Blar i tittel Artikler, rapporter og annet (matematikk og statistikk)

Viser treff 135-154 av 314

    • Homogeneous integrable Legendrian contact structures in dimension five 

      Doubrov, Boris; Medvedev, Alexandr; The, Dennis (Journal article; Tidsskriftartikkel; Peer reviewed, 2019-07-04)
      We consider Legendrian contact structures on odd-dimensional complex analytic manifolds. We are particularly interested in integrable structures, which can be encoded by compatible complete systems of second order PDEs on a scalar function of many independent variables and considered up to point transformations. Using the techniques of parabolic differential geometry, we compute the associated ...

    • Homogeneous Levi non-degenerate hypersurfaces in C3 

      Doubrov, Boris; Medvedev, Alexandr; The, Dennis (Journal article; Tidsskriftartikkel; Peer reviewed, 2020-06-09)
      We classify all (locally) homogeneous Levi non-degenerate real hypersurfaces in C<sup>3</sup> with symmetry algebra of dimension ≥6.

    • Homogeneous Levi non-degenerate hypersurfaces in C^3 

      Doubrov, Boris; Medvedev, Alexandr; The, Dennis (Journal article; Tidsskriftartikkel; Peer reviewed, 2020-06-09)
      We classify all (locally) homogeneous Levi non-degenerate real hypersurfaces in C<sup>3</sup> with symmetry algebra of dimension ≥6.

    • Hyperbolic cone metrics and billiards 

      Erlandsson, Viveka; Leininger, Christopher J.; Sadanand, Chandrika (Journal article; Tidsskriftartikkel; Peer reviewed, 2022-08-31)
      A negatively curved hyperbolic cone metric is called rigid if it is determined (up to isotopy) by the support of its Liouville current, and flexible otherwise. We provide a complete characterization of rigidity and flexibility, prove that rigidity is a generic property, and parameterize the associated deformation space for any flexible metric. As an application, we parameterize the space of ...

    • Hyperspectral imaging for the detection of glioblastoma tumor cells in H&E slides using convolution neural networks 

      Ortega, S.; Halicek, M.; Fabelo, H.; Camacho, R.S.; Plaza, M.L.; Godtliebsen, Fred; Callico, G. M.; Fei, Baowei (Journal article; Tidsskriftartikkel; Peer reviewed, 2020-03-30)
      Hyperspectral imaging (HSI) technology has demonstrated potential to provide useful information about the chemical composition of tissue and its morphological features in a single image modality. Deep learning (DL) techniques have demonstrated the ability of automatic feature extraction from data for a successful classification. In this study, we exploit HSI and DL for the automatic differentiation ...

    • Identifying dietary patterns across age, educational level and physical activity level in a cross-sectional study: the Tromsø Study 2015 - 2016 

      Moe, Åse Mari; Sørbye, Sigrunn Holbek; Hopstock, Laila Arnesdatter; Carlsen, Monica Hauger; Løvsletten, Ola; Ytterstad, Elinor (Journal article; Tidsskriftartikkel; Peer reviewed, 2022-09-15)
      <p><b>Background</b> A healthy diet can decrease the risk of several lifestyle diseases. From studying the health effects of single foods, research now focuses on examining complete diets and dietary patterns reflecting the combined intake of different foods. The main goals of the current study were to identify dietary patterns and then investigate how these differ in terms of sex, age, educational ...

    • Incorporating capture heterogeneity in the estimation of autoregressive coefficients of animal population dynamics using capture–recapture data 

      Nicolau, Pedro Guilherme; Sørbye, Sigrunn Holbek; Yoccoz, Nigel (Journal article; Tidsskriftartikkel; Peer reviewed, 2020-08-31)
      Population dynamic models combine density dependence and environmental effects. Ignoring sampling uncertainty might lead to biased estimation of the strength of density dependence. This is typically addressed using state‐space model approaches, which integrate sampling error and population process estimates. Such models seldom include an explicit link between the sampling procedures and the true ...

    • Instance Segmentation of Microscopic Foraminifera 

      Johansen, Thomas Haugland; Sørensen, Steffen Aagaard; Møllersen, Kajsa; Godtliebsen, Gustav (Journal article; Tidsskriftartikkel; Peer reviewed, 2021-07-16)
      Foraminifera are single-celled marine organisms that construct shells that remain as fossils in the marine sediments. Classifying and counting these fossils are important in paleo-oceanographic and -climatological research. However, the identification and counting process has been performed manually since the 1800s and is laborious and time-consuming. In this work, we present a deep learning-based ...

    • Institutt for matematiske realfag 1972-1992. IMR 20 år. Knutepunkter i instituttets historie og perspektiver på fag og fremtid 

      Jervell, Herman Ruge; Johnsen, Ben (Research report; Forskningsrapport, 1992)

    • Integrability via Geometry: Dispersionless Differential Equations in Three and Four Dimensions 

      Calderbank, David M. J.; Kruglikov, Boris (Journal article; Tidsskriftartikkel; Peer reviewed, 2020-11-25)
      We prove that the existence of a dispersionless Lax pair with spectral parameter for a nondegenerate hyperbolic second order partial differential equation (PDE) is equivalent to the canonical conformal structure defined by the symbol being Einstein–Weyl on any solution in 3D, and self-dual on any solution in 4D. The first main ingredient in the proof is a characteristic property for dispersionless ...

    • Integrable Systems in Four Dimensions Associated with Six-Folds in Gr(4, 6) 

      Doubrov, Boris; Ferapontov, Evgeny V; Kruglikov, Boris; Novikov, Vladimir S (Journal article; Tidsskriftartikkel, 2018-01-29)
      Let Gr(d, n) be the Grassmannian of <i>d</i>-dimensional linear subspaces of an <i>n</i>-dimensional vector space <i>V</i>. A submanifold <i>X</i> ⊂ Gr(<i>d, n</i>) gives rise to a differential system Σ(X) that governs <i>d</i>-dimensional submanifolds of <i>V</i> whose Gaussian image is contained in <i>X</i>. We investigate a special case of this construction where <i>X</i> is a six-fold in Gr(4, ...

    • Inter-outbreak stability reflects the size of the susceptible pool and forecasts magnitudes of seasonal epidemics 

      Rypdal, Martin Wibe; Sugihara, George (Journal article; Tidsskriftartikkel; Peer reviewed, 2019-05-30)
      For dengue fever and other seasonal epidemics we show how the stability of the preceding inter-outbreak period can predict subsequent total outbreak magnitude, and that a feasible stability metric can be computed from incidence data alone. As an observable of a dynamical system, incidence data contains information about the underlying mechanisms: climatic drivers, changing serotype pools, the ecology ...

    • Interplay between advective, diffusive and active barriers in (rotating) Rayleigh-Bénard flow 

      Aksamit, Nikolas Olson; Hartmann, Robert; Lohse, Detlef; Haller, George (Journal article; Tidsskriftartikkel; Peer reviewed, 2023-08-22)
      Our understanding of the material organization of complex fluid flows has benefited recently from mathematical developments in the theory of objective coherent structures. These methods have provided a wealth of approaches that identify transport barriers in three-dimensional (3-D) turbulent flows. Specifically, theoretical advances have been incorporated into numerical algorithms that extract ...

    • Invariant characterization of Liouville metrics and polynomial integrals 

      Kruglikov, Boris (Journal article; Tidsskriftartikkel; Peer reviewed, 2007-09-04)
      A criterion in terms of differential invariants for a metric on a surface to be Liouville is established. Moreover, in this paper we completely solve in invariant terms the local mobility problem of a 2D metric, considered by Darboux: How many quadratic in momenta integrals does the geodesic flow of a given metric possess? The method is also applied to recognition of other polynomial integrals ...

    • Invariants and submanifolds in almost complex geometry 

      Kruglikov, Boris (Chapter; Bokkapittel, 2007-12-20)
      In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of higher-dimensional pseudoholomorphic submanifolds.

    • Invariants of pseudogroup actions: Homological methods and Finiteness theorem 

      Kruglikov, Boris; Lychagin, Valentin V. (Working paper; Arbeidsnotat, 2005-12-07)
      We study the equivalence problem of submanifolds with respect to a transitive pseudogroup action. The corresponding differential invariants are determined via formal theory and lead to the notions of l-variants and l-covariants, even in the case of non-integrable pseudogroup. Their calculation is based on the cohomological machinery: We introduce a complex for covariants, define their cohomology ...

    • Involutivity of field equations 

      Kruglikov, Boris (Working paper; Arbeidsnotat, 2009-02-10)
      We prove involutivity of Einstein and Einstein-Maxwell equations by calculating the Spencer cohomology of these systems. Relation with Cartan method is traced in details. Basic implications through Cartan-Kähler theory are derived.

    • Is there a break in scaling on centennial time scales in Holocene temperature records? 

      Nilsen, Tine; Rypdal, Kristoffer; Fredriksen, Hege-Beate (Conference object; Konferansebidrag, 2017)

    • 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.

    • Joint Invariants of Linear Symplectic Actions 

      Andreassen, Fredrik; Kruglikov, Boris (Journal article; Tidsskriftartikkel; Peer reviewed, 2020-12-07)
      We review computations of joint invariants on a linear symplectic space, discuss variations for an extension of group and space and relate this to other equivalence problems and approaches, most importantly to differential invariants.