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  • Scaling of global temperatures explained by linear energy balance models 

    Rypdal, Kristoffer; Fredriksen, Hege-Beate (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-12)
    <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 

    Myhre, Jonas Nordhaug; Mikalsen, Karl Øyvind; Løkse, Sigurd; Jenssen, Robert (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-12-02)
    In this paper we present a new algorithm for parameter-free 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 5-dimensional CR-manifolds 

    Isaev, Alexander; Kruglikov, Boris (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-11-13)
    We show that for a real-analytic connected holomorphically nondegenerate 5-dimensional CR-hypersurface <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 sub-Riemannian structures 

    Kruglikov, Boris; Vollmer, Andreas; Lukes-Gerakopoulos, Georgios (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-10-01)
    We discuss rank 2 sub-Riemannian structures on low-dimensional 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 

    Rypdal, Kristoffer (Journal article; Tidsskriftartikkel; Peer reviewed, 2018-07-21)
    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 long-memory 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 two-party wire-tap channel of type II 

    Johnsen, Trygve; Verdure, Hugues (Journal article; Tidsskriftartikkel; Peer reviewed; Preprint, 2017-11-15)
    We describe a two-party wire-tap 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 

    Mikalsen, Karl Øyvind; Bianchi, Filippo Maria; Soguero-Ruiz, Cristina; Jenssen, Robert (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 ...
  • Bayesian Computing with INLA: A Review 

    Rue, Håvard; Riebler, Andrea Ingeborg; Sørbye, Sigrunn Holbek; Illian, Janine B.; Simpson, Daniel Peter; Lindgren, Finn Kristian (Journal article; Tidsskriftartikkel, 2016-12-23)
    The key operation in Bayesian inference is to compute high-dimensional integrals. An old approximate technique is the Laplace method or approximation, which dates back to Pierre-Simon Laplace (1774). This simple idea approximates the integrand with a second-order 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 

    Kruglikov, Boris; The, Dennis (Journal article; Tidsskriftartikkel; Peer reviewed, 2014-09-14)
    The infinitesimal symmetry algebra of any Cartan geometry has maximum dimension realized by the flat model, but often this dimension drops significantly when considering non-flat 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 

    Rypdal, Kristoffer (Journal article; Tidsskriftartikkel; Peer reviewed, 2018-07-25)
    Three simple, empirical models for growth of power consumption in the renewable energy sector are compared. These are the exponential, logistic, and power-law models. The exponential model describes growth at a fixed relative growth rate, the logistic model saturates at a fixed limit, while the power-law model describes slowing, but unlimited, growth. The model parameters are determined by regression ...
  • Finite dimensional dynamics for nonlinear filtration equation 

    Akhmetzyanov, Atlas V.; Kushner, Alexei G.; Lychagin, Valentin (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-09-01)
    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 

    Simpson, Daniel; Rue, Håvard; Riebler, Andrea Ingeborg; Martins, Thiago Guerrera; Sørbye, Sigrunn Holbek (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-04-06)
    <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 Monge-Ampère type 

    Doubrov, Boris; Ferapontov, Eugene V.; Kruglikov, Boris; Novikov, Vladimir S. (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-06-08)
    We investigate a class of multi-dimensional two-component systems of Monge-Ampère type that can be viewed as generalisations of heavenly type equations appearing in a self-dual Ricci-flat geometry. Based on the Jordan-Kronecker theory of the skew-symmetric matrix pencils, a classification of normal forms of such systems is obtained. All two-component systems of Monge-Ampère type turn out to be ...
  • Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors 

    Simpson, Daniel; Rue, Håvard; Riebler, Andrea Ingeborg; Martins, Thiago Guerrera; Sørbye, Sigrunn Holbek (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-04-06)
    In this paper, we introduce a new concept for constructing prior distributions. We exploit the natural nested structure inherent to many model components, which defines the model component to be a flexible extension of a base model. Proper priors are defined to penalise the complexity induced by deviating from the simpler base model and are formulated after the input of a user-defined scaling parameter ...
  • Extreme-value statistics from Lagrangian convex hull analysis for homogeneous turbulent Boussinesq convection and MHD convection 

    Pratt, J; Busse, A; Muller, WC; Watkins, NW; Chapman, Sandra (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-06-20)
    We investigate the utility of the convex hull of many Lagrangian tracers to analyze transport properties of turbulent flows with different anisotropy. In direct numerical simulations of statistically homogeneous and stationary Navier–Stokes turbulence, neutral fluid Boussinesq convection, and MHD Boussinesq convection a comparison with Lagrangian pair dispersion shows that convex hull statistics ...
  • Long-range persistence in global surface temperatures explained by linear multibox energy balance models 

    Fredriksen, Hege-Beate; Rypdal, Martin Wibe (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-09-15)
    The temporal fluctuations in global mean surface temperature are an example of a geophysical quantity that can be described using the notions of long-range persistence and scale invariance/scaling, but this description has suffered from lack of a generally accepted physical explanation. Processes with these statistical signatures can arise from nonlinear effects, for instance, through cascade-like ...
  • Submaximally symmetric almost quaternionic structures 

    Kruglikov, Boris; Winther, Henrik; Zalabová, Lenka (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-11-10)
    The symmetry dimension of a geometric structure is the dimension of its symmetry algebra. We investigate symmetries of almost quaternionic structures of quaternionic dimension <i>n</i>. The maximal possible symmetry is realized by the quaternionic projective space H<i>P<sup> n</sup></i>, which is flat and has the symmetry algebra sl(<i>n</i> + 1, H) of dimension 4<i>n</i><sup> 2</sup> + ...
  • Penalised Complexity Priors for Stationary Autoregressive Processes 

    Sørbye, Sigrunn Holbek; Rue, Håvard (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-05-23)
    The autoregressive (AR) process of order p(AR(p)) is a central model in time series analysis. A Bayesian approach requires the user to define a prior distribution for the coefficients of the AR(p) model. Although it is easy to write down some prior, it is not at all obvious how to understand and interpret the prior distribution, to ensure that it behaves according to the users' prior knowledge. In ...
  • Jet-determination of symmetries of parabolic geometries 

    Kruglikov, Boris; The, Dennis (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-04-24)
    We establish 2-jet determinacy for the symmetry algebra of the underlying structure of any (complex or real) parabolic geometry. At non-flat points, we prove that the symmetry algebra is in fact 1-jet determined. Moreover, we prove 1-jet determinacy at any point for a variety of non-flat parabolic geometries—in particular torsion-free, parabolic contact, and several other classes.
  • Fractional Gaussian noise: Prior specification and model comparison 

    Sørbye, Sigrunn Holbek; Rue, Håvard (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-07-07)
    Fractional Gaussian noise (fGn) is a stationary stochastic process used to model anti-persistent or persistent dependency structures in observed time series. Properties of the autocovariance function of fGn are characterised by the Hurst exponent (<i>H)</i>, which in Bayesian contexts typically has been assigned a uniform prior on the unit interval. This paper argues why a uniform prior is ...

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