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Algebraic structures and stochastic differential equations driven by Levy processes
(Peer reviewed; Journal article, 2019)We construct an efficient integrator for stochastic differential systems driven by Lévy processes. An efficient integrator is a strong approximation that is more accurate than the corresponding stochastic Taylor approximation, ... -
Algebraic thinking
(Chapter, 2019) -
Algebraic thinking
(Chapter, 2018)Algebra is one of the most extensively researched areas in mathematics education. Over the past 40 years, many researchers have addressed the problems associated with the learning and teaching of algebra in school and ... -
Algebras of Finite Representation Type
(Master thesis, 2014)In this thesis we are considering finite dimensional algebras. We prove that any basic and indecomposable finite dimensional algebra A over an algebraically closed field k is isomorphic to a bound quiver algebra. Furthermore, ... -
Algorithms For Solving The Learning With Errors Problem
(Master thesis, 2021)Denne avhandlinga ser på fire ulike algoritmar for å løyse "Learning with Errors" (LWE, Læring med Feil) problemet. Den første, BKW-algoritmen, kan samanliknas med gaussisk eliminasjon. Deretter viser vi at LWE kan ... -
Almost finiteness and homology of certain non-free actions
(Peer reviewed; Journal article, 2023)We show that Cantor minimal Z⋊Z2\mathbb{Z}\rtimes\mathbb{Z}_2Z⋊Z2-systems and essentially free amenable odometers are almost finite. We also compute the homology groups of Cantor minimal Z⋊Z2\mathbb{Z}\rtimes\mathbb{Z}_ ... -
Ample Groupoids and their Topological Full Groups
(Doctoral theses at NTNU;2020:292, Doctoral thesis, 2020)In this thesis we study the topological full group of an ample groupoid, with a particular focus on groupoids arising from directed graphs. We mainly address two aspects of the topological full group. The first is to what ... -
An Abel-Jacobi invariant for cobordant cycles
(Journal article; Peer reviewed, 2016)We discuss an Abel-Jacobi invariant for algebraic cobordism cycles whose image in topological cobordism vanishes. The existence of this invariant follows by abstract arguments from the construction of Hodge filtered ... -
An adaptive isogeometric finite element analysis
(Master thesis, 2009)In this thesis we will explore the possibilities of making a finite element solver for partial differential equations using the isogeometric framework established by Hughes et al. Whereas general B-splines and NURBS only ... -
An algorithmic Framework for Multiresolution based non-parametric Regression
(Master thesis, 2017)We study a method to solve non-parametric regression problems in one and two dimensions with statistical multiresolution estimation. We present the non-parametric regression problem, then introduce the multiresolution norm ... -
An Analysis of a Cryptographic Communication Protocol
(Master thesis, 2010)We have considered a cryptographic communication protocol and given a proof for its security. -
An analysis of Norwegian and American interest rates during turbulent times, and prediction of interest rates in a Heat, Jarrow and Morton Model
(Master thesis, 2012)Abstract:In this master thesis the main focus is an analysis of historical interest rates, and the use of historical interest rates in interest rate modeling. The interest rate data used, both in the preliminary analysis ... -
An Analysis of UK Natural Gas Prices Comparing Regression, Neural Nets and Gradient Boosting Techniques
(Master thesis, 2023)I denne masteroppgaven ble det utført en komparativ analyse av de tre ulike modelleringsmetodene: multippel lineær regresjon, gradient boosting metoden XGBoost og det nevrale nettverket Long Short-Term Memory (LSTM). For ... -
An Application of Statistical Learning in Direct Marketing Response Modelling
(Master thesis, 2019)Direkte markedsføring gir selskap en direkte form for kommunikasjon med deres kunder. For a ̊ oppna ̊ den ønskede responsen, er det viktig a ̊ velge en passende ma ̊lgruppe, der- for er responsmodellering en viktig komponent ... -
An Application of the ACER Method to Norwegian Water Level Data: A Comparison of Return Level Estimates
(Master thesis, 2011)In this Master's thesis we have used data from eight different locations in Norway to estimate the distributions of extreme water levels. The locations used are Oslo, Heimsjø, Honningsvåg, Narvik, Harstad, Tregde, Andenes ... -
An embedding of the unit ball that does not embed into a Loewner chain
(Journal article; Peer reviewed, 2019)We construct a holomorphic embedding ϕ:B3→C3 such that ϕ(B3) is not Runge in any strictly larger domain. As a consequence, S≠S1 for n=3. -
An empirical study of the maximum pseudo-likelihood for discrete Markov random fields.
(Master thesis, 2009)In this text we will look at two parameter estimation methods for Markov random fields on a lattice. They are maximum pseudo-likelihood estimation and maximum general pseudo-likelihood estimation, which we abbreviate ... -
An Exploration of Shapley Values for Model Interpretability: Providing a Fair and Accurate Explanation of Black Box Models
(Master thesis, 2023)Shapley-verdier er en populær metode innenfor forklarbar kunstig intelligens på grunn av et solid teoretiske grunnlag for deres korrekthet og rettferdighet. Imidlertid er beregningen av Shapley-verdier kostbar og derfor ... -
An exponential time-differencing method for monotonic relaxation systems
(Journal article; Peer reviewed, 2014)We present first and second-order accurate exponential time differencing methods for a special class of stiff ODEs, denoted as monotonic relaxation ODEs. Some desirable accuracy and robustness properties of our methods are ...