We introduce a notion of productivity (summability) of sequences in a topological group G, parametrized by a given function f : N → ω+1. The extreme case when f is the function taking constant value ω is closely related to the TAP property, the weaker version of the wellknown property NSS. We prove that TAP property coincides with NSS in locally compact groups, ω-bounded abelian groups and coun...

We consider functions of natural numbers which allow a combinatorial interpretation as density functions (speed) of classes of relational structures, such as Fibonacci numbers, Bell numbers, Catalan numbers and the like. Many of these functions satisfy a linear recurrence relation over Z or Zm and allow an interpretation as counting the number of relations satisfying a property expressible in M...

Let β > 1 be an algebraic number. A general definition of a beta-conjugate of β is proposed with respect to the analytical function fβ(z) = −1 + ∑ i≥1 tiz i associated with the Rényi β-expansion dβ(1) = 0.t1t2 . . . of unity. From Szegö’s Theorem, we study the dichotomy problem for fβ(z), in particular for β a Perron number: whether it is a rational fraction or admits the unit circle as natural...

Acknowledgements I first would like to thank my promotor Vincent Blondel for accepting me as his first Ph.D student, and providing me with a challenging research subject. His constructive comments, his pragmatism and his initiative were essential in the realization of this thesis. Several researchers contributed to this thesis. I would like to especially thank Alexander Vladimirov and Yurii Nes...

The representations −→ N 1 + −→ N 2 = D of a natural number D as the sum of two Fibonacci-even numbers −→ N i = F1 ◦ Ni, where ◦ is the circular Fibonacci multiplication, are considered. For the number s(D) of solutions, the asymptotic formula s(D) = c(D)D + r(D) is proved; here c(D) is a continuous, piecewise linear function and the remainder r(D) satisfies the inequality |r(D)| ≤ 5 + ( 1 ln(1...

Generalized estimating equation solvers in R only allow for a few pre-determined options for the link and variance functions. We provide a package, geeM, which is implemented entirely in R and allows for user specified link and variance functions. The sparse matrix representations provided in the Matrix package enable a fast implementation. To gain speed, we make use of analytic inverses of the...

This paper demonstrates that it is possible to relax the commitment to numeric degrees of belief while retaining the desirable features of the Bayesian approach for representing and changing states of belief. We first present an abstract representation of states of belief and an associated notion of conditionalization that subsume their Bayesian counterparts. Next, we provide some symbolic and ...