In this paper we are interesting in the enumeration of rooted labelled trees according to the relationship between the root and its sons. Let Tn;k be the family of Cayley trees on n] such that the root has exactly k smaller sons. In a rst time we give a bijective proof of the fact that jTn+1;kj = ? n k n n?k. Moreover, we use the family Tn+1;0 of Cayley trees for which the root is smaller than ...

1. Synthesis of polyglutamate derivatives from radioactively labelled folic acid, folinic acid and methotrexate has been studied in human phytohaemagglutinin-transformed lymphocytes. 2. With labelled folic acid as the precursor, approximately 20% of the labelled cell folate was found in each of the mono-, tetra-, penta- and hexaglutamate peaks after 72 h of incubation. At earlier times, the amo...

In mdx mice, a model for Duchenne muscular dystrophy, the timing between the replication of myoblasts and their incorporation into myotubes was determined autoradiographically. Thirty-eight mdx mice aged 23 d were injected with tritiated thymidine to label myoblasts replicating early in the dystrophic process. At intervals from 8 h to 30 d after injection the tibialis anterior muscles were remo...

A graphical method is described that allows the determination of specific radioactivities of radioactively labelled hormones. This method combines the self-displacement technique, plotting bound/free ratios versus mass of unlabelled hormone or total radioactivity of labelled preparation added to the receptor preparation, and the maximal binding capacity of the labelled hormone. The procedure pr...

The well-known embedding of intuitionistic logic into classical modal logic means that intuitionistic logic can be viewed as a calculus of labelled deduction on multiple-conclusion sequents, where the labels are the Kripke worlds of the modal embedding. The corresponding natural deduction system constitutes a type system for programs using control operators such as letcc that capture the curren...

There has been much interest in applying techniques that incorporate knowledge from unlabelled data into a supervised learning system but less effort has been made to compare the effectiveness of different approaches on real world problems and to analyse the behaviour of the learning system when using different amount of unlabelled data. In this paper an analysis of the performance of supervise...

Labelled Markov processes (LMPs) are automata whose transitions are given by probability distributions. In this paper we present a ‘universal’ LMP as the spectrum of a commutative C∗-algebra consisting of formal linear combinations of labelled trees. We characterize the state space of the universal LMP as the set of homomorphims from an ordered commutative monoid of labelled trees into the mult...

We describe a theory of labelled structures, which intuitively consist of a labelled shape together with a mapping from labels to data. Labelled structures thus subsume algebraic data types as well as “labelled” types such as arrays and finite maps. This idea of decomposing container structures into shapes and data is an old one; our novel contribution is to explicitly mediate the decomposition...

In this paper, we define new decision procedures for Łukasiewicz logics. They are based on particular integer-labelled hypersequents and of logical proof rules for such hypersequents. These rules being proved strongly invertible our procedures naturally allow one to generate countermodels. From these results we define a “merge”-free calculus for the infinite version of Łukasiewicz logic and pro...