Matematisk institutt
http://hdl.handle.net/10852/5
Tue, 21 Jan 2020 22:33:53 GMT2020-01-21T22:33:53ZA non-Gaussian Ornstein–Uhlenbeck model for pricing wind power futures
http://hdl.handle.net/10852/72329
A non-Gaussian Ornstein–Uhlenbeck model for pricing wind power futures
Benth, Fred Espen
The recent introduction of wind power futures written on the German wind power production index has brought with it new interesting challenges in terms of modelling and pricing. Some particularities of this product are the strong seasonal component embedded in the underlying, the fact that the wind index is bounded from both above and below and also that the futures are settled against a synthetically generated spot index. Here, we consider the non-Gaussian Ornstein–Uhlenbeck type processes proposed by Barndorff-Nielsen and Shephard in the context of modelling the wind power production index. We discuss the properties of the model and estimation of the model parameters. Further, the model allows for an analytical formula for pricing wind power futures. We provide an empirical study, where the model is calibrated to 37 years of German wind power production index that is synthetically generated assuming a constant level of installed capacity. Also, based on 1 year of observed prices for wind power futures with different delivery periods, we study the market price of risk. Generally, we find a negative risk premium whose magnitude decreases as the length of the delivery period increases. To further demonstrate the benefits of our proposed model, we address the pricing of European options written on wind power futures, which can be achieved through Fourier techniques.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/723292018-01-01T00:00:00ZThe motivic Hopf map solves the homotopy limit problem for K-theory
http://hdl.handle.net/10852/72317
The motivic Hopf map solves the homotopy limit problem for K-theory
Østvær, Paul Arne; Röndigs, Oliver; Spitzweck, Markus
We solve affirmatively the homotopy limit problem for (effective) -theory over fields of finite virtual cohomological dimension. Our solution uses the motivic slice filtration and the first motivic Hopf map.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/723172018-01-01T00:00:00ZImpact of Miniaturized Fixed-Bias Multineedle Langmuir Probes on CubeSats
http://hdl.handle.net/10852/72309
Impact of Miniaturized Fixed-Bias Multineedle Langmuir Probes on CubeSats
Marholm, Sigvald; Marchand, Richard; Darian, Diako; Miloch, Wojciech Jacek; Mortensen, Mikael
Kinetic simulation results are presented to study the response of multi-Needle Langmuir Probes of the type used on many satellites. Simulations of isolated probes are used to parametrize the current collected as a function of voltage for a set of densities and temperatures of relevance to Earth ionosphere. These simulations also serve to assess the validity of analytic results obtained from the orbit motion limited (OML) theory used in recent studies. Computed probe characteristics are then fitted with empirical scaling laws and used to account for electron current collected by needle probes on a typical triple CubeSat. These fits are then used to determine the impact of the probes and guards on the spacecraft floating potential for a nominal configuration of bias voltages, over the plasma parameters of interest. In order for the probes to work as intended, they must operate at a positive potential with respect to the ambient plasma. However, results show that for the cases considered, the spacecraft floating potential is so low that the probe with the lowest voltage becomes negative. Possible solutions are examined and proposed to ensure that all probes remain at a positive voltage with respect to surrounding plasma.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/723092019-01-01T00:00:00ZGraded twisting of comodule algebras and module categories
http://hdl.handle.net/10852/72302
Graded twisting of comodule algebras and module categories
Bichon, Julien; Neshveyev, Sergey; Yamashita, Makoto
Continuing our previous work on graded twisting of Hopf algebras and monoidal categories, we introduce a graded twisting construction for equivariant comodule algebras and module categories. As an example we study actions of quantum subgroups of G⊂SL−1(2) on K−1[x,y] and show that in most cases the corresponding invariant rings K−1[x,y]G are invariant rings K[x,y]G′ for the action of a classical subgroup G′⊂SL(2). As another example we study Poisson boundaries of graded twisted categories and show that under the assumption of weak amenability they are graded twistings of the Poisson boundaries.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/723022018-01-01T00:00:00ZX-ray measurements of plunging breaking solitary waves
http://hdl.handle.net/10852/72208
X-ray measurements of plunging breaking solitary waves
Smith, Lisa; Kolaas, Jostein; Jensen, Atle; Sveen, Johan Kristian
The aim of this study is to examine and measure the characteristics of air cavities generated by breaking solitary waves by utilizing a novel tomographic X-ray system. Small scale experiments of solitary waves that propagate on a (1:10) beach are conducted. Waves with amplitude normalized with the water depth, on a flat bottom are investigated by two perpendicular X-ray systems. Images are captured at locations from the surf zone to the swash zone and at maximum runup. A large air tube is observed right after the plunger impacts the dry beach. Void velocity and the shape of the large air tube, are measured and reported. The large air tube evolves from a symmetrical shape with two large air pockets located close to the walls of the wave tank, to an asymmetrical shape. Contrast enhanced X-ray images reveal that the swash tongue surface is unstable and that secondary mixing of air and water occurs. X-ray images from the maximum runup reveal that the air is still entrapped by the thin swash tongue at times close to maximum runup.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/722082018-01-01T00:00:00ZMathematical Modeling of Cerebrospinal Fluid Pulsatility and Pathways
http://hdl.handle.net/10852/72183
Mathematical Modeling of Cerebrospinal Fluid Pulsatility and Pathways
Vinje, Vegard
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/721832019-01-01T00:00:00ZPatient-specific Modeling of the Human Brain using Magnetic Resonance Imaging
http://hdl.handle.net/10852/72174
Patient-specific Modeling of the Human Brain using Magnetic Resonance Imaging
Valnes, Lars Magnus
Dementia is a growing concern for the health-care in the world and most treatment strategies are not successful. Dementia is associated with accumulation of metabolic waste in the form of protein fragments. Recent breakthroughs have suggested that the accumulation of waste is caused by malfunction of clearance mechanism, called the glymphatic system, that provides bulk flow through the extracellular matrix. To what extent this system accelerates transport provided by extracellular diffusion, is an open question. Recent research also shows that transport can be accelerated during sleep and by deep breathing.
In this work, I have investigated the enrichment and clearance of a tracer in the brain using magnetic resonance imaging (MRI), developed methods for constructing computational geometries from MRI and evaluated the tracer diffusion using patient-specific computational simulations. The medical data used in this study are novel imaging recently performed at Rikshopspitalet where MRI tracer was administrated into fluid compartment along the spine and transported up and into the brain. Based on these data I have analyzed the tracer movement, and observed that the tracer had a brain-wide distribution. Additionally, this thesis aims to provide methodology and software tools for constructing computational geometries from brain MRI in a patient-specific manner. In particular, I have solved PDE constrained optimization problems with finite elements to assess the efficiency of the transport mechanism in a patient-specific manner.
Compared to controls, in the patients with dementia the tracers demonstrated a slower clearance. Thus suggesting a brain-wide clearance system and an impairment in the waste-removal in dementia. Additionally, these observations may provide the possibility for a new and more effective method for administrating medicine to the brain. Diffusion coefficients were found to be higher than the expected, henceforth diffusion alone does not explain the clearance of waste from the brain.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/721742020-01-01T00:00:00ZNon-singular simplicial sets
http://hdl.handle.net/10852/72161
Non-singular simplicial sets
Fjellbo, Rune Vegard S.
A simplicial set is said to be non-singular if its non-degenerate simplices are embedded. Let sSet denote the category of simplicial sets. We prove that the full subcategory nsSet whose objects are the non-singular simplicial sets admits a model structure such that nsSet becomes Quillen equivalent to sSet equipped with the standard model structure due to Quillen. The model structure on nsSet is right-induced from sSet and it makes nsSet a proper cofibrantly generated model category. Together with Thomason’s model structure on small categories and Raptis’ model structure on posets these form a square-shaped diagram of Quillen equivalences in which the subsquare of right adjoints commutes.
To establish the model structure referred to above, we first argue that simplicial sets have an analogue of mapping spaces. Namely, let X^K denote the simplicial set whose n-simplices are the simplicial maps Delta^n x K -> X. We prove that X^K is non-singular whenever X is non-singular.
As a related result that is interesting in its own right, we prove that the left Quillen functor of the Quillen equivalence that we establish has an alternate description. The Barratt nerve - denoted B - is the endofunctor that takes a simplicial set to the nerve of the poset of its non-degenerate simplices. The ordered simplicial complex BSd X, namely the Barratt nerve of the Kan subdivision Sd X, is a triangulation of the original simplicial set X in the sense that there is a natural map BSd X -> X whose geometric realization is homotopic to some homeomorphism. This is a refinement to the result that any simplicial set can be triangulated. A simplicial set is said to be regular if each of its non-degenerate simplices is embedded along its n-th face. That BSd X -> X is a triangulation of X is a consequence of the fact that the Kan subdivision makes simplicial sets regular and that B X is a triangulation of X whenever X is regular. In this dissertation, we argue that B - interpreted as a functor from regular to non-singular simplicial sets - is not just any triangulation, but in fact the best. We mean this in the sense that B is the left Kan extension of barycentric subdivision along the Yoneda embedding. Consequently, BSd is indeed the left Quillen functor of a Quillen equivalence - as stated.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/721612018-01-01T00:00:00ZNormal oppdeling og produkt av endelige simplisielle mengder
http://hdl.handle.net/10852/72160
Normal oppdeling og produkt av endelige simplisielle mengder
Fjellbo, Rune Vegard S.
The canonical map from the Kan subdivision of a product of two finite simplicial sets to the product of the Kan subdivisions is a simple map, in the sense that its geometric realization has contractible point inverses.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10852/721602012-01-01T00:00:00ZReliability Analysis of Network Real - Time Kinematic
http://hdl.handle.net/10852/72143
Reliability Analysis of Network Real - Time Kinematic
Ouassou, Mohammed; Natvig, Bent; Jensen, Anna B.O.; Gåsemyr, Jørund Inge
The multistate reliability theory was applied to the network real-time kinematic (NRTK) data processing chain, where the qualities of the network corrections, baseline residuals, and the associated variance-covariance matrices are considered as the system state vectors. The state vectors have direct influence on the rover receiver position accuracy. The penalized honored stochastic averaged standard deviation (PHSASD) is used to map the NRTK sensitive data, represented by the states vectors to different levels of performance. The study shows that the improvement is possible by identification of critical components in the NRTK system and implementation of some parallelism that makes the system more robust.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/721432018-01-01T00:00:00ZA bit of tropical geometry
http://hdl.handle.net/10852/72112
A bit of tropical geometry
Shaw, Kristin; Brugallé, Erwan
This friendly introduction to tropical geometry is meant to be accessible to first year students in mathematics. The topics discussed here are basic tropical algebra, tropical plane curves, some tropical intersections, and Viro's patchworking. Each definition is explained with concrete examples and illustrations. The text is a modification of a translation from a French text by the first author. There is also a newly-added section highlighting new developments and perspectives on tropical geometry. In addition, the final section provides an extensive list of references on the subject.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10852/721122014-01-01T00:00:00ZA tropical intersection product in matroidal fans
http://hdl.handle.net/10852/72110
A tropical intersection product in matroidal fans
Shaw, Kristin
We construct an intersection product on tropical cycles contained in the Bergman fan of a matroid. To do this we first establish a connection between the operations of deletion and restriction in matroid theory and tropical modifications as defined by Mikhalkin in [Proceedings of the International Congress of Mathematicians, Vol. II, European Mathematical Society, Zürich, 2006, pp. 827--852]. This product generalizes the product of Allermann and Rau [Math. Z., 264 (2010), pp. 633--670] and Allermann [Tropical intersection products on smooth varieties, J. Eur. Math. Soc. (JEMS), 14 (2012), pp. 107--126] and also provides an alternative procedure for intersecting cycles which is not based on intersecting with Cartier divisors. Also, we simplify the definition in the case of one-dimensional fan cycles in two-dimensional matroidal fans and give an application of the intersection product to realiability questions in tropical geometry.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10852/721102013-01-01T00:00:00ZLefschetz (1,1) theorem in tropical geometry
http://hdl.handle.net/10852/72109
Lefschetz (1,1) theorem in tropical geometry
Shaw, Kristin; Jell, Philipp; Rau, Johannes
For a tropical manifold of dimension n we show that the tropical homology classes of degree (n-1, n-1) which arise as fundamental classes of tropical cycles are precisely those in the kernel of the eigenwave map. To prove this we establish a tropical version of the Lefschetz (1, 1)-theorem for rational polyhedral spaces that relates tropical line bundles to the kernel of the wave homomorphism on cohomology. Our result for tropical manifolds then follows by combining this with Poincaré duality for integral tropical homology.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/721092018-01-01T00:00:00ZObstructions to approximating tropical curves in surfaces via intersection theory
http://hdl.handle.net/10852/72106
Obstructions to approximating tropical curves in surfaces via intersection theory
Shaw, Kristin; Brugallé, Erwan
We provide some new local obstructions to approximating tropical curves in smooth tropical surfaces. These obstructions are based on a relation between tropical and complex intersection theories, which is also established here. We give two applications of the methods developed in this paper. First we classify all locally irreducible approximable 3-valent fan tropical curves in a fan tropical plane. Secondly, we prove that a generic non-singular tropical surface in tropical projective 3-space contains finitely many approximable tropical lines if it is of degree 3, and contains no approximable tropical lines if it is of degree 4 or more.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10852/721062015-01-01T00:00:00ZWhich principal components are most sensitive in the change detection problem?
http://hdl.handle.net/10852/71996
Which principal components are most sensitive in the change detection problem?
Tveten, Martin
Principal component analysis (PCA) is often used in anomaly detection and statistical process control tasks. For bivariate normal data, we prove that the minor projection (the least varying projection) of the PCA‐rotated data is the most sensitive to distributional changes, where sensitivity is defined as the Hellinger distance between the projections' marginal distributions before and after a change. In particular, this is almost always the case if only one parameter of the bivariate normal distribution changes, that is, the change is sparse. Simulations indicate that the minor projections are the most sensitive for a large range of changes and pre‐change settings in higher dimensions as well, including changes that are very sparse. This motivates using only a few of the minor projections for detecting sparse distributional changes in high‐dimensional data.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/719962019-01-01T00:00:00ZKyle-Back's model with a random horizon
http://hdl.handle.net/10852/71959
Kyle-Back's model with a random horizon
Corcuera, José Manuel; Di Nunno, Giulia
The continuous-time version of Kyle [(1985) Continuous auctions and insider trading, Econometrica53 (6), 1315–1335.] developed by Back [(1992) Insider trading in continuous time, The Review of Financial Studies5 (3), 387–409.] is studied here. In Back’s model, there is asymmetric information in the market in the sense that there is an insider having information on the real value of the asset. We extend this model by assuming that the fundamental value evolves with time and that it is announced at a future random time. First, we consider the case when the release time of information is predictable to the insider and then when it is not. The goal of the paper is to study the structure of equilibrium, which is described by the optimal insider strategy and the competitive market prices given by the market makers. We provide necessary and sufficient conditions for the optimal insider strategy under general dynamics for the asset demands. Moreover, we study the behavior of the price pressure and the market efficiency. In particular, we find that when the random time is not predictable, there can be equilibrium without market efficiency. Furthermore, for the two cases of release time and for classes of pricing rules, we provide a characterization of the equilibrium.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/719592018-01-01T00:00:00ZGLM and GAM modelling of life insurance data
http://hdl.handle.net/10852/71933
GLM and GAM modelling of life insurance data
Rygg, Amanda Haugnes
As an employee you can have a variety of insurances through your employer, one of them being life insurance covering death due to non-occupational illnesses. With such covers it is essential for the insurance company to know which factors impact risk and through this be able to predict the future risks for new policies. As companies enter and leave the portfolio from year to year, it induces shifts in the insured population and with that shifts in the observed death rates. This complicates the modelling of the death rates. In this thesis, we consider Generalized Linear Models (GLMs) and Generalized Additive Models (GAMs) for prediction and smoothing of nonlinear death rate patterns. We will consider different costumer properties for modelling and discuss differences and similarities in smoothing and predictions done by GLMs and GAMs. We, of course, find that death rates due to non-occupational illnesses increase with age. We also find that the death rates decrease over time. We detect significant differences in death rates of people working in companies with different NACE-codes, also known as activity codes. This is a mandatory statistical classification of the economic activities of a company, put down and regulated by the European Union. Here one of the more surprising discoveries is a higher death rate for women engaging in financial and insurance activities, compared to women in other NACE-codes tested, which usually require less education.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/719332019-01-01T00:00:00ZCovariate selection in high-dimensional generalized linear models with measurement error
http://hdl.handle.net/10852/71904
Covariate selection in high-dimensional generalized linear models with measurement error
Sørensen, Øystein; Hellton, Kristoffer Herland; Frigessi Di Rattalma, Arnoldo; Thoresen, Magne
In many problems involving generalized linear models, the covariates are subject to measurement error. When the number of covariates p exceeds the sample size n, regularized methods like the lasso or Dantzig selector are required. Several recent papers have studied methods which correct for measurement error in the lasso or Dantzig selector for linear models in the p > n setting. We study a correction for generalized linear models, based on Rosenbaum and Tsybakov’s matrix uncertainty selector. By not requiring an estimate of the measurement error covariance matrix, this generalized matrix uncertainty selector has a great practical advantage in problems involving high-dimensional data. We further derive an alternative method based on the lasso, and develop efficient algorithms for both methods. In our simulation studies of logistic and Poisson regression with measurement error, the proposed methods outperform the standard lasso and Dantzig selector with respect to covariate selection, by reducing the number of false positives considerably. We also consider classification of patients on the basis of gene expression data with noisy measurements. Supplementary materials for this article are available online.; Covariate selection in high-dimensional generalized linear models with measurement error
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/719042018-01-01T00:00:00ZRelative dynamical degrees of correspondences over a field of arbitrary characteristic
http://hdl.handle.net/10852/71902
Relative dynamical degrees of correspondences over a field of arbitrary characteristic
Truong, Tuyen Trung
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/719022018-01-01T00:00:00ZDetailed measurements of interfacial dynamics in air-water pipe flow
http://hdl.handle.net/10852/71897
Detailed measurements of interfacial dynamics in air-water pipe flow
Ayati, Anis Awal; Vollestad, Petter; Jensen, Atle
Stratified air-water flow in a horizontal pipe is investigated experimentally using particle image velocimetry and conductance probes. This flow regime is characterized by a complex interplay between a turbulent airflow and propagating waves at the interface. The waves are generated by interfacial shear and pressure forces exerted by the faster flowing airflow. The goal of this study is to characterize the waves by means of statistical and spectral methods, and to explore the influence of different wave regimes on the airflow.
Two cases in which the air bulk velocity increases from 2.4 m/s (case A) to 3.5 m/s (case B), while the liquid velocity remains constant at 0.26 m/s, are assessed in detail. Case A belongs to a region of flow conditions in which wave amplitudes grow as a consequence of increasing gas flow rates, i.e., wave growth regime. Meanwhile, case B is in a regime of saturated wave amplitudes. In the first case, the interface was populated by small amplitude 2D waves of relatively small steepness (ak ≈ 0.07). These waves obey Gaussian statistics and are thus considered to be linear. In the second case, the waves are larger, steeper (ak ≈ 0.13) and considerably more irregular. They display non-linear behaviour (steep crests and long troughs) and their exceedance probability distribution deviates significantly from Gaussian statistics. Bicoherence maps show evidence of both overtone and sub-harmonic interactions.
Airflow velocity fields acquired by PIV were subjected to a conditional phase-averaging method based on a steepness criterion. The phase-averaged vorticity field shows evidence of shear-layer separation above the steeper waves of case B. Hence, in addition to non-linear mode interactions and micro-breaking, shear-layer separation may contribute to the transition from the growth regime to the saturation regime.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/718972018-01-01T00:00:00Z