Matematisk institutt
http://hdl.handle.net/10852/5
Thu, 09 Apr 2020 15:08:18 GMT
20200409T15:08:18Z

Assessing graphbased read mappers against a baseline approach highlights strengths and weaknesses of current methods
http://hdl.handle.net/10852/74399
Assessing graphbased read mappers against a baseline approach highlights strengths and weaknesses of current methods
Grytten, Ivar; Rand, Knut D; Nederbragt, Alexander J; Sandve, Geir K
Background
Graphbased reference genomes have become popular as they allow read mapping and followup analyses in settings where the exact haplotypes underlying a highthroughput sequencing experiment are not precisely known. Two recent papers show that mapping to graphbased reference genomes can improve accuracy as compared to methods using linear references. Both of these methods index the sequences for most paths up to a certain length in the graph in order to enable direct mapping of reads containing common variants. However, the combinatorial explosion of possible paths through nearby variants also leads to a huge search space and an increased chance of false positive alignments to highly variable regions.
Results
We here assess three prominent graphbased read mappers against a hybrid baseline approach that combines an initial path determination with a tuned linear read mapping method. We show, using a previously proposed benchmark, that this simple approach is able to improve overall accuracy of readmapping to graphbased reference genomes.
Conclusions
Our method is implemented in a tool Twostep Graph Mapper, which is available at https://github.com/uiobmi/two_step_graph_mapperalong with data and scripts for reproducing the experiments. Our method highlights characteristics of the current generation of graphbased read mappers and shows potential for improvement for future graphbased read mappers.
Wed, 01 Jan 2020 00:00:00 GMT
http://hdl.handle.net/10852/74399
20200101T00:00:00Z

Accelerating deep reinforcement learning strategies of flow control through a multienvironment approach
http://hdl.handle.net/10852/74365
Accelerating deep reinforcement learning strategies of flow control through a multienvironment approach
Rabault, Jean; Kuhnle, Alexander
Deep Reinforcement Learning (DRL) has recently been proposed as a methodology to discover complex active flow control strategies [Rabault et al., “Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control,” J. Fluid Mech. 865, 281–302 (2019)]. However, while promising results were obtained on a simple 2dimensional benchmark flow at a moderate Reynolds number, considerable speedups will be required to investigate more challenging flow configurations. In the case of DRL trained with Computational Fluid Dynamics (CFD) data, it was found that the CFD part, rather than training the artificial neural network, was the limiting factor for speed of execution. Therefore, speedups should be obtained through a combination of two approaches. The first one, which is well documented in the literature, is to parallelize the numerical simulation itself. The second one is to adapt the DRL algorithm for parallelization. Here, a simple strategy is to use several independent simulations running in parallel to collect experiences faster. In the present work, we discuss this solution for parallelization. We illustrate that perfect speedups can be obtained up to the batch size of the DRL agent, and slightly suboptimal scaling still takes place for an even larger number of simulations. This is, therefore, an important step toward enabling the study of more sophisticated fluid mechanics problems through DRL.
Tue, 01 Jan 2019 00:00:00 GMT
http://hdl.handle.net/10852/74365
20190101T00:00:00Z

Stochastic control of general meanfield SPDEs with jumps
http://hdl.handle.net/10852/74325
Stochastic control of general meanfield SPDEs with jumps
Øksendal, Bernt; Sulem, Agnès; Dumitrescu, Roxana
We study optimal control for meanfield stochastic partial differential equations (stochastic evolution equations) driven by a Brownian motion and an independent Poisson random measure, in case of partial information control. One important novelty of our problem is represented by the introduction of general meanfield operators, acting on both the controlled state process and the control process. We first formulate a sufficient and a necessary maximum principle for this type of control. We then prove the existence and uniqueness of the solution of such general forward and backward meanfield stochastic partial differential equations. We apply our results to find the explicit optimal control for an optimal harvesting problem.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/74325
20180101T00:00:00Z

The 2Hessian and sextactic points on plane algebraic curves
http://hdl.handle.net/10852/74319
The 2Hessian and sextactic points on plane algebraic curves
Moe, Karoline; Maugesten, Paul Aleksander
In an article from 1865, Arthur Cayley claims that given a plane algebraic curve there exists an associated 2Hessian curve that intersects it in its sextactic points. In this paper we fix an error in Cayley's calculations and provide the correct defining polynomial for the 2Hessian. In addition, we present a formula for the number of sextactic points on cuspidal curves and tie this formula to the 2Hessian. Lastly, we consider the special case of rational curves, where the sextactic points appear as zeros of the Wronski determinant of the 2nd Veronese embedding of the curve.
Tue, 01 Jan 2019 00:00:00 GMT
http://hdl.handle.net/10852/74319
20190101T00:00:00Z

Singular control of SPDEs with spacemean dynamics
http://hdl.handle.net/10852/74318
Singular control of SPDEs with spacemean dynamics
Agram, Nacira; Hilbert, Astrid; Øksendal, Bernt
We consider the problem of optimal singular control of a stochastic partial differential equation (SPDE) with spacemean dependence. Such systems are proposed as models for population growth in a random environment. We obtain sufficient and necessary maximum principles for these control problems. The corresponding adjoint equation is a reflected backward stochastic partial differential equation (BSPDE) with spacemean dependence. We prove existence and uniqueness results for such equations. As an application we study optimal harvesting from a population modelled as an SPDE with spacemean dependence.
Tue, 01 Jan 2019 00:00:00 GMT
http://hdl.handle.net/10852/74318
20190101T00:00:00Z

Do Japanese and Italian Women Live Longer than Women in Scandinavia?
http://hdl.handle.net/10852/74271
Do Japanese and Italian Women Live Longer than Women in Scandinavia?
Borgan, Ørnulf; Keilman, Nico
Life expectancies at birth are routinely computed from period life tables. When mortality is falling, such period life expectancies will typically underestimate real life expectancies, that is, life expectancies for birth cohorts. Hence, it becomes problematic to compare period life expectancies between countries when they have different historical mortality developments. For instance, life expectancies for countries in which the longevity improved early (like Norway and Sweden) are difficult to compare with those in countries where it improved later (like Italy and Japan). To get a fair comparison between the countries, one should consider cohort data. Since cohort life expectancies can only be computed for cohorts that were born more than a hundred years ago, in this paper we suggest that for younger cohorts one may consider the expected number of years lost up to a given age. Contrary to the results based on period data, our cohort results then indicate that Italian women may expect to lose more years than women in Norway and Sweden, while there are no indications that Japanese women will lose fewer years than women in Scandinavia. The large differences seen for period data may just be an artefact due to the distortion that period life tables imply in times of changing mortality.; Do Japanese and Italian Women Live Longer than Women in Scandinavia?
Tue, 01 Jan 2019 00:00:00 GMT
http://hdl.handle.net/10852/74271
20190101T00:00:00Z

Rational quartic symmetroids
http://hdl.handle.net/10852/74270
Rational quartic symmetroids
Helsø, Martin
We classify rational, irreducible quartic symmetroids in projective 3space. They are either singular along a line or a smooth conic section, or they have a triple point or a tacnode.
Wed, 01 Jan 2020 00:00:00 GMT
http://hdl.handle.net/10852/74270
20200101T00:00:00Z

Datadriven methods for multiple sensor streams, with applications in the maritime industry
http://hdl.handle.net/10852/74263
Datadriven methods for multiple sensor streams, with applications in the maritime industry
Brandsæter, Andreas
Wed, 01 Jan 2020 00:00:00 GMT
http://hdl.handle.net/10852/74263
20200101T00:00:00Z

Diverse personalized recommendations with uncertainty from implicit preference data with the Bayesian Mallows model
http://hdl.handle.net/10852/74215
Diverse personalized recommendations with uncertainty from implicit preference data with the Bayesian Mallows model
Liu, Qinghua; Reiner, Andrew Henry; Frigessi Di Rattalma, Arnoldo; Scheel, Ida
Clicking data, which exists in abundance and contains objective user preference information, is widely used to produce personalized recommendations in webbased applications. Current popular recommendation algorithms, typically based on matrix factorizations, often focus on achieving high accuracy. While achieving good clickthrough rates, diversity of the recommended items is often overlooked. Moreover, most algorithms do not produce interpretable uncertainty quantifications of the recommendations. In this work, we propose the Bayesian Mallows for Clicking Data (BMCD) method, which simultaneously considers accuracy and diversity. BMCD augments clicking data into compatible full ranking vectors by enforcing all the clicked items clicked by a user to be topranked regardless of their rarity. User preferences are learned using a Mallows ranking model. Bayesian inference leads to interpretable uncertainties of each individual recommendation, and we also propose a method to make personalized recommendations based on such uncertainties. With a simulation study and a real life data example, we demonstrate that compared to stateoftheart matrix factorization, BMCD makes personalized recommendations with similar accuracy, while achieving much higher level of diversity, and producing interpretable and actionable uncertainty estimation.
Tue, 01 Jan 2019 00:00:00 GMT
http://hdl.handle.net/10852/74215
20190101T00:00:00Z

Fast Algorithms for Counting Points on Elliptic Curves over Finite Fields
http://hdl.handle.net/10852/74135
Fast Algorithms for Counting Points on Elliptic Curves over Finite Fields
Bocianowski, Sivert
Vi ser på Schoof's og Satoh's algoritmer for opptelling av rasjonale punkter på elliptiske kurver over endelige kropper. Relevant bakgrunn om elliptiske kurver og de padiske tallene. Kort om ECC (elliptic curve cryptography). Implementering av Satoh's algoritme i karakteristikk 2 i Python med SageMath.
Tue, 01 Jan 2019 00:00:00 GMT
http://hdl.handle.net/10852/74135
20190101T00:00:00Z

Multiresolution Bayesian CMB component separation through Wiener filtering with a pseudoinverse preconditioner
http://hdl.handle.net/10852/74120
Multiresolution Bayesian CMB component separation through Wiener filtering with a pseudoinverse preconditioner
Seljebotn, Dag Sverre; Bærland, Trygve; Eriksen, Hans Kristian Kamfjord; Mardal, KentAndre; Wehus, Ingunn Kathrine
We present a Bayesian model for multiresolution component separation for cosmic microwave background (CMB) applications based on Wiener filtering and/or computation of constrained realizations, extending a previously developed framework. We also develop an efficient solver for the corresponding linear system for the associated signal amplitudes. The core of this new solver is an efficient preconditioner based on the pseudoinverse of the coefficient matrix of the linear system. In the full sky coverage case, the method gives an increased speed of the preconditioner, and it is easier to implement in terms of practical computer code. In the case where a mask is applied and priordriven constrained realization is sought within the mask, this is the first time full convergence has been achieved at the full resolution of the Planck data set.
© ESO 2019
Tue, 01 Jan 2019 00:00:00 GMT
http://hdl.handle.net/10852/74120
20190101T00:00:00Z

On environmental contours for marine and coastal design
http://hdl.handle.net/10852/74065
On environmental contours for marine and coastal design
Ross, Emma; Astrup, Ole Christian; BitnerGregersen, Elzbieta; Bunn, Nigel; Feld, Graham; Gouldby, Ben; Huseby, Arne; Liu, Ye; Randell, David; Vanem, Erik; Jonathan, Philip
Environmental contours are used in structural reliability analysis of marine and coastal structures as an approximate means to locate the boundary of the distribution of environmental variables, and hence sets of environmental conditions giving rise to extreme structural loads and responses. Outline guidance concerning the application of environmental contour methods is given in recent design guidelines from many organisations. However there is lack of clarity concerning (a) the differences between approaches to environmental contour estimation reported in the literature, and (b) the relationship between the environmental contour, corresponding to some return period, and the extreme structural response for the same period. Hence there is uncertainty about precisely when environmental contours should be used, and how they should be used well. This article seeks to provide some assistance in understanding the fundamental issues regarding environmental contours and their use in structural reliability analysis. Approaches to estimating the joint distribution of environmental variables, and to estimating environmental contours based on that distribution, are described. Simple freelyavailable software for estimation of the joint distribution, and hence environmental contours, is illustrated. Extra assumptions required to relate the characteristics of environmental contours to structural failure are outlined. Alternative responsebased methods not requiring environmental contours are summarised. The results of an informal survey of the metocean user community regarding environmental contours are presented. Finally, recommendations about when and how environmental contour methods should be used are made.
Wed, 01 Jan 2020 00:00:00 GMT
http://hdl.handle.net/10852/74065
20200101T00:00:00Z

Liquidity induced asset bubbles via flows of ELMMs
http://hdl.handle.net/10852/73990
Liquidity induced asset bubbles via flows of ELMMs
Biagini, Francesca; Mazzon, Andrea; MeyerBrandis, Thilo
We consider a constructive model for asset price bubbles, where the market price $W$ is endogenously determined by the trading activity on the market and the fundamental price $W^F$ is exogenously given, as in [R. Jarrow, P. Protter, and A. Roch, Quant. Finance, 12 (2012), pp. 13391349]. To justify $W^F$ from a fundamental point of view, we embed this constructive approach in the martingale theory of bubbles (see [R. Jarrow, P. Protter, and K. Shimbo, Math. Finance, 20 (2010), pp. 145185] and [F. Biagini, H. Föllmer, and S. Nedelcu, Finance Stoch., 18 (2014), pp. 297326]) by showing the existence of a flow of equivalent martingale measures for $W$, under which $W^F$ equals the expectation of the discounted future cash flow. As an application, we study bubble formation and evolution in a financial network.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/73990
20180101T00:00:00Z

Ship speed prediction based on full scale sensor measurements of shaft thrust and environmental conditions
http://hdl.handle.net/10852/73946
Ship speed prediction based on full scale sensor measurements of shaft thrust and environmental conditions
Brandsæter, Andreas; Vanem, Erik
The primary goal of this study is to adapt and validate various regression models to predict a ship's speed through water based on relevant and available full scale sensor measurements from a ship, including measurements of external environmental forces. The wind is measured by onboard wind sensors, and the effect of the waves is measured by motion reference units (MRUs) installed on the ship, measuring motions in six degrees of freedom; three translational motions and rotations about these. Accurate speed estimates, which relate directly to the estimates of the propulsion efficiency, fuel efficiency and pollution, are vital to be able to optimize ship design and operation. We demonstrate how regression models such as linear regression, projection pursuit (PPT) and generalized additive models (GAM) can be easily implemented for this application. A simple regression model based on the wellestablished relationship between ship speed and shaft thrust represent a benchmark model towards which the other models are compared.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/73946
20180101T00:00:00Z

Alternatives to postprocessing posterior predictive pvalues
http://hdl.handle.net/10852/73939
Alternatives to postprocessing posterior predictive pvalues
Gåsemyr, Jørund Inge; Scheel, Ida
The posterior predictive p value (ppp) was invented as a Bayesian counterpart to classical p values. The methodology can be applied to discrepancy measures involving both data and parameters and can, hence, be targeted to check for various modeling assumptions. The interpretation can, however, be difficult since the distribution of the ppp value under modeling assumptions varies substantially between cases. A calibration procedure has been suggested, treating the ppp value as a test statistic in a prior predictive test. In this paper, we suggest that a prior predictive test may instead be based on the expected posterior discrepancy, which is somewhat simpler, both conceptually and computationally. Since both these methods require the simulation of a large posterior parameter sample for each of an equally large prior predictive data sample, we furthermore suggest to look for ways to match the given discrepancy by a computation‐saving conflict measure. This approach is also based on simulations but only requires sampling from two different distributions representing two contrasting information sources about a model parameter. The conflict measure methodology is also more flexible in that it handles non‐informative priors without difficulty. We compare the different approaches theoretically in some simple models and in a more complex applied example.
Tue, 01 Jan 2019 00:00:00 GMT
http://hdl.handle.net/10852/73939
20190101T00:00:00Z

Respiratory influence on cerebrospinal fluid flow – a computational study based on longterm intracranial pressure measurements
http://hdl.handle.net/10852/73931
Respiratory influence on cerebrospinal fluid flow – a computational study based on longterm intracranial pressure measurements
Vinje, Vegard; Ringstad, Geir; Lindstrøm, Erika Kristina; Valnes, Lars Magnus; Rognes, Marie Elisabeth; Eide, Per Kristian; Mardal, KentAndre
Current theories suggest that waste solutes are cleared from the brain via cerebrospinal fluid (CSF) flow, driven by pressure pulsations of possibly both cardiac and respiratory origin. In this study, we explored the importance of respiratory versus cardiac pressure gradients for CSF flow within one of the main conduits of the brain, the cerebral aqueduct. We obtained overnight intracranial pressure measurements from two different locations in 10 idiopathic normal pressure hydrocephalus (iNPH) patients. The resulting pressure gradients were analyzed with respect to cardiac and respiratory frequencies and amplitudes (182,000 cardiac and 48,000 respiratory cycles). Pressure gradients were used to compute CSF flow in simplified and patientspecific models of the aqueduct. The average ratio between cardiac over respiratory flow volume was 0.21 ± 0.09, even though the corresponding ratio between the pressure gradient amplitudes was 2.85 ± 1.06. The cardiac cycle was 0.25 ± 0.04 times the length of the respiratory cycle, allowing the respiratory pressure gradient to build considerable momentum despite its small magnitude. No significant differences in pressure gradient pulsations were found in the sleeping versus awake state. Pressure gradients underlying CSF flow in the cerebral aqueduct are dominated by cardiac pulsations, but induce CSF flow volumes dominated by respiration.
Tue, 01 Jan 2019 00:00:00 GMT
http://hdl.handle.net/10852/73931
20190101T00:00:00Z

Laplacian Preconditioning of Elliptic PDEs: Localization of the Eigenvalues of the Discretized Operator
http://hdl.handle.net/10852/73929
Laplacian Preconditioning of Elliptic PDEs: Localization of the Eigenvalues of the Discretized Operator
Gergelits, Tomas; Mardal, KentAndre; Nielsen, Bjørn Fredrik; Strakos, Zdenek
In [IMA J. Numer. Anal., 29 (2009), pp. 2442], Nielsen, Tveito, and Hackbusch study the operator generated by using the inverse of the Laplacian as the preconditioner for second order elliptic PDEs $\nabla \cdot (k(x) \nabla u) = f$. They prove that the range of $k(x)$ is contained in the spectrum of the preconditioned operator, provided that $k(x)$ is continuous. Their rigorous analysis only addresses mappings defined on infinite dimensional spaces, but the numerical experiments in the paper suggest that a similar property holds in the discrete case. Motivated by this investigation, we analyze the eigenvalues of the matrix ${L}^{1}{A}$, where ${L}$ and ${{A}}$ are the stiffness matrices associated with the Laplace operator and second order elliptic operators with a scalar coefficient function, respectively. Using only technical assumptions on $k(x)$, we prove the existence of a onetoone pairing between the eigenvalues of ${L}^{1}{A}$ and the intervals determined by the images under $k(x)$ of the supports of the finite element nodal basis functions. As a consequence, we can show that the nodal values of $k(x)$ yield accurate approximations of the eigenvalues of ${L}^{1}{A}$. Our theoretical results, including their relevance for understanding how the convergence of the conjugate gradient method may depend on the whole spectrum of the preconditioned matrix, are illuminated by several numerical experiments.
Tue, 01 Jan 2019 00:00:00 GMT
http://hdl.handle.net/10852/73929
20190101T00:00:00Z

Multigrid Methods for Discrete Fractional Sobolev Spaces
http://hdl.handle.net/10852/73924
Multigrid Methods for Discrete Fractional Sobolev Spaces
Bærland, Trygve; Kuchta, Miroslav; Mardal, KentAndre
Coupled multiphysics problems often give rise to interface conditions naturally formulated in fractional Sobolev spaces. Here, both positive and negative fractionality are common. When designing efficient solvers for discretizations of such problems it would therefore be useful to have a preconditioner for the fractional Laplacian. In this work, we develop an additive multigrid preconditioner for the fractional Laplacian with positive fractionality and show a uniform bound on the condition number. For the case of negative fractionality, we reuse the preconditioner developed for the positive fractionality and leftright multiply a regular Laplacian with a preconditioner with positive fractionality to obtain the desired negative fractionality. Implementational issues are outlined in detail as the differences between the discrete operators and their corresponding matrices must be addressed when realizing these algorithms in code. We finish with some numerical experiments verifying the theoretical findings.
Tue, 01 Jan 2019 00:00:00 GMT
http://hdl.handle.net/10852/73924
20190101T00:00:00Z

Robust meanvariance hedging via Gexpectation
http://hdl.handle.net/10852/73905
Robust meanvariance hedging via Gexpectation
Biagini, Francesca; Mancin, Jacopo; Brandis, Thilo Meyer
In this paper we study mean–variance hedging under the expectation framework. Our analysis is carried out by exploiting the martingale representation theorem and the related probabilistic tools, in a continuous financial market with two assets, where the discounted risky one is modeled as a symmetric martingale. By tackling progressively larger classes of contingent claims, we are able to explicitly compute the optimal strategy under general assumptions on the form of the contingent claim.
Tue, 01 Jan 2019 00:00:00 GMT
http://hdl.handle.net/10852/73905
20190101T00:00:00Z

A duopoly preemption game with two alternative stochastic investment choices
http://hdl.handle.net/10852/73904
A duopoly preemption game with two alternative stochastic investment choices
Dahl, Kristina Rognlien; Stokkereit, Espen
This paper studies a duopoly investment model with uncertainty. There are two alternative irreversible investments. The first firm to invest gets a monopoly benefit for a specified period of time. The second firm to invest gets information based on what happens with the first investor, as well as cost reduction benefits. We describe the payoff functions for both the leader and follower firm. Then, we present a stochastic control game where the firms can choose when to invest, and hence influence whether they become the leader or the follower. In order to solve this problem, we combine techniques from optimal stopping and game theory. For a specific choice of parametres, we show that no pure symmetric subgame perfect Nash equilibrium exists. However, an asymmetric equilibrium is characterized. In this equilibrium, two disjoint intervals of market demand level give rise to preemptive investment behavior of the firms, while the firms otherwise are more reluctant to be the first mover.
Tue, 01 Jan 2019 00:00:00 GMT
http://hdl.handle.net/10852/73904
20190101T00:00:00Z