Recent years have seen a tremendous progress in the microscopic theoretical treatment of surfaces and processes on surfaces. While some decades ago a phenomenological thermodynamic approach was dominant, a variety of surface properties can now be described from first principles, i.e. without invoking any empirical parameters. Consequently, the field of theoretical surface science is no longer l...

In “Is the Frobenius Matrix Norm Induced?”, the authors ask whether the Frobenius and the norms are induced. There, they claimed that the Frobenius norm is not induced and, consequently, conjectured that the norm may not be induced. In this note, it is shown that the Frobenius norm is induced on particular matrix spaces. It is then shown that the norm is in fact induced on a particular matrix-v...

We present an algorithm to evaluate large deviation functions associated to historydependent observables. Instead of relying on a time discretisation procedure to approximate the dynamics, we provide a direct continuous-time algorithm valuable for systems with multiple time scales, thus extending the work of Giardinà, Kurchan and Peliti [1]. The procedure is supplemented with a thermodynamic-in...

Let k be an algebraically closed field of characteristic exponent p ≥ 1. Let G be a connected reductive algebraic group over k and let g be the Lie algebra of G. Note that G acts on G and on g by the adjoint action and on g by the coadjoint action. (For any k-vector space V we denote by V ∗ the dual vector space.) Let GC be the reductive group over C of the same type as G. Let UG be the variety...

Model choice plays an increasingly important role in Statistics. From a Bayesian perspective a crucial goal is to compute the marginal likelihood of the data for a given model. This however is typically a difficult task since it amounts to integrating over all model parameters. The aim of this paper is to illustrate how this may be achieved using ideas from thermodynamic integration or path sam...