We present some old and recent results on rank problems and linearizability of geodesic planar webs

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.

We present a complete description of a class of linearizable planar geodesic webs which contain a parallelizable 3-subweb.

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.

Accurate detection of the borders of skin lesions is a vital first step for computer aided diagnostic systems. This paper presents a novel automatic approach to segmentation of skin lesions that is particularly suitable for analysis of dermoscopic images. Assumptions about the image acquisition, in particular, the approximate location and color, are used to derive an automatic rule to select small ...

We describe how scale space methods can be used for quantitative analysis of blood glucose concentrations from type 2 diabetes patients. Blood glucose values were recorded voluntarily by the patients over one full year as part of a self-management process, where the timeand frequency of the recordings are decided by the patients. This makes a unique datasetin its extent, though with a large variation ...

The group of area preserving diffeomorphisms showed importance in the problems of self-dual gravity and integrability theory. We discuss how representations of this infinite-dimensional Lie group can arise in mathematical physics from pure local considerations. Then using Lie algebra extensions and cohomology we derive the second Plebański equation and its geometry. We do not use Kähler or other ...

This paper develops methodology that provides a toolbox for routinely fitting complex models to realistic spatial point pattern data. We consider models that are based on log-Gaussian Cox processes and include local interaction in these by considering constructed covariates. This enables us to use integrated nested Laplace approximation and to considerably speed up the inferential task. In addition, ...

Detection of objects embedded in tissue, using visible light, is difficult due to light scattering. The optical properties of the surrounding tissue will influence the spectral characteristics of the light interacting with the object, and the spectral signature observed from the object will be directly affected. A method for calibrating the spectral signature of small objects, embedded in translucent ...

In this paper, we study how sea surface temperature variations in the North Atlantic and the Norwegian Sea are correlated with the climate in the Northern Hemisphere in late Holocene. The analysis is performed by testing statistical hypotheses through novel scale space methodologies. In late Holocene, the proposed techniques reveal that the climate development in the subpolar North Atlantic has been ...