Self-Parametrizing System-Focused Atomistic Models

Atomistic-Level Models

Understanding the speciation of mercury throughout the coal-combustion process is crucial to the design of efficient and effective mercury removal technologies. Mercury oxidation takes place through combined homogeneous (i.e., strictly in the gas phase) and heterogeneous (i.e., gas–surface interactions) pathways. Both bench-scale combustion experiments [1] and quantumchemistry-based theoretical...

A self-parametrizing partition model approach to tomographic inverse problems

Partition modelling is a statistical method for nonlinear regression and classification, and is particularly suited to dealing with spatially variable parameters. Previous applications include disease mapping in medical statistics. Here we extend this method to the seismic tomography problem. The procedure involves a dynamic parametrization for the model which is able to adapt to an uneven spat...

Parametrizing Order-Stable Exponential Family Random Graph Models

The Surface Parametrizing Cuboids

We study the surface S̄ parametrizing cuboids: it is defined by the equations relating the sides, face diagonals and long diagonal of a rectangular box. It is an open problem whether a ‘rational box’ exists, i.e., a rectangular box all of whose sides, face diagonals and long diagonal have (positive) rational length. The question is equivalent to the existence of nontrivial rational points on S̄. ...

Towards parametrizing word equations

Classically, in order to resolve an equation u ≈ v over a free monoid X∗, we reduce it by a suitable family F of substitutions to a family of equations uf ≈ vf , f ∈ F , each involving less variables than u ≈ v, and then combine solutions of uf ≈ vf into solutions of u ≈ v. The problem is to get F in a handy parametrized form. The method we propose consists in parametrizing the path traces in t...