Ett informationsblad från matematiska institutionen vid Linköpings universitet. Material till Lite Mat lämnas till Bodil Stavklint firstname.lastname@example.org senast torsdagar kl 08.00.
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Ett informationsblad från matematiska institutionen vid Linköpings universitet
Onsdagen den 17 november, kl. 13.00-14.00 talar Svante Linusson, angående:
A survey on trees in mathematics and biology.
Sammanfattning: A mathematical tree is easy to understand and has been studied not only in pure mathematics. Trees have also been important objects in e.g. optimisation and computer science as for instance search trees, decision trees and computational trees. It would not be unreasonable to believe that such a simple object with many applications would be so thoroughly studied that when questions arise in the new biology related mostly to evolutionary trees, the mathematicians could present all the relevant answers at once. This is however not the case. Several new difficult problems arise.
I will give a survey of interesting theorems/conjectures about trees from both pure mathematics and biology. It is my firm belief that mathematicians have a crucial role in transforming biology into an information science. But also that biology can inspire new beautiful and interesting mathematics.
The talk does not require much prerequisites of the audience. It will be understandable to every mathematician at the department, especially every PhD student.
Lokal: ISY/MAI:s seminarierum Glashuset, ing 25.
Svante Linusson och
Friday, November 12, at 13.15- 15.00
Stochastic iterations, Seminar 4.
Contents: Contraction conditions for stochastic iteration systems; and stochastic iterations of logistic maps.
Lokal: Algoritmen, ISY, Ingång 27 eller 29 , (Hus B).
Friday November 19, at 13.15-15.00.
Stochastic iterations, Seminar 5.
Contents: Stochastic iterations and couplings.
Lokal: Algoritmen, ISY, Ingång 27 eller 29 , (Hus B).
Onsdagen den 17 november kl. 15.15-17.00 talar Professor Aihua Xia, Department of Mathematics and Statistics, University of Melbourne, angående:
Stein's method: from Poisson approximation to a discrete central limit theorem.
Abstract: We want to approximate for and a sum of independent (or weakly dependent) integer-valued random variables with finite second moments. There are two cases to consider.
Case 1: Majority of , , are small, for example, counts the number of occurrences of certain rare events.
Case 2: Majority of , , are relatively large, then the distribution of should behave like a discrete normal.
The first case is well approximated by a Poisson or a modified Poisson such as compound Poisson, Poisson signed measures with errors of approximation estimated by Stein-Chen method. Barbour's probabilistic interpretation of Stein-Chen method for estimating the error of Poisson approximation not only paved a way for investigating Poisson process approximation, but also provided an opportunity for studying other approximations. Xia (1999) gave a purely probabilistic proof of Stein bound for Poisson approximation and the case of approximations by general distributions on the non-negative integers was studied by Brown and Xia (2001). The methods in Brown and Xia (2001) apply to a very large class of approximating distributions on the non-negative integers, including Poisson, binomial, negative binomial as well as a natural class for higher-order approximations by probability distributions rather than signed measures. This offers a comprehensive solution to case 1. In terms of case 2, Goldstein and Xia found a family of discrete distributions which behave in the same way as normal does in the central limit theorem. This talk will cover the following topics:
1. The principle of Stein's method for discrete distribution approximations.
2. Why do we need to have Markov birth-death processes in this exercise?
3. Around Poisson approximation.
4. Polynomial birth-death (PBD) approximation.
5. Zero biasing and a discrete central limit theorem.
Tisdagen den 16 november kl 1315-1500 talar Hans Nyqvist, Stockholms universitet angående:
Optimal design of experiments - a review. Abstract:
Consider an experiment and a model describing the relation between the response variable and the experimental variables or factors. Some introductory examples will show that the precision with which the model parameters are estimated depends on the values on the experimental variables and the allocation of observations to these values, hence emphasizing the importance of a good design. An optimal design of an experiment is defined by an optimisation problem: given a model and a criterion defined on the space of possible designs, find a design that optimise the criterion. Criteria used in practice are often related to the precision of parameter estimators or estimators of functions of parameters. Some general results on optimal design will be presented. A problem with optimal designs is that they generally depend on unknown model parameters. This certainly creates a dilemma: if the parameters are not know, we cannot construct an optimal design and if they are known, we probably don't need an experiment for estimating them. Some approaches to this problem will briefly be mentioned, including optimum on average designs and minimax designs. The minimax designs have shown to be mathematically and numerically intractable. Some newly discovered results have, however, increased our knowledge and indicated a possible way for constructing algorithms for the numerical construction of minimax designs.
Lokal: Kompakta rummet
Olle Eriksson och Anders Grimvall
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
Sidan underhålls av: LiteMat
Senast ändrad: Wed 2012-08-29; 15:43 CEST