We propose parametric geons as a volumetric description of object components for qualitative object recognition. Parametric geons are seven qualitative shape types deened by parameterized equations which control the size and degree of tapering and bending. The models provide global shape constraints which make model recovery procedures robust against noise and minor variations in object shape. ...

We present an algebraic account of the Wasserstein distances Wp on complete metric spaces. This is part of a program of a quantitative algebraic theory of effects in programming languages. In particular, we give axioms, parametric in p, for algebras over metric spaces equipped with probabilistic choice operations. The axioms say that the operations form a barycentric algebra and that the metric...

This paper mainly concerns the study of a large class of variational systems governed by parametric generalized equations, which encompass variational and hemivariational inequalities, complementarity problems, first-order optimality conditions, and other optimization-related models important for optimization theory and applications. An efficient approach to these issues has been developed in o...

Many manifestly non-Hermitian Hamiltonians (typically, PT −symmetric complex anharmonic oscillators) possess a strictly real, “physical” bound-state spectrum. This means that they are (quasi-)Hermitian with respect to a suitable non-standard metric Θ 6= I. The domain D of the existence of this metric is studied here for a nontrivial though still non-numerical four-parametric “benchmark” matrix ...

Kernel smoothing is a widely used non-parametric pattern recognition technique. By nature, it suuers from the curse of dimensionality and is usually diicult to apply to high input dimensions. In this contribution, we propose an algorithm that adapts the input metric used in multivariate regression by minimising a cross-validation estimate of the generalisation error. This allows to automaticall...

We study numerically evolution of metric perturbations during reheating in a model with two fields and a strong parametric resonance. Our calculation is fully nonlinear and includes gravity but is restricted to spherical symmetry. In this model, super-Hubble metric perturbations can grow during reheating only due to effects nonlinear in fluctuations of the fields. We find that they indeed grow ...

Parametric timed automata extend timed automata (Alur and Dill, 1991) in that they allow the specification of parametric bounds on the clock values. Since their introduction in 1993 by Alur, Henzinger, and Vardi, it is known that the emptiness problem for parametric timed automata with one clock is decidable, whereas it is undecidable if the automaton uses three or more parametric clocks. The p...