We compute the algebra of differential invariants of unparametrized curves in the homogeneous G₂ flag varieties, namely in G₂/P. This gives a solution to the equivalence problem for such curves. We consider the cases of integral and generic curves and relate the equivalence problems for all three choices of the parabolic subgroup P.

Many recent works in the field of graph machine learning have introduced pooling operators to reduce the size of graphs. In this article, we present an operational framework to unify this vast and diverse literature by describing pooling operators as the combination of three functions: selection, reduction, and connection (SRC). We then introduce a taxonomy of pooling operators, based on some of ...

Paleoclimate proxy records have non-negligible uncertainties that arise from both the proxy measurement and the dating processes. Knowledge of the dating uncertainties is important for a rigorous propagation to further analyses, for example, for identification and dating of stadial– interstadial transitions in Greenland ice core records during glacial intervals, for comparing the variability in ...

We have implemented a self-consistent feld solver for Hartree–Fock calculations, by making use of Multiwavelets and Multiresolution Analysis. We show how such a solver is inherently a preconditioned steepest descent method and therefore a good starting point for rapid convergence. A distinctive feature of our implementation is the absence of any reference to the kinetic energy operator. This is ...

<p><b>Background</b> A healthy diet can decrease the risk of several lifestyle diseases. From studying the health effects of single foods, research now focuses on examining complete diets and dietary patterns reflecting the combined intake of different foods. The main goals of the current study were to identify dietary patterns and then investigate how these differ in terms of sex, age, educational ...

We study differential invariants of linear differential operators and use them to find conditions for equivalence of differential operators acting on line bundles over smooth manifolds with respect to groups of automorphisms.

The maximal contact symmetry dimensions for scalar ODEs of order ≥ 4 and vector ODEs of order ≥ 3 are well known. Using a Cartan-geometric approach, we determine for these ODEs the next largest realizable (submaximal) symmetry dimension. Moreover, finer curvature-constrained submaximal symmetry dimensions are also classified.

We extend Tanaka theory to the context of supergeometry and obtain an upper bound on the supersymmetry dimension of geometric structures related to strongly regular bracket-generating distributions on supermanifolds and their structure reductions.

Arctic Ocean properties and processes are highly relevant to the regional and global coupled climate system, yet still scarcely observed, especially in winter. Team OCEAN conducted a full year of physical oceanography observations as part of the Multidisciplinary drifting Observatory for the Study of the Arctic Climate (MOSAiC), a drift with the Arctic sea ice from October 2019 to September 2020. ...

Holomorphically homogeneous Cauchy–Riemann (CR) real hypersurfaces <i>M<i/>³⊂C² were classified by Élie Cartan in 1932. In the next dimension, we complete the classification of simply-transitive Levi non-degenerate hypersurfaces <i>M<i/>⁵⊂C³ using a novel Lie algebraic approach independent of any earlier classifications of abstract Lie algebras. Central ...