Matematisk institutt
http://hdl.handle.net/10852/5
Mon, 08 Aug 2022 12:58:52 GMT2022-08-08T12:58:52ZMinimal norm Hankel operators
http://hdl.handle.net/10852/94827
Minimal norm Hankel operators
Brevig, Ole Fredrik
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10852/948272022-01-01T00:00:00ZAlgebraic cobordism and étale cohomology
http://hdl.handle.net/10852/94806
Algebraic cobordism and étale cohomology
Østvær, Paul Arne; Elmanto, Elden; Levine, Marc; Spitzweck, Markus
Thomason’s étale descent theorem for Bott periodic algebraic K–theory is generalized to any MGL module over a regular Noetherian scheme of finite dimension. Over arbitrary Noetherian schemes of finite dimension, this generalizes the analogue of Thomason’s theorem for Weibel’s homotopy K–theory. This is achieved by amplifying the effects from the case of motivic cohomology, using the slice spectral sequence in the case of the universal example of algebraic cobordism. We also obtain integral versions of these statements: Bousfield localization at étale motivic cohomology is the universal way to impose étale descent for these theories. As applications, we describe the étale local objects in modules over these spectra and show that they satisfy the full six functor formalism, construct an étale descent spectral sequence converging to Bott-inverted motivic Landweber exact theories, and prove cellularity and effectivity of the étale versions of these motivic spectra.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10852/948062022-01-01T00:00:00ZMotives and homotopy theory in logarithmic geometry
http://hdl.handle.net/10852/94762
Motives and homotopy theory in logarithmic geometry
Østvær, Paul Arne; Binda, Federico; Park, Doosung
This document is a short user’s guide to the theory of motives and homotopy theory in the setting of logarithmic geometry. We review some of the basic ideas and results in relation to other works on motives with modulus, motivic homotopy theory, and reciprocity sheaves.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10852/947622022-01-01T00:00:00ZThe local cohomology spectral sequence for topological modular forms
http://hdl.handle.net/10852/94744
The local cohomology spectral sequence for topological modular forms
Bruner, Robert R.; Greenlees, John P.C.; Rognes, John
Abstract We discuss proofs of local cohomology theorems for topological modular forms, based on Mahowald–Rezk duality and on Gorenstein duality, and then make the associated local cohomology spectral sequences explicit, including their differential patterns and hidden extensions.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10852/947442022-01-01T00:00:00ZHilbert’s Tenth Problem for Term Algebras with a Substitution Operator
http://hdl.handle.net/10852/94701
Hilbert’s Tenth Problem for Term Algebras with a Substitution Operator
Murwanashyaka, Juvenal
We introduce a first-order theory of finite full binary trees and show that the analogue of Hilbert’s Tenth Problem is undecidable by constructing a many-to-one reduction of Post’s Correspondence Problem.; Hilbert’s Tenth Problem for Term Algebras with a Substitution Operator
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10852/947012022-01-01T00:00:00ZWeak Sequential Theories of Finite Full Binary Trees
http://hdl.handle.net/10852/94700
Weak Sequential Theories of Finite Full Binary Trees
Murwanashyaka, Juvenal
We study a first-order theory of finite full binary trees with an axiom schema of open induction. We show that this theory is sequential by constructing a direct interpretation of Adjunctive Set Theory in a very weak finitely axiomatized subtheory. We show that weakening the latter theory by removal of an axiom which states that the subtree relation is transitive gives a theory that directly interprets Vaught’s weak set theory, a non-finitely axiomatizable fragment of Adjunctive Set Theory.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10852/947002022-01-01T00:00:00ZThe groupoid approach to equilibrium states on right LCM semigroup C*-algebras
http://hdl.handle.net/10852/94698
The groupoid approach to equilibrium states on right LCM semigroup C*-algebras
Neshveyev, Sergey; Stammeier, Nicolai
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10852/946982022-01-01T00:00:00ZThe blood microbiome and its association to cardiovascular disease mortality: case-cohort study
http://hdl.handle.net/10852/94687
The blood microbiome and its association to cardiovascular disease mortality: case-cohort study
Lawrence, Graeme; Midtervoll, Ingvild; Samuelsen, Sven O.; Kristoffersen, Anne K.; Enersen, Morten; Håheim, Lise L.
Background
Little is known about the association between bacterial DNA in human blood and the risk of cardiovascular disease (CVD) mortality.
Methods
A case-cohort study was performed based on a 9 ½ year follow-up of the Oslo II study from 2000. Eligible for this analysis were men born in 1923 and from 1926 to 1932. The cases were men (n = 227) who had died from CVD, and the controls were randomly selected participants from the same cohort (n = 178). Analysis of the bacterial microbiome was performed on stored frozen blood samples for both cases and controls. Association analyses for CVD mortality were performed by Cox proportional hazard regression adapted to the case-cohort design. We used the Bonferroni correction due to the many bacterial genera that were identified.
Results
Bacterial DNA was identified in 372 (82%) of the blood samples and included 78 bacterial genera from six phyla. Three genera were significantly associated with CVD mortality. The genera Kocuria (adjusted hazard ratio (HR) 8.50, 95% confidence interval (CI) (4.05, 17.84)) and Enhydrobacter (HR 3.30 (2.01, 5.57)) indicate an association with CVD mortality with increasing levels. The genera Paracoccus (HR 0.29 (0.15, 0.57)) was inversely related. Significant predictors of CVD mortality were: the feeling of bad health; and the consumption of more than three cups of coffee per day. The following registered factors were borderline significant, namely: a history of heart failure; increased systolic blood pressure; and currently taking antihypertensive drugs now, versus previously.
Conclusions
The increasing levels of two bacterial genera Kocuria (skin and oral) and Enhydrobacter (skin) and low levels of Paracoccus (soil) were associated with CVD mortality independent of known risk factors for CVD.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10852/946872022-01-01T00:00:00ZAnalysis and Numerical Treatment of Nonlinear Hyperbolic Conservation Laws on Graphs
http://hdl.handle.net/10852/94601
Analysis and Numerical Treatment of Nonlinear Hyperbolic Conservation Laws on Graphs
Musch, Markus
Hyperbolic conservation laws are used to model various important applications such as gas flow or traffic flow. Those phenomena are interesting to study in a one-dimensional setting, it would be even more relevant for real world applications, to study those equations on networks. Whilst the theory for hyperbolic conservation laws in 1D is fairly extensive, many questions are still open for the network case. My thesis addresses and solves several of these open questions.
In particular, my thesis addresses the question of well-posedness of hyperbolic conservation laws on networks. The question of well-posedness consists of three sub-questions, which are existence, uniqueness, and stability of a solution. In my thesis I present a fairly general well-posedness theory for a large class of equations that include models of gas flow and traffic flow on networks.
Furthermore, I developed a computer program that allows to compute approximate solutions to said equations and showed that this algorithm converges towards the actual solution. In addition to showing convergence of the algorithm, I also show results on how fast the algorithm converges towards the actual solution. This is important to know for computations of actual use cases.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10852/946012022-01-01T00:00:00ZLongitudinal associations of DNA methylation and sleep in children: a meta-analysis
http://hdl.handle.net/10852/94594
Longitudinal associations of DNA methylation and sleep in children: a meta-analysis
Sammallahti, Sara; Koopman-Verhoeff, M. E.; Binter, Anne-Claire; Mulder, Rosa H.; Cabré-Riera, Alba; Kvist, Tuomas; Malmberg, Anni L. K.; Pesce, Giancarlo; Plancoulaine, Sabine; Heiss, Jonathan A.; Rifas-Shiman, Sheryl L.; Röder, Stefan W.; Starling, Anne P.; Wilson, Rory; Guerlich, Kathrin; Haftorn, Kristine L.; Page, Christian M.; Luik, Annemarie I.; Tiemeier, Henning; Felix, Janine F.; Raikkonen, Katri; Lahti, Jari; Relton, Caroline L.; Sharp, Gemma C.; Waldenberger, Melanie; Grote, Veit; Heude, Barbara; Annesi-Maesano, Isabella; Hivert, Marie-France; Zenclussen, Ana C.; Herberth, Gunda; Dabelea, Dana; Grazuleviciene, Regina; Vafeiadi, Marina; Håberg, Siri E.; London, Stephanie J.; Guxens, Mònica; Richmond, Rebecca C.; Cecil, Charlotte A. M.
Background
Sleep is important for healthy functioning in children. Numerous genetic and environmental factors, from conception onwards, may influence this phenotype. Epigenetic mechanisms such as DNA methylation have been proposed to underlie variation in sleep or may be an early-life marker of sleep disturbances. We examined if DNA methylation at birth or in school age is associated with parent-reported and actigraphy-estimated sleep outcomes in children.
Methods
We meta-analysed epigenome-wide association study results. DNA methylation was measured from cord blood at birth in 11 cohorts and from peripheral blood in children (4–13 years) in 8 cohorts. Outcomes included parent-reported sleep duration, sleep initiation and fragmentation problems, and actigraphy-estimated sleep duration, sleep onset latency and wake-after-sleep-onset duration.
Results
We found no associations between DNA methylation at birth and parent-reported sleep duration (n = 3658), initiation problems (n = 2504), or fragmentation (n = 1681) (p values above cut-off 4.0 × 10–8). Lower methylation at cg24815001 and cg02753354 at birth was associated with longer actigraphy-estimated sleep duration (p = 3.31 × 10–8, n = 577) and sleep onset latency (p = 8.8 × 10–9, n = 580), respectively. DNA methylation in childhood was not cross-sectionally associated with any sleep outcomes (n = 716–2539).
Conclusion
DNA methylation, at birth or in childhood, was not associated with parent-reported sleep. Associations observed with objectively measured sleep outcomes could be studied further if additional data sets become available.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10852/945942022-01-01T00:00:00ZFree Probabilistic and Poisson–Lie Geometric Methods for Quantum Groups: On Strong 1-Boundedness and Coboundary Lie Bialgebras
http://hdl.handle.net/10852/94579
Free Probabilistic and Poisson–Lie Geometric Methods for Quantum Groups: On Strong 1-Boundedness and Coboundary Lie Bialgebras
Elzinga, Floris Eelke
Quantum groups first arose out of the study of integrability in quantum mechanics, presenting a new notion of symmetry extending beyond the traditional group concept. Quantum groups can be thought of as the collection of symmetries of noncommutative spaces, which arise in many areas of modern physics and mathematics.
This thesis deals with two topics in the theory of (operator algebraic) quantum groups.
On the one hand, we study the von Neumann algebras of certain Kac type compact quantum groups. This well-behaved class is amenable to methods from free probability to study their fine analytic structure. We establish several important properties, such as Connes embeddability and strong 1-boundedness, in a number of examples of these quantum groups.
On the other hand, we apply methods from Poisson—Lie geometry to real simple Lie groups, endowing their Lie algebras with coboundary Lie bialgebra structures. The general deformation theory of such Lie groups is poorly understood, but relations between concrete examples using quantum torsors are known. Our results provide an analogue of this quantum phenomenon in the classical setting.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10852/945792022-01-01T00:00:00ZStochastic Volterra integral equations and a class of first-order stochastic partial differential equations
http://hdl.handle.net/10852/94564
Stochastic Volterra integral equations and a class of first-order stochastic partial differential equations
Benth, Fred Espen; Detering, Nils; Krühner, Paul
We investigate stochastic Volterra equations and their limiting laws. The stochastic Volterra equations we consider are driven by a Hilbert space valued Lévy noise and integration kernels may have non-linear dependence on the current state of the process. Our method is based on an embedding into a Hilbert space of functions which allows to represent the solution of the Volterra equation as the boundary value of a solution to a stochastic partial differential equation. We first gather abstract results and give more detailed conditions in more specific function spaces.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10852/945642022-01-01T00:00:00ZStochastic integrals and Gelfand integration in Fréchet spaces
http://hdl.handle.net/10852/94561
Stochastic integrals and Gelfand integration in Fréchet spaces
Benth, Fred Espen; Galimberti, Luca
We provide a detailed analysis of the Gelfand integral on Fréchet spaces, showing among other things a Vitali theorem, dominated convergence and a Fubini result. Furthermore, the Gelfand integral commutes with linear operators. The Skorohod integral is conveniently expressed in terms of a Gelfand integral on Hida distribution space, which forms our prime motivation and example. We extend several results of Skorohod integrals to a general class of pathwise Gelfand integrals. For example, we provide generalizations of the Hida–Malliavin derivative and extend the integration-by-parts formula in Malliavin Calculus. A Fubini-result is also shown, based on the commutative property of Gelfand integrals with linear operators. Finally, our studies give the motivation for two existing definitions of stochastic Volterra integration in Hida space.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10852/945612022-01-01T00:00:00ZDynamic density functional theory for the charging of electric double layer capacitors
http://hdl.handle.net/10852/94553
Dynamic density functional theory for the charging of electric double layer capacitors
Ma, Ke; Janssen, Mathijs Adriaan; Lian, Cheng; Van Roij, René
We consider the charging of a model capacitor comprised of two planar electrodes and an electrolyte. Upon switching on a voltage difference, electric double layers build up in this setup, which we characterize with a classical dynamic density functional theory (DDFT) that accounts for electrostatic correlations and for molecular excluded volume of finite-sized ions and solvent molecules. Our DDFT predicts the electrode charge Q( t) to form exponentially with two timescales: at early times, the system relaxes on the RC time, namely, λ D L/[ D(2 + σ/ λ D )], with λ D being the Debye length, L being the electrode separation, σ being the ion diameter, and D being the ionic diffusivity. Contrasting an earlier DDFT study, this early-time response does not depend on the applied potential. At late times, the capacitor relaxes with a relaxation time proportional to the diffusion time L 2 / D.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10852/945532022-01-01T00:00:00ZSingular Control of Stochastic Volterra Integral Equations
http://hdl.handle.net/10852/94550
Singular Control of Stochastic Volterra Integral Equations
Agram, Nacira; Labed, Saloua; Øksendal, Bernt Karsten; Yakhlef, Samia
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10852/945502022-01-01T00:00:00ZElastic modulus measurements of cooked Lutefisk
http://hdl.handle.net/10852/94547
Elastic modulus measurements of cooked Lutefisk
Feneuil, Blandine; Strøm Lillebø, Eirik; Larris Honstad, Christian; Jensen, Atle; Carlson, Andreas
Lutefisk is a traditional Norwegian Christmas dish, made of dry cod soaked in a lye solution before re-hydrated. We report measurements of tissue rheological properties of cooked Lutefisk. Surprisingly, we find that the elastic modulus does not seem to depend heavily on cooking time, cooking temperature, or the amount of salt, but depends instead mainly on the size of the fish fillets and can be affected by when the cod is fished during the season. Although salting and cooking of the Lutefisk strongly affect the visual aspect of fish fillets, these changes are not found to be correlated with the elastic modulus of the lutefisk when measured with a rheometer.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10852/945472022-01-01T00:00:00ZSelf-exciting jump processes and their asymptotic behaviour
http://hdl.handle.net/10852/94538
Self-exciting jump processes and their asymptotic behaviour
Dahl, Kristina Rognlien; Eyjolfsson, Heidar
The purpose of this paper is to investigate properties of self-exciting jump processes where the intensity is given by an SDE, which is driven by a finite variation stochastic jump process. The value of the intensity process immediately before a jump may influence the jump size distribution. We focus on properties of this intensity function, and show that for each fixed point in time, t≥0, a scaling limit of the intensity process converges in distribution, and the limit equals the strong solution of the square-root diffusion process (Cox–Ingersoll–Ross process) at t. As a particular example, we study the case of a linear intensity process and derive explicit expressions for the expectation and variance in this case.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10852/945382022-01-01T00:00:00ZLieb type convexity for positive operator monotone decreasing functions
http://hdl.handle.net/10852/94537
Lieb type convexity for positive operator monotone decreasing functions
Neumann, Hans Henrich; Yamashita, Makoto
We prove Lieb type convexity and concavity results for trace functionals associated with positive operator monotone (decreasing) functions and certain monotone concave functions, together with strictly positive linear maps of matrices. This gives a partial generalization of Hiai's recent work on trace functionals associated with power functions, by allowing positive operator monotone decreasing functions instead of power maps.Our proof is based on variational formula for trace functionals based on the Legendre transform, and a strengthened convexity of positive operator monotone decreasing functions in a previous work of Kirihata and the second named author. We also provide the generalization to the framework of unital tracial C -algebras based on Petz's work.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10852/945372022-01-01T00:00:00ZWell-posedness theory for nonlinear scalar conservation laws on networks
http://hdl.handle.net/10852/94532
Well-posedness theory for nonlinear scalar conservation laws on networks
Musch, Markus; Fjordholm, Ulrik Skre; Risebro, Nils Henrik
We consider nonlinear scalar conservation laws posed on a network. We define an entropy condition for scalar conservation laws on networks and establish $L^1$ stability, and thus uniqueness, for weak solutions satisfying the entropy condition. We apply standard finite volume methods and show stability and convergence to the unique entropy solution, thus establishing existence of a solution in the process. Both our existence and stability/uniqueness theory is centred around families of stationary states for the equation. In one important case – for monotone fluxes with an upwind difference scheme – we show that the set of (discrete) stationary solutions is indeed sufficiently large to suit our general theory. We demonstrate the method's properties through several numerical experiments.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10852/945322022-01-01T00:00:00ZA decision support system for safer airplane landings: Predicting runway conditions using XGBoost and explainable AI
http://hdl.handle.net/10852/94531
A decision support system for safer airplane landings: Predicting runway conditions using XGBoost and explainable AI
Midtfjord, Alise Danielle; De Bin, Riccardo; Huseby, Arne Bang
The presence of snow and ice on runway surfaces reduces the available tire-pavement friction needed for retardation and directional control and causes potential economic and safety threats for the aviation industry during the winter seasons. To activate appropriate safety procedures, pilots need accurate and timely information on the actual runway surface conditions. In this study, XGBoost is used to create a combined runway assessment system, which includes a classification model to identify slippery conditions and a regression model to predict the level of slipperiness. The models are trained on weather data and runway reports. The runway surface conditions are represented by the tire-pavement friction coefficient, which is estimated from flight sensor data from landing aircrafts. The XGBoost models are combined with SHAP approximations to provide a reliable decision support system for airport operators, which can contribute to safer and more economic operations of airport runways. To evaluate the performance of the prediction models, they are compared to several state-of-the-art runway assessment methods. The XGBoost models identify slippery runway conditions with a ROC AUC of 0.95, predict the friction coefficient with a MAE of 0.0254, and outperforms all the previous methods. The results show the strong abilities of machine learning methods to model complex, physical phenomena with a good accuracy.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10852/945312022-01-01T00:00:00Z