Institutt for matematikk og statistikk
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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 ... 
On integrability of certain rank 2 subRiemannian structures
(Journal article; Tidsskriftartikkel; Peer reviewed, 20171001)We discuss rank 2 subRiemannian structures on lowdimensional manifolds and prove that some of these structures in dimensions 6, 7 and 8 have a maximal amount of symmetry but no integrals polynomial in momenta of low degrees, except for those coming from the Killing vector fields and the Hamiltonian, thus indicating nonintegrability of the corresponding geodesic flows. 
The Life and Death of the Recent Global Warming Hiatus Parsimoniously Explained
(Journal article; Tidsskriftartikkel; Peer reviewed, 20180721)The main features of the instrumental global mean surface temperature (GMST) are reasonably well described by a simple linear response model driven by anthropogenic, volcanic and solar forcing. This model acts as a linear longmemory filter of the forcing signal. The physical interpretation of this filtering is the delayed response due to the thermal inertia of the ocean. This description is ... 
Flags of almost affine codes and the twoparty wiretap channel of type II
(Journal article; Tidsskriftartikkel; Peer reviewed; Preprint, 20171115)We describe a twoparty wiretap channel of type II in the framework of almost affine codes. Its cryptological performance is related to some relative profiles of a pair of almost affine codes. These profiles are analogues to relative generalized Hamming weights in the linear case. 
Time series cluster kernel for learning similarities between multivariate time series with missing data
(Journal article; Tidsskriftartikkel; Peer reviewed, 20171206)<p>Similaritybased 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 ... 
Modelling high intensity laser pulse propagation in air using the modified Kortewegde Vries equation
(Master thesis; Mastergradsoppgave, 20180601)Ultrafast laser pulse experiments and applications are entering a phase that challenges the validity of mathematical models utilised to model longer pulses in nonlinear optics. This thesis aims to propose a possible mathematical model for high intensity laser pulse propagation in air through a multiple scales expansion of Maxwell’s equations and discuss a method on how to solve the corresponding ... 
Bayesian Computing with INLA: A Review
(Journal article; Tidsskriftartikkel, 20161223)The key operation in Bayesian inference is to compute highdimensional integrals. An old approximate technique is the Laplace method or approximation, which dates back to PierreSimon Laplace (1774). This simple idea approximates the integrand with a secondorder Taylor expansion around the mode and computes the integral analytically. By developing a nested version of this classical idea, combined ... 
The gap phenomenon in parabolic geometries
(Journal article; Tidsskriftartikkel; Peer reviewed, 20140914)The infinitesimal symmetry algebra of any Cartan geometry has maximum dimension realized by the flat model, but often this dimension drops significantly when considering nonflat geometries, so a gap phenomenon arises. For general (regular, normal) parabolic geometries of type (G,P), we use Tanaka theory to derive a universal upper bound on the submaximal symmetry dimension. We use Kostant’s version ... 
Empirical Growth Models for the Renewable Energy Sector
(Journal article; Tidsskriftartikkel; Peer reviewed, 20180725)Three simple, empirical models for growth of power consumption in the renewable energy sector are compared. These are the exponential, logistic, and powerlaw models. The exponential model describes growth at a fixed relative growth rate, the logistic model saturates at a fixed limit, while the powerlaw model describes slowing, but unlimited, growth. The model parameters are determined by regression ... 
Finite dimensional dynamics for nonlinear filtration equation
(Journal article; Tidsskriftartikkel; Peer reviewed, 20170901)We construct new finite dimensional submanifolds in the solution space of nonlinear differential filtration equations and describe the corresponding evolutionary dynamics. This method is implemented in a computer program of symbolic computations Maple. 
You Just Keep on Pushing My Love over the Borderline: A Rejoinder
(Journal article; Tidsskriftartikkel; Peer reviewed, 20170406)<i>INTRODUCTION</i>: The point of departure for our paper is that most modern statistical models are built to be flexible enough to model diverse data generating mechanisms. Good statistical practice requires us to limit this flexibility, which is typically controlled by a small number of parameters, to the amount “needed” to model the data at hand. The Bayesian framework provides a natural method ... 
On a class of integrable systems of MongeAmpère type
(Journal article; Tidsskriftartikkel; Peer reviewed, 20170608)We investigate a class of multidimensional twocomponent systems of MongeAmpère type that can be viewed as generalisations of heavenly type equations appearing in a selfdual Ricciflat geometry. Based on the JordanKronecker theory of the skewsymmetric matrix pencils, a classification of normal forms of such systems is obtained. All twocomponent systems of MongeAmpère type turn out to be ...