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

v10 2004

Matematiska kollokviet

Onsdagen den 3 mars, kl. 13.00-14.00 talar Dr. Federico Incitti, Rome,

Bruhat order on the involutions of classical Weyl groups

Sammanfattning: It is known that a Coxeter group , partially ordered by the Bruhat order, is a graded poset, with rank function given by the length, and that it is EL-shellable, hence Cohen-Macaulay, and Eulerian.
We wish to investigate whether a particular subposet of , namely that induced by the set of involutions of , which we denote by Invol(), is endowed with similar properties.
The problem arises from a geometric question. In fact, as well as the Bruhat order on the symmetric group encodes the cell decomposition of Shubert varieties, the Bruhat order on its involutions, considered for the first time by Richardson and Springer in 1990 in a more general context, describes the cell decomposition of some symmetric varieties.
In this talk we prove that if is a classical Weyl group, then the poset Invol() is graded, with rank function given by the average between the length and the absolute length, and that it is EL-shellable, hence Cohen-Macaulay, and Eulerian.
The proofs are combinatorial and use the descriptions of classical Weyl groups in terms of permutation groups: the symmetric group for type , the hyperoctahedral group for type and the even-signed permutation group for type .
In particular we obtain, as new results, a combinatorial description of the absolute length of the involutions in classical Weyl groups, and a combinatorial description of the covering relation in the hyperoctahedral group and in the even-signed permutation group.
It is also conjectured that the result proved for classical Weyl groups actually holds for every Coxeter group.

Onsdagen den 10 mars, kl. 13.00-14.00 talar Prof.Alexander Stolin, Chalmers

Deformation quantization, Yang-Baxter equation and algebraic orbit method

Sammanfattning: Abstract. The fact that any Poisson bracket on a manifold leads to a star-product on was explained by M. Kontsevich a few years ago. However finding of the explicit formulas in concrete cases is still an open problem. In my talk I will explain relations between quantization of the Kirillov-Kostant bracket on certain orbits of the co-adjoint representation of the simple complex finite dimensional Lie algebra and certain representations of . Relations with the dynamical YBE will be also explained.

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

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

Seminarium i optimeringslära

Onsdagen den 3 mars, kl 14.00-15.00 talar Kaj Holmberg,

Determining the Existence or Nonexistence of a Compatible OSPF Metric

Abstract: Many telecommunication networks use IP (Internet Protocol) with OSPF (Open Shortest Path First) and ECM (Equal Cost Multipath) for deciding the routing of traffic. Each router sends the traffic on the shortest path to the destination, and splits the traffic evenly if there is more than one shortest path. The network operator can not decide directly how to send the traffic, but can assign the link weights (metric) used in the calculation the shortest paths. Given the weights, it is quite easy to calculate the traffic. However, if one would like to obtain a certain traffic pattern, one must find the weights giving that traffic pattern (weights compatible with the traffic pattern). This can be viewed as an inverse problem. For certain traffic patterns there are no compatible weights, i.e. the traffic pattern will never be obtained. There is usually no preference between different sets of compatible weights, so the main question is whether or not there exists a set of compatible weights for a desired traffic pattern. We investigate the problem, and find necessary and sufficient conditions for the existence of compatible weights for a set of given desired shortest path graphs. A polynomial algorithm that answers the question whether or not there exists a compatible metric is presented. The method also identifies the conflicting parts of the desired graphs.

Lokal: Kompakta rummet.

Välkomna
Kaj Holmberg

Seminarium i matematisk statistik

Bayesian identification of genetically diverged groups of individuals using multilocus genetic markers

Sammanfattning: In structured populations allele frequencies at multiple marker loci are known to be affected by forces like random genetic drift, migration, and mutation. When a population becomes split with negligible consequent migration between the distinct parts, then over time genetic profiles of individuals originating from different parts tend to resemble each other less than profiles sampled from the same part. Probabilistic Bayesian methods based on latent class models are widely used for identification of diverged groups on the basis of multilocus marker data. Inference on the number of latent classes (K) supported by the data is typically done by sequential analyses conditioned on an increasing value of K. We describe a partition-based approach where sampling units (individuals, groups, populations) can be classified into diverged groups while simultaneously making inference about the number of classes needed for appropriate data description. Our approach is based on a full Bayesian model, from which marginal posterior distribution can be derived for K or other quantities of interest. This approach also enables "model-averaged" clustering on the basis of a posterior distance measure, which is particularly useful when the posterior distribution over the partition space is relatively flat. Apart from simple cases where the posterior is available in analytical form, we use Markov chain Monte Carlo methods to estimate the posterior distribution.

Lokal: ISY/MAI:s seminarierum Glashuset

Välkomna !
Timo Koski

Presentation av examensarbeten

Fredagen den 27 februari kl 10.15 presenterar teknologerna Erik Johansson och Lena Jonsson sitt examensarbete i optimeringslära.

Väginvesteringar för säker virkesleverans en optimeringsmodell och två heuristiker

Abstract: Väginvesteringar är kostsamma men nödvändiga för att skogsindustrin ska kunna säkerställa tillgången på råvara under hela året. Samtidigt är problemet att välja de mest lämpliga vägarna att uppgradera tidsödande att lösa med en optimerande heltalsmodell. I examensarbetet presenteras en optimerande modell samt två heuristiker som minskar lösningstiden. Den första bygger på idén att lösa linjära nätverksproblem upprepade gånger med bågkostnader som tar hänsyn till uppgraderingskostnader och som uppdateras mellan lösningarna. Den andra är en konstruktiv heuristik som väljer vägar att uppgradera på ett sätt som påminner om Prims algoritm.

Lokal: Kompakta rummet, ing 23 bv

Välkomna!
Mathias Henningsson och Jenny Karlsson

Tisdagen den 2 mars kl. 15.15 presenterar Vanesa Isovic sitt examensarbete i matematisk statistik.

Undersökning av ekvivalensen mellan susceptibilitetstest utförda med många infallsriktningar

Sammanfattning: Elektromagnetisk strålning kan störa elektronik-utrustning. Med tanke på att elektronik i ökande utsträckning används i moderna säkerhetssystem, har EMC-provning (Electromagnetic Compatibility) och skärmning av elektronisk utrustning mycket stor betydelse.
Vid EMC-provning av elektronisk utrustning i mikrovågsområdet kan det krävas tusentals olika infallsriktningar/polarisationer för att träffa den infallsriktningen där känsligheten mot elektromagnetisk strålning är störst. I praktiken har man emellertid oftast endast råd att prova med ett litet antal infallsriktningar och polarisationer.
I detta examensarbete för civilingenjörsexamen föreslås en frekvenssubstitutionsmetod som bara använder ett fåtal infallsriktningar och polarisationer, men ett frekvensintervall runtomkring den aktuella frekvensen. En statistisk modell för den elektromagnetiska kopplingen studeras också.
Frekvenssubstitutionsmetoden verkar fungera för alla frekvenser förutom vid testobjektens resonansfrekvenser. Chi2-fördelningen med en frihetsgrad kan användas som en grov skattning av fördelningsfunktionen för den elektromagnetiska kopplingen.

Lokal: Kompakta rummet

Välkomna!
Pontus Andersson

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.