The main focus of this thesis is to evaluate $k_r(n,\delta)$, the minimal number of $r$-cliques in graphs with $n$ vertices and minimum degree~$\delta$. A fundamental result in Graph Theory states that a triangle-free graph ...

We compute the groups H*(Aut(F$_{n}$);M) and H*(Out(F$_{n}$);M) in a stable range, where M is obtained by applying a Schur functor to H$_{Q}$ or H$_{Q}$, respectively the first rational homology and cohomology of F$_{n}$. ...

We analyse the steady-state behaviour of two different models with collaborating queues: that is, models in which "customers" can be served by many types of "servers", and "servers" can process many types of "customers". The ...

We congratulate the authors on their stimulating contribution to the burgeoning high-dimensional inference literature. The bootstrap offers such an attractive methodology in these settings, but it is well-known that its ...

On a complex variety X, two different approaches to K-theory are available: the algebraic K-theory of the variety, and the topological K-theory of the underlying topological space. In this context, the algebraic variant ...

Abstract Background Genome-wide association studies (GWAS) are a widely used study design for detecting genetic causes of complex diseases. Current studies provide good coverage of common causal SNPs, but not rare ones. A ...

Abstract Background The epidermal growth factor receptor (EGFR) signaling pathway plays a key role in regulation of cellular growth and development. While highly studied, it is still not fully understood how the signal is ...

Floer theory is a rich collection of tools for studying symplectic manifolds and their Lagrangian submanifolds with the help of holomorphic curves. Its origins lie in estimating the numbers of equilibria in Hamiltonian ...

The connective constant $μ$($G$) of an infinite transitive graph $G$ is the exponential growth rate of the number of self-avoiding walks from a given origin. In earlier work of Grimmett and Li, a locality theorem was proved ...

Correlation inequalities are presented for ferromagnetic Potts models with external field, using the random cluster representation of Fortuin and Kasteleyn, together with the FKG inequality. These results extend and simplify ...

The increasing penetration of electric vehicles over the coming decades, taken together with the high cost to upgrade local distribution networks and consumer demand for home charging, suggest that managing congestion on ...

In this paper we consider random planar maps weighted by the self-dual Fortuin--Kasteleyn model with parameter $q \in (0,4)$. Using a bijection due to Sheffield and a connection to planar Brownian motion in a cone we obtain ...

The 1-2 model on the hexagonal lattice is a model of statistical mechanics in which each vertex is constrained to have degree either 1 or 2. There are three edge directions, and three corresponding parameters a, b, c. It ...

The hexagonal polygon model arises in a natural way via a transformation of the 1-2 model on the hexagonal lattice, and it is related to the high temperature expansion of the Ising model. There are three types of edge, and ...

Let V be a fi nite graph and let ∅ : V → V be an irreducible train track map whose mapping torus has word-hyperbolic fundamental group G. Then G acts freely and cocompactly on a CAT(0) cube complex. Hence, if F is a ...

We introduce a sheaf of infinite order differential operators D on smooth rigid analytic spaces that is a rigid analytic quantisation of the cotangent bundle. We show that the sections of this sheaf over sufficiently small ...

Let X be a smooth rigid analytic space. We prove that the category of co-admissible D-cap-modules on a smooth rigid analytic space supported on a closed smooth subvariety is naturally equivalent to the category of co-admissible ...

The $\alpha$-sandwiched Rényi divergence satisfies the data processing inequality, i.e. monotonicity under quantum operations, for $\alpha$ $\geq$ 1/2. In this article, we derive a necessary and sufficient algebraic condition ...