Department of Mathematics
Nye registreringer

BlackLitterman portfolio allocation using Local Gaussian Correlation
(Master thesis, 20240427) 
Rolling Stiefel Manifolds Equipped with αMetrics
(Journal article; Peer reviewed, 2023)We discuss the rolling, without slipping and without twisting, of Stiefel manifolds equipped with 𝛼metrics, from an intrinsic and an extrinsic point of view. We, however, start with a more general perspective, namely, ... 
Shift modules, strongly stable ideals, and their dualities
(Journal article; Peer reviewed, 2023)We enrich the setting of strongly stable ideals (SSI): We introduce shift modules, a module category encompassing SSIs. The recently introduced duality on SSIs is given an effective conceptual and computational setting. ... 
A Bayesian Lasso based sparse learning model
(Journal article; Peer reviewed, 2023)The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse ... 
Exploring Spline Based Models in glmmTMB
(Master thesis, 20240603)In recent times the Rpackage glmmTMB has been extended to facilitate spline regression. In this thesis we implement spline based smoothers in glmmTMBmodels and compare them to generalized additive models from mgcv and ... 
Exceptional families of measures on Carnot groups
(Journal article; Peer reviewed, 2023)We study the families of measures on Carnot groups that have vanishing p module, which we call Mp exceptional families. We found necessary and sufficient Conditions for the family of intrinsic Lipschitz surfaces passing ... 
Symmetric Spaces Rolling on Flat Spaces
(Journal article; Peer reviewed, 2023)The objective of the current paper is essentially twofold. Firstly, to make clear the difference between two notions of rolling a Riemannian manifold over another, using a language accessible to a wider audience, in ... 
A robust solution strategy for the CahnLarché equations
(Journal article; Peer reviewed, 2023)In this paper we propose a solution strategy for the CahnLarché equations, which is a model for linearized elasticity in a medium with two elastic phases that evolve subject to a GinzburgLandau type energy functional. ... 
Portfolio Selection with a RankDeficient Covariance Matrix
(Journal article; Peer reviewed, 2024)In this paper, we consider optimal portfolio selection when the covariance matrix of the asset returns is rankdeficient. For this case, the original Markowitz’ problem does not have a unique solution. The possible solutions ... 
On the formulation of energy conservation in the eeKdV equation
(Journal article; Peer reviewed, 2024)The Kortewegde Vries (KdV) equation is a wellknown model equation for unidirectional shallowwater (long) surface waves. The equation includes dispersion and weak nonlinearity. The derivation of the equation originates ... 
WellPosedness for the Extended Schrödinger–Benjamin–Ono System
(Journal article; Peer reviewed, 2024) 
A finite mixture analysis of structural breaks in the G7 gross domestic product series
(Journal article; Peer reviewed, 2023)In this paper we apply a clustering procedure to detect trend changes in macroeconomic data, focusing on the GDP time series for the G7 countries. A finite mixture of regression models is considered to show different ... 
The Rectangle Complex of a Relation
(Journal article; Peer reviewed, 2023)We construct a simplicial complex, the rectangle complex of a relation R, and show that it is homotopy equivalent to the Dowker complex of . This results in a short and conceptual proof of functorial versions of Dowker’s ... 
Strongly interacting solitary waves for the fractional modified Kortewegde Vries equation
(Journal article; Peer reviewed, 2023)We study one particular asymptotic behaviour of a solution of the fractional modified Kortewegde Vries equation (also known as the dispersion generalised modified BenjaminOno equation): ∂tu + ∂x(−Dαu + u3) = 0. The ... 
Determining homology of an unknown space from a sample
(Journal article; Peer reviewed, 2023)The homology of an unknown subspace of Euclidean space can be determined from the intrinsic Čech complex of a sample of points in the subspace, without reference to the ambient Euclidean space. More precisely, given a ... 
Sudden wave flooding on steep rock shores: a clear but hidden danger
(Journal article; Peer reviewed, 2024)It is shown that very steep coastal profiles can give rise to unexpectedly large wave events at the coast. We conduct a statistical analysis of runs from a nearshore Boussinesqtype model to demonstrate that under certain ... 
Local limit theorems for a directed random walk on the backbone of a supercritical oriented percolation cluster
(Journal article; Peer reviewed, 2023)We consider a directed random walk on the backbone of the supercritical oriented percolation cluster in dimensions d+1 with d≥3 being the spatial dimension. For this random walk we prove an annealed local central limit ... 
Asymptotic N solitonlike solutions of the fractional Korteweg–de Vries equation
(Journal article; Peer reviewed, 2023)We construct Nsoliton solutions for the fractional Korteweg–de Vries (fKdV) equation ∂tu−∂x(∣D∣αu−u2)=0, in the whole subcritical range α∈(1/2,2). More precisely, if Qc denotes the ground state solution associated ... 
Profunctors Between Posets and Alexander Duality
(Journal article; Peer reviewed, 2023)We consider profunctors f : P −→Q between posets and introduce their graph and ascent. The profunctors Pro(P, Q) form themselves a poset, and we consider a partition I F of this into a downset I and upset F, called a ... 
Plant Identification with Computer Vision and Improvement Through Location Data
(Master thesis, 20240603)Det ˚a kunne riktig identifisere arter er et veldig viktig verktøy i kampen for ˚a bevare artsmangfoldet i verden, men dette er kunnskap som er enten forbeholdt eksperter, eller s˚a er det veldig tidskrevende for ufagkyndige. ...