MAT-nytt. Aktuelt. Nr. 4 Desember 2008

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1 MAT-nytt Nyhetsbrev fra Matematisk institutt Universitetet i Bergen Nr. 4 Desember 2008 Instituttleders hjørne Med dette takker eg av som instituttleiar og ynskjer Stein Arild velkommen tilbake i stolen! Takk for all støtte og hjelp eg har fått i år frå mange dyktige medarbeidarar. Og til slutt God jul og Godt Nyttår! Helge Vet du om noe matematikkrelatert som burde tas opp i nyhetsbrevet? Er det noen feil eller mangler under noe av det som er tatt opp? Alle innspill tas imot med stor takk. Send e-post til kristine.lysnes@math.uib.no Aktuelt Registrering av publikasjoner i Frida Frist for registrering av publikasjoner for 2008 er 15. februar Overføring av ferie samt fraværmelding i julen Vi minne om melding om overføring av ferie til neste år og fravær/ferie i forbindelse med jule- og nyttårshelgen (se Det er anledning til å overføre 14 feriedager (yrkesdager) til nest år. Reiseregning - litt nytt Fra er det innført fordelsbeskatning ved reiser i utlandet. Reiser du etter regulativ, må du dokumentere overnattingsutgifter (eks frokost). Det er den positive differansen som er skattepliktig. I den elektroniske reiseregningen er det på slutten lagt inn et område hvor slike opplysninger skal gis. Vanligvis vil skatten bli beregnet og trukket senere. Les mer her og

2 finn oppdatert skjema for reiseregningen: Semesterstart vår 2009 Semesteret starter 5.1, mens forlesingene starter påfølgende uke eller uken etter, sjekk din timeplan! (logg inn med brukernavn og passord) Nye medarbeidere Denis Gaidashev was employed as a postdoctoral fellow in the CAPA group 6 th of October, having been a postdoctoral fellow at the University of Toronto, KTH, Stockholm and Universite de Montreal. Denis Gaidashev obtained his PhD degree from the University of Texas at Austin. His research is mainly in dynamical systems, mostly focusing on renormalization - a technique which is used to study various universality phenomena so common in dynamics, and which is also very useful for an analysis of ergodic properties of dynamical systems. He strives to find a good balance between analytic, numerical and rigorous computer-assisted approaches in his work. He also has a side interest in integrable PDE's and hydrodynamics. Ferenc Bartha, who s full name is Bartha Ferenc Ágoston, is a Ph.D. in the CAPA group since 10 th of October, working with Dr. Warwick Tucker. His field of interest is dynamical systems and rigorous scientific computations. He is currently trying to improve certain numerical methods for solving PDEs. Ferenc Bartha is from Szeged, Hungary and made his studies in mathematics at the University of Szeged. He finished his major (=5 years university education, equals to bachelor + master together) in the spring of 2008, in his thesis he has proven the existence of a Morse-decomposition of the global attractor of state dependent delayed differential equations with a certain type of Lipschitz delays and threshold delays. Arne Johannes Holmin er ansatt som Universitetsstipendiat fra 1. november. Han er tilknyttet statistikkgruppen. Han tok mastergrad statistikk - dataanalyse her ved instituttet i september i år. Jan Ole Skogestad ble tilsatt som Universitetsstipendiat fra 1.desember. Han skal jobbe med multiskalametoder for flerfaseflyt i porøse medier med Jan M. Nordbotten som veileder. Jan Ole Skogestad kommer fra jobb i SINTEF Petroleumsforskning AS, avdeling Boring og brønnkonstruksjon i Bergen. Han har mastergrad i anvendt matematikk/hydrodynamikk og havmodellering her fra instituttet (vår 2007).

3 Nye artikler Berntsen, Jarle; Xing, Jiuxing; Davies, Alan M: Numerical studies of internal waves at a sill: Sensitivity to horizontal grid size and subgrid scale closure. Abstract: A non-hydrostatic terrain following model in cross sectional form is applied to study the generation and propagation of tidally forced internal waves near a sill in an idealized loch. On inflow internal waves are generated behind the sill, and they propagate from the sill. There is a transfer of energy from the barotropic tide to internal waves and then to irreversible mixing. The range of length scales involved goes from the scale of the forced tide to scales associated with wave breaking. This wide range of scales makes it very difficult to resolve all relevant length scales with a numerical model using a uniform finite difference grid. The sensitivity of the numerical results to the grid resolution and the parameterisation of subgrid scale mixing is investigated. Initial calculations are performed with constant values of viscosity and diffusivity, and subsequently they are repeated using large eddy simulations and including Richardson number dependant vertical mixing. In the studies with sub-critical flow over the sill, the results are robust to changes in the grid size. With stronger forcing, the flow over the sill becomes super-critical during maximum inflow, and the frequency and the nature of the internal waves generated in the lee of the sill becomes grid size dependant. For the super-critical case, the solution is sensitive to the subgrid scale closure scheme. Calculations show that with constant and small values of vertical viscosity and diffusivity, strong internal waves are generated on inflow in the lee of the sill. When using Richardson number dependant vertical viscosity and diffusivity, more of the tidal energy goes into vertical irreversible mixing, and less into internal waves. Continental Shelf Research 2008 ;Volum 28.(10-11) s Berre, Inga; Cement, Francois; Lien, Martha; Mannseth, Trond: Data driven reparameterization structure for estimation of fluid conductivity. IAHS-AISH publication 2008 ;Volum 320. s Berre, Inga; Lien, Martha; Mannseth, Trond: A multi-level strategy for regularized parameter identification using nonlinear reparameterization with sample application for reservoir characterization. Abstract: Level-set methods are popular for identifying piecewise constant structures. We propose an approach inspired by the level-set idea to identify coarse scale features of a scalar field, where the transitions between different regions can be both sharp and smooth. The nonlinear and coarse reparameterization structure provides regularization on the inverse problem, which is important if the quality of the available information is poor. In our identification strategy, the resolution of the representation of the parameter function is refined gradually; for several inverse problems, the nonlinearity of the problem is correspondingly carefully increased. Hence, when using a gradient-based optimization routine, the approach may reduce the risk of getting trapped in a local minimum of the objective function. We demonstrate the identification strategy for estimation of fluid conductivity in a porous medium based on sparsely distributed, transient data. The methodology is well suited for determining channels and barriers as well as smooth structures based on limited information. Journal of Physics, Conference Series 2008 ;Volum 135. Kleppe, Tore Selland; Skaug, Hans Julius: Building and Fitting Non-Gaussian Latent Variable Models via the Moment-Generating Function. Abstract: For certain classes of hierarchical models, it is easy to derive an expression for the joint moment-generating function (MGF) of data, whereas the joint probability density has an intractable form which typically involves an integral. The most important example is the class

4 of linear models with non-gaussian latent variables. Parameters in the model can be estimated by approximate maximum likelihood, using a saddlepoint-type approximation to invert the MGF. We focus on modelling heavy-tailed latent variables, and suggest a family of mixture distributions that behaves well under the saddlepoint approximation (SPA). It is shown that the well-known normalization issue renders the ordinary SPA useless in the present context. As a solution we extend the non-gaussian leading term SPA to a multivariate setting, and introduce a general rule for choosing the leading term density. The approach is applied to mixed-effects regression, time-series models and stochastic networks and it is shown that the modified SPA is very accurate. Scandinavian Journal of Statistics 2008 ;Volum 35.(4) s Knutsen, Andreas Leopold: A note on Seshadri constants on general $K3$ surfaces. Comptes rendus de l'académie des sciences. Série 1, Mathématique 2008 ;Volum 346. s Knutsen, Andreas Leopold; Sernesi, Edoardo; Flamini, Flaminio; Pacienza, Gianluca. Nodal curves with general moduli on K3 surfaces. Communications in Algebra 2008 ;Volum 36. s Kozlov, Roman: Exponential operator splitting time integration for spectral methods. Journal of Computational and Applied Mathematics 2008 ;Volum 222.(2) s Kozlov, Roman: High-order conservative discretizations for some cases of the rigid body motion. Physics Letters A 2008 ;Volum 373.(1) s Nordbotten, Jan Martin; Bjørstad, Petter Erling: On the relationship between the multiscale finite-volume method and domain decomposition preconditioners. Abstract: In this paper, we review the classical nonoverlapping domain decomposition (NODD) preconditioners, together with the newly developed multiscale control volume (MSCV) method. By comparing the formulations, we observe that the MSCV method is a special case of a NODD preconditioner. We go on to suggest how the more general framework of NODD can be applied in the multiscale context to obtain improved multiscale estimates. Computational Geosciences 2008 ;Volum 12.(3) s Paulsen, Jostein: Optimal dividend payments and reinvestments of diffusion processes with both fixed and proportional costs. Abstract: Assets are assumed to follow a diffusion process subject to some conditions. The owners can pay dividends at their discretion, but whenever assets reach zero, they have to reinvest money so that assets never go negative. With each dividend payment there is a fixed and a proportional cost, and so with reinvestments. The goal is to maximize the expected value of discounted net cash flow, i.e., dividends paid minus reinvestments. It is shown that there can be two different solutions depending on the model parameters and the costs as follows. (1) Whenever assets reach a barrier $y^*$ they are reduced to $y^*-\delta^*$ through a dividend payment, and whenever they reach 0 they are increased to $\gamma^*\leq y^*- \delta^*$ by a reinvestment. (2) There is no optimal policy, but the value function is approximated by policies of the form described in (1) for increasing barriers. We provide criteria to decide whether an optimal solution exists, and when it does not, we show how to calculate the value function. We discuss how the problem can be solved numerically and give numerical examples. SIAM Journal of Control and Optimization 2008 ;Volum 47.(5) s

5 Paulsen, Jostein: Ruin models with investment income. Probability Surveys& IMS Lecture Notes 2008 ;Volum 5. s Paulsen, Jostein; Lunde, Astrid; Skaug, Hans Julius: Fitting mixed-effects models when data are left truncated. Abstract: Damage sizes, i.e. all damages occurring to a policy and not only those that are reported to an insurance company, are modelled as a linear mixed model. Only those damages that are larger than their deductibles are reported to the company, and this fact should be taken into account when analyzing such data. In statistical terms, the problem is to make inference in a linear mixed model with left truncated data. Estimation methods based on a Monte Carlo simulation of the likelihood are proposed, and extensive simulations to evaluate the quality of the methods are reported. The proposed methods are then used to analyze claimsizes for some marine insurance data, where shipowners represent random effects and technical data about the ships represent fixed effects. Insurance, Mathematics & Economics 2008 ;Volum 43.(1) s Rødseth, Øystein J: Addendum to "Distribution of points on the circle" [J. Number Theory 127 (1) (2007) ]. Abstract: In an earlier paper we gave a result relating the value of an exponential sum with the distribution of summands in the arcs of the unit circle in the complex plane. In a marginal case, this result is superseded by a result of Lev. In this addendum we use an idea of Lev to give a new proof of our earlier result and to improve upon the marginal result. Journal of Number Theory 2008 ;Volum 128.(6) s Skaug, Hans Julius; Berube, Martine; Rew, Mary Beth; Palsbøll, Per: Genetic analyses reveal promiscuous mating in female minke whales, Balaenoptera acutorostrata. Journal of Cetacean Research and Management 2008 ;Volum 9. s Titelman, Josefin; Riemann, Lasse; Holmfeldt, Karin; Nilsen, Trygve: Copepod feeding stimulates bacterioplankton activities in a low phosphorus system. Abstract: Zooplankton sloppy feeding releases high-quality dissolved organic matter, which is readily used by microbes. We hypothesized that in phosphorus (P) limited environments, released dissolved DNA may be a particularly important source of P for bacteria. In an incubation experiment with water from the Bothnian Bay, Sweden, we investigated the shortterm effect of copepod feeding activity on bacterial production, DNA uptake and phosphatase activity. Consistent patterns in bacterial activity measures suggested that copepod feeding activity stimulated phosphatase activity, DNA uptake and production. The P taken up as dissolved DNA exceeded cellular P requirements. We speculate that bacterioplankton cells in the Bothnian Bay store excess P intracellularly during times of extensive sloppy feeding, which may then subsequently be utilized to prevent P limitation of growth. Aquatic Biology 2008 ;Volum 2.(2) s Tucker, Warwick; Johnson, Tomas: Rigorous parameter reconstruction for differential equations with noisy data. Abstract: We present a method that given a data set, a finitely parametrized system of ordinary differential equations (ODEs), and a search space of parameters discards portions of the search space that are inconsistent with the model ODE and data. The method is completely rigorous as it is based on validated integration of the vector field. As a consequence, no consistent parameters can be lost during the pruning phase. For data sets with moderate levels of noise, this yields a good reconstruction of the underlying parameters. Several examples are included to illustrate the merits of the method. Automatica 2008 ;Volum 44. s

6 Nye doktorgrader Birgitte Eikemo: Simulering av væskeflyt i komplekse porøse media Birgitte Eikemo disputerte onsdag 3.desember 2008 for Phd-graden ved Universitetet i Bergen med avhandlinga: Fast Solvers for Computing Transport in Unfractured and Fractured Porous Media I oljeindustrien er det viktig å kunne forstå flytmønster i oljereservoar for å optimere utvinning frå eksisterande olje- og gassfelt, samt å finne nye førekomstar. Også når det gjeld grunnvatn, som er ei vanleg kjelde for drikkevatn i mange land, er forståinga av væskeflyt viktig. Det vil normalt ta mange hundre år frå vatn filtrerer inn frå overflata til det igjen dukker opp i ei kjelde. For å sikre grunnvatnkjelder mot ureiningar er det avgjerande å kunne forstå korleis ureiningar vil spreie seg i berggrunnen. For å få kunnskap om dette er det nødvendig å rekne ut korleis væskene i berggrunnen beveger seg. Væskeflyt i porøse media er modellert ved hjelp av system av partielle differensiallikningar. Slike system kan berre løysast ved hjelp av datasimuleringar. Temaet i avhandlinga er knytta til utvikling og bruk av numeriske teknikkar i slike simuleringar. Det er fokusert på å utvikle raske løysingsmetodar som kan handtere kompliserte geometriar. Dette er spesielt viktig når væskeflyten er dominert av forkastningar eller sprekksystem, som også gjev store variasjonar i bergartsdata. Komplekse geometriar med forkastningar og sprekker representerar generelt store utfordringar for datasimuleringane. Resultata i oppgåva gjev eit betre grunnlag for korleis ein kan forstå slike komplekse modellar, og er også eit grunnlag for betre modellering av slike system. Veiledere: Helge K. Dahle, Knut-Andreas Lie og Geir Terje Eigestad Nye mastergrader Arne Johannes Holmin: Statistical analysis of data from the Simrad MS70 multibeam sonar. Arne Johannes Holmin hadde 5. september avsluttende mastergradseksamen i Statistikk Dataanalyse. Veileder: Dag Tjøstheim. Andreas Hillersøy Henriksen: Statistiske metoder på nedbørsdata. Andreas Hillersøy Henriksen hadde 12. september avsluttende mastergradseksamen i Statistikk Dataanalyse. Veileder: Hans A. Karlsen

7 Andreas Hammer: Vertically averaged models for CO 2 storage in porous media. Andreas Hammer hadde 8. desember avsluttende mastergradseksamen i Anvendt og Beregningsorientert matematikk Miljømatematikk. Veileder: Jan Martin Nordbotten. Ingrid Langfeldt Gould: Stochastic chain-ladder models in nonlife insurance. Ingrid Langfeldt Gould hadde 10. desember avsluttende mastergradseksamen i Statistikk Finansteori og forsikringsmatematikk. Veileder: Trygve Nilsen. Kristin Eik: Om fluidregistrering for medisinske bilete. Kristin Eik hadde 11. desember avsluttende mastergradseksamen i Anvendt og Beregningsorientert matematikk Bildebehandling. Veileder: Antonella Zanna Munthe-Kaas. Thomas Djønne: Sammenligning av Dersimonian-Lairds og Paule-Mandels metode for meta-analyse. Thomas Djønne hadde 12. desember avsluttende mastergradseksamen i Statistikk Dataanalyse. Veileder: Ivar Heuch. Sturla Bingen: Dualgraden til noen determinentelle varieteter. Sturla Bingen hadde 16. desember avsluttende mastergradseksamen i Matematikk Algebraisk geometri. Veiledere: Andreas Leopold Knutsen og Kristian Ranestad (UiO). David L. Rabenorolahy: Relaxation schemes for degenerate parabolic convection-diffusion equations with a discontinuous coefficient. David L. Rabenorolahy hadde 17. desember avsluttende mastergradseksamen i Anvendt og Beregningsorientert matematikk Reservoarmekanikk. Veileder: Henrik Kalisch. Ledige stillinger Postdoktor ved BCCS En treårig stilling som postdoktor er ledig ved Bergen Center for Computational Science (BCCS). Søknadsfrist er 11. januar Forsker ved BCCS En toårig stilling som forsker i Grid Computing er ledig ved Unifob AS, BCCS innen High Performance Computing Laboratory (Parallab). Søknadsfrist 9. februar 2009 Lærervikariat Marikollen skole. De kontaktet oss direkte fra Marikollen skole, en ungdomsskole som ligger i Åsane bydel, og ønsket seg (helst) en nyutdannet master- eller bachelorstudent til et ledig et 70% vikariat i matematikk og naturfag på 10. trinn fra Er du interessert, vennligst søk

8 på stillingen via Finn.no (kode ) eller ta kontakt med rektor: Johnny Tindvik tlf mail: Matematikk-humor