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.

This thesis is concerned with the (non)existence of Killing Tensors in Koutras-McIntosh spacetimes. Killing tensors are of particular interest in general relativity, because these correspond to conserved quantities for the geodesic motion. For instance, Carter found such a conserved quantity in the Kerr metric which he used to explicitly integrate the geodesic equations. The equation defining ...

Simple climate models have gathered much attention as they have suggested the possibility of abrupt climate change associated with tipping points. Several simple climate models are found to have multiple equilibria, but in most cases similar equilibria do not appear or become too difficult to find in complex, fully coupled earth system models. In this thesis, we investigate a simple climate model, ...

This thesis is concerned with classification and regression using deep learning applied to fish otolith images. Otoliths (earstones) are calcified structures in the inner ear of vertebrates, and are used, for instance, in fish stock assessment and fish age determination. We use convolutional neural networks – a class of deep learning models - on two specific problems: discrimination between Northeast ...

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 ...

Symmetries and differential invariants of viscid flows with viscosity depending on temperature on a space curve are given. Their dependence on thermodynamic states of media is studied, and a classification of thermodynamic states is given.

In this paper we give an algorithm to round the floating point output of a semidefinite programming solver to a solution over the rationals or a quadratic extension of the rationals. This algorithm does not require the solution to be strictly feasible and works for large problems. We apply this to get sharp bounds for packing problems, and we use these sharp bounds to prove that certain optimal ...

Symmetries and the corresponding fields of differential invariants of the inviscid flows on a curve are given. Their dependence on thermodynamic states of media is studied, and a classification of thermodynamic states is given.

The categories pCS(X,Pro(k)) of precosheaves and CS(X,Pro(k)) of cosheaves on a small Grothendieck site X, with values in the category Pro(k) of prok-modules, are constructed. It is proved that pCS(X,Pro(k)) satisfies the AB4 and AB5* axioms, while CS(X,Pro(k)) satisfies AB3 and AB5*. Homology theories for cosheaves and precosheaves, based on quasi-projective resolutions, are constructed and investigated.