Browsing Institutt for matematikk og statistikk by Issue Date

Now showing items 41-60 of 389

    • Compatibility, multi-brackets and integrability of systems of PDEs 

      Kruglikov, Boris; Lychagin, Valentin V. (Journal article; Tidsskriftartikkel; Peer reviewed, 2008-02-20)
      We establish an efficient compatibility criterion for a system of generalized complete intersection type in terms of certain multi-brackets of differential operators. These multi-brackets generalize the higher Jacobi- Mayer brackets, important in the study of evolutionary equations and the integrability problem. We also calculate Spencer δ-cohomology of generalized complete intersections and ...

    • Estimation of Ambiguity Functions With Limited Spread 

      Hindberg, Heidi; Olhede, Sofia C. (Research report; Forskningsrapport, 2008-04-07)
      This paper proposes a new estimation procedure for the ambiguity function of a non-stationary time series. The stochastic properties of the empirical ambiguity function calculated from a single sample in time are derived. Different thresholding procedures are introduced for the estimation of the ambiguity function. Such estimation methods are suitable if the ambiguity function is only non-negligible ...

    • Two models of population genetics 

      Skancke, Jørgen (Master thesis; Mastergradsoppgave, 2008-06-02)
      The production of proteins in a cell is a regulated process. This means that the cell will only produce a type of protein when that type is needed. A fundamental step where this regulation occurs is at gene transcription. It is observed that transcription is regulated differently for different genes, and the question is therefore asked: why has evolution come up with different modes of transcriptional ...

    • Large eddy simulation of homogeneous isotropic turbulence 

      Zeigler, Harald Bergersen (Master thesis; Mastergradsoppgave, 2008-06-02)
      The theme for the master thesis is simulation of homogeneous, isotropic turbulence. I have shown that the energy of the velocity field is decaying in time, but the comparison to the reference solution is however invalid, due to the fact that the reference solution may have scalings that are not obvious to the observer, and that my own simulation results seemed to behave quite strange, with a sudden ...

    • Modeling temporal fluctuations in avalanching system 

      Rypdal, Martin; Rypdal, Kristoffer (Working paper; Arbeidsnotat, 2008-07-22)
      We demonstrate how to model the toppling activity in avalanching systems by stochastic differential equations (SDEs). The theory is developed as a generalization of the classical mean field approach to sandpile dynamics by formulating it as a generalization of Itoh’s SDE. This equation contains a fractional Gaussian noise term representing the branching of an avalanche into small active clusters, ...

    • A stochastic theory for temporal fluctuations in self-organized critical systems 

      Rypdal, Martin; Rypdal, Kristoffer (Working paper; Arbeidsnotat, 2008-07-22)
      A stochastic theory for the toppling activity in sandpile models is developed, based on a simple mean-field assumption about the toppling process. The theory describes the process as an anti-persistent Gaussian walk, where the diffusion coefficient is proportional to the activity. It is formulated as a generalization of the Itˆo stochastic differential equation with an anti-persistent fractional ...

    • Point classification of 2nd order ODEs: Tresse classification revisited and beyond 

      Kruglikov, Boris (Chapter; Bokkapittel, 2008-09-26)
      In 1896 Tresse gave a complete description of relative differential invariants for the pseudogroup action of point transformations on the 2nd order ODEs. The purpose of this paper is to review, in light of modern geometric approach to PDEs, this classification and also discuss the role of absolute invariants and the equivalence problem.

    • Geodesic Webs on a Two-Dimensional Manifold and Euler Equations 

      Goldberg, Vladislav V.; Lychagin, Valentin V. (Journal article; Tidsskriftartikkel; Peer reviewed, 2008-10-30)
      We prove that any planar 4-web defines a unique projective structure in the plane in such a way that the leaves of the web foliations are geodesics of this projective structure. We also find conditions for the projective structure mentioned above to contain an affine symmetric connection, and conditions for a planar 4-web to be equivalent to a geodesic 4-web on an affine symmetric surface. Similar ...

    • Geodesic Webs and PDE Systems of Euler Equations 

      Goldberg, Vladislav V.; Lychagin, Valentin V. (Journal article; Tidsskriftartikkel; Peer reviewed, 2008-10-30)
      We find necessary and sufficient conditions for the foliation defined by level sets of a function f(x1, ..., xn) to be totally geodesic in a torsion-free connection and apply them to find the conditions for d-webs of hypersurfaces to be geodesic, and in the case of flat connections, for d-webs (d ≥ n + 1) of hypersurfaces to be hyperplanar webs. These conditions are systems of generalized Euler ...

    • Unsupervised segmentation of skin lesions 

      Møllersen, Kajsa (Master thesis; Mastergradsoppgave, 2008-11-15)
      During the last decades, the incidence rate of cutaneous malignant melanoma, a type of skin cancer developing from melanocytic skin lesions, has risen to alarmingly high levels. As there is no effective treatment for advanced melanoma, recognizing the lesion at an early stage is crucial for successful treatment. A trained expert dermatologist has an accuracy of around 75 % when diagnosing melanoma, ...

    • On Rank Problems for Planar Webs and Projective Structures 

      Lychagin, Valentin V.; Goldberg, Vladislav V. (Chapter; Bokkapittel, 2008-12-03)
      We present some old and recent results on rank problems and linearizability of geodesic planar webs

    • 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.

    • Geodesic Webs of Hypersurfaces 

      Goldberg, Vladislav V.; Lychagin, Valentin V. (Working paper; Arbeidsnotat, 2008-12-11)
      In the present paper we study geometric structures associated with webs of hypersurfaces. We prove that with any geodesic (n + 2)-web on an n-dimensional manifold there is naturally associated a unique projective structure and, provide that one of web foliations is pointed, there is also associated a unique affine structure. The projective structure can be chosen by the claim that the leaves of all ...

    • On a class of linearizable planar geodesic webs 

      Goldberg, Vladislav V.; Lychagin, Valentin V. (Working paper; Arbeidsnotat, 2008-12-13)
      We present a complete description of a class of linearizable planar geodesic webs which contain a parallelizable 3-subweb.

    • Finite Larmor radius influence on MHD solitary waves 

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

    • 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.

    • Distributing a private key generator in Ad hoc Networks 

      Stenberg, Eystein Måløy (Master thesis; Mastergradsoppgave, 2009-05-15)
      A Mobile Ad hoc Network (MANET) is a wireless network that does not rely on a fixed infrastructure. These characteristics make algorithms that route network traffic particularly vulnerable to attack. Mechanisms used to protect against such attacks often depend on cryptographic keys. Since the nodes in a MANET have limited resources, designing methods for cryptographic key management is ...

    • Applying the ICM algorithm for separating pictures consisting of two main parts, background and object application to fMRI recordings and mole pictures 

      Larsen, Are (Master thesis; Mastergradsoppgave, 2009-05-15)
      This work concentrates on using the ICM algorithm for image restoration. The algorithm has been applied to fMRI recordings and mole pictures

    • Multi-fractal stochastic modeling of the auroral electrojet index 

      Sund, Martin Jong Yul Shon (Master thesis; Mastergradsoppgave, 2009-12-15)
      In this thesis we have analyzed the Auroral Electrojet (AE) Index over the years 2000 to 2005, a time series consisting of over 3 000 000 data points. The aim is to describe this data as a multi-fractal stochastic process. We first introduce a class of random multiplicative measures, which provide the multi-fractality in the stochastic processes that will be defined later. We also review the ...