Ett informationsblad från matematiska institutionen vid Linköpings universitet. Material till Lite Mat lämnas till Maud Lindström litemat@mai.liu.se senast torsdagar kl 12.00.

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***LITE MAT***

Ett informationsblad från matematiska institutionen vid Linköpings universitet

v22 2004

Viktigt inför delårsrapporten 1 januari - 30 juni 2004

Reseräkningar (konterade och attesterade) avseende våren lämnas till Inger Pettersson senast OBS! 28 juni.

Lönematerial avseende våren skall vara Marthina respektive Monika tillhanda senast 7 juni.

Den 7 juni är sista dag att internfakturera andra enheter inom LiU/HU. Jag vill ha underlag till internfakturor senast 2 juni. Underlag till externfakturor och omföringar vill jag ha före midsommar.

Tänk på att ansöka om ev reseförskott redan nu. Under v 29-31 kan inga reseförskott utbetalas.

Ulla Segring

Matematiska kollokviet

Tisdagen den 1 juni, kl. 13.15-14.15 talar Professor Sergei Avdonin, University of Alaska, Fairbanks,

Boundary control method in inverse problems of mathematical physics

Sammanfattning: The boundary control (BC) method reveals that the two central problems of the theory of inverse problems and control theory have a direct connection with each other. The first one, together with the recovery of the coefficients, consists in the construction of a map extending the solution inside the domain, from the data on their behavior on the boundary. The second one is the controllability of the corresponding initial boundary value problem. Roughly speaking, the BC method gives the realization for distributed systems of R. Kalman's idea that the controllable (or observable) part of a system can be identified. One of the important results of the BC method is obtaining multidimensional analogs of the Gelfand-Levitan-Krein-Marchenko equations. It is interesting to note that these equations have a clear control-theoretic meaning which makes their derivation much more simple than the original derivation of one-dimensional versions.
The BC method was first proposed for the multidimensional wave equation (Belishev, 1987) and was extended to non-self-adjoint inverse problems, to the heat equation and several other types of PDEs. In the first part of this talk we shall describe the main ideas of this method on a classical example of the (1d) string equation. Then we shall discuss new controllability and indentification results for the Schrödinger equation and for the wave equation on graphs.

Lokal: ISY/MAI:s seminarierum Glashuset, ing 25.

Välkomna!
Vladimir Kozlov,
Svante Linusson och
Stefan Rauch-Wojciechowski

Seminarium i Matematisk Statistik

Onsdagen den 26 maj kl 15.15-17.00

Computational strategies for analyzing data in gene expression microarray experiments

Dr. Tero Aittokallio Turku Centre of Computer Science (TUCS) & Turku Centre of Biotechnology, University of Turku, Finland

Sammanfattning: Microarray analysis has become a widely used method for monitoring gene expression levels on a genomic scale. Although this powerful new research tool has been enthusiastically applied in many fields of biomedical research, accurate analysis and interpretation of the data have provided many challenges. Several analysis steps are needed to convert thousands of noisy data points into reliable and interpretable biological information. In this talk, some of the common themes in DNA microarray data analysis are overviewed and their relative merits and potential pitfalls discussed. Conventional analysis steps, including data normalization followed by class comparison, class prediction, and class discovery are demonstrated on real DNA microarray experiments. More sophisticated analysis methods beyond classification seek to elucidate interactions between elements in a genetic network from microarray data. Efficiency of a simple Boolean network paradigm for inferring genetic regulato ry interactions is tested in a simulation study.

Lokal: Glashuset

Välkomna !
Timo Koski
Matematiska institutionen
Information: tikos@mai.liu.se, tfn: 28 1454

Ämnesdidaktiska seminariet

Fredagen den 28 maj, kl. 10.15-11.15, talar Prof. Norma Presmeg, Illinois State University, om Visualization and generalization in the learning of mathematics. Sammanfattning: Ever since Albert Einstein credited his visual imagery as the source of his remarkable creativity, the role and function of visually mediated thought processes in mathematics has been a topic of interest. Early research (Presmeg, 1985) showed that visual representation of mathematical concepts has both power and pitfalls in mathematics teaching and learning. In an intense three-year study, the thinking of 54 high school "visualizers" revealed that all of the various difficulties they experienced in learning mathematics were rooted in one way or another with the mathematical requirement of generalization. In this presentation I shall describe how these issues led me to investigate the uses of metaphor and metonymy in the teaching and learning of mathematics, and later to the power of Peircean semiotics in investigating various kinds of representations of mathematical concepts at the high school and undergraduate university levels.

Lokal: ISY/MAI:s seminarierum Glashuset, ing. B25.

Välkomna!
Ämnesdidaktiska gruppen
Information: Christer Bergsten, chber@mai.liu.se, tfn: 282984

Seminarium i Beräkningsvetenskap

Torsdagen den 27 maj kl 13.15 talar professor Per Lötstedt, Uppsala, om Computational methods for electromagnetic problems in the frequency domain

Abstract: Integral equations are discretized and solved to determine the scattering of an incoming electromagnetic wave by an object. The resulting system of linear equations is solved by an iterative Krylov method. The matrix-vector multiplications are replaced by evaluations with the fast multipole method. Many incident waves correspond to many right hand sides and simplifications are possible thanks to their smooth dependence of a parameter. The same idea can be applied to problems with many frequencies when the system matrix varies continuously. Examples of scattering calculations will be presented with millions of unknown variables and many hundreds of right hand sides. This talk is based on work by Martin Nilsson and on collaborative work with him. His PhD thesis at http://www.it.uu.se/research/diss/ contains a more detailed accoun of these matters.

Lokal: Kompakta rummet

Välkomna!
Lars Eldén

Seminarium i Statistik

Tisdagen den 25 maj, kl 13-15 talar Kalle Wahlin

Extracting the essence of process-based models of the flow of nitrogen through catchments

Process-oriented models of the flow of nitrogen through catchments can have very complex dynamic properties. We introduced several types of ensemble runs that can provide informative summaries of meteorologically normalised model outputs and also clarify the extent to which such outputs are related to various model parameters. Specifically, we showed how nitrogen and water travel times in the unsaturated and saturated zones can be assessed. Studies of the catchment model INCA-N revealed that the temporal distribution of the modelled water quality response to changes in fertiliser application was determined primarily by the hydromechanical model parameters, whereas the magnitude of the total intervention effect was influenced mainly by the parameters governing the turnover of nitrogen in soil. In addition, the nitrogen travel times in this model were invariably shorter than the water travel times, due to preferential removal of the nitrogen that has unusually long residence times.gh to correctly explain the widespread observations of slow water quality responses to changes in agricultural practices.

Lokal: Kompakta rummet, ingång 23

Välkomna!

Licentiatseminarier

Tisdagen den 25 maj kl 13.15 presenterar fil.mag. Johan Lundvall sin lic. avhandling med titeln

Reconstruction of Velocity Data using Adjoint Optimization

Abstract: In many application areas there is a growing interest in data assimilation or data reconstruction. Data assimilation is a process for integrating observed or measured data into a physical model. The problem originates from a vast array of different topics: traditionally in metereological and oceanographic modelling, and recently from non-invasive medical measurement devices such as magnetic resonance imaging. The measured data may contain inaccurancies and random noise, given with low spatial and/or temporal resolution.
This thesis presents a method for solving reconstruction problems in fluid dynamics using optimal control theory. The problem considered here includes a known partial differential equation and some spatially and temporarily sparsely distributed data with an unknown initial state. From a given velocity field , a flow field is determined which satisfies a given system of partial differential equations and minimizes . The function is known at the boundary and the initial condition is used as design variable. The optimization problem is solved using adjoint formulation.

Lokal: Glashuset

Välkomna
Per Weinerfelt

Torsdagen den 3 juni kl 10.15 presenterar fil.mag. Peter Brostöm sin licenciat avhandling med titeln

Optimization in the Design of OSPF Telecommunication Networks

Abstract: This thesis address optimization problems related to the design of IP (Internet Protocol) networks. One of the most commonly used IGP's (Interior Gateway Protocols) in telecommunication networks is the OSPF (Open Shortest Path First) protocol with ECM (Equal Cost Multipath) distribution. This link state based protocol uses link weights, which usually are set by an network operator, for providing routers necessary information regarding how traffic should be routed. By shortest path computations, router decide by themselves how to distribute the traffic.
One problem considered in this thesis is the problem of designing networks which are capable of accommodating large parts of the traffic when network components fails. Link failures are the most common failures, and this is the kind of disturbance which is considered. A multiobjective optimization model is presented and we search for pareto-optimal solutions using a two-phased weight based search method. This method tries to minimize the design cost simultaneously as the level of network survivability is maximized. This method uses the fact that is is easy to compute how traffic is distributed when the OSPF metric is known.
In contrary, it is a much more difficult task to determine if there are any OSPF weights that yield a desired flow distribution. This is a topic which also is studied in the thesis. Necessary conditions, which flow patterns must fulfill for being identical to the shortest paths obtained from OSPF weights, are reported. Sufficient conditions for a special type of flow patterns are also presented. The thesis also contains a polynomial method which can be used for detecting impossibilities in a set of flow patterns when this set do not correspond to the shortest paths of any OSPF weights.
Flow patterns are the basis for a new model which is developed for designing IP networks where OSPF and ECM distribution is used. This model uses a set of in-graphs in order to represent weights implicitly. The model also uses a new set of constraints used for modeling ECM distribution. The usefulness of the model is verified by computational experiments.

Lokal: BL32

Välkomna
Kaj Holmberg

Doktorandkurser Tillämpad matematik

Läsåret 2004-2005 ges följande doktorandkurser vid TM:

Höstterminen 2004
Dynamiska system, 5p (Stefan Rauch)
Fourieranalys, 5p (Bengt Ove Turesson)
Matematikens historia, 3p (Olle Axling)

Vårterminen 2005
Icke-linjär analys, 5p (Vladimir Kozlov)
Kombinatorik, 5p (Svante Linusson)
Topologi, 5p (Vitalij Tjatyrko)

Detaljerad information om kurserna kommer senare.

Välkomna!
Svante Linusson, Bengt Ove Turesson

OBS: Material till Lite Mat lämnas fr o m va 22 till Bodil Stavklint senast torsdagar kl 08.00. Obs tiden.

Mer information om MAI finns på MAIs hemsida.
Material till Lite Mat lämnas till Bodil Stavklint senast torsdagar kl 08.00.
Linköpings universitet, 581 83 Linköping
Tel 013-281000, Fax 013-149403, Email: litemat@mai.liu.se.