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Now showing items 360-379 of 389
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Tangent and normal bundles in almost complex geometry
(Journal article; Tidsskriftartikkel; Peer reviewed, 2005-06-10)We define and study pseudoholomorphic vector bundles structures, particular cases of which are tangent and normal bundle almost complex structures. As an application we deduce normal forms of 1-jets of almost complex structures along a pseudoholomorphic submanifold. In dimension four we relate these normal forms to the problem of pseudoholomorphic foliation of a neighborhood of a curve and the ... -
Temporal evolution of under-ice meltwater layers and false bottoms and their impact on summer Arctic sea ice mass balance
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023-03-31)Low-salinity meltwater from Arctic sea ice and its snow cover accumulates and creates under-ice meltwater layers below sea ice.These meltwater layers can result in the formation of new ice layers, or false bottoms, at the interface of this low-salinity meltwater and colder seawater. As part of the Multidisciplinary drifting Observatory for the Study of the Arctic Climate (MOSAiC), we used a ... -
Theory of linear G-difference equations
(Journal article; Tidsskriftartikkel; Peer reviewed, 1997-12-17)We introduce the notion of difference equation defined on a structured set. The symmetry group of the structure determines the set of difference operators. All main notions in the theory of difference equations are introduced as invariants of the action of the symmetry group. Linear equations are modules over the skew group algebra, solutions are morphisms relating a given equation to other ... -
Thousand years of winter surface air temperature variations in Svalbard and northern Norway reconstructed from ice-core data
(Journal article; Tidsskriftartikkel; Peer reviewed, 2011)Two isotopic ice core records from western Svalbard are calibrated to reconstruct more than 1000 years of past winter surface air temperature variations in Longyearbyen, Svalbard, and Vardø, northern Norway. Analysis of the derived reconstructions suggests that the climate evolution of the last millennium in these study areas comprises three major sub-periods. The cooling stage in Svalbard (ca. ... -
The three missing terms in Ramanujan’s septic theta function identity
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023-02-23)On page 206 in his lost notebook, Ramanujan recorded the following enigmatic identity for his theta function φ(q): φ(e^{−7π√7}) = 7^{−3/4}φ(e^{−π√7}){1 + ( )^{2/7} + ( )^{2/7} + ( )^{2/7}}. We give the three missing terms. In addition, we calculate the class invariant G_{343} and further special values of φ(e^{−nπ}), for n = 7, 21, 35, and 49. -
A threshold cointegration analysis of Norwegian interest rates
(Master thesis; Mastergradsoppgave, 2012-04)In this thesis we generalize the Hansen and Seo test in the R package tsDyn, which tests a linear cointegration model against a two-regime threshold cointegration model, to the case of three regimes in the alternative hypothesis. As the Lagrange Multiplier test statistic used in the Hansen and Seo test in tsDyn is different from the LM statistic described in Hansen and Seo (2002), we generalize ... -
Time series cluster kernel for learning similarities between multivariate time series with missing data
(Journal article; Tidsskriftartikkel; Peer reviewed, 2017-12-06)<p>Similarity-based approaches represent a promising direction for time series analysis. However, many such methods rely on parameter tuning, and some have shortcomings if the time series are multivariate (MTS), due to dependencies between attributes, or the time series contain missing data. In this paper, we address these challenges within the powerful context of kernel methods by proposing the ... -
The Tipping Effect of Delayed Interventions on the Evolution of COVID-19 Incidence
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-04-23)We combine infectious disease transmission and the non-pharmaceutical (NPI) intervention response to disease incidence into one closed model consisting of two coupled delay differential equations for the incidence rate and the time-dependent reproduction number. The model contains three parameters, the initial reproduction number, the intervention strength, and the response delay. The response is ... -
Tipping points and crises in financial markets
(Master thesis; Mastergradsoppgave, 2015-05-15)Electricity spot markets and other financial markets are complex systems, and it is difficult to forecast their behaviour, especially uncontrolled and unmanageable situations, such as power crises and deflation of financial bubbles. An energy crisis is any price rise in the supply of energy resources to an economy. It has undesirable consequences, occasionally irreversible. The most known of these ... -
A toolbox for fitting complex spatial point process models using integrated nested Laplace approximation (INLA)
(Journal article; Tidsskriftartikkel; Peer reviewed, 2012)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, ... -
Total Variation Graph Neural Networks
(Journal article; Tidsskriftartikkel, 2023-07)Recently proposed Graph Neural Networks (GNNs) for vertex clustering are trained with an unsupervised minimum cut objective, approximated by a Spectral Clustering (SC) relaxation. However, the SC relaxation is loose and, while it offers a closed-form solution, it also yields overly smooth cluster assignments that poorly separate the vertices. In this paper, we propose a GNN model that computes cluster ... -
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 ... -
Towers of Betti Numbers of Matroids and Weight Distribution of Linear Codes and their Duals
(Master thesis; Mastergradsoppgave, 2015-05-15)The main notion behind the study of matroids is linear dependence. In this thesis, we give a survey of the concepts and properties of linear error-correcting codes over finite fields being dependent only on the matroids derived from these codes. In particular, the weight distributions of linear codes, and their extensions, over bigger fields are only dependent on the N-graded Betti numbers of these ... -
Trans-dimensional inference over Bayesian neural networks
(Master thesis; Mastergradsoppgave, 2021-06-03)Trans-dimensional Bayesian inference for multi-layer perceptron architectures of varying size by reversible jump Markov chain Monte Carlo is developed and examined for its theoretical and practical merits and considerations. The algorithm features the No-U-Turn Sampler and Hamiltonian Monte Carlo for within-dimension moves, and makes use of a delayed-rejection sampler while exploring a variety of ... -
Two models of population genetics
(Master thesis; Mastergradsoppgave, 2008-06-02)The production of proteins in a cell is a regulated process. This means that the cell will only produce a type of protein when that type is needed. A fundamental step where this regulation occurs is at gene transcription. It is observed that transcription is regulated differently for different genes, and the question is therefore asked: why has evolution come up with different modes of transcriptional ... -
A Two-Component Generalization of the Integrable rdDym Equation
(Journal article; Tidsskriftartikkel; Peer reviewed, 2012)We find a two-component generalization of the integrable case of rdDym equation. The reductions of this system include the general rdDym equation, the Boyer-Finley equation, and the deformed Boyer-Finley equation. Also we find a Bäcklund transformation between our generalization and Bodganov's two-component generalization of the universal hierarchy equatio -
Understanding Pooling in Graph Neural Networks
(Journal article; Tidsskriftartikkel; Peer reviewed, 2022-07-21)Many recent works in the field of graph machine learning have introduced pooling operators to reduce the size of graphs. In this article, we present an operational framework to unify this vast and diverse literature by describing pooling operators as the combination of three functions: selection, reduction, and connection (SRC). We then introduce a taxonomy of pooling operators, based on some of ... -
The Unidirectional Pulse Propagation Equation for Cylindrical Vector modes
(Master thesis; Mastergradsoppgave, 2015-07-27)A new model for the unidirectional pulse propagation equations (UPPE) was developed by Per Jacobsen[1], this model is based on the assumption of cylindrical vector (CV) modes. The model will be strong for CV type electrical eld representations where only a few modes will be excited. In this thesis we will investigate the model further. The model will be implemented as a pseudo spectral method where ... -
Unsupervised segmentation of skin lesions
(Master thesis; Mastergradsoppgave, 2008-11-15)During the last decades, the incidence rate of cutaneous malignant melanoma, a type of skin cancer developing from melanocytic skin lesions, has risen to alarmingly high levels. As there is no effective treatment for advanced melanoma, recognizing the lesion at an early stage is crucial for successful treatment. A trained expert dermatologist has an accuracy of around 75 % when diagnosing melanoma, ... -
The use of elliptic curves in cryptography
(Master thesis; Mastergradsoppgave, 2007-06)The use of elliptic curves in cryptography was suggested independently by Neal Koblitz and Victor Miller in 1985. Being a relatively new field, there is still a lot of ongoing research on the subject, but elliptic curve cryptography, or ECC for short, has already been implemented in real-life applications. Its strength was proved in 2003 when the U.S. National Security Agency adopted ECC for protecting ...
