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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, 15-May-2009)

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Abstract: This work concentrates on using the ICM algorithm for image restoration. The algorithm has been applied to fMRI recordings and mole pictures

URI: http://hdl.handle.net/10037/2071

File(s) in this item: 1

thesis.pdf (3.404Mb)

A piece-wise affine contracting map with positive entropy

Kruglikov, Boris; Rypdal, Martin (Working paper; Arbeidsnotat, 10-Apr-2005)

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Abstract: We construct the simplest chaotic system with a two-point attractor.

URI: http://hdl.handle.net/10037/1863

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article.pdf (74.93Kb)
A propagation-separation approach to estimate the autocorrelation in a time-series

Polzehl, J; Divine, Dmitry V; Godtliebsen, Fred (Journal article; Tidsskriftartikkel; Peer reviewed, 2008)

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URI: http://hdl.handle.net/10037/3132

File(s) in this item: 1

article.pdf (500.3Kb)

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

Rypdal, Martin; Rypdal, Kristoffer (Journal article; Tidsskriftartikkel; Peer reviewed, 2008)

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URI: http://hdl.handle.net/10037/3144

File(s) in this item: 1

article.pdf (840.9Kb)

A threshold cointegration analysis of Norwegian interest rates

Larsen, Berner (Master thesis; Mastergradsoppgave, Apr-2012)

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Abstract:

In this thesis we generalize the Hansen and Seo test in the R package tsDyn, which tests a linear cointegration model against a two-regime threshold cointegration model, to the case of three regimes in the alternative hypothesis. As the Lagrange Multiplier test statistic used in the Hansen and Seo test in tsDyn is different from the LM statistic described in Hansen and Seo (2002), we generalize both these LM statistics, and show that they are equal under certain conditions. The grid search algorithm, which is necessary when maximizing this LM statistic, is also extended to the case of three regimes, and it is rewritten such that if the cointegration value is given, it really maximizes the LM statistic under the constraints specified by the user. In our empirical studies we have examined thoroughly the bivariate time series consisting of the monthly NIBOR rates of the maturities tomorrow next and 12 months. When modeling this bivariate time series, we find strong evidence for a two-regime TVECM being superior to a linear VECM, and in our out-of-sample forecasting the two-regime SETAR model gives much better prediction of the cointegration relation than an AR model. When testing a two-regime SETAR model for the cointegration relation against a three-regime model, the two-regime model cannot be rejected at any reasonable significance level. In addition, we show how influential a few outliers may be by removing them from the time series and rerunning some of the statistical tests. Also, we have tested all the 66 possible pairs of Norwegian interest rates for cointegration, and we have tested the term spread of each pair for threshold effects, i.e., testing a linear model against a two-regime model, as well as testing a two-regime model against a three-regime model. We find a lot of cointegrated pairs, and we find evidence for a two-regime model in approximately 50 % of the cases, and evidence for a three-regime model in some cases in this univariate time series analysis. At last, we simulate a bivariate time series with a three-regime threshold cointegration model as data generation process, and estimate a three-regime threshold cointegration model from this simulated time series. Thus, we illustrate that the thresholds which our version of the Hansen and Seo test detects as optimal, are close to the original thresholds used in the simulation. As expected, a linear model for this bivariate time series is strongly rejected, and there is strong evidence for a three-regime threshold model for the cointegration relation being superior to both a linear model and a two-regime threshold model.

URI:

http://hdl.handle.net/10037/4370

File(s) in this item: 1

thesis.pdf (1.462Mb)

Bayesian modeling and significant features exploration in wavelet power spectra

Divine, Dmitry V; Godtliebsen, Fred (Journal article; Tidsskriftartikkel; Peer reviewed, 2007)

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URI: http://hdl.handle.net/10037/3130

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article.pdf (373.4Kb)

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Abstract:	We find an invariant characterization of planar webs of maximum rank. For 4-webs, we prove that a planar 4-web is of maximum rank three if and only if it is linearizable and its curvature vanishes. This result leads to the direct web-theoretical proof of the Poincar´e’s theorem: a planar 4- web of maximum rank is linearizable. We also find an invariant intrinsic characterization of planar 4-webs of rank two and one and prove that in general such webs are not linearizable. This solves the Blaschke problem “to find invariant conditions for a planar 4-web to be of rank 1 or 2 or 3”. Finally, we find invariant characterization of planar 5-webs of maximum rank and prove than in general such webs are not linearizable.
Description:	Dette er forfatternes aksepterte versjon.
URI:	http://hdl.handle.net/10037/2049

Abstract:	If E is an elliptic curve, then the Galois group of the extension generated by the n-torsion points acts on these points. We prove a quadratic reciprocity law involving this group action. This law is an extension of the usual quadratic reciprocity law.
Description:	This is a preprint of an article to be published in Acta Scientiarum Mathematicarum
URI:	http://hdl.handle.net/10037/1607

Abstract:	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 evaluate the formal functional dimension of the solutions space. The results are applied to establish new integration methods and solve several differential-geometric problems.
Description:	Dette er forfatternes aksepterte versjon
URI:	http://hdl.handle.net/10037/2048

Abstract:	We classify the almost complex structures on homogeneous spaces M = G/H of real dimension less than or equal to 6 with semi-simple isotropy group H.
URI:	http://hdl.handle.net/10037/4372

Abstract:	In this note we discuss some formal properties of universal linearization operator, relate this to brackets of non-linear differential operators and discuss application to the calculus of auxiliary integrals, used in compatibility reductions of PDEs.
URI:	http://hdl.handle.net/10037/2125

Abstract:	This work concentrates on using the ICM algorithm for image restoration. The algorithm has been applied to fMRI recordings and mole pictures
URI:	http://hdl.handle.net/10037/2071

Abstract:	We construct the simplest chaotic system with a two-point attractor.
URI:	http://hdl.handle.net/10037/1863

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