Matematisk institutt
http://hdl.handle.net/10852/5
Mon, 26 Oct 2020 12:53:15 GMT2020-10-26T12:53:15ZTangent Structure of Non-Commutative Rings
http://hdl.handle.net/10852/80673
Tangent Structure of Non-Commutative Rings
Patrono, Richard Pedersen
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/806732020-01-01T00:00:00ZThe Fourier-Stieltjes algebra of a C*-dynamical system II
http://hdl.handle.net/10852/80643
The Fourier-Stieltjes algebra of a C*-dynamical system II
Bedos, Erik Christopher; Conti, Roberto
We continue our study of the Fourier–Stieltjes algebra associated to a twisted (unital, discrete) C*-dynamical system and discuss how the various notions of equivalence of such systems are reflected at the algebra level. As an application, we show that the amenability of a system, as defined in our previous work, is preserved under Morita equivalence.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/806432020-01-01T00:00:00ZRobust preconditioning for coupled Stokes–Darcy problems with the Darcy problem in primal form
http://hdl.handle.net/10852/80608
Robust preconditioning for coupled Stokes–Darcy problems with the Darcy problem in primal form
Holter, Karl Erik; Kuchta, Miroslav; Mardal, Kent-Andre
The coupled Darcy–Stokes problem is widely used for modeling fluid transport in physical systems consisting of a porous part and a free part. In this work we consider preconditioners for monolithic solution algorithms of the coupled Darcy–Stokes problem, where the Darcy problem is in primal form. We employ the operator preconditioning framework and utilize a fractional solver at the interface between the problems to obtain order optimal schemes that are robust with respect to the material parameters, i.e. the permeability, viscosity and Beavers–Joseph–Saffman condition. Our approach is similar to that of Holter et al. (2020), but since the Darcy problem is in primal form, expressing mass conservation at the interface involves the normal derivative, which introduces some mathematical challenges. These challenges will be specifically addressed in this paper, in particular we will employ fractional Laplacians at the interface. Numerical experiments illustrating the performance are provided. The preconditioner is posed in non-standard Sobolev spaces which may be perceived as an obstacle for its use in applications. However, we detail the implementational aspects and show that the preconditioner is quite feasible to realize in practice.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/806082020-01-01T00:00:00ZDiscontinuous Galerkin methods for multiphase flow
http://hdl.handle.net/10852/80602
Discontinuous Galerkin methods for multiphase flow
Landet, Tormod Ravnanger
This thesis describes a finite element method for simulation of free-surface flows, such as ocean waves, using the discontinuous Galerkin method. Free-surface flows where there is a large difference in density between two immiscible fluids will have a large jump in the magnitude of the momentum field at the interface between the two fluids. Such discontinuities create problems for higher-order discretisations, which are more computationally efficient where the solution is smooth, but need careful handling near discontinuities in order to avoid Gibbs oscillations. This thesis shows how slope limiting can be used to stabilise the momentum equation in an exactly mass conserving discontinuous Galerkin finite element discretisation of the Navier–Stokes equation. The stabilised method is tested on a range of well known 2D and 3D free-surface-flow test cases. The results are in good agreement with published experimental results, and also give the expected higher-order convergence rates for smooth solutions.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/806022020-01-01T00:00:00ZProjecting onto Helson matrices in Schatten classes
http://hdl.handle.net/10852/80560
Projecting onto Helson matrices in Schatten classes
Brevig, Ole Fredrik; Miheisi, Nazar
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10852/805602021-01-01T00:00:00ZComputations in A1-homotopy theory. Contractibility and enumerative geometry
http://hdl.handle.net/10852/80256
Computations in A1-homotopy theory. Contractibility and enumerative geometry
Pauli, Sabrina
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/802562020-01-01T00:00:00ZDødelighet ved hoftebrudd: Analyser av kohort og matchet kohort data
http://hdl.handle.net/10852/80243
Dødelighet ved hoftebrudd: Analyser av kohort og matchet kohort data
Nordby, Katrine
Hoftebrudd innebærer brudd i lårhalsen eller i området ved den lille og store lårbensknuten. Vi vet at 70% av individer med hoftebrudd er kvinner og også at 70% av disse individene er over 70 år. I denne oppgaven er vi interessert i dødeligheten ved hoftebrudd. Vi skal utføre en kohortstudie der vi analyserer et datasett bestående av individer som var 50 år eller eldre i folke- og boligtellingen i Norge i 2001. Vi vil gjøre diverse undersøkelser for å beskrive dødeligheten for ulike kovariater. I hovedsak er vi interessert i å undersøke hvordan diverse kovariater påvirker dødeligheten ved hoftebrudd. Store kohortanalyser kan være både tidkrevende og kostbare. Matchede kohortanalyser der vi ser på en submengde av kohorten er et alternativ for å få ned kostnadene og tiden det tar å utføre analysene. Vi skal i denne oppgaven også utføre matchede kohortanalyser der vi matcher eksponerte individer med ikke-eksponerte individer ved hjelp av gitte matchingsvariable. Vi er interessert i hvor stor submengde, eller mer presist hvor mange ikke-eksponerte indivder vi trenger å matche hvert eksponert individ med for å oppnå omtrent like god presisjon i resultatene som ved den fulle kohorten.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/802432020-01-01T00:00:00ZParallel subsampling MCMC and the Perturbed Subset Parameter Approximation
http://hdl.handle.net/10852/80220
Parallel subsampling MCMC and the Perturbed Subset Parameter Approximation
Wollbraaten, Fredrik Lundvall
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/802202020-01-01T00:00:00ZSome new theoretical and computational results around the Jacobian conjecture
http://hdl.handle.net/10852/80184
Some new theoretical and computational results around the Jacobian conjecture
Truong, Tuyen Trung
In this paper, we study a so-called Condition C1 on square matrices with complex coefficients and a weaker Condition C2. For Druzkowski maps Condition C2 is equivalent to the Jacobian conjecture. We show that these conditions satisfy many good properties and in particular are satisfied by a dense subset of the set of square matrices of a given rank [Formula: see text]. Based on this, we propose a heuristic argument for the truth of the Jacobian conjecture. We propose some new equivalent formulations and some generalizations of the Jacobian conjecture, and some approaches (including computer algebra and numerical methods) toward resolving it. We show that some of these equivalent formulations are automatically satisfied by generic Druzkowski matrices. Applications and experimental results are included.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/801842020-01-01T00:00:00ZVariance and interest rate risk in unit-linked insurance policies
http://hdl.handle.net/10852/80155
Variance and interest rate risk in unit-linked insurance policies
Baños, David; Lagunas, Marc; Ortiz-Latorre, Salvador
One of the risks derived from selling long-term policies that any insurance company has arises from interest rates. In this paper, we consider a general class of stochastic volatility models written in forward variance form. We also deal with stochastic interest rates to obtain the risk-free price for unit-linked life insurance contracts, as well as providing a perfect hedging strategy by completing the market. We conclude with a simulation experiment, where we price unit-linked policies using Norwegian mortality rates. In addition, we compare prices for the classical Black-Scholes model against the Heston stochastic volatility model with a Vasicek interest rate model.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/801552020-01-01T00:00:00ZFinding the needle in the haystack: Fine-tuning transformers to classify protest events in a sea ofnews articles, with Bayesian uncertainty measures
http://hdl.handle.net/10852/79984
Finding the needle in the haystack: Fine-tuning transformers to classify protest events in a sea ofnews articles, with Bayesian uncertainty measures
Ghai, Chris
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/799842020-01-01T00:00:00ZFully-dynamic risk-indifference prices and no-good-deal bounds
http://hdl.handle.net/10852/79946
Fully-dynamic risk-indifference prices and no-good-deal bounds
Bion-Nadal, Jocelyne; Di Nunno, Giulia
The seller's risk-indifference price evaluation is studied. We propose a dynamic risk-indifference pricing criterion derived from fully-dynamic risk measures on the $L_p$-spaces for $p\in [1,\infty]$. The concept of fully-dynamic risk measures extends the one of dynamic risk measures by adding the actual possibility of changing the risk perspectives over time. This family is then characterized by a double time index. Our framework fits well the study of both short- and long-term investments. In this paper we analyze whether the risk-indifference pricing criterion actually provides a proper convex price system. It turns out that, depending on $p$, this is not always the case. Then an extension of the framework beyond $L_p$ becomes necessary. Furthermore, we consider the relationship of the fully-dynamic risk-indifference price with no-good-deal bounds. We shall provide necessary and sufficient conditions on the fully-dynamic risk measures so that the corresponding risk-indifference prices satisfy the no-good-deal bounds. Remarkably, the use of no-good-deal bounds also provides a method to select the risk measures and thus construct a proper fully-dynamic risk-indifference price system within the $L_2$-spaces.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/799462020-01-01T00:00:00ZOn quantum channels and attractors
http://hdl.handle.net/10852/79761
On quantum channels and attractors
Søisdal, Stian Bergersen
The main aim of the thesis is to study attractors for certain iterated function systems arising from quantum channels on finite dimensional C*-algebras. I will show the existence of attractors on the density operators by strictly contractive quantum channels. Moreover, with the strictly contractive quantum channels on the probability vectors, I will reconstruct some of the more famous fractals as attractors and illustrating them in the probability vectors of dimension up to four. Furthermore, with the strictly contractive quantum channels on the 2 by 2 matrices, I will reconstruct further famous fractals as attractors and illustrate them on the 2 by 2 density matrices.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/797612020-01-01T00:00:00ZOption Pricing with Neural Networks
http://hdl.handle.net/10852/79745
Option Pricing with Neural Networks
Nilsen, Henrik
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/797452020-01-01T00:00:00ZModelling Car Insurance Data with Individual Effects
http://hdl.handle.net/10852/79744
Modelling Car Insurance Data with Individual Effects
Tresselt, Hanne Jahreie
We show how both Poisson regression and recurrent events models can be used to model the number of claims to expect on a car insurance policy. We also show that the same is true when these models are extended to include a random effect/frailty. We then look at the effect of different assumptions made regarding the distribution of this random effect/frailty, through simulated data sets, one where we do not know the true distribution and several where we controlled the distribution and variance of the random effect/frailty. The results showed that the choice of frailty did seem to have an impact on the estimation of expected number of claims. They also indicated that the choice of distribution to use for the frailty was more important for data with a higher degree of heterogeneity than for data with a lower degree of heterogeneity.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/797442020-01-01T00:00:00ZDynamical Entropy
http://hdl.handle.net/10852/79717
Dynamical Entropy
Schwartz, Gaute
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/797172020-01-01T00:00:00ZSeifert Manifolds as Circle Manifolds
http://hdl.handle.net/10852/79714
Seifert Manifolds as Circle Manifolds
Gåsøy, Joakim
Seifert manifolds play a crucial role in the classification of 3-manifolds, as they occupy six of the eight geometries proposed by Thurston. In this thesis we determine which Seifert manifolds can be given a smooth action from the circle group. We show how the stabilizer groups and orbit space of this circle manifold relate to the Seifert invariants and base space of the Seifert manifold. In particular, we give a smooth circle action to Brieskorn manifolds and spherical space forms and calculate their stabilizer groups. Additionally, we show that the orbit space is an orbifold.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/797142020-01-01T00:00:00ZPhotoemissive charging of the Mercury Magnetospheric Orbiter studied by means of 3D Particle-In-Cell simulations
http://hdl.handle.net/10852/79678
Photoemissive charging of the Mercury Magnetospheric Orbiter studied by means of 3D Particle-In-Cell simulations
Nielsen, Trym Erik
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/796782020-01-01T00:00:00ZModeling of Blood Flow in Zebrafish With Cancer
http://hdl.handle.net/10852/79643
Modeling of Blood Flow in Zebrafish With Cancer
Ibrahim, Soran Najat
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/796432020-01-01T00:00:00ZMultiple imputation for Cox regression with sampled cohort data
http://hdl.handle.net/10852/79641
Multiple imputation for Cox regression with sampled cohort data
Njøs, Aleksander
In nested case-control and case-cohort studies of time-to-events, covariate information is collected for all individuals in the sampled cohort. Often information on some of the covariates are easily available for the entire cohort while some can only be collected for a limited amount of individuals; those in the sampled cohort. Multiple imputation, an algorithm for handling missing data, can be used to impute (``fill inn'') covariate values, that have not been collected for individuals in the remaining part of the cohort, a small to moderately number of times. Then, Cox regression estimates from each imputed dataset (cohort) can be combined according to Rubin's rules. Multiple imputation used in this setting has previously been shown to give more efficient inferences by utilising more of the available information outside the sampled cohorts. However, in studies with very large cohorts, multiple imputation for the entire cohort might be very demanding or even infeasible. In this thesis, existing methods for multiple imputation of missing values (by chance) in sampled cohort studies, in their original and an adapted form, are used to impute values in a superset of the sampled cohort. Imputing values missing by design in the superset motivates estimating the regression coefficients with nested case-control or case-cohort estimators. The results from simple simulations experiments show good performance with respect to bias and efficiency. For very large cohorts, the number of controls in a nested case-control superset or the size of the subcohort in a case-cohort superset, determines the size of the part of the cohort that is to be imputed, and superset imputation therefore looks like a promising method when imputation of the entire cohort is not possible.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/796412020-01-01T00:00:00Z