Institutt for matematikk og statistikk
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A Step Towards Deep Learningbased CADs for Cancer Analysis in Medical Imaging
(Master thesis; Mastergradsoppgave, 20190601)In 2018, cancer was the second leading cause of death worldwide. Early detection can reduce mortality. Screening programs intended for early detection increases the workload for clinicians. To improve efficiency CAD systems would be highly beneficial. We have developed CAD systems using deep learning, for automatic tissue segmentation and prediction of diagnosis in lung and breast cancer. The ... 
Condition Monitoring System for Internal Blowout Prevention (IBOP) in Top Drive Assembly System using Discrete Event Systems and Deep Learning Approaches
(Conference object; Konferansebidrag, 20200719)<p>Offshore oil drilling is a complex process that requires careful coordination of hardware and control systems. Fault monitoring systems play an important role in such systems for safe and profitable operations. Thus, predictive maintenance and monitoring operating conditions of drilling systems are critical to the overall production cycle. In this paper, we are addressing the topic of condition ... 
Statistical estimation of global surface temperature response to forcing under the assumption of temporal scaling
(Journal article; Tidsskriftartikkel; Peer reviewed, 20200408)Reliable quantification of the global mean surface temperature (GMST) response to radiative forcing is essential for assessing the risk of dangerous anthropogenic climate change. We present the statistical foundations for an observationbased approach using a stochastic linear response model that is consistent with the longrange temporal dependence observed in global temperature variability. We ... 
Spectral clustering with graph neural networks for graph pooling
(Journal article; Tidsskriftartikkel; Peer reviewed; Conference object; Konferansebidrag, 2020)Spectral clustering (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster. However, the eigendecomposition of the Laplacian is expensive and, since clustering results are graphspecific, pooling methods based on SC must perform a ... 
Reservoir computing approaches for representation and classification of multivariate time series
(Journal article; Tidsskriftartikkel; Peer reviewed, 20200629)Classification of multivariate time series (MTS) has been tackled with a large variety of methodologies and applied to a wide range of scenarios. Reservoir computing (RC) provides efficient tools to generate a vectorial, fixedsize representation of the MTS that can be further processed by standard classifiers. Despite their unrivaled training speed, MTS classifiers based on a standard RC ... 
A boundary integral approach to the modeling of surface waves in a wave tank
(Master thesis; Mastergradsoppgave, 20200614)Boundary integral equations (BIEs) are used to model surface waves in a wave tank. Assuming an ideal fluid, the velocity of the fluid can be considered as a potential flow and be modeled by the Laplace equation on the domain. The domain in this case will be a section of a wave channel with an incoming wave from the right, a rigid bottom, a reflective wall on the right and a time varying surface that ... 
A bidirectional pulse propagation model for extreme nonlinear optics: derivation and implementation.
(Master thesis; Mastergradsoppgave, 20200513)With growing capabilities of highintensity laser beams to generate ultrashort pulses of light, the simulation of pulse propagation in nonlinear media is expected to catch up with the frontline experimental setups. Among the challenges of nonlinear material response modeling is the ability to capture the backscatter effect  a phenomenon inherently elusive for the wellestablished methods of ... 
Validation of prediction models of severe disease course and nonachievement of remission in juvenile idiopathic arthritis part 2: Results of the Nordic model in the Canadian cohort
(Journal article; Tidsskriftartikkel; Peer reviewed, 20200115)<b>Background</b> Validated clinical prediction models to identify children with poor prognosis at the time of juvenile idiopathic arthritis (JIA) diagnosis would be very helpful for tailoring treatments, and avoiding under or overtreatment. Our objective was to externally validate Nordic clinical prediction models in Canadian patients with JIA. <b>Methods</b> We used data from 513 subjects ... 
Joint Invariants of Symplectic and Contact Lie Algebra Actions
(Master thesis; Mastergradsoppgave, 20200623)By restricting generating functions of infinitesimal symmetries of symplectic and contact vector spaces to quadratic forms, we obtain a finitedimensional Lie subalgebra, consisting of vector fields isomorphic to the linear symplectic or conformal symplectic algebra. This allows us to look for joint invariants of the diagonal action of g on product manifolds. We find an explicit recipe for creating ... 
Differential Invariants of Symplectic and Contact Lie Algebra Actions
(Master thesis; Mastergradsoppgave, 20200623)In this thesis we consider the equivalence problem for symplectic and conformal symplectic group actions on submanifolds and functions. We solve the equivalence problem for general submanifolds by means of computing differential invariants and describing all the invariants of the associated group action by appealing to the LieTresse theorem. 
Homogeneous Levi nondegenerate hypersurfaces in C^3
(Journal article; Tidsskriftartikkel; Peer reviewed, 20200609)We classify all (locally) homogeneous Levi nondegenerate real hypersurfaces in C<sup>3</sup> with symmetry algebra of dimension ≥6. 
Higher Weight Spectra of Veronese Codes
(Journal article; Tidsskriftartikkel; Peer reviewed, 20191018)We study qary linear codes C obtained from Veronese surfaces over finite fields.We show how one can find the higher weight spectra of these codes, or equivalently, the weight distribution of all extension codes of C over all field extensions of the ground field. Our methods will be a study of the StanleyReisner rings of a series of matroids associated to each code C. 
The Four Faces of Hyperelliptic curves
(Master thesis; Mastergradsoppgave, 20200513)In this thesis we will look at elliptic and hyperelliptic curves. There are three abelian groups that are isomorphic to hyperelliptic curves. The Jacobian of hyperelliptic curves, the ideal class group and the form class group, will all be defined and given abelian group structure. We will give an algorithm for point addition and point doubling done exclusively in the jacobian of the curve. ... 
Spatial trend analysis of gridded temperature data at varying spatial scales
(Journal article; Tidsskriftartikkel; Peer reviewed, 20200228)Classical assessments of trends in gridded temperature data perform independent evaluations across the grid, thus, ignoring spatial correlations in the trend estimates. In particular, this affects assessments of trend significance as evaluation of the collective significance of individual tests is commonly neglected. In this article we build a space–time hierarchical Bayesian model for temperature ... 
Symmetric NonNegative Forms and Sums of Squares
(Journal article; Tidsskriftartikkel; Peer reviewed, 20200521)We study symmetric nonnegative forms and their relationship with symmetric sums of squares. For a fixed number of variables <i>n</i> and degree 2<i>d</i>, symmetric nonnegative forms and symmetric sums of squares form closed, convex cones in the vector space of <i>n</i>variate symmetric forms of degree 2<i>d</i>. Using representation theory of the symmetric group we characterize both cones in a ... 
Food recommendation using machine learning for physical activities in patients with type 1 diabetes
(Journal article; Tidsskriftartikkel; Peer reviewed, 2019)Physical activities have a significant impact on blood glucose homeostasis of patients with type 1 diabetes. Regular physical exercise provides many proven health benefits and is recommended as part of a healthy lifestyle. However, one of the main side effects of physical activities is hypoglycemia (low blood glucose). Fear of hypoglycemia generally leads to the patients not participating in ... 
Poincaré function for moduli of differentialgeometric structures
(Journal article; Tidsskriftartikkel, 2019)The Poincaré function is a compact form of counting moduli in local geometric problems. We discuss its property in relation to V. Arnold’s conjecture, and derive this conjecture in the case when the pseudogroup acts algebraically and transitively on the base. Then we survey the known counting results for differential invariants and derive new formulae for several other classification problems in ... 
Integrable Systems in Four Dimensions Associated with SixFolds in Gr(4, 6)
(Journal article; Tidsskriftartikkel; Preprint; Manuskript, 20180129)Let Gr(d, n) be the Grassmannian of <i>d</i>dimensional linear subspaces of an <i>n</i>dimensional vector space <i>V</i>. A submanifold <i>X</i> ⊂ Gr(<i>d, n</i>) gives rise to a differential system Σ(X) that governs <i>d</i>dimensional submanifolds of <i>V</i> whose Gaussian image is contained in <i>X</i>. We investigate a special case of this construction where <i>X</i> is a sixfold in Gr(4, ... 
Dispersionless integrable hierarchies and GL(2,R) geometry
(Journal article; Tidsskriftartikkel; Peer reviewed, 20191008)Paraconformal or GL(2, ℝ) geometry on an <i>n</i>dimensional manifold <i>M</i> is defined by a field of rational normal curves of degree <i>n</i> – 1 in the projectivised cotangent bundle <i>ℙT*M</i>. Such geometry is known to arise on solution spaces of ODEs with vanishing Wünschmann (Doubrov–Wilczynski) invariants. In this paper we discuss yet another natural source of <i>GL</i>(2, ℝ) structures, ... 
Differential invariants of Kundt waves
(Journal article; Tidsskriftartikkel; Peer reviewed, 20190717)Kundt waves belong to the class of spacetimes which are not distinguished by their scalar curvature invariants. We address the equivalence problem for the metrics in this class via scalar differential invariants with respect to the equivalence pseudogroup of the problem. We compute and finitely represent the algebra of those on the generic stratum and also specify the behavior for vacuum Kundt ...