Spectral clustering (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster. However, the eigendecomposition of the Laplacian is expensive and, since clustering results are graph-specific, pooling methods based on SC must perform a ...

Boundary integral equations (BIEs) are used to model surface waves in a wave tank. Assuming an ideal fluid, the velocity of the fluid can be considered as a potential flow and be modeled by the Laplace equation on the domain. The domain in this case will be a section of a wave channel with an incoming wave from the right, a rigid bottom, a reflective wall on the right and a time varying surface that ...

<b>Background</b> Validated clinical prediction models to identify children with poor prognosis at the time of juvenile idiopathic arthritis (JIA) diagnosis would be very helpful for tailoring treatments, and avoiding under- or over-treatment. Our objective was to externally validate Nordic clinical prediction models in Canadian patients with JIA. <b>Methods</b> We used data from 513 subjects ...

In this thesis we consider the equivalence problem for symplectic and conformal symplectic group actions on submanifolds and functions. We solve the equivalence problem for general submanifolds by means of computing differential invariants and describing all the invariants of the associated group action by appealing to the Lie-Tresse theorem.

We study q-ary linear codes C obtained from Veronese surfaces over finite fields.We show how one can find the higher weight spectra of these codes, or equivalently, the weight distribution of all extension codes of C over all field extensions of the ground field. Our methods will be a study of the Stanley-Reisner rings of a series of matroids associated to each code C.

Classical assessments of trends in gridded temperature data perform independent evaluations across the grid, thus, ignoring spatial correlations in the trend estimates. In particular, this affects assessments of trend significance as evaluation of the collective significance of individual tests is commonly neglected. In this article we build a space–time hierarchical Bayesian model for temperature ...

Physical activities have a significant impact on blood glucose homeostasis of patients with type 1 diabetes. Regular physical exercise provides many proven health benefits and is recommended as part of a healthy lifestyle. However, one of the main side effects of physical activities is hypoglycemia (low blood glucose). Fear of hypoglycemia generally leads to the patients not participating in ...

Let Gr(d, n) be the Grassmannian of <i>d</i>-dimensional linear subspaces of an <i>n</i>-dimensional vector space <i>V</i>. A submanifold <i>X</i> ⊂ Gr(<i>d, n</i>) gives rise to a differential system Σ(X) that governs <i>d</i>-dimensional submanifolds of <i>V</i> whose Gaussian image is contained in <i>X</i>. We investigate a special case of this construction where <i>X</i> is a six-fold in Gr(4, ...

Kundt waves belong to the class of spacetimes which are not distinguished by their scalar curvature invariants. We address the equivalence problem for the metrics in this class via scalar differential invariants with respect to the equivalence pseudo-group of the problem. We compute and finitely represent the algebra of those on the generic stratum and also specify the behavior for vacuum Kundt ...

In this paper we discuss some of the mathematical and numerical issues that have to be addressed when calculating wave scattering using the Ewald Oseen scattering (EOS) formulation which is newly developed for solving linear and nonlinear scattering problems. The discussion is framed in context of light scattering by objects whose optical response can be of a nonlinear and/or inhomogeneous nature. ...