Institutt for matematikk og statistikk: Recent submissions
Now showing items 141-160 of 394
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G(3)-supergeometry and a supersymmetric extension of the Hilbert–Cartan equation
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-10-23)We realize the simple Lie superalgebra <i>G</i>(3) as supersymmetry of various geometric structures, most importantly super-versions of the Hilbert–Cartan equation (SHC) and Cartan's involutive PDE system that exhibit <i>G</i>(2) symmetry. We provide the symmetries explicitly and compute, via the first Spencer cohomology groups, the Tanaka–Weisfeiler prolongation of the negatively graded Lie ... -
Hyperspectral imaging for the detection of glioblastoma tumor cells in H&E slides using convolution neural networks
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-03-30)Hyperspectral imaging (HSI) technology has demonstrated potential to provide useful information about the chemical composition of tissue and its morphological features in a single image modality. Deep learning (DL) techniques have demonstrated the ability of automatic feature extraction from data for a successful classification. In this study, we exploit HSI and DL for the automatic differentiation ... -
Towards detection and classification of microscopic foraminifera using transfer learning
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-02-06)<p>Foraminifera are single-celled marine organisms, which may have a planktic or benthic lifestyle. During their life cycle they construct shells consisting of one or more chambers, and these shells remain as fossils in marine sediments. Classifying and counting these fossils have become an important tool in e.g. oceanography and climatology. <p>Currently the process of identifying and counting ... -
Snow avalanche segmentation in SAR images with Fully Convolutional Neural Networks
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-11-10)Knowledge about frequency and location of snow avalanche activity is essential for forecasting and mapping of snow avalanche hazard. Traditional field monitoring of avalanche activity has limitations, especially when surveying large and remote areas. In recent years, avalanche detection in Sentinel-1 radar satellite imagery has been developed to improve monitoring. However, the current state-of-the-art ... -
Estimation of Blood Glucose Concentration During Endurance Sports
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-07-21)In this paper, we describe a new statistical approach to estimate blood glucose concentration along time during endurance sports based on measurements of glucose concentration in subcutaneous interstitial tissue. The final goal is the monitoring of glucose concentration in blood to maximize performance in endurance sports. Blood glucose concentration control during and after aerobic physical ... -
Hierarchical Representation Learning in Graph Neural Networks with Node Decimation Pooling
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-12-31)In graph neural networks (GNNs), pooling operators compute local summaries of input graphs to capture their global properties, and they are fundamental for building deep GNNs that learn hierarchical representations. In this work, we propose the Node Decimation Pooling (NDP), a pooling operator for GNNs that generates coarser graphs while preserving the overall graph topology. During training, the ... -
A polymatroid approach to generalized weights of rank metric codes
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-09-15)We consider the notion of a (<i>q,m)</i>-polymatroid, due to Shiromoto, and the more general notion of (<i>q,m</i>)-demi-polymatroids, and show how generalized weights can be defined for them. Further, we establish a duality for these weights analogous to Wei duality for generalized Hamming weights of linear codes. The corresponding results of Ravagnani for Delsarte rank metric codes, and Martínez-Peñas ... -
Relative generalized Hamming weights of affine Cartesian codes
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-03-10)We explicitly determine all the relative generalized Hamming weights of affine Cartesian codes using the notion of footprints and results from extremal combinatorics. This generalizes the previous works on the determination of relative generalized Hamming weights of Reed–Muller codes by Geil and Martin, as well as the determination of all the generalized Hamming weights of the affine Cartesian codes ... -
Integrability via Geometry: Dispersionless Differential Equations in Three and Four Dimensions
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-11-25)We prove that the existence of a dispersionless Lax pair with spectral parameter for a nondegenerate hyperbolic second order partial differential equation (PDE) is equivalent to the canonical conformal structure defined by the symbol being Einstein–Weyl on any solution in 3D, and self-dual on any solution in 4D. The first main ingredient in the proof is a characteristic property for dispersionless ... -
Homogeneous Levi non-degenerate hypersurfaces in C3
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-06-09)We classify all (locally) homogeneous Levi non-degenerate real hypersurfaces in C<sup>3</sup> with symmetry algebra of dimension ≥6. -
Blow-ups and infinitesimal automorphisms of CR-manifolds
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-03-07)For a real-analytic connected CR-hypersurface M of CR-dimension n⩾1 having a point of Levi-nondegeneracy the following alternative is demonstrated for its symmetry algebra s=s(M): (i) either dims=n2+4n+3 and M is spherical everywhere; (ii) or dims⩽n2+2n+2+δ2,n and in the case of equality M is spherical and has fixed signature of the Levi form in the complement to its Levi-degeneracy locus. A version ... -
Incorporating capture heterogeneity in the estimation of autoregressive coefficients of animal population dynamics using capture–recapture data
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-08-31)Population dynamic models combine density dependence and environmental effects. Ignoring sampling uncertainty might lead to biased estimation of the strength of density dependence. This is typically addressed using state‐space model approaches, which integrate sampling error and population process estimates. Such models seldom include an explicit link between the sampling procedures and the true ... -
Risk-Averse Food Recommendation Using Bayesian Feedforward Neural Networks for Patients with Type 1 Diabetes Doing Physical Activities
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-11-12)<p><i>Background.</i> Since physical activity has a high impact on patients with type 1 diabetes and the risk of hypoglycemia (low blood glucose levels) is significantly higher during and after physical activities, an automatic method to provide a personalized recommendation is needed to improve the blood glucose management and harness the benefits of physical activities. This paper aims to reduce ... -
Generalized eigenvalue methods for Gaussian quadrature rules
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020)A quadrature rule of a measure <i>µ</i> on the real line represents a conic combination of finitely many evaluations at points, called nodes, that agrees with integration against <i>µ</i> for all polynomials up to some fixed degree. In this paper, we present a bivariate polynomial whose roots parametrize the nodes of minimal quadrature rules for measures on the real line. We give two symmetric ... -
A Step Towards Deep Learning-based CADs for Cancer Analysis in Medical Imaging
(Master thesis; Mastergradsoppgave, 2019-06-01)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, 2020-07-19)<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, 2020-04-08)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 observation-based approach using a stochastic linear response model that is consistent with the long-range temporal dependence observed in global temperature variability. We ... -
Spectral clustering with graph neural networks for graph pooling
(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 graph-specific, pooling methods based on SC must perform a ... -
Reservoir computing approaches for representation and classification of multivariate time series
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-06-29)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, fixed-size 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, 2020-06-14)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 ...