Tree series transformations computed by bottom-up and top-down tree series transducers are called bottomup and top-down tree series transformations, respectively. (Functional) compositions of such transformations are investigated. It turns out that the class of bottom-up tree series transformations over a commutative and complete semiring is closed under left-composition with linear bottom-up t...

A composition of the positive integer n is a representation of n as an ordered sum of positive integers n = a1 + a2 + · · ·+ am. It is well known that there are 2n−1 compositions of n. An inversion in a composition is a pair of summands {ai, aj} for which i < j and ai > aj . The number of inversions of a composition is an indication of how far the composition is from a partition of n, which by ...

Motivated by mass-spectrometry protein sequencing, we consider the problem of reconstructing a string from the multisets of its substring composition. We show that all strings of length 7, one less than a prime and one less than twice a prime, can be reconstructed uniquely up to reversal. For all other lengths, we show that unique reconstruction is not always possible and provide sometimes-tigh...

We report mass-dependent and mass-independent Ca isotopic variations in nine chondrites from three groups: carbonaceous, ordinary and enstatite chondrites. There is about 0.25‰ per amu, i.e., 1‰ in Ca/Ca, variation in chondrites: carbonaceous chondrites have the lightest Ca isotopes, enstatite chondrites have modeled bulk Earth like Ca isotopes, and ordinary chondrites are in between. The corre...

Architectural Description Languages (ADLs) allow developers to describe the architecture of a software system but provide only limited support for their execution. In this paper, we present ACL/1, an XML based Application Composition Language, that describes the architectural view of a software system while at the same time enabling the execution of the software application. As we will show, ou...

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Using generating functions and limit theorems, we obtain a stochastic description of Carlitz compositions of large integer n (i.e. compositions two successive parts of which are different). We analyze: the number M of parts, the number of compositions T (m,n) with m parts, the distribution of the last part size, the correlation between two successive parts, leading to a Markov chain. We describ...

The aim of this talk is to convince the reader that there are a lot of interesting statistical problems in presentday life science data analysis which seem ultimately connected with compositional statistics.

Concave compositions are ordered partitions whose parts are decreasing towards a central part. We study the distribution modulo a of the number of concave compositions. Let c(n) be the number of concave compositions of n having even length. It is easy to see that c(n) is even for all n 1. Refining this fact, we prove that #{n < X : c(n) ⌘ 0 (mod 4)} p X and also that for every a > 2 and at leas...