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 2001

Matematiska kollokviet

Fredagen den 23 februari, kl. 13.15 - 14.15 talar Dr. Maria Roginskaya, Chalmers,

Some criteria for Riesz sets

Sammanfattning: The F. and M. Riesz theorem says that, as soon as a finite measure on an interval has Fourier transform supported on the positive half line, the measure has no singular part. A Riesz set (on or ) is a set such that, as soon as a finite measure has Fourier transform supported on the set, the measure has no singular part. I'm going to show some examples of Riesz and non-Riesz sets, and discuss two types of criteria for a set to be Riesz.

Fredagen den 2 mars, kl. 13.15 - 14.15 talar Dr. Stephen Buckley, National University of Ireland, Maynooth,

Gromov hyperbolicity

Sammanfattning: We define Gromov hyperbolicity and discuss one area (in Several Complex Variables) where it arises. Although useful, this concept is still somewhat mysterious. For instance, the literature gives no good guide as to how one can determine whether or not the quasihyperbolic metric on a bounded Euclidean domain is hyperbolic. We discuss new results that answer this and related problems, and shed a little more light on hyperbolicity.

Lokal: MAI:s seminarierum Beurling

Välkomna!

Lars-Erik Andersson, Anders Björn, Svante Linusson och Stefan Rauch-Wojciechowski

Licentiat-seminarium

Onsdagen den 28 februari kl. 10.30 presenterar Charlotte Karlsson sin uppsats

Estimating and Forecasting Cyclical Fluctuations - A Study of the Industrial Production for Paper and Pasteboard in Sweden.

Opponent är Lars-Erik Öller, Konjunkturinstitutet i Stockholm.

Sammanfattning: Time series data concerning the forest industry and especially the paper industry is characterised by large cyclical fluctuations. In this thesis we study two approaches to estimate and extract cyclical fluctuations. Our first approach focus on simplicity and motivate the X-11 procedure. The second approach with Structural Time Series Models is more complicated since the method simultaneously estimate, extract and forecast a cyclical component. For the studied variable, Industrial Production for Paper and Pasteboard in Sweden, the dating of the turning points in the estimated cyclical component correspond approximately to known and verified turning points.

In decision processes about investments and budgets, decision inputs in form of long-term forecasts of the cyclical component are important. It is therefore interesting to study if there is any suitable method for making forecasts of future cyclical behaviour and especially the turning points. Among the methods we study for this purpose, Seasonal Auto Regressive Integrated Moving Average Models (SARIMA), Periodic Auto Regressive Models (PAR) and Structural Time Series Models (STSM), the latter performs best. The thesis includes a description of how the suggested method works in reality. Given that structural time series models are used both to estimate, extract and forecast the cycle, the user will receive knowledge of coming peaks almost one year ahead, while a signal for a trough is given approximately at the time of the forecasting.

Lokal: Kepler (E330), Fysikhuset.

Välkomna!
Stig Danielsson

Seminarium i optimeringslära

Onsdagen den 28 februari kl 13.15-14 håller PO Lindberg ett seminarium:

Traffic Equilibria without Route-Flows - A Link-Flow Cutting-plane Method for the Traffic Assignment Problem.

The Traffic Assignment Problem (TAP) is a much studied Operations Research problem, that can be stated as a convex optimization problem. The rich structure of this problem has inspired many different solution approaches. One of the earliest is the classical Frank-Wolf (F-W) method, which does line searches in the link flow space, but builds link flows from route flows. It has fast initial convergence, but very slow final convergence. The F-W method has been improved upon by adding simplicial decomposition, giving faster convergence. Even better convergence is achieved by disaggregate simplicial decomposition, which iterates in the space of route flows.

The convergence rate of all these primal methods is hampered by the fact that the route flows typically are not unique, although the link flows are. (This gives a case for dual methods, which however are not covered in the seminar.) We will suggest an alternative, cutting-plane method, for the TAP working in the link flow space.

The set of link- and route-flows fulfilling the origin/destination demand constraints forms a convex polytope, P. The objective in the optimization formulation of the TAP, however, only contains the link flow variables. Hence, the optimization could in principle be performed over the projection of the polytope P onto the link flow space. The problem is to find a good description of .

In the seminar, I will describe how facets of can be generated. The ensuing method for the TAP works by minimizing the original objective over relaxations of , successively adding the ``most violated'' facet. For a given relaxation of , the optimization can be done efficiently since we have separable objective and linear constraints.

Lokal: Kompakta rummet

Välkomna!

Seminarium i statistik

Fredag 2 mars kl 13-15:

Deliang Chen, Geovetenskapligt centrum, Göteborgs universitet.

Multimode probability distributions of climatic variables: A universal feature of the climate system?

A detailed study on extremes of a climatic or hydrological valuable requires a understanding and determination of its probability distribution. Quite often a single mode probability distribution is used to fit observation. Based on a theoretical discussion on physical background and mathematical implication of the dynamics of the non-linear climate system, we argue that probability distribution of a climatic variable may be better described as a weighted sum of a number of normal distributions which result from different physical mechanisms/processes. To confirm this, we focused on probability distributions of a number of climatic variables. The climatic variables analyzed can be classified as those derived from well known dynamics and those from less known dynamics. As an example for the later class daily surface air pressure and temperature in Stockholm/Uppsala from March 1, 1822 to October 4, 1999 is used. The existence of multimode can be confirmed by testing the significance of every individual distribution (mode) using Minimum Description Length (MDL) as a criteria. The determination of the characteristics of each mode is considered as a non-linear fitting problem. Mathematically, this problem can be solved by employing the Levenberg-Marguardt iterative scheme.

Based on the analysis of the data set covering a large range of temporal and spatial scales, it is shown that multimode is most likely a universal feature in the climatic system. Further, the multimodes identified for the first class data correspond well with the well known dynamics behind the phenomena, which provides a proof of the hypothesis. If the multimodes identified can be associated with distinctive processes, it would provide a way to link the change in the occurrence of extremes to the dynamics of the respective processes.

Lokal: Kompakta rummet

Välkomna!
Åsa Forsman

Seminarium i matematisk statistik

Onsdag 7 mars, 13.15 - 15.00 håller John Noble, matematisk statistik, ett seminarium

The Inviscid Burgers Equation and the Action Functional of Brownian Motion

The viscosity solution, of the Inviscid Burgers Equation is considered. The solution may be represented in terms of critical points of an associated action functional. But it is shown, using a simple time dependent potential, that these critical points are not necessarily the minimising ones and will be the attracting critical points when these two things are different.

This, of course, contradicts the well known theorem of Varadhan from the theory of large deviations. It is shown where the problem occurs with the proof of Schilder's theorem; the unit ball in does not satisfy the required compactness criterion that one would expect following the well known and basic Banach Alaoglu theorem.

Lokal: MAI:s seminarierum Beurling.

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

Presentation av examensarbeten

Tisdagen den 27 februari kl 13.15 presenterar Jonna Gill sitt examensarbete i tillämpad matematik: Studier av generaliserade Birkhoffpolytoper.

Denna rapport studerar en polytop M(m,n,k) som är en generalisering a Birkhoffpolytopen, och M(m,n,k) definieras av att dess hörn är alla (0,1)-matriser av storlek m/n som har exakt k ettor, högst en etta i varje rad och högst en etta i varje kolonn.

En del enkla och grundläggande egenskaper hos M(m,n,k) undersöks här, samt två olika sätt att representera M(m,n,k):s sidor vilka kan utgöra bra redskap för att vidare undersöka denna polytop. Dels kan M(m,n,k):s sidor representeras som kvadratiska (0,1)-matriser, och dels som bipartita grafer.

Lokal: MAI:s seminarierum Beurling.

Välkomna!
Svante Linusson

Torsdagen den 1 mars kl 13.15 presenterar Peter Broström  (MatNat)  sitt examensarbete:

Solving the Forwarding Problem using Taburoute

Abstract: In this paper we present a solution method for the Forwarding problem. This problem is to move piles of saw- and pulplogs on a harvesting area to adjacent forest roads. In order to solve this problem, Taburoute, a Tabu search heuristic have been modified and implemented. The algorithm considers a sequence of adjacent solutions obtained by repeatedly removing a pile of timber from its current route and reinserting it into another route. During the computation of the algorithm, infeasible solutions are allowed. This work is performed within a research project between Linköping University, SkogForsk and Holmen Skog. We compare our results with those obtained by another method, based on Repeated Matching, within this project. We find that our developed procedure produce competitive results for this type of problem.

Lokal: MAI:s seminarierum Beurling

Välkomna!
Maud Göthe Lundgren och Mikael Rönnqvist

Fredagen den 2 mars klockan 10.15 presenterar Joakim Isaksson (I-linjen) sitt examensarbete:

Generering av effektiva returflöden och kostnadsdelning i skogsindustrin

Sammanfattning: Examensarbetet som legat till grund för den här rapporten är består av två separata problem, båda med anknytning till skogsindustrin. Det ena problemet är att generera returflöden. Carlsson & Rönnqvist (1998) har med hjälp av det klassiska transportproblemet som grund utvecklat en modell av ett transportproblem som tar hänsyn till returflöden. I sin implementering av modellen har de använt sig av kolumngenerering. Kolumnerna genererar de från en pool i vilken alla möjliga returflöden innehållande två jobb ligger. Det är till det problem som Carlsson & Rönnqvist (1998) beskriver som det i den här rapporten föreslås en alternativ kolumngenereringsmetod. Returflöden genereras i denna alternativa metod med hjälp av en tidsbegränsad billigaste vägalgoritm. Fördelen med denna metod är att det inte är några problem att generera flöden innehållande fler än två jobb, till skillnad från metoden då kolumner genereras från en pool.

Det andra problemet går ut på att fördela kostnader som uppstår då företag inom skogsindustrin gemensamt planerar sina transporter. Om de gemensamt planerar sina transporter finns det fler möjliga flöden att välja bland, det är då troligt att det går att hitta en totalt sett billigare lösning. I rapporten föreslås en metod för kostnadsdelning som bygger på kooperativ spelteori. Modellen bygger på  att  man ska hitta en lösning i mitten på spelets core, då en lösning i mitten på core kan betraktas som rättvis. Modellen testas på två fall som bygger  på  realistiska  data från skogsindustrin.

Lokal: Kompakta rummet

Välkomna!
Maud Göthe Lundgren och Mikael Rönnqvist

 
  Mer information om MAI finns på under 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

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