Artikler, rapporter og annet (matematikk og statistikk)
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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 ... 
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; Manuskript; 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 ...