A probabilistic graphical model encodes conditional independences among random variables, which is related to factorisable distributions. Moreover, the entropy of a probability distribution on a set of discrete random variables is always bounded by the entropy of its factorisable counterpart. This is due to the submodularity of entropy on the set of discrete random variables. Submodular functio...

Recent advances in computational methods allow the Characteristic and Acyclic Polynomials of a Chemical Graph to be calculated easily. A consequence of this is that checking for a zero-value remainder after computer assisted polynomial division is sometimes the simplest way of testing suspected factors of a chemical graph. The technique is simple enough to apply on a routine basis when characte...

We classify compactification lattices for supersymmetric Z2×Z2 orbifolds. These lattices include factorisable as well as non-factorisable six-tori. Different models lead to different numbers of fixed points/tori. A lower bound on the number of fixed tori per twisted sector is given by four, whereas an upper bound consists of 16 fixed tori per twisted sector. Thus, these models have a variety of...

A notion of a coring extension is defined and it is shown to be equivalent to the existence of an additive functor between comodule categories that factorises through forgetful functors. This correspondence between coring extensions and factorisable functors is illustrated by functors between categories of descent data. A category in which objects are corings and morphisms are coring extensions...

Future hadron collider experiments will allow for a detailed investigation of t ¯ t spin correlation effects. In this talk, recent progress in the theoretical description of these effects is reported. In particular, next-to-leading order results for the t ¯ t spin correlations in q ¯ q → t ¯ tX are presented, using various spin quantization axes. Top quark pair production and decay can be descr...

We find a canonical form for pure states of a general multipartite system, in which the constraints on the coordinates (with respect to a factorisable orthonormal basis) are simply that certain ones vanish and certain others are real. For identical particles they are invariant under permutations of the particles. As an application, we find the dimension of the generic local equivalence class.

This thesis examines the non-leptonic B-decays within QCD factorisation and beyond, to challenge the assumptions and limitations of the method. We analyse the treatment of the distribution amplitudes of light mesons and present a new model described by simple physical parameters. The leading twist distribution amplitudes of light mesons describe the leading non-perturbative hadronic contributio...

Abstract Models whose associated likelihood functions fruitfully factorise are an important minority allowing elimination of nuisance parameters via partial likelihood, operation that is valuable in both Bayesian and frequentist inferences, particularly when the number not small. After some general discussion we focus on marginal factorisations, which difficult to ascertain from elementary calc...

Let n S-valued categorical variables be jointly distributed according to a distribution known only up to an unknown normalising constant. For an unnormalised joint likelihood expressible as a product of factors, we give an algebraic recursion which can be used for computing the normalising constant and other summations. A saving in computation is achieved when each factor contains a lagged subs...