Mastergradsoppgaver i teknologi - industriell matematikk

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Mastergradsoppgaver i teknologi - industriell matematikk

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• Empirisk analyse og stokastisk modellering av temporale fluktuasjoner i den norske pengemarkedsrenta

  Løvsletten, Ola (Master thesis; Mastergradsoppgave, 01-Jun-2010)

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  Abstract:

  I denne oppgaven analyserer vi den norske pengemarkedsrenta NIBOR (3 mnd). Vi fokuserer spesielt p\aa\ modeller som beskriver den karakteristiske potenslovskaleringen vi ser i data. Eksempler p\aa\ slike modeller er stabile L\'{e}vy-prosesser, trunkerte stabile L\'{e}vy-prosesser og multifraktale prosesser. Vi finner at modellen Markov Switching Multifractal gjenskaper de viktigste strukturelle egenskapene til rentefluktasjonene samtidig som den er egnet til volatilitetsvarsling. Vi utf\o rer en statistisk test p\aa\ hvordan denne modellen takler prediksjonsproblemet.

  URI:

  http://hdl.handle.net/10037/2666

  File(s) in this item: 1

  thesis.pdf   (4.125Mb)
• Multi-fractal stochastic modeling of the auroral electrojet index

  Sund, Martin Jong Yul Shon (Master thesis; Mastergradsoppgave, 15-Dec-2009)

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  Abstract:

  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 theory of fractal dimensions and scaling functions, before introducing the Multifractal Model of Asset Returns (MMAR), Mandelbrot (1997). The scaling properties of various versions of the MMAR model are compared with the scaling function of the AE Index, and through this we describe the multi-fractal properties of the AE Index. Additionally, we have studied probability density functions (pdf) at different time scales, and used this to compare the stochastic models with the AE data. Finally we have tested our diagnostic tools on simulated multi-fractal models. These experiments show that the methods are capable of detecting multi-fractality. The results are good if we average over several independent realizations of the processes.

  URI:

  http://hdl.handle.net/10037/2374

  File(s) in this item: 1

  thesis.pdf   (4.105Mb)
• Two models of population genetics

  Skancke, Jørgen (Master thesis; Mastergradsoppgave, 02-Jun-2008)

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  Abstract:

  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 regulation for different genes? Mathematical models of biological evolution are important for two reasons: 1) aiding researchers in understanding how complex biological systems have emerged and 2) enabling modelers to predict future outcomes of evolution. In this work, models of evolution of natural populations are applied to better understand the mechanisms of gene regulation in E. coli by investigating two predictor arguments of gene regulatory mode, namely the demand rule and the rule of minimal error load. Two models of population genetics are derived: the Wright-Fisher model and the Moran model. These discrete stochastic models are approximated to continuous stochastic models and to continuous deterministic mean field models. The continuous stochastic models are used to investigate the demand rule, while the continuous deterministic models are used to investigate the rule of minimal error load. In the continuous limits it is found that both discrete Wright-Fisher and Moran models can be described by the same equations. Two special cases are investigated in the model derivations: variable population size for the Wright-Fisher model and non-zero selection coefficients for continuous approximation of the Moran model. The models show that the demand rule describes well the evolution for the most basic mode of gene regulation, and that the rule of minimal error load describes the evolution for a larger group of gene regulation modes. It is concluded that one should use the rule of minimal error load to investigate advanced systems of gene regulation. The demand rule is correct only as a special case for the most basic mode of gene regulation.

  URI:

  http://hdl.handle.net/10037/1649

  File(s) in this item: 1

  thesis.pdf   (640.0Kb)
• Large eddy simulation of homogeneous isotropic turbulence

  Zeigler, Harald Bergersen (Master thesis; Mastergradsoppgave, 02-Jun-2008)

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  Abstract:

  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 fall of energy in the first time-steps, which I have no explanation for why happened. The thesis consists of a rather large theory section and a smaller discussion in the end. Chapters 3 and 4 are mainly introductory and addressing the theme and job description. They also serve as mild introductions to tuirbulence theory as well as mathematical, numerical subjects. Overall, the reader is assumed not to be very familiar with mathematical terms, applied mathematics and physics, so many terms are explained. The provided theory is designed to teach a reader totally unfamiliar with science some things, but not all. The author has not forgot about the experienced reader who may be an expert in the field, and the level of the thesis should be high enough for that person also to maintain interest while reading.

  URI:

  http://hdl.handle.net/10037/1642

  File(s) in this item: 1

  thesis.pdf   (653.3Kb)

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