Matematisk institutt
http://hdl.handle.net/10852/6
Sat, 11 Jul 2020 15:48:25 GMT2020-07-11T15:48:25ZPincherle's theorem in reverse mathematics and computability theory
http://hdl.handle.net/10852/77797
Pincherle's theorem in reverse mathematics and computability theory
Normann, Dag; Sanders, Sam
We study the logical and computational properties of basic theorems of uncountable mathematics, in particular Pincherle's theorem, published in 1882. This theorem states that a locally bounded function is bounded on certain domains, i.e. one of the first ‘local-to-global’ principles. It is well-known that such principles in analysis are intimately connected to (open-cover) compactness, but we nonetheless exhibit fundamental differences between compactness and Pincherle's theorem. For instance, the main question of Reverse Mathematics, namely which set existence axioms are necessary to prove Pincherle's theorem, does not have an unique or unambiguous answer, in contrast to compactness. We establish similar differences for the computational properties of compactness and Pincherle's theorem. We establish the same differences for other local-to-global principles, even going back to Weierstrass. We also greatly sharpen the known computational power of compactness, for the most shared with Pincherle's theorem however. Finally, countable choice plays an important role in the previous, we therefore study this axiom together with the intimately related Lindelöf lemma.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/777972020-01-01T00:00:00ZIntensive breast screening in BRCA2 mutation carriers is associated with reduced breast cancer specific and all cause mortality
http://hdl.handle.net/10852/77669
Intensive breast screening in BRCA2 mutation carriers is associated with reduced breast cancer specific and all cause mortality
Evans, Dafydd Gareth; Harkness, Elaine F.; Howell, Anthony; Wilson, Mary; Hurley, Emma; Holmen, Marit Muri; Tharmaratnam, Kukatharmini; Hagen, Anne Irene; Lim, Yit Yoong; Maxwell, Anthony James; Møller, Pål
Background
The addition of annual MRI screening to mammography has heightened optimism that intensive screening along with improved treatments may substantially improve life expectancy of women at high risk of breast cancer. However, survival data from BRCA2 mutation carriers undergoing intensive combined breast screening are scarce.
Methods
We have collated the results of screening with either annual mammography or mammography with MRI in female BRCA2 mutation carriers in Manchester and Oslo and use a Manchester control group of BRCA2 mutation carriers who had their first breast cancer diagnosed without intensive screening.
Results
Eighty-seven BRCA2 mutation carriers had undergone combined (n = 34) or mammography (n = 53) screening compared to 274 without such intensive screening. Ten year breast cancer specific survival was 100 % in the combined group (95 % CI 82.5–100 %) and 85.5 % (95 % CI 72.6–98.4 %) in the mammography group compared to 74.6 % (95 % CI 66.6–82.6 %) in the control group. Better survival was driven by lymph node status (negative in 67 % of screened vs 39 % of unscreened women; p < 0.001) and a significantly greater proportion of intensively screened women had invasive breast cancers <2 cm at diagnosis (74.6 % vs 50.4 %; p = 0.002).
Conclusion
Intensive combined breast cancer screening with annual MRI and mammography appears to improve survival from breast cancer in BRCA2 mutation carriers. Data from larger groups are required to confirm the effectiveness of combined screening in BRCA2 carriers.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10852/776692016-01-01T00:00:00ZAccounting for grouped predictor variables or pathways in high-dimensional penalized Cox regression models
http://hdl.handle.net/10852/77565
Accounting for grouped predictor variables or pathways in high-dimensional penalized Cox regression models
Belhechmi, Shaima; Bin, Riccardo D; Rotolo, Federico; Michiels, Stefan
Background
The standard lasso penalty and its extensions are commonly used to develop a regularized regression model while selecting candidate predictor variables on a time-to-event outcome in high-dimensional data. However, these selection methods focus on a homogeneous set of variables and do not take into account the case of predictors belonging to functional groups; typically, genomic data can be grouped according to biological pathways or to different types of collected data. Another challenge is that the standard lasso penalisation is known to have a high false discovery rate.
Results
We evaluated different penalizations in a Cox model to select grouped variables in order to further penalize variables that, in addition to having a low effect, belong to a group with a low overall effect; and to favor the selection of variables that, in addition to having a large effect, belong to a group with a large overall effect. We considered the case of prespecified and disjoint groups and proposed diverse weights for the adaptive lasso method. In particular we proposed the product Max Single Wald by Single Wald weighting (MSW*SW) which takes into account the information of the group to which it belongs and of this biomarker. Through simulations, we compared the selection and prediction ability of our approach with the standard lasso, the composite Minimax Concave Penalty (cMCP), the group exponential lasso (gel), the Integrative L1-Penalized Regression with Penalty Factors (IPF-Lasso), and the Sparse Group Lasso (SGL) methods. In addition, we illustrated the methods using gene expression data of 614 breast cancer patients.
Conclusions
The adaptive lasso with the MSW*SW weighting method incorporates both the information in the grouping structure and the individual variable. It outperformed the competitors by reducing the false discovery rate without severely increasing the false negative rate.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/775652020-01-01T00:00:00ZPoincaré-Friedrichs inequalities of complexes of discrete distributional differential forms
http://hdl.handle.net/10852/77419
Poincaré-Friedrichs inequalities of complexes of discrete distributional differential forms
Christiansen, Snorre H; Licht, Martin Werner
We derive bounds for the constants in Poincaré–Friedrichs inequalities with respect to mesh-dependent norms for complexes of discrete distributional differential forms. A key tool is a generalized flux reconstruction which is of independent interest. The results apply to piecewise polynomial de Rham sequences on bounded domains with mixed boundary conditions.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/774192020-01-01T00:00:00ZTowards definition of the risk premium function
http://hdl.handle.net/10852/77360
Towards definition of the risk premium function
Krecar, Nikola; Benth, Fred Espen; Gubina, Andrej
Successful trading in electricity markets relies on the market actor's ability to accurately forecast the electricity price. The fundamental electricity price models use market information, provided by various price drivers, including the residual that contains a risk premium. In the past, researchers investigating risk premium focused primarily on daily spot price levels, ignoring the intraday information hindering the accurate risk premium determination. This paper presents a new KGB Method for modelling of risk premium, based on “ex-ante” approach focused on a yearly product. The method involves a novel KGB Model and its linearized formulation, the KGB Linear Model, which enables capturing the influence of renewable energy sources on risk premium. The four key drivers of the KGB Linear Model were used providing an insight into the influence of RES generation on risk premium evolution. The method was tested on historical data from the German electricity market. The results for the 2010-2014 period reveal overall influence of PV production share on risk premium is greater than that of wind production share, both increasing the risk premium due to their variability and uncertainty. Using the KGB Method, market actors can forecast risk premium using information readily available to them.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/773602020-01-01T00:00:00ZGranular viscosity from plastic yield surfaces: The role of the deformation type in granular flows
http://hdl.handle.net/10852/77353
Granular viscosity from plastic yield surfaces: The role of the deformation type in granular flows
Rauter, Matthias; Barker, T.; Fellin, W.
Numerical simulations of granular flows with Navier–Stokes type models emerged in the last decade, challenging the well established depth-averaged models. The structure of these equations allows for extension to general rheologies based on complex and realistic constitutive models. Substantial effort has been put into describing the effect of the shear rate, i.e. the magnitude of the velocity gradient, on the shear stress. Here we analyse the effect of the deformation type. We apply the theories of Mohr–Coulomb and Matsuoka–Nakai to calculate the stresses under different deformation types and compare results to the theory of Drucker–Prager, which is formulated independently of the deformation type. This model is particularly relevant because it is the basis for many granular rheologies, such as the –rheology. All models have been implemented into the open-source toolkit OpenFOAM® for a practical application. We found that, within the context of these models, the deformation type has a large influence on the stress. However, for the geometries considered here, these differences are limited to specific zones which have little influence on the landslide kinematics. Finally we are able to give indicators on when the deformation type should be considered in modelling of landslides and when it can be neglected.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10852/773532020-01-01T00:00:00ZConvergence rates for stochastic and degenerate-parabolic balance laws
http://hdl.handle.net/10852/77339
Convergence rates for stochastic and degenerate-parabolic balance laws
Storrøsten, Erlend Briseid
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10852/773392016-01-01T00:00:00ZA high order time discretization of the solution of the non-linear filtering problem
http://hdl.handle.net/10852/77316
A high order time discretization of the solution of the non-linear filtering problem
Crisan, Dan; Ortiz-Latorre, Salvador
The solution of the continuous time filtering problem can be represented as a ratio of two expectations of certain functionals of the signal process that are parametrized by the observation path. We introduce a class of discretization schemes of these functionals of arbitrary order. The result generalizes the classical work of Picard, who introduced first order discretizations to the filtering functionals. For a given time interval partition, we construct discretization schemes with convergence rates that are proportional with the m-power of the mesh of the partition for arbitrary m∈N. The result paves the way for constructing high order numerical approximation for the solution of the filtering problem.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/773162019-01-01T00:00:00ZGeneralized Periodic Vehicle Routing and Maritime Surveillance
http://hdl.handle.net/10852/77314
Generalized Periodic Vehicle Routing and Maritime Surveillance
Fauske, Maria Fleischer; Mannino, Carlo; Ventura, Paolo
Planning maritime surveillance activities in military operations and long-term defense planning is a huge task that is done manually today. Because maritime surveillance resources are extremely expensive, the potential cost savings of using optimization models to do such planning are large. In this paper, we developed a methodology for making maritime surveillance planning more efficient. The purpose of our tool is to find routes for the force elements involved in maritime surveillance operations, where the goal is to keep a maritime picture sufficiently updated. Our problem may be viewed as a variant of the classical periodic vehicle routing problem, but it differs from this problem in some major aspects. To cope with the specific issues of our problem, we introduce a novel time-indexed formulation, where each variable is associated with a set of contiguous time periods. We defined and implemented a branch-and-price procedure to solve this formulation to exact optimality. Moreover, to tackle instances of practical size, we defined and applied efficient and effective heuristic techniques for solving the pricing problem. We show how our approach can plan up to 72-hour realistic missions with routing ships.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/773142019-01-01T00:00:00ZThe geometry of SDP-exactness in quadratic optimization
http://hdl.handle.net/10852/77082
The geometry of SDP-exactness in quadratic optimization
Cifuentes, Diego; Harris, Corey; Sturmfels, Bernd
Consider the problem of minimizing a quadratic objective subject to quadratic equations. We study the semialgebraic region of objective functions for which this problem is solved by its semidefinite relaxation. For the Euclidean distance problem, this is a bundle of spectrahedral shadows surrounding the given variety. We characterize the algebraic boundary of this region and we derive a formula for its degree.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/770822019-01-01T00:00:00ZCross-streamer wavefield interpolation using deep convolutional networks
http://hdl.handle.net/10852/77027
Cross-streamer wavefield interpolation using deep convolutional networks
Greiner, Thomas Larsen; Kolbjørnsen, Odd; Lie, Jan Erik; Harris Nilsen, Espen; Kjeldsrud Evensen, Andreas; Gelius, Leiv-J.
Seismic exploration in complex geological settings and shallow geological targets has led to a demand for higher spatial and temporal resolution in the final migrated image. Seismic data from conventional marine acquisition lacks near offset and wide azimuth data, which limits imaging in these settings. In addition, large streamer separation introduce aliasing of spatial frequencies across the streamers. A new marine survey configuration, known as TopSeis, was introduced in 2017 in order to address the shallow-target problem. However, introduction of near offset data has shown to be challenging for interpolation and regularization, using conventional methods. In this paper, we investigate deep learning as a tool for interpolation beyond spatial aliasing across the streamers, in the shot domain. The proposed method is based on imaging techniques from single-image super resolution (SISR). The model architecture consist of a deep convolutional neural network (CNN) and a periodic resampling layer for upscaling to the non-aliased wavefield. We demonstrate the performance of proposed method on representative broad-band synthetic data and TopSeis field data from the Barents Sea.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/770272019-01-01T00:00:00ZSub-voxel Perfusion Modeling in Terms of Coupled 3d-1d Problem
http://hdl.handle.net/10852/77026
Sub-voxel Perfusion Modeling in Terms of Coupled 3d-1d Problem
Holter, Karl Erik; Kuchta, Miroslav; Mardal, Kent-Andre
We study perfusion by a multiscale model coupling diffusion in the tissue and diffusion along the one-dimensional segments representing the vasculature. We propose a block-diagonal preconditioner for the model equations and demonstrate its robustness by numerical experiments. We compare our model to a macroscale model by Tofts [Modelling in DCE MRI, 2012].
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/770262019-01-01T00:00:00ZFree nilpotent groups are C*-superrigid
http://hdl.handle.net/10852/76934
Free nilpotent groups are C*-superrigid
Omland, Tron
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/769342019-01-01T00:00:00ZDynamic risk measure for BSVIE with jumps and semimartingale issues
http://hdl.handle.net/10852/76933
Dynamic risk measure for BSVIE with jumps and semimartingale issues
Agram, Nacira
Risk measure is a fundamental concept in finance and in the insurance industry. It is used to adjust life insurance rates. In this article, we will study dynamic risk measures by means of backward stochastic Volterra integral equations (BSVIEs) with jumps. We prove a comparison theorem for such a type of equations. Since the solution of a BSVIEs is not a semimartingale in general, we will discuss some particular semimartingale issues.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/769332019-01-01T00:00:00ZParametric jet interpolation for Stein manifolds with the density property
http://hdl.handle.net/10852/76932
Parametric jet interpolation for Stein manifolds with the density property
Ramos-Peon, Alexandre; Ugolini, Riccardo
Given a Stein manifold with the density property, we show that under a suitable topological condition it is possible to prescribe derivatives at a finite number of points to automorphisms depending holomorphically on a Stein parameter. This is an Oka property of the manifold and is related to its holomorphic flexibility.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/769322019-01-01T00:00:00ZComparison of Computational Fluid Dynamics Simulations and Experiments for Stratified Air-Water Flows in Pipes
http://hdl.handle.net/10852/76856
Comparison of Computational Fluid Dynamics Simulations and Experiments for Stratified Air-Water Flows in Pipes
Chinello, Gabriele; Ayati, Anis Awal; McGlinchey, Don; Ooms, Gorik; Henkes, Ruud
Stratified gas–liquid flow is a flow regime typically encountered in multiphase pipelines. The understanding and modeling of this regime is of engineering importance especially for the oil and gas industry. In this work, simulations have been conducted for stratified air–water flow in pipes. We solved the Reynolds-averaged Navier–Stokes (RANS) equations with the volume of fluid (VOF) method. The aim of this work was to evaluate the performance of the k–ω shear stress transport (SST) turbulence model with and without damping of the turbulence at the gas–liquid interface. Simulation results were compared with some of the latest experimental results found in the literature. A comparison between the simulated velocity and kinetic energy profiles and the experimental results obtained with the particle image velocimetry (PIV) technique was conducted. The characteristics of the interfacial waves were also extracted and compared with the experiments. It is shown that a proper damping of the turbulence close to the interface is needed to obtain agreement with the experimental pressure drop and liquid hold-up. In its current form, however, RANS with the k–ω turbulence model is still not able to give an accurate prediction of the velocity profiles and of the interface waves.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/768562019-01-01T00:00:00ZMean-field stochastic control with elephant memory in infinite time horizon
http://hdl.handle.net/10852/76818
Mean-field stochastic control with elephant memory in infinite time horizon
Agram, Nacira; Øksendal, Bernt
Our purpose of this paper is to study stochastic control problems for systems driven by mean-field stochastic differential equations with elephant memory, in the sense that the system (like the elephants) never forgets its history. We study both the finite horizon case and the infinite time horizon case.
- In the finite horizon case, results about existence and uniqueness of solutions of such a system are given. Moreover, we prove sufficient as well as necessary stochastic maximum principles for the optimal control of such systems. We apply our results to solve a mean-field linear quadratic control problem.
- For infinite horizon, we derive sufficient and necessary maximum principles.
As an illustration, we solve an optimal consumption problem from a cash flow modelled by an elephant memory mean-field system.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/768182019-01-01T00:00:00ZB-spline-like bases for C2 cubics on the Powell–Sabin 12-split
http://hdl.handle.net/10852/76790
B-spline-like bases for C2 cubics on the Powell–Sabin 12-split
Lyche, Tom; Muntingh, Georg
For spaces of constant, linear, and quadratic splines of maximal smoothness on the Powell–Sabin 12-split of a triangle, the so-called S-bases were recently introduced. These are simplex spline bases with B-spline-like properties on the 12-split of a single triangle, which are tied together across triangles in a Bézier-like manner.
In this paper we give a formal definition of an S-basis in terms of certain basic properties. We proceed to investigate the existence of S-bases for the aforementioned spaces and additionally the cubic case, resulting in an exhaustive list. From their nature as simplex splines, we derive simple differentiation and recurrence formulas to other S-bases. We establish a Marsden identity that gives rise to various quasi-interpolants and domain points forming an intuitive control net, in terms of which conditions for C0-, C1-, and C2-smoothness are derived.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/767902019-01-01T00:00:00ZRigidity theory for C*-dynamical systems and the "Pedersen rigidity problem", II
http://hdl.handle.net/10852/76781
Rigidity theory for C*-dynamical systems and the "Pedersen rigidity problem", II
Kaliszewski, S.; Omland, Tron; Quigg, John
This is a follow-up to a paper with the same title and by the same authors. In that paper, all groups were assumed to be abelian, and we are now aiming to generalize the results to nonabelian groups. The motivating point is Pedersen’s theorem, which does hold for an arbitrary locally compact group [Formula: see text], saying that two actions [Formula: see text] and [Formula: see text] of [Formula: see text] are outer conjugate if and only if the dual coactions [Formula: see text] and [Formula: see text] of [Formula: see text] are conjugate via an isomorphism that maps the image of [Formula: see text] onto the image of [Formula: see text] (inside the multiplier algebras of the respective crossed products). We do not know of any examples of a pair of non-outer-conjugate actions such that their dual coactions are conjugate, and our interest is therefore exploring the necessity of latter condition involving the images; and we have decided to use the term “Pedersen rigid” for cases where this condition is indeed redundant. There is also a related problem, concerning the possibility of a so-called equivariant coaction having a unique generalized fixed-point algebra, that we call “fixed-point rigidity”. In particular, if the dual coaction of an action is fixed-point rigid, then the action itself is Pedersen rigid, and no example of non-fixed-point-rigid coaction is known.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/767812019-01-01T00:00:00ZA simplification problem in manifold topology
http://hdl.handle.net/10852/76730
A simplification problem in manifold topology
Jahren, Bjørn; Hausmann, Jean-Claude
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/767302019-01-01T00:00:00Z