theorem, every positive integer is uniquely written as a sum of distinct non-adjacent Fibonacci terms. In this paper, we investigate the asymptotic formula of the number of binary expansions $<x$ that have no adjacent terms,…

In this paper, given a simple linear recurrence sequence of algebraic numbers, which has either a dominant characteristic root or exactly two characteristic roots of maximal modulus, we give some explicit lower bounds for the index beyond…

In this article we introduce a dual of the uniform boundedness principle which does not require completeness and gives an indirect means for testing the boundedness of a set. The dual principle, although known to the analyst and despite its…

We present a new recursive generation algorithm for prefix normal words. These are binary strings with the property that no substring has more 1s than the prefix of the same length. The new algorithm uses two operations on binary strings,…

We consider a measure of similarity for infinite words that generalizes the notion of asymptotic or natural density of subsets of natural numbers from number theory. We show that every overlap-free infinite binary word, other than the…

There is a growing body of results in the theory of discrete point sets and tiling systems giving conditions under which such systems are pure point diffractive. Here we look at the opposite direction: what can we infer about a discrete…

Let $M$ be a fixed positive integer. Let $(R_{j}(n))_{n\ge 1}$ be a linear recurrence sequence for every $j=0,1,\ldots, M$, and we set $f(n)=(R_0\circ \cdots \circ R_M)(n)$, where $(S\circ T)(n)= S(T(n))$. In this paper, we obtain…

This paper describes an alternative method of generating fixed points of certain substitution systems. This method centres on taking infinite words consisting of one repeated letter per word. These infinite words are then interlaced to form…

The nonlinear recurrences we consider here include the functions $3x(1-x)$ and $\cos(x)$, which possess attractive fixed points $2/3$ and $0.739...$ (Dottie's number). Detailed asymptotics for oscillatory convergence are found, starting…

We investigate the number of symmetric matrices of non-negative integers with zero diagonal such that each row sum is the same. Equivalently, these are zero diagonal symmetric contingency tables with uniform margins, or loop-free regular…

A speedup, like a time change in discrete time dynamics, is a way of moving faster through the orbits of a dynamical system. Linearly recurrence is a stronger form of minimality for subshifts, shared by e.g.\ all primitive substitution…

Random substitutions are a natural generalisation of their classical `deterministic' counterpart, whereby at every step of iterating the substitution, instead of replacing a letter with a predetermined word, every letter is independently…

Couplings in complex real-world systems are often nonlinear and scale-dependent. In many cases, it is crucial to consider a multitude of interlinked variables and the strengths of their correlations to adequately fathom the dynamics of a…

We investigate the behavior of the periods and border lengths of random words over a fixed alphabet. We show that the asymptotic probability that a random word has a given maximal border length $k$ is a constant, depending only on $k$ and…

Deciding the positivity of a sequence defined by a linear recurrence and initial conditions is, in general, a hard problem. When the coefficients of the recurrences are constants, decidability has only been proven up to order 5. The…

A positive linear recurrence sequence is of the form $H_{n+1} = c_1 H_n + \cdots + c_L H_{n+1-L}$ with each $c_i \ge 0$ and $c_1 c_L > 0$, with appropriately chosen initial conditions. There is a notion of a legal decomposition (roughly,…