DFG Research Center MATHEON Mathematics for key ...co-at-work.zib.de/berlin2009/downloads/2009-10-08/2009-10-08-0930-M… · Mathematics for key technologies DFG Research Center MATHEON

DFG Research Center MATHEONMathematics for key technologies

DFG Research Center MATHEON

Mathematics for key technologies:Modelling, simulation, and optimization

of real-world processes

CO@W Berlin

Martin GrötschelOctober 7, 2009

DFG Research Center Matheon 2

Outline

MATHEON Introduction

A: Life Sciences

B: Logistics, Traffic, Telecommunication Networks

C: Production

D: Circuit Simulation and Opto-Electronic Devices

E: Finance

F: Visualization

Z: Education, Outreach, Administration


German Research Foundation (DFG)


DFG Coordinated Programs

Ordered by amount of funding:

Research units (Forschergruppen)

Priority programs (Schwerpunktsprogramme)

Research training groups (Graduiertenkollegs)

Collaborative research centers (Sonderforschungsbereiche)

Research Centers (Forschungszentren)

Excellence Initiative:

Graduate schools (Graduiertenschulen)

Excellence clusters (Exzellenzcluster) (excellence cluster ≈ research center + graduate school)


DFG Research Centers

Flexibility indistributing fundschoosing research focuses

Internal and external evaluation for high research standards

Structural impact bycreating new branches of researchenhancing technology transfer into applications, namely key technologiesbuilding and extending networks


Overview DFG Research Centers

rcomOcean margins, Bremen (2001)

CFNFunctional nanostructures, Karlsruhe (2001)

Rudolf-Virchow-CenterExperimental biomedicine, Würzburg (2001)

MATHEONMathematics for key technologies, Berlin (2002)

CMPBMolecular physiology of the brain, Göttingen (2002)

CRTDRegenerative therapies, Dresden (2006)


History of the DFG Research Center MATHEON

2000 first call, open topics 89 proposalsBerlin proposal I

early 2001 second call, special topic 14 proposals“Modelling and simulation in science,engineering, and social sciences”Berlin proposal II

July 2001 detailed proposal (approx. 400 pages) 3 finalists

January 2002 final international peer review

May 2002 “the winner takes it all ... Berlin” 1 winner

November 2005 submission new proposal (540+1000 pages)

January 2006 peer review by the DFG

May 2006 MATHEON prolongation until May 2010

2006—2011 Berlin Mathematical School (BMS)

October 2009 submission of next (and last) proposal

May 2010 MATHEON prolongation until May 2014


MATHEON Application and Reapplication

November 2001400 pages

November 2005540 pages + 1000 pages on CD


Opening Ceremony 2002

Audimax, TU Berlin: more than 1000 guests at the opening ceremony on November 20, 2002


Festival of Mathematics 2006

Approximately 1000 participants, Audimax, TU Berlin, on November 16, 2006


Supporting Institutions (Trägerinstitute)

Freie Universität BerlinInstitute of Mathematics and Computer Science

Humboldt-Universität zu BerlinInstitute of Mathematics and Institute of Computer Science

Technische Universität Berlin (Host university, Sprecheruniversität)Institute of Mathematics

Weierstraß Institute for Applied Analysis and Stochastics (WIAS)

Zuse Institute Berlin (ZIB)


Funding 2007 (Million Euros per Year)

DFG 5.6TU, HU, FU, ZIB, WIAS 3.0State of Berlin 0.1Technology Foundation Berlin 0.05Total budget: 8.75plus significant industry fundingGrant period: 4+4+4* years* subject to successful peer review

6 full professors (2+2+2)7 junior research groups (3+2+2)

65 researchers21 research students

Total: about 200 members, including ~40 professors


Central Location of MATHEON

3rd floor of math building at TU Berlin


MATHEON Executive Board

Alexander MielkeWIAS/HU

Volker MehrmannTU, Chair

Peter DeuflhardZIB/FU

Jürg KramerHU

Konrad PolthierFU

Andreas BleyTU

Christoph SchütteFU, Deputy Chair


Mathematical Fields

I Optimization and discrete mathematicsWerner Römisch, Martin Skutella, Günter M. Ziegler

II Numerical analysis and scientific computingRalf Kornhuber, Reinhold Schneider, Harry Yserentant

III Applied and stochastic analysisPeter Imkeller, Caroline Lasser, Alexander Mielke


Application Areas

A Life sciencesAlexander Bockmayr, Peter Deuflhard, Christof Schütte

B Logistics, traffic, and telecommunication networksMartin Grötschel, Rolf Möhring, Martin Skutella

C ProductionCarsten Carstensen, Dietmar Hömberg, Fredi

D Circuit simulation and opto-electronic devicesVolker Mehrmann, Alexander Mielke, Frank Schmidt

E FinanceDirk Becherer, Peter Imkeller

F VisualizationKonrad Polthier, John M. Sullivan, Günter M.

Z Education, Outreach, AdministrationJürg Kramer

from 6/2010


Spin-Off Companies

Indeed Visual Concepts (www.amiravis.com):3D data visualization (Amira), today: Mercury

JCMwave (www.jcmwave.com):Simulation software for nano-optical components

atesio (www.atesio.de):Plan, configure, and optimize telecommunication networks

Löbel, Borndörfer & Weider GbR (www.lbw-berlin.de)Optimization and consulting for public transport

Synoptio (www.synoptio.net)Mathematical consulting and software

Lenné 3D (www.lenne3d.de)Digital botany and real-time landscapes

inbion GmbH (inbion.math.fu-berlin.de)Bioinformatics solutions for life sciences

and more


Selection of Industry Cooperations

BASF, Bayer, Schering, ...

Siemens, IBM, Infineon, Microsoft, NEC, Philips, ...

Deutsche Telekom (T-Systems), E-Plus, ...

DaimlerChrysler, BMW, Volkswagen, Tebis, Bosch, ...

Deutsche Bahn, BVG, IVU, Lufthansa, ABB, ADAC, Herlitz, ...

EdF, Vattenfall, E.ON Gastransport, DREWAG, BHP Billiton, ...

AMRO Bank, Bankgesellschaft Berlin, Commerzbank, Deutsche Bank, IKB, Reuters Financial Software, ...

Numerous small and medium enterprises (SME)


Outline


A: Life Sciences


C: Production


E: Finance

F: Visualization



A: Life Sciences

Topics:

computer-assisted surgery

patient-specific therapy planning

protein data base analysis

protein conformation dynamics

systems biology

pharmacokinetics

Domains of Expertise

Mathematical modelling of molecular processes

Computational surgery and therapy planning

Mathematical systems biology


A1: Hyperthermia Treatment Planning

Regional Hyperthermia: local tumor heating by radiowave radiation

Aim: optimal control of antennas

Problems: handling of state constraintsperfusion modelling


A1: Interior Point Methods in Function Space

Idea: model state constraints by barrier functionals

homotopy in function space

inexact Newton path-following

adaptive multilevel method

Homotopy Path:

existence and convergence

Lipschitz continuity

Lavrentiev Regularization:

regular Lagrange multipliers


A2: Osteotomic Surgery Planning

Towards forward dynamics for a human knee joint

Patient-specific geometry

Finite element discretization

Time integration with inequality constraints

Unconditionally stableFew spurious oscillations

Static two-body contact problemsMortar discretizationParametrized boundariesMultigrid convergence


A2: Two-Body Contact Problems

Fast solvers for multi-body contact problems

Monotone multigrid: asymptotic multigrid convergence rate

Nonsmooth Newton multigrid: faster than equivalent linear problem!


A2: Real-World Data

Example using real-world data

Distal femur and proximal tibia from the Visible Human data set

Contact between the bones; foundation as rigid obstacle

Three grid levels, ≈220,000 degrees of freedom


A3: Noise Reduction in fMRI

fMRI — functional Magnetic Resonance Imaging

Aim: Noise reduction while preserving shapes of activation areas.Method:Structural adaptive denoising (lower right)


A4: Towards a Mathematics of Biomolecular Flexibility

Conformation Dynamics

1.3 µs simulation of 12-Alanine with implicit solvent

Three conformations visible: conformation switches on nanosecond timescale

Aims: Efficient sampling of state space, identification of conformations, intra-conformation flexibility, accurate transition rates, transition pathways


target

activesite

amira@ZIB

ligand

target structure

diffe

rent

con

form

atio

nsConformation Dynamics & Ligand Design

A4: Towards a Mathematics of Biomolecular Flexibility


A6: Stochastic Modelling in Pharmacokinetics

Pharmacokinetics:

Absorption

Distribution

Metabolism

Excretion

of drugs in the body

Aim: Mathematical modelling and theoretical analysis of pharmacokinetics processes, including variability & uncertainty

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A6: Stochastic Modelling in Pharmacokinetics

Model design: development of consistent and modular pharmacokinetic models

Hybrid stochastic-deterministic models: coupling pharmacokinetic models to cellular processes

Non-linear sensitivity analysis: analyzing the effects of parameter variability

))(div()( tuFtut ⋅−=∂

Software: Virtual Lab for Modelling and Simulation in Pharmacokinetics (coop CiT)


A8: Systems Biology

Molecular biology:study components of a biological system in isolation

Systems biology:understand how the components interact to perform biological function


A8: Gene Regulatory Networks

Discrete modeling approach: discrete variables and parameters

Logical analysis of the network dynamics model checking

Incorporating time constraints hybrid discrete/continuous modeling

Relating topology and dynamics of the network


Outline


A: Life Sciences


C: Production


E: Finance

F: Visualization




Topics:planning of optical, multilayer, and UMTS telecommunication networksline planning, periodic timetabling, and revenue management in public transport networksoptimization in logistics, scheduling and material flowsoptimization under uncertaintysymmetries in integer programminggame theoretic methods in network design

Domains of ExpertiseTelecommunication Logistics Traffic and transport Energy and utilities


B3: Integrated Planning of Multi-layer Networks

Telecom network planning:

Discrete link capacities

Node hardware

Survivable routing

Multi-layer networks:

Several technological layers (IP, SDH, WDM) with strong interdependencies

Upper layer links are lower layer paths

Goal: integrated planning of all layers


B4: UMTS Radio Network Design

Antenna

Cell

Find antenna locations and configuration for optimal network

Capacity

Coverage

Cost

Task

Network adjusts transmit powers continuously to traffic and radio conditions

Coverage depends on interference

Strong coupling between cells

Soft capacity

Evaluation of expected performance costly

Challenges with UMTS


B7: Focus 2: Wireless Networks

Motivation: provide location-based services (emergency, commercial) to mobile network users.

Aim: localize a mobile device using available information (without e.g. additional GPS).

One basic mathematical question: What is the information gain when superposing the geometric knowledge from two different cellular networks?


B8: Flows over Time

Applications

Control of traffic lights

Flow of materials in storage areasShunting of trains

Routing in a container terminal


B8: Flows over Time

Static network flows + time dimensions = flows over time

Task:

maximize throughput within a given time or

minimize time for a given throughput

Challenge:

develop theory and methods for efficient handling of real-world problems

exploit underlying network structureexplore complexity and develop algorithmshandle large networks


B13: Applications & Industrial Cooperations

flexible resource assignment impact on duration and cost

The goal is to find anoptimal project duration(cost for resource assignment vs. out-of-service cost)optimal resource assignment(capacity constraint, resource leveling)

Time-Cost-Tradeoff Problem combined with resource-leveling

Turnaround Scheduling: Resource planning for large-scale maintenance projects during shutdown of chemical plants


B14: Combinatorial Aspects of Logistics

Task: online/offline control of logistics systems

Practice: nothing like the logistics problem (specific aspects in each application)

Wanted: identify and tackle core models/approaches,e.g. reoptimization for online problems

Applications: vehicle dispatching, elevator control,automated transportation systems, ...


B14: Some Applications

Scheduling of laser welding robots in car body manufacturing (Volkswagen):

During welding each robot is fed by a laser source

Goal: minimize number of required laser sources

Control of destination-call elevator systems (Kollmorgen Steuerungstechnik):

Passenger specifies destination already when calling an elevator

Goal: small average/maximal waiting and journey times


B15: Service Design in Public Transport

Line Planning

two objectives: minimizing traveling times and costs

multi-commodity flow model

column generation approach

cooperation with ViP (Potsdam)

Timetabling

based on periodic event scheduling model

minimum cycle basis approach

cooperation with BVG (Berlin)


B15: Service Design in Public Transport

Fare Planning

maximizing revenue, profit, demand

discrete choice demand function

nonlinear optimization approach

Integrated Service Planning

complex interdependencies between individual problems

analyses of variable demand

Goal: decision support tool

SERVICE

DEMAND


B16: Mechansims for Network Design Problems

solve a combinatorial optimization problem

distribute the resulting cost among the users

establish fairness although users act selfishly (i.e. try to manipulate the algorithm) machine scheduling


Outline


A: Life Sciences


C: Production


E: Finance

F: Visualization



C: Production

Topics:

phase transitions in steels and solder alloys

production of semiconductor crystals

modeling of active and passive behavior of functional materials

online production planning

growth of thin films


Automotive

Energy

Phase Transitions


C7: Application Background

Optimal planning of electricity production and trading:

Several uncertainty factors and risks must be taken into account.

Mean-risk optimization of electricity production in liberalized markets


C7: Models and Results

Suitable Framework: Risk-averse stochastic programming

Challenges:

1. Justified finite approximations of stochastic parameters (energy demands, market prices)

2. Risk-aversion strategies

such that the resulting problems are numerically tractable

Results:

1. Scenario tree approximation methods based on stability theorems

2. Probabilistic constraints, polyhedral risk measures

Concrete Application: Medium-term optimization model for a municipal power company


C9: Applications of Semiconductor Crystals

Light-emitting diodes:Lifetime: ≈ 10 years

Light extraction efficiency > 32%(light bulb: ≈10%)

Blue laser:

Its use in DVD players admits up to 10-fold capacity of disc

SiC-based electronics still works at 600°C; SiC sensors placed close to car

engines save resources and costs


C9: Physical Vapor Transport Method

polycrystalline SiC powder sublimates inside induction-heated graphite crucible at 2000 – 3000 K and ≈20 hPa

a gas mixture consisting of Ar (inert gas), Si, SiC2, Si2C, ... is created

an SiC single crystal grows on a cooled seed

SiC seed crystal

2000-3000 K

SiC source powder

coil for induction heating

insulated graphite crucible


C10: Drag-out Problem for Rotating Disks

Industrial application: Fluid dynamical of PET polymer production

Steady-state solutions for angular velocities Ω=0.277, 1.0, 3.0

Comparison of FEM results to solutions of the asymptotic meniscus model (left, at constant radius r=9) and characteristics of

hyperbolic regime (right, at constant Ω=0.277).

Researchers: K. Afanasiev, A. Münch, B. Wagner, Appl. Math. Mod., 2007.


C11: Phase Transitions in Steel

Thermomechanical modelling of phase transitions in steelphysical properties of steel can be modified by heat treatmentwe consider three physical quantities which are associated by coupled partial and ordinary differential equationstemperature stress/displacement phase distributiondistribution of (metallurgical) phases corresponds to different degrees of hardness and ductilityphases exhibit different densities, thereby hardening may lead to distortion, i.e. undesired alterations in size and shape

Inhomogeneous cooling of a hot slab leads to a corresponding formation of the hard steel phase martensite which causes distortion.


C11: Heat Treatment — Simulation and Optimization

Challenges

thermomechanical modelling

adaptive numerical simulation

optimal control of hardening subject to distortion

laser welding and remelting

Adaptive simulation of laser surface hardening.


C14: Precipitation in GaAs Crystals

GaAs has a broad range of applications e.g. in micro- and optoelectronic devices

Heat treatment of GaAs wafer at ≈ 950 °C induces unwanted liquid As-rich precipitates

Can we prevent precipitation? Can we limit it to a homogeneous distribution?

Industrial partners:


C15: Magnetic Thin Films

A prime example of a pattern forming system with multiple scales and omnipresent in modern information technologies MRAMs, Spintronics

Non-Convexity & Non-Locality Pattern-Formation

Micromagnetic model: (director field)


C17: Separation Problems in Solders

Technological challenge: lead-free solder alloys

joint reliability: thermomechanically induced phase separation

First two images: Böhme/Müller, Lehrstuhl für Kontinuumsmechanik und Materialtheorie, TU Berlin

Goal: robust and reliable numerical simulation

coupled systems of PDEs: anisotropic phase-field models with logarithmic potential + linear elasticity [Dreyer (WIAS) & Müller (TUB)]

fast solvers: adaptive monotone multigrid methods


C18: Shape-memory Alloys

Shape-memory alloys and other multifunctional materials react on exterior stimuli like

temperature changes, electric or magnetic fields, light

viaelastic deformations and phase transformations (shape changes)polarization, magnetization, ...

Hysteretic behavior has its origin in time-dependent microstructures

Applicationsmedical area: superelastic grippers, dental wires, stents

MEMS: micro grippers, --valves and --pumps


C20: Modelling Car Frames

Aim: To model frames of automobiles with as a structure made of flexible beams connected together by rigid joints.

Challenge:

Modelling of compression, elongation and bending of the beams together and computation of the state energy from only the positions and orientations of the end points of the beams.

Optimize the structure through economic use of material while maintaining the static and dynamic properties under various load scenarios.


Outline


A: Life Sciences


C: Production


E: Finance

F: Visualization




Topics:

shape memory alloys in airfoils

production of semiconductor crystals

methanole fuel cell optimization

metamaterials


Electronic devices

Photonic devices


D1: Switched Systems of DAEs

Complex dynamical systems switching in time and frequency:

Electronic circuits: different device models used for different frequencies

Mechanical systems: robot manipulators or automatic gear-boxes (with DaimlerChrysler)

Biological systems: act differently depending on day cycles or on the nutrition

Traffic systems: operate differently depending on delays


D7: Numerical Simulation of Integrated Circuits

Coupling between circuits and components

Required by technological progress, miniaturization, detailed physical modeling

Mathematical Challenges

Stable computation of tractability index

Consistent initialization

Stable treatment of high order derivatives

Project focus

Apply algorithmic differentiation instead of numerical differentiation

Improve algorithms for index computation

Improve algorithms for consistent initialization


D13: Coupled Systems

Goals

Efficient numerical methods for coupled systemscoupling of different simulatorserror estimators step-size and convergence controller for coupled simulators

Model reduction for coupled systemspreservation of interconnection structure preservation of subsystem properties error estimates for the entire system


D14: Nonlinear and Dispersive Effects in Fiber Optics

Generalized Nonlinear Schrödinger Equation (GNLS)

Soliton Propagation Modulation Instability Supercontinuum Generation


D15: Photonic Crystal Fibers

Eigenvalue problems for Maxwell’s equations

Goal: Optimization of Geometry High order edge elementsAdaptive finite elements

Visualization of an PhC-eigenmode

courtesy Crystal Fibre, S.A.

PhC-fiber


Outline


A: Life Sciences


C: Production


E: Finance

F: Visualization



E: Finance

Topics:

measurement and hedging of risks

interaction models for asset price fluctuation


Risk management and hedging

Simulation and calibration


E1: Motivation

Understanding statistical properties of price processes is of paramount importance for financial industry

Statistical models reproduce observed data, but do not give insight into casual connections

Agent based models are an attempt to understand fundamental mechanisms driving financial markets

Project E1 investigates an agent based model on the level of order book dynamics

More information and an applet version of the simulation tool are available on the project's homepage:www.wias-berlin.de/research-groups/stochsys/dfg.html

http://www.wias-berlin.de/research-groups/stochsys/dfg.html






E2: Project Aims

Aim: Improve means of controlling financial risk due to climateRelevance: 20—30% of world wide economy affected by weather

Difficulty: Climate is a complex system


E2: Hedging

Hedging of weather dependent income fluctuationsAim: Dynamic hedging with exchange-traded climate securities

Relevant and practical suggestions allowing to mitigate weather risk

Case Study: Weather derivatives based on Heating Degree Days

Result: The optimal investment in HDD derivatives is given by


E5: Main Problem and Goals


Outline


A: Life Sciences


C: Production


E: Finance

F: Visualization



F: Visualization

Topics:

discrete differential geometry

geometry processing

image processing

virtual reality PORTAL


Geometry Processing

Image Processing

Interactive Graphics


F1: Discrete Surface Parametrizations

In computer graphics and numerics, surfaces in space are represented by surface meshes

Our aim: Develop theory and applications for surface meshes by discretizing the notions and methods of classical differential geometry

This is the paradigm of discrete differential geometry

Leads to “smart” discretizations

Examples of discrete minimal surfaces. They are discrete analogs of classical minimal surfaces


F2: Atlas-based 3D Image Segmentation

Applications

Geometry Reconstructionfrom 2D and 3d image data

Analysis of Shape Variability based on statistical shape models

Clinical Therapy and Surgery Planning


F4: Geometric Shape Optimization

Reverse engineeringClass-A surfaces for automotive design

Industry cooperation: Tebis AG

Thin shell simulationEfficient simulation of cloth dynamics

Cooperation: Columbia University, USA

Surface reconstructionReconstruction from 3D laser scans

Industry cooperation: Tube Experts



3D mesh compression

Efficient storage of huge geometries with millions of triangles

Fast online transfer of 3D data sets

Goal: new industry standards such as Java 3D and MPEG-4

Industry cooperation: mental images GmbH



Multimedia & Outreach: The award-winning video MESH

A journey through the geometry of polyhedral meshes

From Plato to contemporary geometry processing

Cooperation: Beau Janzen, Zipheron Design Labs


F5: Mathematics in Virtual Reality

Real-time Simulation of Fluid Motionbased on the discrete smoke ring flow.

Non-Euclidean Spaces:Interactive visualization and navigation.

Interactive Visualization and Modelingof integrable systems, e.g. K-surfaces.

Applications


F5: Mathematics in Virtual Reality

Cooperations & Outreach

Portal:Frequent demos for VIPs

3D-Lab at TU Berlin (EFRE):3D printer and scanner

Interactive navigation through scanned construction sites


F6: Multilevel Methods on Manifold Meshes

Surface Parameterization

permits high-quality regular remeshing

gives rise to subdivision hierarchies

New Quad-Cover algorithm generates regular surface parameterizations automatically[Eurographics, 2007]

1. Irregular scan data

2. Parameterization

3. Multi-resolution mesh


Outline


A: Life Sciences


C: Production


E: Finance

F: Visualization




Topics:

modern mathematics at school

school teachers at universities

network of math-science oriented schools

public awareness of Mathematics

media presence


Education

Training

Course Design


Z1.1: Current Mathematics at Schools

Aim: Enlarging the impact of Matheon with respect to the mathematical education at Berlin schools

Concept of the seminar courseBased on the new school law in Berlin

Introduce modelling problems at schools in cooperation with Matheon scientists

Didactic support by the delegated teachers

"Facharbeit" at the end of the course

School mathematics

Seminar course

University mathematics

Analysis

Linearalgebra/

Analyticalgeometry

Stochastic

MatheonModelling, simulation and optimization


Mathematical modelling


Z1.2: Teachers at Universities

Aim: Solidifying and extending the cooperation between schools and universities

School teachers at universityStrengthening the teachers’/teacher students’ competence with respect to practical needs through a close cooperation among delegated teachers, scientists and students in:

Lectures

Seminars

Exercises

Practical courses in schools

Examinations

Financial and organizational support through the delegation of teachers by the Senatsverwaltung für Bildung, Wissenschaft und Forschung


Refreshing and completing the teachers’ mathematical and didactical knowledge

Promotion of mathematically talented students of the “Network Schools” and acquisition of university credits before entering the university

Advising and influencing the designof new curricula

Developing concepts for furtherance of highly talented pupils starting in grade 5


Network of math-science oriented schools

Further development of mathematical education in schools by:

Foto: Heike Zappe, Humboldt-Universität zu Berlin



Public awareness of mathematics

Improvement of the image of mathematics in the public at large by:

Didactical advice concerning organization and implementation of the online competition “Digitaler Adventskalender”

Support in organizing and carrying out the “Berliner Tag der Mathematik” and “Mathematikolympiade”

Organization and didactical support of activities at the intersection of school and university such as

“Rent the Center”

Summer School “Lust auf Mathematik”


Z1.3: Visualization of Algorithms

Visage Software for education

Based on the interactive geometry software Cinderella a software package for teaching graph algorithms is developed.

Features:

Free experimentation environment for graphs and algorithms

Creation of internet-based, interactive tutoring systems

Providing ready-to-use teaching material


Z1.3: Visualization of Algorithms

Experiences in school

Proving the software in school

Development of new didactic concepts

Evaluation of material and methods in everyday school life

Free experimentation environment for graphs and algorithms

Film

DFG Research Center MATHEONMathematics for key technologies

DFG Research Center MATHEON

Mathematics for key technologies:Modelling, simulation, and optimization


Martin GrötschelThe End

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DFG Research Center MATHEON Mathematics for key ...co-at-work.zib.de/berlin2009/downloads/2009-10-08/2009-10-08-0930-M… · Mathematics for key technologies DFG Research Center MATHEON