LiU
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Matematiska Institutionen
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.
Vi har dessutom ett arkiv av gamla nummer.
Ett informationsblad från matematiska institutionen vid Linköpings universitet
v21 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.
Onsdagen den 19 maj, kl. 13.00-14.00 talar Dr. Krzysztof Marciniak, ITN
Geometric approach to Dirac theory of constrained Hamiltonian systems
Sammanfattning:
Given a foliation 
of a manifold 
, a distribution 
in
transversal to and a Hamiltonian system on we present a geometrical
method of reducing this system on the foliation . We analyse its relation
with the classical ideas of P.A.M. Dirac on constrained Hamiltonian systems
(Dirac reduction) and with the more modern theory of J. Marsden and T.
Ratiu. Our method is constructive and "constraint-independent" in the sense
that it does not depend on the functions that define the foliation . As a
consequence, in case of a second class constraints (in the terminology of
Dirac) one can perform not only usual Dirac reduction of Poisson
(Hamiltonian) systems to submanifolds but also other types of reductions.
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
Lokal: ISY/MAI:s seminarierum Glashuset, ing B25.
Välkomna!
Ämnesdidaktiska gruppen
Information: Christer Bergsten, chber@mai.liu.se, tfn 282984
OBS ! Datum och lokal
Måndag den 17 maj, 15.15 - 17.00, talar Dr. Harry Hurd Department of Statistics, University of North Carolina, Chapel Hill
Spatial Probabilities for Clusters Based on Correlation Distance
Sammanfattning: Clustering based on the correlation distance is often desirable because of the inherent scale invariance. Since scale invariance essentially tranforms the problem to the hypersphere, we use spherical caps as a means to measure the spatial size of a cluster. Using this idea, we show that an analysis of the clusters specified by cutting the dendrogram tree at various levels can provide an understanding of the spatial makeup of the data. For example, several senses of p-value for clusters can be determined. Examples are given from the analysis of microarray data.
Lokal: Kompakta rummet
Välkomna !
Timo Koski
Information: tikos@mai.liu.se, tfn: 28 1454
Onsdagen den 26 maj kl 15.15-17.00, talar Dr. Tero Aittokallio Turku Centre of Computer Science (TUCS) & Turku Centre of Biotechnology, University of Turku, Finland
Computational strategies for analyzing data in gene expression microarray experiments
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
Onsdagen den 19 maj kl 10.15 talar Åke Björck under rubriken
Bidiagonal Decomposition and Least Squares Problems
Lokal: Seminarierummet Algoritmen på ISY
Välkomna!
Lars Eldén
Multicommodity Flow Problems
Convex Multicommodity Flow Problems (CMFP:s) appear in many transportation and communication problems, in particular traffic assignment and telecom message routing.
CMFP:s tend to be huge, whence specialized methods often are needed. The dominating method in practice is the Frank-Wolfe method, which has fast initial but slow asymptotic convergence. Faster (origin based) methods have been suggested recently, though.
For this problem class, we suggest a new bidual approach, that promises to be both fast and accurate.
The dual problem to a differentiable, strictly convex CMFP is an (essentially) unconstrained problem with piecewise differentiable strictly concave objective
We have devised a dual ascent scheme for this problem. It is based on
Välkomna!
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!
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
Tid: tisdag 18 maj kl 13.15
Lokal: R42
Hans Lundmark och Jörgen Blomvall
Schedule
The course will be given in two parts (I-II) in Linköping, at Campus Valla of LiU/LiTH.
40, August-September, 2004, 2h per week,
with possible extension to
October 2004.
Preliminary Topics
Possible Additional/Alternative Topics
Examination
Home work: analytic problems, computer assignments. Presentations by participants.
Homepage
http://www.mai.liu.se/~tikos/kurser/bayesmcmc.html
Course Literature:
Support Literature:
Timo Koski
tikos@mai.liu.se, tfn: 013 - 28 1454.
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
Enumerering av lösningar till det binära kappsäcksproblemet
Sammanfattning: Kappsäcksproblemet består i att välja vilka av n stycken element
som ska packas i en kappsäck. Varje element har en given vikt och kappsäcken har
en viktbegränsning, vilken inte får överskridas. En optimallösning till
problemet fås genom att summan av elementens värde maximeras. I detta arbete
söks inte endast den optimala lösningen till problemet, utan alla lösningar vars
målfunktionsvärde är lika med eller överskrider ett givet värde. Syftet med
arbetet är att utveckla en lösningsmetod för problemet att enumerera ett antal
när-optimala lösningar till det binära kappsäcksproblemet, att implementera
metoden i programmeringsspråket C, samt att utvärdera lösningsmetoden på
testproblem. Metoden som utvecklats bygger på en trädsökningsmetod, Expknap, som
tagits fram av David Pisinger vid Köpenhamns Universitet ([3]). Denna metod har
sedan modifierats för att kunna lösa det beskrivna enumereringsproblemet.
Resultaten visar att den modifierade versionen av Expknap tar fram korrekta
lösningar. Tester har utförts på problem med mellan 5 och 200 variabler med
exekveringstider mellan 0.161 och 12036.7 sekunder och mellan 4-34 551 536 120
stycken lösningar har maximalt enumererats. Dessa exekveringstider gäller då man
sökt tillåtna lösningar med ett målfunktionsvärde med lägsta värde på 0.1 % från
det optimala målfunktionsvärdet. Samtliga tester har utförts på en PC med en AMD
Athlon 800 MHz processor.
Lokal: Kompakta rummet
Välkomna!
Maud Göthe-Lundgren
Fredag den 14 maj presenteras två examensarbeten inom pedagogiskt arbete, lärarprogrammet, vid Matematiska institutionen.
kl. 10.15-11.00, Maria Artursson: "Plus, minus, delat, gånger, att tänka och att använda hjärnan" En studie av elevers och deras lärares uppfattningar om matematik. Opponent är Anna Aronsson.
kl. 11.15-12.00 Anna Aronsson: "Att gå från det konkreta till det abstrakta, att det blir konkret för barnen" En undersökning av hur lärare använder och värderar olika laborativa material i matematikundervisningen i år 1-3. Opponent är Maria Artursson Seminarieledare: Christer Bergsten
Lokal: Hus B, ingång 23, 1 trappa, Determinanten.
Välkommen!
Maria Bjerneby Häll och Christer Bergsten
OBS: Material till Lite Mat nästa vecka v22 måste lämnas onsdag kl 12.00
Mer information om MAI finns på MAIs hemsida.
Material till Lite Mat lämnas till Maud Lindström senast
torsdagar kl 12.00.
Tel 013-281405, Fax 013-149403, Email: litemat@mai.liu.se.
Sidan underhålls av: LiteMat
litemat@mai.liu.se
Senast ändrad: Wed 2012-08-29; 15:43 CEST