Browsing Artikler, rapporter og annet (matematikk og statistikk) by Title

Now showing items 89-108 of 314

    • Exact semidefinite programming bounds for packing problems 

      Dostert, Maria; de Laat, David; Moustrou, Philippe (Journal article; Tidsskriftartikkel; Peer reviewed, 2021-05-25)
      In this paper we give an algorithm to round the floating point output of a semidefinite programming solver to a solution over the rationals or a quadratic extension of the rationals. This algorithm does not require the solution to be strictly feasible and works for large problems. We apply this to get sharp bounds for packing problems, and we use these sharp bounds to prove that certain optimal ...

    • Examples of integrable sub-Riemannian geodesic flows 

      Kruglikov, Boris (Journal article; Tidsskriftartikkel; Peer reviewed, 2001-10-22)
      We exhibit examples of sub-Riemannian metrics with integrable geodesic flows and positive topological entropy.

    • Exceptionally simple PDE 

      The, Dennis (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-11-08)
      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 ...

    • Exceptionally simple super-PDE for F (4) 

      Santi, Andrea; The, Dennis (Journal article; Tidsskriftartikkel; Peer reviewed, 2024-02-01)
      For the largest exceptional simple Lie superalgebra F(4), having dimension (24|16), we provide two explicit geometric realizations as supersymmetries, namely as the symmetry superalgebra of super-PDE systems of second and third order respectively.

    • Existence of close pseudoholomorphic disks for almost complex manifolds and an applications to Kobayashi-Royden pseudonorm 

      Kruglikov, Boris (Journal article; Tidsskriftartikkel; Peer reviewed, 2000-02-23)
      It is proved in the paper that near every pseudoholomorphic disk on an almost complex manifold a disk of almost the same size in any close direction passes. As an application the Kobayashi-Royden pseudonorm for almost complex manifolds is defined and studied.

    • Explainability in subgraphs-enhanced Graph Neural Networks 

      Guerra, Michele; Bianchi, Filippo Maria; Scardapane, Simone; Spinelli, Indro (Journal article; Tidsskriftartikkel, 2023)
      Recently, subgraphs-enhanced Graph Neural Networks (SGNNs) have been introduced to enhance the expressive power of Graph Neural Networks (GNNs), which was proved to be not higher than the 1-dimensional Weisfeiler-Leman isomorphism test. The new paradigm suggests using subgraphs extracted from the input graph to improve the model’s expressiveness, but the additional complexity exacerbates an ...

    • Explicit values for Ramanujan's theta function φ(q) 

      Berndt, Bruce C.; Rebák, Örs (Journal article; Tidsskriftartikkel; Peer reviewed, 2022-01-09)
      This paper provides a survey of particular values of Ramanujan's theta function φ(q) = ∑ q^(n^2), n = −∞ ... ∞, when q = e^(−π√n), where n is a positive rational number. First, descriptions of the tools used to evaluate theta functions are given. Second, classical values are briefly discussed. Third, certain values due to Ramanujan and later authors are given. Fourth, the methods that are used to ...

    • The expressive power of pooling in Graph Neural Networks 

      Bianchi, Filippo Maria; Lachi, Veronica (Journal article; Tidsskriftartikkel; Peer reviewed, 2023)
      In Graph Neural Networks (GNNs), hierarchical pooling operators generate local summaries of the data by coarsening the graph structure and the vertex features. While considerable attention has been devoted to analyzing the expressive power of message-passing (MP) layers in GNNs, a study on how graph pooling affects the expressiveness of a GNN is still lacking. Additionally, despite the recent advances ...

    • Extreme Event Statistics in Dst, SYM-H, and SMR Geomagnetic Indices 

      Bergin, A.; Chapman, Sandra; Watkins, N.W.; Moloney, N.R.; Gjerløv, Jesper (Journal article; Tidsskriftartikkel; Peer reviewed, 2023-03-20)
      Extreme space weather events are rare, and quantifying their likelihood is challenging, often relying on geomagnetic indices obtained from ground-based magnetometer observations that span multiple solar cycles. The Dst index ring-current monitor, derived from an hourly average over four low-latitude stations, is a benchmark for extreme space weather events, and has been extensively studied ...

    • 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 ...

    • Factorisation patterns of division polynomials 

      Verdure, Hugues (Journal article; Tidsskriftartikkel; Peer reviewed, 2004-05)
      The choice of an elliptic curve for the implementa- tion of an elliptic curve cryptosystem requires count- ing the number of points on such a curve over a fi- nite field. An improvement of Schoof’s algorithm for counting the number of rational points on an ellip- tic curve defined over a finite field takes advantage of some factor of the division polynomials. In this paper, we study the ...

    • Families of Gröbner Degenerations, Grassmannians and Universal Cluster Algebras 

      Bossinger, Lara; Mohammadi, Fatemeh; Nájera Chávez, Alfredo (Journal article; Tidsskriftartikkel; Peer reviewed, 2021-06-10)
      Let V be the weighted projective variety defined by a weighted homogeneous ideal J and C a maximal cone in the Gröbner fan of J with m rays. We construct a flat family over A<sup>m</sup> that assembles the Gröbner degenerations of V associated with all faces of C. This is a multi-parameter generalization of the classical one-parameter Gröbner degeneration associated to a weight. We explain how our ...

    • Feedback Differential Invariants 

      Lychagin, Valentin V. (Journal article; Tidsskriftartikkel, 2008-12-07)
      The problem of feedback equivalence for control systems is considered. An algebra of differential invariants and criteria for the feedback equivalence for regular control systems are found.

    • Feedback Equivalence of 1-dimensional Control Systems of the 1-st Order 

      Lychagin, Valentin V. (Working paper; Arbeidsnotat, 2008-12-09)
      The problem of local feedback equivalence for 1-dimensional control systems of the 1-st order is considered. The algebra of differential invariants and criteria for the feedback equivalence for regular control systems are found.

    • 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.

    • Finite Larmor radius influence on MHD solitary waves 

      Mjølhus, Einar (Journal article; Tidsskriftartikkel; Peer reviewed, 2009)

    • A finite volume flux coordinate independent approach 

      Wiesenberger, Matthias; Held, Markus (Journal article; Tidsskriftartikkel; Peer reviewed, 2023-07-03)
      We present a novel family of schemes as the merging between a one-dimensional advection scheme with the flux coordinate independent approach. The scheme can be used to discretize the field-aligned NavierStokes equations in three dimensions. Our approach consists of three major steps: (i) the formulation of the one-dimensional scheme in a locally field-aligned coordinate system, (ii) a numerical ...

    • Finite-sample properties of estimators for first and second order autoregressive processes 

      Sørbye, Sigrunn Holbek; Nicolau, Pedro Guilherme; Rue, Håvard (Journal article; Tidsskriftartikkel; Peer reviewed, 2021-12-05)
      The class of autoregressive (AR) processes is extensively used to model temporal dependence in observed time series. Such models are easily available and routinely fitted using freely available statistical software like R. A potential problem is that commonly applied estimators for the coefficients of AR processes are severely biased when the time series are short. This paper studies the ...

    • Flags of almost affine codes and the two-party wire-tap channel of type II 

      Johnsen, Trygve; Verdure, Hugues (Journal article; Tidsskriftartikkel; Manuskript; 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.

    • Food recommendation using machine learning for physical activities in patients with type 1 diabetes 

      Ngo, Phuong; Tayefi, Maryam; Nordsletta, Anne Torill; Godtliebsen, Fred (Journal article; Tidsskriftartikkel; Peer reviewed, 2019)
      Physical activities have a significant impact on blood glucose homeostasis of patients with type 1 diabetes. Regular physical exercise provides many proven health benefits and is recommended as part of a healthy lifestyle. However, one of the main side effects of physical activities is hypoglycemia (low blood glucose). Fear of hypoglycemia generally leads to the patients not participating in ...