This note proves the existence of universal rational parametrizations. The description involves homogeneous coordinates on a toric variety coming from a lattice polytope. We first describe how smooth toric varieties lead to universal rational parametrizations of certain projective varieties. We give numerous examples and then discuss what happens in the singular case. We also describe rational ...

It has long been known that maximum likelihood estimation in a Poisson model reproduces the chain-ladder technique. We revisit this model. A new canonical parametrisation is proposed to circumvent the inherent identification problem in the parametrisation. The maximum likelihood estimators for the canonical parameter are simple, interpretable and easy to derive. The boundary problem where all o...

Numerical simulations of neutron star mergers represent an essential step toward interpreting the full complexity multimessenger observations and constraining properties supranuclear matter. Currently, are limited by array factors, including computational performance input physics uncertainties, such as equation state. In this work, we expand range nuclear phenomenology efficiently available to...

In the paper an innovative alternative to automatic image parametrization on multiple resolutions, based on texture description with specialized association rules, and image evaluation with machine learning methods is presented. The algorithm ArTex for parameterizing textures with association rules belonging to structural parametrization algorithms was developed. In order to improve the classif...

A procedure for constructing solutions to the Riemann problem for gas dynamics with a general convex equation of state is given. Approximate procedures, involving a local parametrization of the equation of state, are introduced in order to calculate numerical fluxes in conservative finite difference schemes. This leads to difference schemes which are as accurate and almost as fast as the analog...

This paper concerns the use of the finite signalto-noise (FSN) model to design a state estimator. First, the sufficient conditions for the existence of the state estimator are provided. These conditions are expressed in terms of linear matrix inequalities (LMIs) and the parametrization of all the solutions is provided. Then an LMI based estimator design is addressed and the algorithm to solve t...