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»AndereProjekte imBereich„Lebenswis-senschaften“widmen sichder computer-gestütztenOperations-planung.«MAX MUSTERMANN

MATHEON | U1

DFG Research Center MATHEON

Mathematics for Key Technologies

Mathematics is the FutureMATHEON

MAT H E O N

Creative and Efficient

mathematics, optimization, numerical analysis, scientific com-puting, as well as applied and stochastic analysis.

True to its motto “Mathematics is the Future”, MATHEON

works to promote the intrinsic fascination of mathematics. Theproject’s target groups are the wider public and particularlyschools. A number of projects aim to show students how funand interesting mathematics can be. Such projects include theMathematical Advent Calendar, the MATHEredaktiON schoolnewspaper project as well as numerous lectures and work-shops.

MATHEON’s high level of scientific excellence has receivedworldwide recognition. More and more companies are comingto depend on the know-how of the center’s mathematicianswhen looking for solutions to the widest range of questions. Thecreativity and efficacy of the research activities conducted atMATHEON have consistently won over its partners in businessand industry.

www.matheon.de

Mathematics is creative. Mathematics is exciting andmultifaceted. Mathematics is the future. Withoutmathematics, modern key technologies would be

unimaginable. In fact, without mathematics, the entire universewould most likely remain a complete mystery to us.

The DFG Research Center MATHEON was established in2002 as a means by which mathematics could be used to helpincrease the efficiency of technological developments. Thecenter is run by the mathematics departments at Berlin’s threemajor universities – the Technical University, the Free Universityand Humboldt University – as well as by the Zuse Institute Ber-lin (ZIB) and the Weierstrass Institute for Applied Analysis andStochastics (WIAS). With the support of the German ResearchFoundation (DFG), MATHEON aims to develop tailored solutionsfor the complex problems of modern key technologies.

MATHEON’s primary fields of application are life sciences,traffic and telecommunications networks and logistics, produc-tion, circuit simulation and opto-electronic devices, financeand visualization. Scientists at MATHEON are involved in about70 projects aimed at finding solutions for basic mathematicalproblems in each of these fields. The approximately 200 scien-tists model, simulate and optimize real-world processes usingmethods taken from the mathematical sub-fields of discrete

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L IFE SCIENCES

Counting on a Cure

Additional projects in the “Life Sciences” research field aredevoted to computer-assisted surgery planning, which allow forthe comparison of various options before the actual operationon the basis of a simulation of increasingly detailed and realis-tic models of soft tissue, bone and human movements. A furthertopic in the field of computer-assisted medicine is the search forentirely new perspectives for the optimal design of prosthesesadapted to individual anatomy.

www.matheon.de/research

Diabetes, cancer and Creutzfeldt-Jacob disease areexamples of illnesses that – either directly or indirectly –affect large numbers of people. In many cases, these

diseases can still not be cured because they are based on verycomplicated processes, which to this day are not completelyunderstood. Nevertheless, in recent decades, enormousadvances have been made, many of which were made possibleby the use of mathematical methods.

Mathematics has assumed a significant role in manybranches of the life sciences, such as in the development ofnew medications, therapies and cures. MATHEON’s “LifeSciences” research area testifies to the growing importance ofthis field. Its research activities make it possible for importantbiological and medical processes to be mathematically mod-eled, tested in virtual laboratories, adapted and optimized.

Projects in the “Life Sciences” application area are engagedin developing new medications and planning their targetedeffects. Research on the characteristics of particular moleculesis simultaneously conducted with the analysis of molecular net-works. This work, in turn, sets the foundations for the develop-ment of mathematical tools for the modeling of cellular andphysiological processes in systems biology and pharmaco-kinetics.

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TRAFFIC AND TELECOMMUNICATION NETWORKS AND LOGISTICS

Networks for an Organized World

MATHEON’s current projects include planning the network forUMTS cellular phones and developing the best design for thelandline telephone network of Germany’s National Researchand Education Network (DFN-Verein). The time-table forBerlin’s subway system was also optimized here, along with per-sonnel scheduling for bus drivers and the commuter railwaysystem in the capital as well as in many other regions. Workschedules for the “golden angels” of the ADAC, Germany’semergency roadside assistance company, as well as the routeplans for automated transportation vehicles in the container ter-minal of Hamburg’s port have also been calculated using algo-rithms originally from MATHEON. Before long, the elevator thattakes you to the floor you want with the least waiting time pos-sible will also be controlled by an algorithm developed atMATHEON.

www.matheon.de/research

We encounter networks everyday and everywhere.Tightly interwoven street, bus, railway and airline net-works form the backbone of local and global mobility,

and logistical networks lay the groundwork for efficient produc-tion and the reliable supply of goods. Without high-capacitycommunications networks and transferring data, it would beimpossible to surf the Internet or even make a phone call.Countless factors influence and affect the quality, costs andsafety of these networks. Traditional approaches to planning nolonger suffice when attempting to grasp complex interrelationsnor when seeking optimal solutions to problems that arise.

World-class experts involved in MATHEON’s “Logistics, Trafficand Telecommunications Networks” application area developmathematical methods for modeling, simulation, optimizing andcontrolling complicated flows of materials, people, energy,financial transactions and information. The goal of these meth-ods is to make decisions – out of the almost infinite range ofpossibilities – that maximize the benefits for clients. Among themethods applied and further developed are linear, integral andstochastic optimization, graph theory and combinatorics. Oursuccess – and that which has been achieved as a result ofcooperating with several industry partners – is reflected in thefact that our research is followed around the world.

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PRODUCTION

Efficient Production Thanks to Mathematics

An additional area of research entails the mathematical model-ing and simulation of shape memory alloys. Even after consider-able deformation, objects made from these materials are ableto “remember” their original shape and, under certain condi-tions, reform themselves into their original shape. A few sampleapplications for shape memory alloys include those in modernengines, sensors and medical stents.

Semiconductor materials play a crucial role in producingboth chips and solar cells used to generate power. The model-ing and production processes for semiconductors representanother focus of MATHEON. For example, a method for growingsemiconductor crystals using gallium arsenide (GaAs) has beenmodeled, simulated and optimized here. Other researchersfocus on thin liquid film, drop deposition and the effect of lighton semiconductor processes, which are very important, forexample, for the production of modern solar cells.

www.matheon.de/research

Production processes in modern key technologies, such assemiconductor engineering, photovoltaics and medicalengineering, are becoming more and more complex.

Moreover, new materials are now making previously impossiblefunctions feasible. Real challenges have arisen as a result ofthe need to control complicated steps in development, produc-tion and processing. A major contribution to meeting thesechallenges has been made by the methods of mathematicalmodeling, simulation and optimization.

MATHEON’s “Production” application area concentratesespecially on multifunctional materials but also on importantaspects of electricity generation.

Modern steel plays a central role in a number of studies.Owing to its material properties, more and more demands arebeing made on steel to serve as the base material for numerousindustrial applications.

These demands can only be met if scientists can compre-hend and control the phase transitions encountered in the pro-duction and processing stages, such as the changes in physicalproperties under varying heat conditions. Our mathematicalmethods also help these processes to be implemented in con-crete industrial applications, such as in computer-guided lasersand welding robots.

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CIRCUIT SIMULATION AND OPTO-ELECTRONIC DEVICES

Mathematics for the Chips of Tomorrow

A number of research projects are focused on quickly and reli-ably simulating the three-dimensional diffusion of electromag-netic waves. These play an important role, for example, in thedevelopment of new nano-optical components, such as mini-ature lasers and new generations of solar cells. An equallyimportant research topic is the delineating and simulating ofoptical systems using quantum mechanical models.

Another important research focus involves the modeling andnumerical simulation of increasingly more complicated inte-grated circuits for new generations of chips by means of so-called algebraic differential equations. This type of equation isalso used to delineate and electronically control complicatedsystems, such as modern automotive transmissions, in the bestway possible.

www.matheon.de/research

The invention of the transistor, laser and microchip weremilestones in the history of technical progress. Along withever more powerful computer processors, these inventions

have revolutionized our everyday lives. At the same time, inte-grated circuits are becoming more and more complex; thecomponents used in transistors are getting smaller and smaller;production cycles are growing shorter and shorter; and thetechnical aspects of putting things into production are gettingmore and more complex. In addition to electricity, light is alsocoming to play an increasingly important role in technical appli-cations, for example, in solar cells, lasers and fiber optic lines.

For many years, mathematical modeling and numerical simu-lation have been successfully employed in electrical technologi-cal developments. However, to a growing extent, these estab-lished methods have been reaching their limits. As a result ofadvances in miniaturization and new applications, physicaleffects that up to now were either not encountered or playedabsolutely no role at all must now be understood and mastered.The constantly growing complexity of products also necessitatesnew mathematical approaches.

The scientists at MATHEON working in the “Circuit Simulationand Opto-Electronic Devices” application area are committedto meeting these new challenges.

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FINANCE

Limiting Risks

Lastly, for the general evaluation of economic instruments andtheir associated financial risks, scientists at MATHEON determinenew statistical and numerical mathematical methods usinghigh-dimensional models, and they develop effective algorithmsas well.

www.matheon.de/research

The world of finance is getting more and more complex.New derivatives capture the market, hedging becomesmore and more important, and the interdependence

between global and local markets increases. For banks and theinsurance industry, risk factors such as climate change andrising raw materials costs are increasingly important. The stan-dard textbook models no longer suffice to explain financialmarkets.

One result is the increasing demand for mathematical solu-tions. Methods based on probability theory and statistics aremore and more often being used to analyze financial risks intheir various guises. This has led MATHEON’s “Finance” researchdivision to undertake various research projects using mathe-matical modeling, simulation and optimization. For many yearsnow, Berlin and MATHEON’s “Finance” applications area, inparticular, have played a leading role in this field.

Mathematicians at MATHEON study pricing processes forgoods being traded on different markets. They are alsoresearching safety measures while taking into consideration riskfactors associated with changes in weather and climate.

MATHEON plays a leading role in the search for dynamicinvestment strategies with the optimal criteria for minimizingrisk.

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VISUALIZATION

Virtual Imaging

computer graphics. Multistage algorithms are also developedfor industrial applications and computer graphics for whichlarge surface networks must be efficiently processed. Thesealgorithms are in particular demand in the automotive industry.

In addition, the results of the work conducted at MATHEON

are also used in producing computer games and large films.Image segmentation, i.e., the detection and identification of

objects using existing anatomical knowledge, is the basis forapplications in computer-aided therapy and operation plan-ning. New methods are also being developed for visualizingquantum molecular systems occurring in chemistry and physics.

Lastly, MATHEON’s 3-D portal makes mathematical visualiza-tion possible and permits the experimental diagramming of cur-vilinear spaces and the examination of geometric optimizingfunctions in biophysics and material sciences.

www.matheon.de/research

Today, the calculations involved in the observation of scien-tific and technological processes or in measuring andimaging procedures are producing increasingly complex

and comprehensive forms of data. And yet, people are not ableto directly access the information contained in these calcula-tions and techniques. The data only becomes accessible once ithas been processed, filtered and visualized in a form peopleare used to. Visualization is also necessary and helpful when itcomes to electronically diagramming or manipulating complex3-D objects. Whether for diagramming free-form architecture,designing new automobile bodies using CAD, or creatingrealistic computer animation for films, new mathematical meth-ods of describing and processing objects on a computer havebecome basic prerequisites.

The researchers in MATHEON’s “Visualization” research fielddevelop efficient algorithms for the visual analysis of largeamounts of data. When it comes to transferring “old” geometryinto a computerized form, i.e., “discrete geometry”, our scien-tists number among the world’s leading experts. In its widestsense, discrete geometry analyzes the interplay between 3-Dobjects and their computerized representations. In doing so, itplays a supporting role in the processing and optimization ofpolyhedric forms in industrial applications, such as CAD and

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EDUCATION

Improving Mathematics Education

piled. Colleagues participate in a diverse array of commissions,with the goal of integrating the vitality and versatility of mathe-matics into everyday classroom life and teaching plans.

www.matheon.de/research

Mathematical education in Germany was under scrutinyeven before the first PISA study was undertaken. Thestudy did not give particularly good grades to German

students, and the educational system was criticized as well.Large numbers of students still have the preconception thatmathematics is boring, incomprehensible and pointless. Thereadiness of a certain segment of teachers to rebut this preju-dice by bringing excitement and diversity to their classrooms isanother element that could be addressed in the future.

In order to improve this situation, MATHEON has introducedan “Education” application area. Scientists in this field strive todevelop new concepts for educating teachers. MATHEON is alsoinvolved in advanced and continuing education and uses thepractical experience of three teachers in its project’s ongoingwork. Berlin’s Senate Department for Education, Science andResearch has delegated each of these teachers to MATHEON fora year to aid in this research. In the context of Berlin’s networkof schools with high reputations in mathematics and natural sci-ences, the participating teachers and scientists are alsoinvolved in programs supporting gifted students.

New teaching and learning materials are also developedand tested at MATHEON. New content development and modelsfor classroom teaching as well as teaching plans are also com-

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EDUCATION

Awakening Student Interest

to conduct research and interview scientists, after which theycan go on to compose articles to be published in their schoolnewspapers.

One of the annual highlights of MATHEON’s school activitiesis the Digital Advent Calendar. Every day from December 1 to24, young people are invited to solve a new tricky mathematicalproblem posted on the Internet, and a number of valuableindustry-sponsored prizes can be won. Each year, nearly 10.000students and adults and a growing number of people from allover the world participate in this “math calendar.”

www.matheon.de/schools

MATHEON has initiated a range of projects aimed at get-ting students interested in and enthusiastic aboutmathematics as early as possible. In cooperation with

mathematics teachers, MATHEON organizes project weeks atBerlin schools during which games are used to introduce stu-dents in the fifth and sixth grades to mathematical topics. Atthe same time, these project weeks provide teachers with newideas for integrating practical, real-life applications into theirteaching.

Each year, older students meet for a week outside Berlin fora summer school program called “Feeling like Math”, wherethey work on exciting mathematical subjects under the supervi-sion of MATHEON scientists.

A series of lectures under the motto “MathInside” is held forstudents at Urania Berlin three times each school year. Allschools in Berlin and Brandenburg are invited to the lecturesdelivered by MATHEON members. MATHEON also offers a selec-tion of tours and lectures to school groups from all over Ger-many and abroad. The “Rent the Center” program also offers acatalogue of mathematics-related lectures, which schools canbook for specific groups or classes.

The MATHEredatiON program brings together journalists fromschool newspapers five times a year at participating institutes

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TECHNOLOGY TRANSFER

Mathematics is the Mother of Invention

have developed software that is being used profitably in indus-try and business. Several mathematical methods and conceptshave been and are being further developed in a series of com-panies founded to bring them to maturity and then profession-ally market them.

MATHEON organizes regular workshops for industry and busi-ness so as to be able to sound out the potential for mathemati-cal solution-finding approaches in ongoing projects in industrialresearch and development. Special seminars are used to com-municate the current state of mathematical research “in a user-friendly way”. Moreover, MATHEON makes great efforts to pro-vide the next generation with excellent, application-orientedqualifications in the fields of both engineering and mathe-matics.

www.matheon.de/transfer

Mathematicians are famous for seeking out “problems”– the more complex, the more exciting. And whatcould be more complex than reality, especially when it

involves new developments in modern key technologies? Forthis reason, the scientists at MATHEON are always searching fornew mathematical challenges arising from industrial and busi-ness practices. Industry and business, in turn, are increasinglyemploying mathematics to structure and transfer complex prob-lems into technical, quantitative models. Mathematicalapproaches allow problems to be better understood, to recog-nize what is essential, to make predictions in difficult situationsand to make better decisions.

MATHEON offers industries its internationally recognizedexpertise in the complete spectrum of applied mathematics.Moreover, MATHEON provides access to a worldwide networkof excellent contacts in the research areas of mathematics,computer science, the natural sciences, economics, engineeringand medicine.

In recent years, MATHEON’s offerings have convinced over100 companies from Germany and abroad to cooperate withMATHEON scientists in applied research projects, many of whichhave led to innovative solutions in various industries. For exam-ple, MATHEON scientists have filed a number of patents and

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MAT H E O N

MATHEON is actively engaged in finding innova-tive solutions in a number of fields includingthe following:

■ Architecture & Construction Industries■ Automotive Engineering & Machine

Manufacturing■ Banking & Insurance■ Electronic & Semiconductor Industries■ Energy & Water Supply■ Logistics■ Media & Entertainment■ Medical Engineering■ Pharmaceuticals■ Processing Industries■ Telecommunications■ Transport & Traffic

A selection of our numerous projects conducted incooperation with partners in business and industrycan be found on the Internet.

CONTACT:MATHEON Technology TransferTel.: +49 (0)30 314–2 92 75E-Mail: transfer@matheon.de

www.matheon.de/transfer

MATHEON

Media and Public Relations

MATHEON’s press office is the point of contact forboth journalists and interested members of the pub-lic. The office promotes the fascinating world ofmathematics and supplies the public with whateverinformation they may need. Its many activitiesinclude (but are not limited to!) arranging forexperts to speak on various issues, organizing visitsto either of its 3-D projection rooms and its 3-Dlaboratory, arranging discussions with scientists,and organizing exciting lectures. If you sign up forour mailing list, we will send you the current pressreleases. You can also subscribe to our newsletter,which appears on an irregular basis. Furthermore,all other MATHEON publications can be procuredfrom the press office, which is also available to helpwith images, films and other visual media.MATHEON’s press office also confers an annualmedia prize open to young journalists for the bestprint article on mathematics and its applications.

CONTACT:MATHEON Press OfficeTel.: +49 (0)30 314–2 92 74E-Mail: kellermann@matheon.de

www.matheon.de/press

Imprint

PUBLISHER:DFG Research Center MATHEON

c/o Technische Universität BerlinMedia and Public RelationsStrasse des 17. Juni 136, D-10623 BerlinTel.: +49 (0)30 314–2 92 74E-Mail: kellermann@matheon.dewww.matheon.de

EDITOR: Rudolf Kellermann

PHOTOGRAPHY: Kay Herschelmannwww.kayherschelmann.de

COVER GRAFIC 3: Charles Gunn, MATHEON

LAYOUT AND PRODUCTION:deutsch-türkischer fotosatz, Berlin (dtf)E-Mail: satz@dtf-berlin.de

TRANSLATION: The Hagedorn Groupwww.hagedorn-group.com

PUBLICATION DATE:January 2008

We would like to thank the following for their gener-ous support: Verkehrsbetriebe Potsdam;Dr. Michael Hünerbein, Helios Clinics, Departmentof Surgery and Surgical Oncology, Berlin-Buch;Andreas-Oberschule Berlin (Gymnasium)

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