For the largest exceptional simple Lie superalgebra F(4), having dimension (24|16), we provide two explicit geometric realizations as supersymmetries, namely as the symmetry superalgebra of super-PDE systems of second and third order respectively.

Recently, subgraphs-enhanced Graph Neural Networks (SGNNs) have been introduced to enhance the expressive power of Graph Neural Networks (GNNs), which was proved to be not higher than the 1-dimensional Weisfeiler-Leman isomorphism test. The new paradigm suggests using subgraphs extracted from the input graph to improve the model’s expressiveness, but the additional complexity exacerbates an ...

In Graph Neural Networks (GNNs), hierarchical pooling operators generate local summaries of the data by coarsening the graph structure and the vertex features. While considerable attention has been devoted to analyzing the expressive power of message-passing (MP) layers in GNNs, a study on how graph pooling affects the expressiveness of a GNN is still lacking. Additionally, despite the recent advances ...

We investigate the utility of the convex hull of many Lagrangian tracers to analyze transport properties of turbulent flows with different anisotropy. In direct numerical simulations of statistically homogeneous and stationary Navier–Stokes turbulence, neutral fluid Boussinesq convection, and MHD Boussinesq convection a comparison with Lagrangian pair dispersion shows that convex hull statistics ...

Let V be the weighted projective variety defined by a weighted homogeneous ideal J and C a maximal cone in the Gröbner fan of J with m rays. We construct a flat family over A^m that assembles the Gröbner degenerations of V associated with all faces of C. This is a multi-parameter generalization of the classical one-parameter Gröbner degeneration associated to a weight. We explain how our ...

The problem of local feedback equivalence for 1-dimensional control systems of the 1-st order is considered. The algebra of differential invariants and criteria for the feedback equivalence for regular control systems are found.

The class of autoregressive (AR) processes is extensively used to model temporal dependence in observed time series. Such models are easily available and routinely fitted using freely available statistical software like R. A potential problem is that commonly applied estimators for the coefficients of AR processes are severely biased when the time series are short. This paper studies the ...

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 ...

Heterogeneity between individuals has attracted attention in the literature of survival analysis for several decades. Widowed individuals also differ; some are more frail than others and thereby have a higher risk of dying. The traditional hazard rate in a survival model is a measure of population risk and does not provide direct information on the unobservable individual risk. A frailty model is ...