Matematisk institutt
http://hdl.handle.net/10852/5
Sat, 13 Oct 2018 14:00:47 GMT
20181013T14:00:47Z

Poisson and Martin boundaries of discrete quantum groups: a noncommutative and categorical perspective
http://hdl.handle.net/10852/65045
Poisson and Martin boundaries of discrete quantum groups: a noncommutative and categorical perspective
Malacarne, Sara
Quantum groups are a noncommutative extension of the notion of a group and first appeared in the context of quantum mechanics. Now the theory of quantum groups has further developed and has become interesting in its own right. In this work we study compact and discrete quantum groups, the latter in connection with random walks and probabilistic boundaries.
Random walks on classical groups have been extensively studied and the associated probabilistic boundaries which encode information on their asymptotic behaviour, that is, what happens after an infinite number steps, have been obtained in a number of cases. In this work we concentrate on the quantum setting where the theory is still not so clear. We compute these boundaries for particular discrete quantum groups using both a functional analytic and categorical approach. It turns out in fact that the interconnection between the two offers a very powerful tool for gaining insights into this topic.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/65045
20180101T00:00:00Z

Optimal spline spaces for L2 nwidth problems with boundary conditions
http://hdl.handle.net/10852/64835
Optimal spline spaces for L2 nwidth problems with boundary conditions
Floater, Michael S.; Sande, Espen
In this paper we show that, with respect to the L2 norm, three classes of functions in Hr(0,1) , defined by certain boundary conditions, admit optimal spline spaces of all degrees ≥r−1 , and all these spline spaces have uniform knots.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/64835
20180101T00:00:00Z

Alternating Sign Matrices, Related (0, 1)Matrices, and the Smith Normal Form
http://hdl.handle.net/10852/64834
Alternating Sign Matrices, Related (0, 1)Matrices, and the Smith Normal Form
Brualdi, R.A.; Dahl, Geir
We investigate the Smith Normal Form (SNF) of alternating sign matrices (ASMs) and related matrices of 0’s and 1’s ((0, 1)matrices). We identify certain classes of ASMs and (0, 1)matrices whose SNFs are (0, 1)matrices. We relate some of our work to various ranks, in particular, the (0, 1)rank of a (0, 1)matrix, that is, the bipartite partition number of a bipartite graph.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/64834
20180101T00:00:00Z

The interval structure of (0,1)matrices
http://hdl.handle.net/10852/64833
The interval structure of (0,1)matrices
Brualdi, R.A.; Dahl, Geir
Let A be an n × n (0, ∗)matrix, so each entry is 0 or ∗. An Ainterval matrix is a (0, 1)matrix obtained from A by choosing some ∗’s so that in every interval of consecutive ∗’s, in a row or column of A, exactly one ∗ is chosen and replaced with a 1, and every other ∗ is replaced with a 0. We consider the existence questions for Ainterval matrices, both in general, and for specific classes of such A defined by permutation matrices. Moreover, we discuss uniqueness and the number of Apermutation matrices, as well as properties of an associated graph.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/64833
20180101T00:00:00Z

Alternating Sign Matrices and Hypermatrices, and a Generalization of Latin Squares
http://hdl.handle.net/10852/64832
Alternating Sign Matrices and Hypermatrices, and a Generalization of Latin Squares
Brualdi, R.A.; Dahl, Geir
An alternating sign matrix, or ASM, is a (0, ±1)matrix where the nonzero entries in each row and column alternate in sign. We generalize this notion to hypermatrices: an n × n × n hypermatrix A = [aijk] is an alternating sign hypermatrix, or ASHM, if each of its planes, obtained by fixing one of the three indices, is an ASM. Several results concerning ASHMs are shown, such as finding the maximum number of nonzeros of an n × n × n ASHM, and properties related to Latin squares. Moreover, we investigate completion problems, in which one asks if a subhypermatrix can be completed (extended) into an ASHM. We show several theorems of this type.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/64832
20170101T00:00:00Z

Statistical solutions and Onsager’s conjecture
http://hdl.handle.net/10852/64831
Statistical solutions and Onsager’s conjecture
Fjordholm, Ulrik Skre; Wiedemann, Emil
We prove a version of Onsager’s conjecture on the conservation of energy for the incompressible Euler equations in the context of statistical solutions, as introduced recently by Fjordholm et al. (2017). As a byproduct, we also obtain an alternative proof for the conservative direction of Onsager’s conjecture for weak solutions, under a weaker Besovtype regularity assumption than previously known.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/64831
20170101T00:00:00Z

Quantifying the Ocean, Freshwater and Human Effects on YeartoYear Variability of OneSeaWinter Atlantic Salmon Angled in Multiple Norwegian Rivers
http://hdl.handle.net/10852/64809
Quantifying the Ocean, Freshwater and Human Effects on YeartoYear Variability of OneSeaWinter Atlantic Salmon Angled in Multiple Norwegian Rivers
Villar, Jaime Otero; Jensen, Arne Johan; L'abeeLund, Jan Henning; Stenseth, Nils Christian; Storvik, Geir Olve; Vøllestad, Leif Asbjørn
Many Atlantic salmon, Salmo salar, populations are decreasing throughout the species' distributional range probably due to several factors acting in concert. A number of studies have documented the influence of freshwater and ocean conditions, climate variability and human impacts resulting from impoundment and aquaculture. However, most previous research has focused on analyzing single or only a few populations, and quantified isolated effects rather than handling multiple factors in conjunction. By using a multiriver mixedeffects model we estimated the effects of oceanic and river conditions, as well as human impacts, on yeartoyear and betweenriver variability across 60 time series of recreational catch of oneseawinter salmon (grilse) from Norwegian rivers over 29 years (1979–2007). Warm coastal temperatures at the time of smolt entrance into the sea and increased water discharge during upstream migration of mature fish were associated with higher rod catches of grilse. When hydropower stations were present in the course of the river systems the strength of the relationship with runoff was reduced. Catches of grilse in the river increased significantly following the reduction of the harvesting of this lifestage at sea. However, an average decreasing temporal trend was still detected and appeared to be stronger in the presence of salmon farms on the migration route of smolts in coastal/fjord areas. These results suggest that both ocean and freshwater conditions in conjunction with various human impacts contribute to shape interannual fluctuations and betweenriver variability of wild Atlantic salmon in Norwegian rivers. Current global change altering coastal temperature and water flow patterns might have implications for future grilse catches, moreover, positioning of aquaculture facilities as well as the implementation of hydropower schemes or other encroachments should be made with care when implementing management actions and searching for solutions to conserve this species.
Sat, 01 Jan 2011 00:00:00 GMT
http://hdl.handle.net/10852/64809
20110101T00:00:00Z

Fully pseudospectral solution of the conformally invariant wave equation near the cylinder at spacelike infinity. II: Schwarzschild background
http://hdl.handle.net/10852/64802
Fully pseudospectral solution of the conformally invariant wave equation near the cylinder at spacelike infinity. II: Schwarzschild background
Frauendiener, Jörg; Hennig, J.
It has recently been demonstrated (Frauendiener and Hennig 2014 Class. Quantum Grav. 31 085010) that the conformally invariant wave equation on a Minkowski background can be solved with a fully pseudospectral numerical method. In particular, it is possible to include spacelike infinity into the numerical domain, which is appropriately represented as a cylinder, and highly accurate numerical solutions can be obtained with a moderate number of gridpoints. In this paper, we generalise these considerations to the sphericallysymmetric wave equation on a Schwarzschild background. In the Minkowski case, a logarithmic singularity at the future boundary is present at leading order, which can easily be removed to obtain completely regular solutions. An important new feature of the Schwarzschild background is that the corresponding solutions develop logarithmic singularities at infinitely many orders. This behaviour seems to be characteristic for massive spacetimes. In this sense this work is indicative of properties of the solutions of the Einstein equations near spatial infinity. The use of fully pseudospectral methods allows us to still obtain very accurate numerical solutions, and the convergence properties of the spectral approximations reveal details about the singular nature of the solutions on spacelike and null infinity. These results seem to be impossible to achieve with other current numerical methods. Moreover, we describe how to impose conditions on the asymptotic behaviour of initial data so that the leadingorder logarithmic terms are avoided, which further improves the numerical accuracy.
© 2017 IOP Publishing
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/64802
20170101T00:00:00Z

Financial asset price bubbles under model uncertainty
http://hdl.handle.net/10852/64801
Financial asset price bubbles under model uncertainty
Biagini, Francesca; Mancin, Jacopo
We study the concept of financial bubbles in a market model endowed with a set P of probability measures, typically mutually singular to each other. In this setting, we investigate a dynamic version of robust superreplication, which we use to introduce the notions of bubble and robust fundamental value in a way consistent with the existing literature in the classical case P={P}. Finally, we provide concrete examples illustrating our results.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/64801
20170101T00:00:00Z

Option pricing under timevarying riskaversion with applications to risk forecasting
http://hdl.handle.net/10852/64800
Option pricing under timevarying riskaversion with applications to risk forecasting
Kiesel, Rüdiger; Rahe, Florentin
We present a twofactor optionpricing model, which parsimoniously captures the difference in volatility persistences under the historical and riskneutral probabilities. The model generates an Sshaped pricing kernel that exhibits timevarying risk aversion. We apply our model for two purposes. First, we analyze the risk preference implied by S&P500 index options during 2001–2009 and find that riskaversion level strongly increases during stressed market conditions. Second, we apply our model for ValueatRisk (VaR) forecasts during the subprime crisis period and find that it outperforms several leading VaR models.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/64800
20170101T00:00:00Z

Numerical simulations of a sounding rocket in ionospheric plasma: Effects of magnetic field on the wake formation and rocket potential
http://hdl.handle.net/10852/64799
Numerical simulations of a sounding rocket in ionospheric plasma: Effects of magnetic field on the wake formation and rocket potential
Darian, Diako; Marholm, Sigvald; Paulsson, Joakim John Paul; Miyake, Y.; Usui, H.; Mortensen, Mikael; Miloch, Wojciech Jacek
The charging of a sounding rocket in subsonic and supersonic plasma flows with external magnetic field is studied with numerical particle‐in‐cell (PIC) simulations. A weakly magnetized plasma regime is considered that corresponds to the ionospheric F2 layer, with electrons being strongly magnetized, while the magnetization of ions is weak. It is demonstrated that the magnetic field orientation influences the floating potential of the rocket and that with increasing angle between the rocket axis and the magnetic field direction the rocket potential becomes less negative. External magnetic field gives rise to asymmetric wake downstream of the rocket. The simulated wake in the potential and density may extend as far as 30 electron Debye lengths; thus, it is important to account for these plasma perturbations when analyzing in situ measurements. A qualitative agreement between simulation results and the actual measurements with a sounding rocket is also shown.
© 2017 American Geophysical Union
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/64799
20170101T00:00:00Z

A Convergent Finite Difference Scheme for the Variational Heat Equation
http://hdl.handle.net/10852/64798
A Convergent Finite Difference Scheme for the Variational Heat Equation
Coclite, Giuseppe Maria; Ridder, Johanna; Risebro, Nils Henrik
The variational heat equation is a nonlinear, parabolic equation not in divergence form that arises as a model for the dynamics of the director field in a nematic liquid crystal. We present a finite difference scheme for a transformed, possibly degenerate version of this equation and prove that a subsequence of the numerical solutions converges to a weak solution. This result is supplemented by numerical examples that show that weak solutions are not unique and give some intuition about how to obtain a viscosity type solution.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/64798
20170101T00:00:00Z

Impacts of the lowlevel jet's negative wind shear on the wind turbine
http://hdl.handle.net/10852/64797
Impacts of the lowlevel jet's negative wind shear on the wind turbine
Gutierrez, Walter; RuizColumbie, Arquimedes; Tutkun, Murat; Castillo, Luciano
Nocturnal lowlevel jets (LLJs) are defined as relative maxima in the vertical profile of the horizontal wind speed at the top of the stable boundary layer. Such peaks constitute major power resources for wind turbines. However, a wind speed maximum implies a transition from positive wind shears below the peak to negative ones above. The effect that such a transition has on wind turbines has not been thoroughly studied.
This research study employed a methodical approach to the study of negative wind shear's impacts on wind turbines. Up to now, the presence of negative shears inside the turbine's rotor in relation to the presence of positive shears has been largely ignored. A parameter has been proposed to quantify that presence in future studies of LLJ–windturbine interactions. Simulations were performed using the NREL aeroelastic simulator FAST code. Rather than using synthetic profiles to generate the wind data, all simulations were based on real data captured at the high frequency of 50 Hz, which allowed us to perform the analysis of a turbine's impacts with reallife, small scales of wind motions.
It was found that the presence of negative wind shears at the height of the turbine's rotor appeared to exert a positive impact on reducing the motions of the nacelle and the tower in every direction, with oscillations reaching a minimum when negative shears covered the turbine swept area completely. Only the tower wobbling in the spanwise direction was amplified by the negative shears; however, this occurred at the tower's slower velocities and accelerations. The forces and moments were also reduced by the negative shears. The aforementioned impacts were less beneficial in the rotating parts, such as the blades and the shafts. Finally, the variance in power production was also reduced. These findings can be very important for the next generation of wind turbines as they reach deeper into LLJ's typical heights.
The study demonstrated that the presence of negative shears is significant in reducing the loading on wind turbines. A major conclusion of this study is that the wind turbines of the future should probably be designed with the aim of reaching the top of the nightly boundary layer more often and therefore the altitudes where negative shears are more frequent. Doing so will help to reduce the positive shear's associated damage and to capture the significant LLJ energy.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/64797
20170101T00:00:00Z

Er maskinlæring framtida i Skatteetaten?
http://hdl.handle.net/10852/64796
Er maskinlæring framtida i Skatteetaten?
Løland, Anders; Berset, Anders; Hobæk Haff, Ingrid
Skatteetaten bruker i dag prediktive metoder til blant annet utvelgelse til kontroll av merverdiavgiftsoppgaver og til å forbedre og effektivisere innkreving av skatter. Dette har vist seg å gi økt proveny og en mer effektiv utnyttelse av ressursene. Framover ønsker Skatteetaten å få utviklet nye modeller som vil forenkle rapporteringen for den delen av næringslivet som opererer innenfor lovverket, og samtidig gjør kampen mot svart økonomi mer effektiv. Derfor har etaten inngått partnerskap med Big Insight, som er et såkalt Senter for forskningsdrevet innovasjon. Big Insight består av forskningspartnere, private bedrifter og offentlige etater, og skal forske på innovative statistikk og maskinlæringsmetoder for å løse viktige problemer. Hovedformålet med samarbeidet mellom Skatteetaten og Big Insight er å utvikle metodikk som gjør det mulig å ta i bruk stadig nye datakilder og økte datamengder for å målrette veiledning, kommunikasjon, forebygging og forenkling av kontrollarbeidet.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/64796
20170101T00:00:00Z

Multivariate statistical modelling of compound events via paircopula constructions: Analysis of floods in Ravenna (Italy)
http://hdl.handle.net/10852/64795
Multivariate statistical modelling of compound events via paircopula constructions: Analysis of floods in Ravenna (Italy)
Bevacqua, Emanuele; Maraun, Douglas; Hobæk Haff, Ingrid; Widmann, Matrin; Vrac, Mathieu
Compound events (CEs) are multivariate extreme events in which the individual contributing variables may not be extreme themselves, but their joint – dependent – occurrence causes an extreme impact. Conventional univariate statistical analysis cannot give accurate information regarding the multivariate nature of these events. We develop a conceptual model, implemented via paircopula constructions, which allows for the quantification of the risk associated with compound events in presentday and future climate, as well as the uncertainty estimates around such risk. The model includes predictors, which could represent for instance meteorological processes that provide insight into both the involved physical mechanisms and the temporal variability of compound events. Moreover, this model enables multivariate statistical downscaling of compound events. Downscaling is required to extend the compound events' risk assessment to the past or future climate, where climate models either do not simulate realistic values of the local variables driving the events or do not simulate them at all. Based on the developed model, we study compound floods, i.e. joint storm surge and high river runoff, in Ravenna (Italy). To explicitly quantify the risk, we define the impact of compound floods as a function of sea and river levels. We use meteorological predictors to extend the analysis to the past, and get a more robust risk analysis. We quantify the uncertainties of the risk analysis, observing that they are very large due to the shortness of the available data, though this may also be the case in other studies where they have not been estimated. Ignoring the dependence between sea and river levels would result in an underestimation of risk; in particular, the expected return period of the highest compound flood observed increases from about 20 to 32 years when switching from the dependent to the independent case.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/64795
20170101T00:00:00Z

A HidaMalliavin white noise calculus approach to optimal control
http://hdl.handle.net/10852/64794
A HidaMalliavin white noise calculus approach to optimal control
Agram, Nacira; Øksendal, Bernt
The classical maximum principle for optimal stochastic control states that if a control û is optimal, then the corresponding Hamiltonian has a maximum at u=û. The first proofs for this result assumed that the control did not enter the diffusion coefficient. Moreover, it was assumed that there were no jumps in the system. Subsequently, it was discovered by Shige Peng (still assuming no jumps) that one could also allow the diffusion coefficient to depend on the control, provided that the corresponding adjoint backward stochastic differential equation (BSDE) for the firstorder derivative was extended to include an extra BSDE for the secondorder derivatives. In this paper, we present an alternative approach based on Hida–Malliavin calculus and white noise theory. This enables us to handle the general case with jumps, allowing both the diffusion coefficient and the jump coefficient to depend on the control, and we do not need the extra BSDE with secondorder derivatives. The result is illustrated by an example of a constrained linearquadratic optimal control.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/64794
20180101T00:00:00Z

Some existence results for advanced backward stochastic differential equations with a jump time
http://hdl.handle.net/10852/64792
Some existence results for advanced backward stochastic differential equations with a jump time
Jeanblanc, Monique; Agram, Nacira; Lim, Thomas
In this paper, we are interested by advanced backward stochastic differential equations (ABSDEs), in a probability space equipped with a Brownian motion and a single jump process, with a jump at time τ. ABSDEs are BSDEs where the driver depends on the future paths of the solution. We show, that under immersion hypothesis between the Brownian filtration and its progressive enlargement with τ, assuming that the conditional law of τ is equivalent to the unconditional law of τ, and a Lipschitz condition on the driver, the ABSDE has a solution.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/64792
20170101T00:00:00Z

Optimal control of forward–backward meanfield stochastic delayed systems
http://hdl.handle.net/10852/64791
Optimal control of forward–backward meanfield stochastic delayed systems
Agram, Nacira; Engen Røse, Elin
We study methods for solving stochastic control problems of systems offorward–backward meanfield equations with delay, in finite and infinite time horizon.Necessary and sufficient maximum principles under partial information are given. The results are applied to solve a meanfield recursive utility optimal problem.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/64791
20170101T00:00:00Z

A versatile strategy for the implementation of adaptive splines
http://hdl.handle.net/10852/64790
A versatile strategy for the implementation of adaptive splines
Bressan, Andrea; Mokris, Dominik
This paper presents an implementation framework for spline spaces over Tmeshes (and their ddimensional analogs). The aim is to share code between the implementations of several spline spaces. This is achieved by reducing evaluation to a generalized Bézier extraction.
The approach was tested by implementing hierarchical Bsplines, truncated hierarchical Bsplines, decoupled hierarchical Bsplines (a novel variation presented here), truncated Bsplines for partially nested refinement and hierarchical LRsplines.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/64790
20170101T00:00:00Z

A spacetime random field model for electricity forward prices
http://hdl.handle.net/10852/64789
A spacetime random field model for electricity forward prices
Benth, Fred Espen; Paraschiv, Florentina
Stochastic models for forward electricity prices are of great relevance nowadays, given the major structural changes in the market due to the increase of renewable energy in the production mix. In this study, we derive a spatiotemporal dynamical model based on the HeathJarrowMorton (HJM) approach under the Musiela parametrization, which ensures an arbitragefree model for electricity forward prices. The model is fitted to a unique data set of historical price forward curves. As a particular feature of the model, we disentangle the temporal from spatial (maturity) effects on the dynamics of forward prices, and shed light on the statistical properties of risk premia, of the noise volatility term structure and of the spatiotemporal noise correlation structures. We find that the shortterm risk premia oscillates around zero, but becomes negative in the long run. We identify the Samuelson effect in the volatility term structure and volatility bumps, explained by market fundamentals. Furthermore we find evidence for coloured noise and correlated residuals, which we model by a Hilbert spacevalued normal inverse Gaussian Lévy process with a suitable covariance functional. (Best Energy Paper Award, ECOMFIN 2016, Paris)
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/64789
20170101T00:00:00Z