Existence, uniqueness and approximation for stochastic Schrodinger equation: the Poisson case

In quantum physics, recent investigations deal with the so-called "quantum trajectory" theory. Heuristic rules are usually used to give rise to "stochastic Schrodinger equations" which are stochastic differential equations of non-usual type describing the physical models. These equations pose tedious problems in terms of mathematical justification: notion of solution, existence, uniqueness, justification... In this article, we concentrate on a particular case: the Poisson case. Random measure theory is used in order to give rigorous sense to such equations. We prove existence and uniqueness of a solution for the associated stochastic equation. Furthermore, the stochastic model is physically justified by proving that the solution can be obtained as a limit of a concrete discrete time physical model.Comment: 35 page

Existence of graphs with sub exponential transitions probability decay and applications

In this paper, we present a complete proof of the construction of graphs with bounded valency such that the simple random walk has a return probability at time $n$ at the origin of order $exp(-n^{\alpha}),$ for fixed $\alpha \in [0,1[$ and with Folner function $exp(n^{\frac{2\alpha}{1-\alpha}})$. We begin by giving a more detailled proof of this result contained in (see \cite{ershdur}). In the second part, we give an application of the existence of such graphs. We obtain bounds of the correct order for some functional of the local time of a simple random walk on an infinite cluster on the percolation model.Comment: 46 page

Top Quark Modelling and Tuning at CMS

Recent measurements dedicated to improving the understanding of modelling top quark pair (${\text{t}\overline{\text{t}}}$) production at the LHC are summarised. These measurements, performed with proton-proton collision data collected by the CMS detector at $\sqrt{s}=$ 13 TeV, probe the underlying event in ${\text{t}\overline{\text{t}}}$ events, and use the abundance of jets in ${\text{t}\overline{\text{t}}}$ events to study the substructure of jets. A new set of tunes for PYTHIA 8, and their performance with ${\text{t}\overline{\text{t}}}$ data, are also discussed.Comment: Proceedings for the 11th International Workshop on Top Quark Physics (TOP2018

‘Do larger molars and robust jaws in early hominins represent dietary adaptation?’ A New Study in Tooth Wear

Diet imposes significant constraints on the biology and behaviour of animals. The fossil record suggests that key changes in diet have taken place throughout the course of human evolution. Defining these changes enables us to understand the behaviour of our extinct fossil ancestors. Several lines of evidence are available for studying the diet of early hominins, including craniodental morphology, palaeoecology, dental microwear and stable isotopes. They do, however, often provide conflicting results. Using dental macrowear analysis, this new UCL Institute of Archaeology project will provide an alternative source of information on early hominin diet. Dental macrowear has often been used to analyse diet in archaeological populations, but this will be the first time that this type of detailed study has been applied to the early hominin fossil record