Matematisk institutt
http://hdl.handle.net/10852/5
Fri, 23 Mar 2018 05:11:10 GMT
20180323T05:11:10Z

Nodal finite element de Rham complexes
http://hdl.handle.net/10852/61204
Nodal finite element de Rham complexes
Christiansen, Snorre H; Hu, Jun; Hu, Kaibo
We construct 2D and 3D finite element de Rham sequences of arbitrary polynomial degrees with extra smoothness. Some of these elements have nodal degrees of freedom and can be considered as generalisations of scalar Hermite and Lagrange elements. Using the nodal values, the number of global degrees of freedom is reduced compared with the classical Nédélec and Brezzi–Douglas–Marini finite elements, and the basis functions are more canonical and easier to construct. Our finite elements for H(div) with regularity r=2 coincide with the nonstandard elements given by Stenberg (Numer Math 115(1):131–139, 2010). We show how regularity decreases in the finite element complexes, so that they branch into known complexes. The standard de Rham complexes of Whitney forms and their higher order version can be regarded as the family with the lowest regularity. The construction of the new families is motivated by finite element systems.
This is a postpeerreview, precopyedit version of an article published in Numerische Mathematik. The final authenticated version is available online at: http://dx.doi.org/10.1007/s002110170939x
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61204
20170101T00:00:00Z

Convergence of a Godunov scheme for conservation laws with a discontinuous flux lacking the crossing condition
http://hdl.handle.net/10852/61200
Convergence of a Godunov scheme for conservation laws with a discontinuous flux lacking the crossing condition
Karlsen, Kenneth Hvistendahl; Towers, John D.
stability for entropy solutions of nonlinear degenerate parabolic convection–diffusion equations with discontinuous coefficients, Skr. K. Nor. Vidensk. Selsk. 3 (2003) 1–49], singles out the vanishing viscosity solution whether or not the crossing condition is satisfied, and has a discrete version satisfied by the Godunov variant of the finite difference scheme of [S. Diehl, On scalar conservation laws with point source and discontinuous flux function, SIAM J. Math. Anal. 26(6) (1995) 1425–1451]. We show that the solutions produced by that scheme converge to the unique vanishing viscosity solution. The scheme does not require a Riemann solver for the discontinuous flux problem. This makes its implementation simple even when the flux is multimodal, and there are multiple flux crossings.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61200
20170101T00:00:00Z

Modeling the Premium in NonLife Insurance  a Comparison of Generalized Linear and Generalized Linear Mixed Models
http://hdl.handle.net/10852/61164
Modeling the Premium in NonLife Insurance  a Comparison of Generalized Linear and Generalized Linear Mixed Models
Ha, Tam
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61164
20170101T00:00:00Z

Analysis of ContractforDifference with Vasicek Process and Cointegrated System in Stock Market and Nordic Electricity Market
http://hdl.handle.net/10852/61163
Analysis of ContractforDifference with Vasicek Process and Cointegrated System in Stock Market and Nordic Electricity Market
Huang, Bo
This thesis aims at pricing ContractforDifference (CFD) in stock market, and Electricity Price Area Differential (EPAD) in the Nord Pool. For CFD, our model consists of Geometric Brownian Motion and Vasicek process. For EPAD, we apply cointegrated system to build a model, with and without Vasicek process. Both parts claim calculable results. And they are given by a series of analysis and calculationwork. Reader will also encounter some figures of simulation by R.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61163
20170101T00:00:00Z

Bsplines in Machine Learning
http://hdl.handle.net/10852/61162
Bsplines in Machine Learning
Douzette, Andre Sevaldsen
In the recent decade, artificial intelligence and machine learning has become increasingly popular for solving complex realworld problems. In particular problems which was believed to be very hard or in some cases impossible by computers have seen a surge in interest from both academia but also the indus try. A recent example is the defeat of the worlds best Go player by Googles AlphaGo using deep neural networks. At the core of neural networks is the a part of the neurons called an activation function. This function is of mayor significance in how the network operates, but is often overlooked. One most often picks one of the commonly chosen nonadaptive functions as activation function. There have been research into using adaptive sigmoid or ReLU functions, but these have the drawbacks that the adaptations caused by data from one local region would effect the global domain. We therefore propose to use adaptive spline functions with free knots. Research into the field of spline networks have been limited in sophistication, with interpolating cubic splines being the most researched. The implementation in this thesis is using splines with Bsplines as a basis, and is therefore free to use any polynomial degree.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61162
20170101T00:00:00Z

Local Euler obstructions of toric varieties
http://hdl.handle.net/10852/61063
Local Euler obstructions of toric varieties
Utstøl Nødland, Bernt Ivar
We use Matsui and Takeuchi's formula for toric Adiscriminants to give algorithms for computing local Euler obstructions and dual degrees of toric surfaces and 3folds. In particular, we consider weighted projective spaces. As an application we give counterexamples to a conjecture by Matsui and Takeuchi. As another application we recover the wellknown fact that the only defective normal toric surfaces are cones.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/61063
20180101T00:00:00Z

Invariance of the Cuntz splice
http://hdl.handle.net/10852/61045
Invariance of the Cuntz splice
Eilers, Søren; Restorff, Gunnar; Ruiz, Efren; Sørensen, Adam Peder Wie
We show that the Cuntz splice induces stably isomorphic graph C∗algebras. This result is a key step towards the recent complete classification of unital graph C∗algebras both with respect to Ktheoretical classification and with respect to geometrical classification in terms of an equivalence relation on the underlying graphs.
This is a postpeerreview, precopyedit version of an article published in Mathematische Annalen. The final authenticated version is available online at: http://dx.doi.org/10.1007/s002080171570y
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61045
20170101T00:00:00Z

Vanishing cotangent cohomology for Plücker algebras
http://hdl.handle.net/10852/61001
Vanishing cotangent cohomology for Plücker algebras
Christophersen, Jan Arthur; Ilten, Nathan Owen
We use representation theory and Bott’s theorem to show vanishing of higher cotangent cohomology modules for the homogeneous coordinate ring of Grassmannians in the Plücker embedding. As a byproduct, we answer a question of Wahl about the cohomology of the square of the ideal sheaf for the case of Plücker relations. We obtain slightly weaker vanishing results for the cotangent cohomology of the coordinate rings of isotropic Grassmannians.
This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Algebra on 31 Jan 2017, available online: http://www.tandfonline.com/10.1080/00927872.2016.1249373
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61001
20170101T00:00:00Z

Alternative models for reinsurance in Solvency II
http://hdl.handle.net/10852/60967
Alternative models for reinsurance in Solvency II
Dang, John Nguyen
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/60967
20170101T00:00:00Z

Integrated analysis of DNAmethylation and gene expression using highdimensional penalized regression: a cohort study on bone mineral density in postmenopausal women
http://hdl.handle.net/10852/60926
Integrated analysis of DNAmethylation and gene expression using highdimensional penalized regression: a cohort study on bone mineral density in postmenopausal women
Lien, Tonje G; Borgan, Ørnulf; Reppe, Sjur; Gautvik, Kaare; Glad, Ingrid K
Background
Using highdimensional penalized regression we studied genomewide DNAmethylation in bone biopsies of 80 postmenopausal women in relation to their bone mineral density (BMD). The women showed BMD varying from severely osteoporotic to normal. Global gene expression data from the same individuals was available, and since DNAmethylation often affects gene expression, the overall aim of this paper was to include both of these omics data sets into an integrated analysis.
Methods
The classical penalized regression uses one penalty, but we incorporated individual penalties for each of the DNAmethylation sites. These individual penalties were guided by the strength of association between DNAmethylations and gene transcript levels. DNAmethylations that were highly associated to one or more transcripts got lower penalties and were therefore favored compared to DNAmethylations showing less association to expression. Because of the complex pathways and interactions among genes, we investigated both the association between DNAmethylations and their corresponding cis gene, as well as the association between DNAmethylations and translocated genes. Two integrating penalized methods were used: first, an adaptive groupregularized ridge regression, and secondly, variable selection was performed through a modified version of the weighted lasso.
Results
When information from gene expressions was integrated, predictive performance was considerably improved, in terms of predictive mean square error, compared to classical penalized regression without data integration. We found a 14.7% improvement in the ridge regression case and a 17% improvement for the lasso case. Our version of the weighted lasso with data integration found a list of 22 interesting methylation sites. Several corresponded to genes that are known to be important in bone formation. Using BMD as response and these 22 methylation sites as covariates, least square regression analyses resulted in R2=0.726, comparable to an average R2=0.438 for 10000 randomly selected groups of DNAmethylations with group size 22.
Conclusions
Two recent types of penalized regression methods were adapted to integrate DNAmethylation and their association to gene expression in the analysis of bone mineral density. In both cases predictions clearly benefit from including the additional information on gene expressions.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/60926
20180101T00:00:00Z

On a selection problem for small noise perturbation in the multidimensional case
http://hdl.handle.net/10852/60921
On a selection problem for small noise perturbation in the multidimensional case
Pilipenko, Andrey; Proske, Frank Norbert
The problem on identification of a limit of an ordinary differential equation with discontinuous drift that perturbed by a zeronoise is considered in multidimensional case. This problem is a classical subject of stochastic analysis, see, for example, [6, 29, 11, 20]. However the multidimensional case was poorly investigated. We assume that the drift coefficient has a jump discontinuity along a hyperplane and is Lipschitz continuous in the upper and lower halfspaces. It appears that the behavior of the limit process depends on signs of the normal component of the drift at the upper and lower halfspaces in a neighborhood of the hyperplane, all cases are considered.
Electronic version of an article published as Pilipenko, Andrey, and Frank Norbert Proske. "On a selection problem for small noise perturbation in the multidimensional case." Stochastics and Dynamics (2018): 1850045. https://doi.org/10.1142/S0219493718500454 © World Scientific Publishing Company https://www.worldscientific.com/worldscinet/sd
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/60921
20170101T00:00:00Z

The Cone Conjecture for Some CalabiYau Varieties
http://hdl.handle.net/10852/60868
The Cone Conjecture for Some CalabiYau Varieties
Skauli, Bjørn
In this thesis we give an introduction to the Minimal Model Program and the MorrisonKawamata cone conjecture. We then present some known results on anticanonical hypersurfaces building up to the result proven by Kollár in relating the nef cone of an ample anticanonical hypersurface to the nef cone of the ambient variety. We will present the proof of this in detail including the definitions and necessary background material to follow the proof. We give our own proofs for several of the background results including two proofs done by toric geometry. Then we give examples illustrating how possible extension of Kollár’s result fail. Most of the examples here are new. We then move on to proving the MorrisonKawamata cone conjecture for the nef cone on the Enriques CalabiYau, and more generally on CalabiYau varieties arising as certain finite étale quotients. This is already proven, but our proof of the cone conjecture is based on a different idea, although both ultimately rely on the Torelli theorem. We then study certain CalabiYau complete intersections in products of projective spaces and in particular prove the MorrisonKawamata cone conjecture for the movable cone. This generalizes known constructions and results. Here the results and proofs are new, although many ideas are inspired by earlier work. Finally we prove the MorrisonKawamata cone conjecture for the movable cone for an anticanonical hypersurface in the blowup of projective space in one and two points, and compute the birational automorphism group for these CalabiYau varieties. To our knowledge the results of this final section are new.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/60868
20170101T00:00:00Z

Experiments of Breaking Waves in Pipes and Flumes
http://hdl.handle.net/10852/60469
Experiments of Breaking Waves in Pipes and Flumes
Smith, Lisa
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/60469
20180101T00:00:00Z

GSuite HyperBrowser: integrative analysis of dataset collections across the genome and epigenome
http://hdl.handle.net/10852/60459
GSuite HyperBrowser: integrative analysis of dataset collections across the genome and epigenome
Simovski, Boris; Vodak, Daniel; Gundersen, Sveinung; Domanska, Diana Ewa; Azab, Abdulrahman; Holden, Lars; Holden, Marit; Grytten, Ivar; Rand, Knut Dagestad; Drabløs, Finn Sverre; Johansen, Morten; Mora, Antonio M.; LundAndersen, Christin; Fromm, Bastian; Eskeland, Ragnhild; Gabrielsen, Odd Stokke; Ferkingstad, Egil; Nakken, Sigve; Bengtsen, Mads; Nederbragt, Alexander Johan; Thorarensen, Hildur Sif; Andreas Akse, Johannes; Glad, Ingrid Kristine; Hovig, Johannes Eivind; Sandve, Geir Kjetil
Background: Recent largescale undertakings such as ENCODE and Roadmap Epigenomics have generated experimental data mapped to the human reference genome (as genomic tracks) representing a variety of functional elements across a large number of cell types. Despite the high potential value of these publicly available data for a broad variety of investigations, little attention has been given to the analytical methodology necessary for their widespread utilisation. Findings: We here present a first principled treatment of the analysis of collections of genomic tracks. We have developed novel computational and statistical methodology to permit comparative and confirmatory analyses across multiple and disparate data sources. We delineate a set of generic questions that are useful across a broad range of investigations and discuss the implications of choosing different statistical measures and null models. Examples include contrasting analyses across different tissues or diseases. The methodology has been implemented in a comprehensive opensource software system, the GSuite HyperBrowser. To make the functionality accessible to biologists, and to facilitate reproducible analysis, we have also developed a webbased interface providing an expertly guided and customizable way of utilizing the methodology. With this system, many novel biological questions can flexibly be posed and rapidly answered. Conclusions: Through a combination of streamlined data acquisition, interoperable representation of dataset collections and customizable statistical analysis with guided setup and interpretation, the GSuite HyperBrowser represents a first comprehensive solution for integrative analysis of track collections across the genome and epigenome. The software is available at: https://hyperbrowser.uio.no
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/60459
20170101T00:00:00Z

Verification and Validation of a Monolithic FluidStructure Interaction Solver in FEniCS. A comparison of mesh lifting operators.
http://hdl.handle.net/10852/60349
Verification and Validation of a Monolithic FluidStructure Interaction Solver in FEniCS. A comparison of mesh lifting operators.
Slyngstad, Andreas Strøm
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/60349
20170101T00:00:00Z

Pricing of Spreads and Other Options in Cointegrated Markets
http://hdl.handle.net/10852/60347
Pricing of Spreads and Other Options in Cointegrated Markets
You, Elena
In this thesis we analyze spread functions in the cointegrated market, with dynamics based on different combinations of Brownian motions and OrnsteinUhlenbeck processes, and their structural differences. Theoretical and computational methods for pricing these options are explored, and we will discuss the parameters and dynamics of the price functions by examining analytical expressions and numerical simulations. The extention of cointegrated spreads to quanto options is also touched upon. We use the meanreversal, stationary dynamic of OrnsteinUhlenbeck spreads to suggest a model on the form of an European putoption to approximate quanto options in cointegrated markets, which are based on a product of spreads.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/60347
20170101T00:00:00Z

Fiducial and Objective Bayesian Inference: History, Theory, and Comparisons
http://hdl.handle.net/10852/60343
Fiducial and Objective Bayesian Inference: History, Theory, and Comparisons
Rønneberg, Leiv Tore Salte
In 1930, Fisher presented his fiducial argument as a solution to the "fundamen tally false and devoid of foundation" practice of using Bayes’ theorem with uniform priors to represent ignorance about a parameter. His solution resulted in an “objec tive” posterior distribution on the parameter space, but was the subject of a long controversy in the statistical community. The theory was never fully accepted by his contemporaries, notably the NeymanWald school of thought, and after Fisher’s death in 1962 the theory was largely forgotten, and widely considered his "biggest blunder". In the past 20 years or so, his idea has received renewed attention, from numer ous authors, yielding several more modern approaches. The common goal of these approaches is to obtain an objective distribution on the parameter space, summa rizing what might be reasonably learned from the data – without invoking Bayes’ theorem. Similarly, from the Bayesian paradigm, approaches have been made to create prior distributions that are in a sense objective, based either on invariance arguments, or on entropy arguments – yielding an “objective” posterior distribution, given the data. This thesis traces the origins of these two approaches to objective statistical inference, examining the underlying logic, and investigates when they give equal, similar or vastly different answers, given the same data.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/60343
20170101T00:00:00Z

American Options in Financial Quotes
http://hdl.handle.net/10852/60342
American Options in Financial Quotes
Saakvitne, Jo Albertsen
We build a mathematical model for the risk involved when a person makes a binding fixedprice offer to buy or sell something that fluctuates in value. This situation often arises in financial markets, where such an offer is called a quote. Quotes involve a risk for the person giving them, and an opportunity for the person receiving them. We investigate two different versions of quotes: offers that cannot be canceled before a certain time has passed ("minimum resting times"), and quotes that are automatically canceled if the price moves past a specified barrier ("last look"). Our model of financial quotes is in many respects similar to option pricing models. Quotes with minimum resting times are in a certain sense similar to American options, and quotes with last look are similar to American barrier options. There are also differences however, for example are the time scales of financial quotes orders of magnitude shorter than the time scales of traditional options. These differences lead us to use different modeling approaches than what is used for traditional option pricing models, in particular we investigate optimal stopping problems for the class of integervalued Levy processes. We develop both explicit formulas and numerical algorithms.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/60342
20170101T00:00:00Z

Comparison of two lower bounds for availabilities in multistate monotone systems an established one and a new one
http://hdl.handle.net/10852/60341
Comparison of two lower bounds for availabilities in multistate monotone systems an established one and a new one
Abrahamsen, Tobias
The lower bounds are used to determine availabilities of a system, and are used in many different companies. Such is for example a company that supplies water to a city. The company would most likely want to know how reliable the water system is. Does the water system deliver minimum 40% or more of its water capacity to the city? It is important to have a lower bound that is close to the real value. I will therefore in this paper show, and explain, what a Multistate Monotone System (MMS) is, and compare two lower bounds. The bounds are a new lower bound and an established lower bound. I will also present the theorems linked to the bounds, and establish some points to make computer implementation easier. I am also going to show something that I have figured out, a new theorem, and an algorithm which makes it easier to identify minimal cut vectors. Part of the computer code will be discussed and explained, where some of the algorithms will be shown as Pseudocode. The computer simulation gives data that will be shown in plots and used to compare the two bounds. The comparison of the two bounds shows that the new bound is better than the established bound.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/60341
20170101T00:00:00Z

Transfinite surface interpolation over irregular nsided domains
http://hdl.handle.net/10852/60339
Transfinite surface interpolation over irregular nsided domains
Kåshagen, Carl Emil
Parametric representations of surfaces in ComputerAided Geometric Design (CAGD) are often based on connected patches with rectangular parameter domains. Given a loop of four space curves and normalderivative curves, we want to find a parametric surface that interpolates the boundary data in a C^1continuous way. The Coons patch developed by Steven A. Coons in the 1960s, is a well known technique for constructing such surfaces. However, the need to construct patches with nonrectangular domains can often occur within a rectangular patch framework. In a recent paper by Várady, Rockwood & Salvi (2011), three different methods which generalizes the original Coons patch to match n boundary curves using irregular nsided domains, were presented. Another transfinite interpolation method called cubic mean value interpolation based on mean value coordinates was introduced by Floater & Schulz (2008). The purpose of this thesis is to review and compare these methods. All the methods were successfully implemented in MATLAB®. We discuss the pros and cons of the different constructions, and provide several numerical examples to compare the shape qualities and computational efficiency.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/60339
20170101T00:00:00Z