It has long been suspected that Active Galactic Nuclei are powered by accretion of matter onto massive black holes and this belief implies their presence in the nuclei of most nearby galaxies as ”relics” of past activity. Just a few years ago this was considered a paradigm but, recently, new ground-based and Hubble Space Telescope observations are producing a breakthrough in our knowledge on ma...

We present a (co)algebraic treatment of iteration-free dynamic modal logics such as Propositional Dynamic Logic (PDL) and Game Logic (GL), both without star. The main observation is that the program/game constructs of PDL/GL arise from monad structure, and the axioms of these logics correspond to certain compatibilty requirements between the modalities and this monad structure. Our main contrib...

The Laplace-Beltrami operator for graphs has been been widely used in many machine learning issues, such as spectral clustering and transductive inference. Functions on the nodes of a graph with vanishing Laplacian are called harmonic functions. In differential geometry, the Laplace-de Rham operator generalizes the Laplace-Beltrami operator. It is a differential operator on the exterior algebra...

The Laplace-Beltrami operator of a smooth Riemannian manifold is determined by the Riemannian metric. Conversely, the heat kernel constructed from the eigenvalues and eigenfunctions of the Laplace-Beltrami operator determines the Riemannian metric. This work proves the analogy on Euclidean polyhedral surfaces (triangle meshes), that the discrete heat kernel and the discrete Riemannian metric (u...

We draw connections between the field of contact topology and the study of Beltrami fields in hydrodynamics on Riemannian manifolds in dimension three. We demonstrate an equivalence between Reeb fields (vector fields which preserve a transverse nowhere-integrable plane field) up to scaling and rotational Beltrami fields on three-manifolds. Thus, we characterise Beltrami fields in a metric-indep...

In this paper, we propose a stress-based crossover (SX) operator to solve the checkerboardlike material distributation and disconnected topology that is common for simple genetic algorithm (SGA) to structural topology optimization problems (STOPs). A penalty function is defined to evaluate the fitness of each individual. A number of constrained problems are adopted to experiment the effectivene...

Subdivision surfaces are proven to be a powerful tool in geometric modeling and computer graphics, due to the great flexibility they offer in capturing irregular topologies. This paper discusses the robust and efficient implementation of an isogeometric discretization approach to partial differential equations on surfaces using subdivision methodology. Elliptic equations with the Laplace-Beltra...