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

v9 2004

Matematiska kollokviet

Onsdagen den 25 februari, kl. 13.00-14.00 talar Andreas Rietz,

Noncoercive contact problems with friction

Sammanfattning: I open this talk by discussing the mathematical properties of contact problems with friction. I then focus on noncoercive contact problems, that occur for example when the body has no prescribed displacements. Some recent results on the existence of solutions are presented and these results are interpreted mechanically in terms of dynamical stability. I also present the main ideas on how to derive these results.

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.

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

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

Seminars on Model-Based Phylogenetic Inference

Lecture II

Onsdag den 25 februari kl. 15.1516.30
Lokal: Glashuset.

Sammanfattning: Mer om Markovkedjor i kontinuerlig tid: forward equations, transitionsmatrisens egenskaper, uniformizability, jämviktsfördelning.

Timo Koski
Information: tikos@mai.liu.se, tfn: 28 1454

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 examensarbete

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

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 013-100746, Email: litemat@mai.liu.se.