Institutt for matematikk og statistikk
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Climate variability in the subarctic area for the last 2 millennia
(Journal article; Tidsskriftartikkel; Peer reviewed, 20180125)To put recent climate change in perspective, it is necessary to extend the instrumental climate records with proxy data from paleoclimate archives. Arctic climate variability for the last 2 millennia has been investigated using statistical and signal analyses from three regionally averaged records from the North Atlantic, Siberia and Alaska based on many types of proxy data archived in the ... 
Differential invariants of EinsteinWeyl structures in 3D
(Journal article; Tidsskriftartikkel; Peer reviewed, 20180522)Einstein–Weyl structures on a threedimensional manifold <i>M</i> are given by a system <i>E</i> of PDEs on sections of a bundle over <i>M</i>. This system is invariant under the Lie pseudogroup <i>G</i> of local diffeomorphisms on <i>M</i>. Two Einstein–Weyl structures are locally equivalent if there exists a local diffeomorphism taking one to the other. Our goal is to describe the quotient equation ... 
Reflection groups, arrangements, and invariant real varieties
(Journal article; Tidsskriftartikkel; Peer reviewed, 20171018)Let <i>X</i> be a nonempty real variety that is invariant under the action of a reflection group <i>G</i>. We conjecture that if <i>X</i> is defined in terms of the first <i>k</i> basic invariants of <i>G</i> (ordered by degree), then <i>X</i> meets a <i>k</i>dimensional flat of the associated reflection arrangement. We prove this conjecture for the infinite types, reflection groups of rank at most ... 
On the Isotypic Decomposition of Cohomology Modules of Symmetric Semialgebraic Sets: Polynomial Bounds on Multiplicities
(Journal article; Tidsskriftartikkel; Peer reviewed, 20180430)We consider symmetric (under the action of products of finite symmetric groups) real algebraic varieties and semialgebraic sets, as well as symmetric complex varieties in affine and projective spaces, defined by polynomials of degrees bounded by a fixed constant <i>d</i>. We prove that if a Specht module, S<sup>λ</sup>, appears with positive multiplicity in the isotypic decomposition of the ... 
On the equivariant Betti numbers of symmetric definable sets: vanishing, bounds and algorithms
(Journal article; Tidsskriftartikkel; Peer reviewed, 20180302)Let R be a real closed field. We prove that for any fixed <i>d</i>, the equivariant rational cohomology groups of closed symmetric semialgebraic subsets of R<sup><i>k</i></sup> defined by polynomials of degrees bounded by <i>d</i> vanishes in dimensions <i>d</i> and larger. This vanishing result is tight. Using a new geometric approach we also prove an upper bound of [mathematical formula] on the ... 
Assessing the performance of the BARCAST climate field reconstruction technique for a climate with longrange memory
(Journal article; Tidsskriftartikkel; Peer reviewed, 20180629)The skill of the stateoftheart climate field reconstruction technique BARCAST (Bayesian Algorithm for Reconstructing Climate Anomalies in Space and Time) to reconstruct temperature with pronounced longrange memory (LRM) characteristics is tested. A novel technique for generating fields of target data has been developed and is used to provide ensembles of LRM stochastic processes with a prescribed ... 
Clustering and climate associations of Kawasaki Disease in San Diego County suggest environmental triggers
(Journal article; Tidsskriftartikkel; Peer reviewed, 20181112)Kawasaki Disease (KD) is the most common cause of pediatric acquired heart disease, but its etiology remains unknown. We examined 1164 cases of KD treated at a regional children’s hospital in San Diego over a period of 15 years and uncovered novel structure to disease incidence. KD cases showed a welldefined seasonal variability, but also clustered temporally at much shorter time scales (days to ... 
Spatiotemporal variability of Arctic summer temperatures over the past 2 millennia
(Journal article; Tidsskriftartikkel; Peer reviewed, 20180424)<p>In this article, the first spatially resolved and millenniumlength summer (June–August) temperature reconstruction over the Arctic and subArctic domain (north of 60°N) is presented. It is based on a set of 44 annually dated temperaturesensitive proxy archives of various types from the revised PAGES2k database supplemented with six new recently updated proxy records. As a major advance, an ... 
Projectable Lie algebras of vector fields in 3D
(Journal article; Tidsskriftartikkel; Peer reviewed, 20180615)Starting with Lie’s classification of finitedimensional transitive Lie algebras of vector fields on <b>C<sup>2</sup></b> we construct transitive Lie algebras of vector fields on the bundle <b>C<sup>2</sup> x C</b> by lifting the Lie algebras from the base. There are essentially three types of transitive lifts and we compute all of them for the Lie algebras from Lie’s classification. The simplest ... 
Exceptionally simple PDE
(Journal article; Tidsskriftartikkel; Peer reviewed, 20171108)We give local descriptions of parabolic contact structures and show how their flat models yield explicit PDE having symmetry algebras isomorphic to all complex simple Lie algebras except <math><msub is="true"><mrow is="true"><mi mathvariant="fraktur" is="true">sl</mi></mrow><mrow is="true"><mn is="true">2</mn></mrow></msub></math>. This yields a remarkably uniform generalization of the Cartan–Engel ... 
Control of Blood Glucose for Type1 Diabetes by Using Reinforcement Learning with Feedforward Algorithm
(Journal article; Tidsskriftartikkel; Peer reviewed, 20181230)<p><i>Background</i>: Type1 diabetes is a condition caused by the lack of insulin hormone, which leads to an excessive increase in blood glucose level. The glucose kinetics process is difficult to control due to its complex and nonlinear nature and with state variables that are difficult to measure.</p> <p><i>Methods</i>: This paper proposes a method for automatically calculating the basal and ... 
Kayas identitet og valgets kval
(Chronicle; Kronikk, 20170821)<i>Ingress</i>: Det Kayas identitet viser oss er for det første at for å redusere utslippene må vi gjøre noe med befolkningsveksten og/eller en eller flere av de tre intensitetene. 
Rigidity of 2step carnot groups
(Journal article; Tidsskriftartikkel; Peer reviewed, 20170619)In the present paper we study the rigidity of 2step Carnot groups, or equivalently, of graded 2step nilpotent Lie algebras. We prove the alternative that depending on bidimensions of the algebra, the Lie algebra structure makes it either always of inﬁnite type or generically rigid, and we specify the bidimensions for each of the choices. Explicit criteria for rigidity of pseudo Hand <i>J</i>type ... 
Bayesian analysis of temporal and spatial trends of house prices in Norway
(Master thesis; Mastergradsoppgave, 20180921)The goal of this thesis is to analyse the temporal and spatial trends of house prices in Norway in a Bayesian setting. We will perform regression analysis of the data which will be modelled using structured additive regression models. This choice was made because structured additive regression models can be put into a computational framework of latent Gaussian models that can be analysed using ... 
Mathematics of Viral Infections: A Review of Modeling Approaches and A CaseStudy for Dengue Dynamics
(Master thesis; Mastergradsoppgave, 20180920)In this thesis we use mathematical models to study the mechanisms by which diseases spread. Transmission dynamics is modelled by the class of SIR models, where the abbreviation stands for susceptible (S), infected (I) and recovered (R). These models are also called compartmental models, and they serve as the basic mathematical framework for understanding the complex dynamics of infectious diseases. ... 
The NISK 2018 Proceedings: Message from the Programme Chairs
(Journal article; Tidsskriftartikkel; Peer reviewed, 2018)This NISK Journal volume 11 is the published proceedings of the papers presented at NISK 2018: the 11th Norwegian Information Security Conference 2018 held on September 1820, 2018 in Longyearbyen, Svalbard. The aim of the NISK conference series is to be the principal Norwegian research venue for presenting and discussing developments in the field of ICT security and privacy, and bringing together ... 
Frailty in Survival Analysis of Widowhood Mortality
(Journal article; Tidsskriftartikkel; Peer reviewed, 20181002)Heterogeneity between individuals has attracted attention in the literature of survival analysis for several decades. Widowed individuals also differ; some are more frail than others and thereby have a higher risk of dying. The traditional hazard rate in a survival model is a measure of population risk and does not provide direct information on the unobservable individual risk. A frailty model is ... 
Scaling of global temperatures explained by linear energy balance models
(Journal article; Tidsskriftartikkel; Peer reviewed, 201712)<i>Introduction</i>: Scale invariance of natural variability of global surface temperatures is often interpreted as a signature of nonlinear dynamics. However, the observed scaling can be adequately explained by linear energy balance involving subsystems with different response times. 
Robust clustering using a kNN mode seeking ensemble
(Journal article; Tidsskriftartikkel; Peer reviewed, 20171202)In this paper we present a new algorithm for parameterfree clustering by mode seeking. Mode seeking, especially in the form of the mean shift algorithm, is a widely used strategy for clustering data, but at the same time prone to poor performance if the parameters are not chosen correctly. We propose to form a <i>clustering ensemble</i> consisting of repeated and bootstrapped runs of the recent kNN ... 
On the symmetry algebras of 5dimensional CRmanifolds
(Journal article; Tidsskriftartikkel; Peer reviewed, 20171113)We show that for a realanalytic connected holomorphically nondegenerate 5dimensional CRhypersurface <i>M</i> and its symmetry algebra <i>s</i> one has either: (i) dim <i>s</i> = 15 and <i>M</i> is spherical (with Levi form of signature either (2,0), or (1,1), everywhere), or (ii) dim <i>s</i> ≤ 11 where dim <i>s</i> = 11 can only occur if on a dense open subset <i>M</i> is spherical with Levi ...