In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of higher-dimensional pseudoholomorphic submanifolds.

We prove involutivity of Einstein and Einstein-Maxwell equations by calculating the Spencer cohomology of these systems. Relation with Cartan method is traced in details. Basic implications through Cartan-Kähler theory are derived.

We establish 2-jet determinacy for the symmetry algebra of the underlying structure of any (complex or real) parabolic geometry. At non-flat points, we prove that the symmetry algebra is in fact 1-jet determined. Moreover, we prove 1-jet determinacy at any point for a variety of non-flat parabolic geometries—in particular torsion-free, parabolic contact, and several other classes.

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 Koutras–McIntosh family of metrics include conformally flat pp-waves and the Wils metric. It appeared in a paper of 1996 by Koutras–McIntosh as an example of a pure radiation spacetime without scalar curvature invariants or infinitesimal symmetries. Here we demonstrate that these metrics have no 'hidden symmetries', by which we mean Killing tensors of low degrees. For the particular case of Wils ...

Med LK20 Fagfornyelsen innføres det nye læreplaner i skolen, der antall kompetansemål i de ulike fagene er noe redusert for å gi mer rom til dybdelæring, samt at læreplanene i matematikk og fysikk har et større fokus på utforsking, modellering og bruk av numeriske metoder enn tidligere (Ludvigsen et al., 2015; Utdanningsdirektoratet, 2020, 2021). I dette bidraget presenterer vi hvordan en gruppe ...

In order to have a scaling description of the climate system that is not inherently non-stationary, the rapid shifts between stadials and interstadials during the last glaciation (the Dansgaard-Oeschger events) cannot be included in the scaling law. The same is true for the shifts between the glacial and interglacial states in the Quaternary climate. When these events are omitted from a scaling ...

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 ...

A large fraction of the Electronic Health Records consists of clinical multivariate time series. Building models for extracting information from these is important for improving the understanding of diseases, patient care and treatment. Such time series are oftentimes particularly challenging since they are characterized by multiple, possibly dependent variables, length variability and irregular ...