We consider a q-analogue of abstract simplicial complexes, called q-complexes, and discuss the notion of shellability for such complexes. It is shown that q-complexes formed by independent subspaces of a q-matroid are shellable. Further, we explicitly determine the homology of q-complexes corresponding to uniform q-matroids. We also outline some partial results concerning the determination of homology ...

The arithmetic mean/geometric mean inequality (AM/GM inequality) facilitates classes of nonnegativity certificates and of relaxation techniques for polynomials and, more generally, for exponential sums. Here, we present a first systematic study of the AM/GM-based techniques in the presence of symmetries under the linear action of a finite group. We prove a symmetry-adapted representation theorem and ...

Statistiske metoder som regresjonsanalyse og kausale design basert på naturlige eksperi-menter har etter hvert blitt hyllevare innen de fleste fag som behandler store datamengder,ikke minst innen epidemiologi, meteorologi og klimavitenskap.1 Et eksempel er prinsipalkomponentanalyse (PCA), som brukes til å finne karakteristiske mønstre i geofysiske felt.Mønstrene, eller prinsipalkomponentene, ...

The global atmospheric circulation is fundamental for the local weather and climate by redistributing energy and moisture. To the present day, there is a knowledge gap at which spatial scales the energy and its components are transported. Therefore, we separate the meridional atmospheric energy transport in the ERA5 reanalysis by the spatial scales, the quasi-stationary and transient flow patterns, ...

A negatively curved hyperbolic cone metric is called rigid if it is determined (up to isotopy) by the support of its Liouville current, and flexible otherwise. We provide a complete characterization of rigidity and flexibility, prove that rigidity is a generic property, and parameterize the associated deformation space for any flexible metric. As an application, we parameterize the space of ...

Lattice conditional independence models [Andersson and Perlman, Lattice models for conditional independence in a multivariate normal distribution, Ann. Statist. 21 (1993), 1318–1358] are a class of models developed first for the Gaussian case in which a distributive lattice classifies all the conditional independence statements. The main result is that these models can equivalently be described via ...

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 ...