Mastergradsoppgaver i teknologi - industriell matematikk
https://hdl.handle.net/10037/227
2024-10-08T19:33:03ZOverlevelsesanalyse med tidsavhengige forklaringsvariabler med bruk av Cox proporsjonal hasard regresjonsmodell
https://hdl.handle.net/10037/8421
Nilsen, Irmelin Kristin<br />
I denne mastergradsoppgaven ble det brukt overlevelsesanalyse med tidsavhengige variabler til å estimere en Cox proporsjonal hasard regresjonsmodell. Variablene stammet fra forskningsprosjektet ''Kvinner og kreft'' (The Norwegian Women and Cancer post genome cohort study - NOWAC) ved universitetet i Tromsø og besto av 57 561 kvinner. Modellen ble brukes til lage en modell av hasard raten til kvinnene og å finne hvilken av forklaringsvariabelen som hadde en effekt på overlevelsesevnen til kvinner.<br />
2015-12-15T00:00:00ZOverlevelsesanalyse med tidsavhengige forklaringsvariabler med bruk av Cox proporsjonal hasard regresjonsmodellNilsen, Irmelin KristinI denne mastergradsoppgaven ble det brukt overlevelsesanalyse med tidsavhengige variabler til å estimere en Cox proporsjonal hasard regresjonsmodell. Variablene stammet fra forskningsprosjektet ''Kvinner og kreft'' (The Norwegian Women and Cancer post genome cohort study - NOWAC) ved universitetet i Tromsø og besto av 57 561 kvinner. Modellen ble brukes til lage en modell av hasard raten til kvinnene og å finne hvilken av forklaringsvariabelen som hadde en effekt på overlevelsesevnen til kvinner.UiT Norges arktiske universitetUiT The Arctic University of NorwayYtterstad, ElinorMaster thesisMastergradsoppgaveThe formation of optical shocks for paraxial pulses propagating in weakly nonlinear and weakly dispersive materials
https://hdl.handle.net/10037/7378
Ottesen, Therese Dagsvik<br />
In this thesis leading order asymptotic equations describing the propagation of approximately paraxial pulses in a weakly nonlinear and weakly dispersive medium are derived using the method of multiple scales, and the formation of optical shocks in the nondispersive, purely paraxial case is investigated. How the state of polarization influences the shock have in particularly been looked in to.<br />
2014-06-02T00:00:00ZThe formation of optical shocks for paraxial pulses propagating in weakly nonlinear and weakly dispersive materialsOttesen, Therese DagsvikIn this thesis leading order asymptotic equations describing the propagation of approximately paraxial pulses in a weakly nonlinear and weakly dispersive medium are derived using the method of multiple scales, and the formation of optical shocks in the nondispersive, purely paraxial case is investigated. How the state of polarization influences the shock have in particularly been looked in to.UiT Norges arktiske universitetUiT The Arctic University of NorwayJakobsen, PerMaster thesisMastergradsoppgaveDiscrimination of cod otolith shapes by two different Fourier methods
https://hdl.handle.net/10037/5977
Henriksen, Are Murberg<br />
In this thesis we have applied Fisher’s discrimination method to cod samples to discriminate between cod
originating from the coastal cod stock and cod originating from the arctic cod stock. The discrimination
is based on Fourier coefficients extracted from cod otolith contours. We have optimized and compared
two different Fourier methods of extracting these coefficients. These methods are evaluated and compared
in terms of discrimination results and robustness.<br />
2013-12-16T00:00:00ZDiscrimination of cod otolith shapes by two different Fourier methodsHenriksen, Are MurbergIn this thesis we have applied Fisher’s discrimination method to cod samples to discriminate between cod
originating from the coastal cod stock and cod originating from the arctic cod stock. The discrimination
is based on Fourier coefficients extracted from cod otolith contours. We have optimized and compared
two different Fourier methods of extracting these coefficients. These methods are evaluated and compared
in terms of discrimination results and robustness.UiT Norges arktiske universitetUiT The Arctic University of NorwayHolbek Sørbye, SigrunnHarbitz, AlfMaster thesisMastergradsoppgaveEmpirisk analyse og stokastisk modellering av temporale fluktuasjoner i den norske pengemarkedsrenta
https://hdl.handle.net/10037/2666
Løvsletten, Ola<br />
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.<br />
2010-06-01T00:00:00ZEmpirisk analyse og stokastisk modellering av temporale fluktuasjoner i den norske pengemarkedsrentaLøvsletten, OlaI 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.Universitetet i TromsøUniversity of TromsøRypdal, MartinMaster thesisMastergradsoppgaveMulti-fractal stochastic modeling of the auroral electrojet index
https://hdl.handle.net/10037/2374
Sund, Martin Jong Yul Shon<br />
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.<br />
2009-12-15T00:00:00ZMulti-fractal stochastic modeling of the auroral electrojet indexSund, Martin Jong Yul ShonIn 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.Universitetet i TromsøUniversity of TromsøMjølhus, EinarMaster thesisMastergradsoppgaveTwo models of population genetics
https://hdl.handle.net/10037/1649
Skancke, Jørgen<br />
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.<br />
2008-06-02T00:00:00ZTwo models of population geneticsSkancke, JørgenThe 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.Universitetet i TromsøUniversity of TromsøFlå, TorMaster thesisMastergradsoppgaveLarge eddy simulation of homogeneous isotropic turbulence
https://hdl.handle.net/10037/1642
Zeigler, Harald Bergersen<br />
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.<br />
2008-06-02T00:00:00ZLarge eddy simulation of homogeneous isotropic turbulenceZeigler, Harald BergersenThe 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.Universitetet i TromsøUniversity of TromsøWasberg, Carl-ErikGjesdal, ThorMjølhus, EinarMaster thesisMastergradsoppgave