1 Summary including Mission and Vision Statement - KTH

Enclosure 1: Summary Center for Industrial and Applied Mathematics

1 Summary including Mission and Vision Statement

As the world is becoming technologically more advanced and the innovation cycles are gettingshorter, Swedish industry is faced with new challenges. New knowledge will be increasinglyimportant for keeping a competitive edge. Modeling complex technological systems requiresabstraction, and thus mathematics. In our computerized world, key technologies are increas-ingly dependent on mathematics. Indeed, mathematics is the language of all modern scienceand engineering and is playing an increasingly profound role in industrial development.

Nevertheless, there remains a wide gap between core mathematics and true applications.Industrial applications must often resort to “quick and dirty” solutions since economic con-siderations demand that time horizons be short. There are few engineers in industry whocan afford the time needed to understand advanced mathematical techniques, even if thebenefits of such a strategy are recognized. Likewise, many mathematicians lack basic insightinto industrial problems, even if these provide highly interesting mathematical problems. Itis obvious that much could be gained by narrowing this gap.

Our mission is to form a Center for Industrial and Applied Mathematics (CIAM), in whichresearchers from both core mathematics and applied mathematics collaborate with industryto create a bridge between a broad area of mathematics and industrial applications. Thepurpose is twofold: (i) to develop new mathematics that is relevant for applications and todisseminate these results to industry; and (ii) to educate a new generation of mathematicianswith a profound understanding and experience of applications of mathematics.

The Center will be operated by a consortium of experts in analysis, discrete mathematicsand combinatorics, stochastics, numerics, optimization, systems theory, and computer science– international leaders in their respective fields – from two distinguished departments, tobring to the fore the applied and applicable aspects of modern mathematics, in particular to

• create an optimal interface with Swedish industry for sharing knowledge about uses ofmathematics and for solving problems requiring new mathematics,

• educate a new generation of mathematicians for whom the best scientific training inmodern mathematics is combined with substantial exposure to industrial and real-world problems,

• engage all participants (students, postdocs, faculty, visitors) in research on cutting-edgeapplicable mathematics.

The research program is application-driven and will be carried out in collaboration withindustrial partners. Interesting mathematical problems of importance to industry will beidentified for research and education. Several members of this consortium have on-goingindustrial projects on which we can build. However, the added value provided by the Centeris to allow for a broader perspective in applying mathematics to real-world problems. Indeed,many industrial problems are complex, and an integrated approach incorporating a widerspectrum of competences is needed.

Our vision is that the full potential of the resource provided by mathematics is madeavailable to Swedish industry to enhance its competitiveness. We seek to provide Sweden withwell-educated industrial mathematicians, as future opportunities for industrial developmentemerge and products, processes, and services become more sophisticated and efficient. Thisis crucial for Sweden’s ability to meet the technological challenges of the future and transmittechnological breakthroughs into innovations.

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Enclosure 2: Research Program Center for Industrial and Applied Mathematics

2 Research Program and the Scientific Basis and Fu-

ture Impact of the Center

Mathematical techniques, based both on theoretical analysis and on computer implementa-tions and simulations, are used for many benefits to society; for instance, for the planning oftraffic in a city or on the internet, for analyzing the genome, for predicting and controllingthe spread of infectious diseases in animals and people, for understanding global warming,and for developing the mathematical algorithms that underlie various imaging modalities— including the biomedical imaging devices that are rendering exploratory surgery a thingof the past. All these applications, and many more, are based on mathematical modelsand techniques. These models and techniques are often highly complex and require deepmathematical understanding to apply reliably. Furthermore, for the development of and forimprovements to such technology new mathematics must be developed.

2.1 Background

The members of the consortium behind this proposal can together report a considerablenumber of prior industrial projects. The Center for Industrial and Applied Mathematics(CIAM) will build on our extensive networks, both with industrial partners and with Euro-pean research consortia, and on our experience with PSCI (Parallel and Scientific ComputingInstitute), a Competence Center sponsored by Vinnova.

PSCI, which is hosted by the Computer Science Department and is directed by one of theco-applicant of this proposal (Bjorn Engquist), was started in 1995 and is now in its tenthand last year. The study and applications of mathematical models have been an integral partof all projects at PSCI. Typical examples are Maxwell’s equations for antenna design andstealth technology (Ericsson, Saab, Allgon), Navier-Stokes equations for aerodynamics andcombustion (Volvo Aero, Saab, ABB Flakt, Bofors), differential-algebraic equations for cellsimulation (Biovitrum), molecular dynamical systems and diffusion equations for materialscience (Hoganas, Sandvik) and shallow water equations for modeling flow in the Baltic(SMHI). This research has resulted in innovations that have already been implemented inproduction and also produced Masters and Doctoral graduates who now are employed inSwedish industry.

In the Mathematics Department, the Division of Optimization and Systems Theory hasan extensive network of industrial partners such as ABB, Ericsson, Volvo, Bombardier, AssiDoman, Frovi, and RaySearch Laboratories AB. The group participates in European con-sortia such as ERNSI, RECSYS, HYCON and ERCIM and is also involved in the Europeannetwork of excellence Euro NGI concerning the next generation of the Internet. Several in-dustrial graduate projects have been successfully completed in cooperation with industrialpartners. Former PhD students are now strategically positioned in industry, and they area link to a much wider set of problems of interest to the Center. The research has led toseveral patents.

In the Division of Mathematics there has been a fruitful collaboration with Yale Uni-versity (R. R. Coifman) concerning applications of wavelets to image data compression,especially seismic data, that has led to extensive industrial collaboration. One of the origi-nators of the wavelets technology, Jan-Olov Stromberg, is a member of our consortium. Hehas one patent approved (in the United States, in the area of seismic data compression) andone pending patent (in Sweden, in the area of video compression). An industrial partner in

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Sweden is Sidec, which is a spin-off company from the Karolinska Institutet.Dynamical Systems, an area of strength in the Mathematics Department, has possible

applications to control engineering, weather forecast and molecular dynamics. Another areaof strength is harmonic analysis — in particular its computational aspects. There is ongoingcollaboration with Ericsson and Coding Technologies. Also, research of industrial potentialis carried out in image processing and medical signal processing using wavelet tools, togetherwith different groups at the Karolinska Institutet.

Consequently, the members of the consortium can together report a considerable numberof prior industrial projects. What is new in this proposal is a concerted effort to broaden theperspective through collaboration and to involve a fuller spectrum of mathematical tools.

The members of the consortium are of very high international standing. Among theco-applicants of this proposal there are three members of the Royal Swedish Academy ofSciences (KVA) and two members of the Royal Swedish Academy of Engineering Sciences(IVA). Members of the consortium are often invited plenary speakers at important congresses,e.g. there are six invitations to address the International Congress of Mathematicians, andnumerous prizes have been awarded to them.

2.2 Main goals

The core activities of the Center will be research projects oriented toward problems of indus-trial relevance. The research focus will include optimization theory, numerical mathematics,dynamical systems, and combinatorics, and will have applications in a wide range of areassuch as telecommunications, information technology, automotive, aerospace, chemical, pulpand paper, metallurgy, power, robotics, medical and pharmaceutical industries, which allrepresent strategically important segments of Swedish industry. In the projects new and ap-plicable mathematics will be developed, students will be trained in industrial and appliedmathematics, and postdocs and visitors will enrich the mathematical community. All of theprojects will be designed to have mathematicians working together with industrial scientistsinterested in the applications of mathematics. Consequently, an important goal is to edu-cate a new generation of mathematicians with a profound understanding and experience ofapplications of mathematics.

Another goal is that CIAM will provide applied mathematics at KTH with an interfacethat will help in establishing industrial contacts that support PhD projects. It will alsoprovide a good infrastructure that will support KTH in EU funded collaboration.

We set up the following milestones for mid-term evaluation during the third year:

• At least one PhD project in each of the key-technology areas of Enclosure 2 will bewell under way. Each project will have a reference group with representatives from theindustrial partner and at least two research groups in CIAM.

• Scientific and industrial networks will have been established for securing sustainablefuture funding of the Center. Initiatives for future EU funded project will have beentaken.

• A forum in which industrial scientists can share their knowledge and expertise with in-terested mathematicians will have been established. A portfolio of identified industrialproblems where mathematics is needed will have been created.

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• All planned postdoctoral fellows will have been hired, and they will have been inte-grated in the projects. A guest researcher program will have been established.

• An international Masters Program in Industrial and Applied Mathematics will havebeen established and is running.

• A joint colloquium series in Industrial and Applied Mathematics will have been runningregularly.

2.3 Mathematical topics

We first list a number of mathematical areas in which the consortium can offer world-leadingexpertise and which are of importance in applications.

Discrete mathematics and combinatorics

Information plays a central role in modern society and this creates surprisingly many interest-ing and challenging problems. Cryptography, traditionally the art of protecting informationfrom the enemy, has expanded to encompass much more. Today we want digital signatures,replacing traditional signatures and possibly adding new functionality not possible before,digital money, digital elections, auctions over the internet, transfer of cryptographic cre-dentials between nontrusting networks, etc. Even defining security and desired functionalityis in many applications a difficult task, but the main problem is of course to design goodprotocols.

Many cryptographic protocols have been designed by engineers and programmers withoutsufficient mathematical foundation, and over time some have been broken while others haveremained resilient to attacks. This is similar to a situation where buildings and bridgesare constructed, some fall down and some do not — a situation that society would findunacceptable and would devote substantial resources to, in order to find a quick remedy.Designing protocols together with mathematical proofs of security avoids such problems,and hence setting cryptography on firm theoretical foundations is of crucial importance.

From a different angle, both storage and transmission of information are subject to er-ror and hence we need error detection and error correction, traditionally done with errorcorrecting codes. Many basic issues here remain unsolved, and such a basic question as theoptimal rate of a code tolerating a given level of error is still not settled.

Other information related areas, where discrete methods are necessary and which con-stitute possible areas of future investigations are numerous. Let us give a few examples.Computational biology is by now a subject in its own right, but it has strong connectionswith combinatorics and complexity theory. The recent success of efficient algorithms designedfor quantum computers and the possibility that such computers will be physically possiblecalls for a rethinking of many classical algorithms. Quantum information theory offers a newmeeting ground between discrete mathematicians and theoretical physicists around questionsthat are of great interest in future applications. Cellular phone systems need sophisticatedalgorithms for several subtasks, ranging from compression to congestion control, to operatesmoothly and efficiently.

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Optimization

Faster computers and improved methods have made the use of optimization increase sig-nificantly for wide areas of industrial and applied problems. This development has madeit possible to solve optimization problems of a size and complexity that were not consid-ered tractable a couple of decades back. We have recently witnessed the formulation ofmore sophisticated and large-scale optimization problems from various research areas suchas stochastic modeling, combinatorics, applied harmonic analysis and systems and control.An example is the inclusion of robustness in the models, to allow for solutions that are lesssensitive to parameter inaccuracy. To take this one step further, one may consider a stochas-tic model (e.g., optimal flow through hydro power plants), leading to problems of larger sizeand complexity.

We have good methodological knowledge, and are also currently running a number ofapplied projects in different areas. Extending optimization to new difficult applications willbe a vital factor in helping Swedish companies face international competition. The use ofoptimization helps improving various parts of a company’s operations. It could for exampleconcern decreasing costs, shortening lead-time, or improving design. Such improvements arevery important for the company to be competitive. Problems arising from many diverseapplications may lead to the same type of optimization problem. There is a big potentialfor successful formulation and solution of important industrial optimization problems bycombining expertise from applications and optimization methodology within the frameworkof the center. As this proposal is written, the 8th SIAM Conference on Optimization is heldin Stockholm with a member of the consortium as co-chair. This is the first SIAM conferenceever held outside of North-America.

Applied harmonic analysis - wavelets

The theory of wavelets has been a continuing success story, not least in view of its many spec-tacular applications. Functions (or data) are broken up in building blocks (or base functions)each with rather good localization both in space and in frequency. A classical case in point,among many, is the very efficient data compression system based on wavelets used by FBI’sregister for finger prints. Often one wants to analyse a signal’s frequency content without los-ing the information about localization as with the Fourier transform. The wavelet is a goodtool for this. We have used this for example for studying vibrations in defect bearings. Thefrequency is often parametrized by a scale parameter and using wavelets one gets a multiscaledecomposition of the data. Multiresolution approximation of surfaces and curves is a majorproblem in applications. Indeed, technology in the form of laser scanners is now availableto sample real-world three-dimensional data with a very high level of detail. For a typicalobject, scanners generate huge amounts of coordinate point data with limited informationabout the connectivity of the individual points. The problem is to reconstruct a surface fromthis data. Wavelets are basic in this construction. The surface should be described in a waythat allows for processing such as compression, denoising, filtering and texturing. New waysof reconstructing and describing three-dimensional objects can lead to significantly improvedcompression algorithms and facilitate other processing.

The wavelet construction is very flexible and there are algorithms that adjust the waveletsto the dataset to obtain a best basis for the purpose for which it is used. In this way a programcan use a training set of data for learning, to find the best basis for increasing the ability ofthe program to discriminate between different classes of signals.

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Systems theory for complex systems

Mathematical systems theory, which is motivated by applications in automatic control, signalprocessing and many other areas where a cybernetic perspective is required, makes wideuse of results from algebra, analysis, operator theory, algebraic and differential geometry,topology, global analysis and optimization. Hence it constitutes in itself a bridge on onehand to core mathematics and on the other hand to applied industrial problems.

A case in point are the global-analysis approaches studied by one of the proposers, wherecontrol systems or spectral estimation filters are studied as a smoothly parametrized manifoldof such objects, satisfying suitable complexity constraints required by the application, andthe parameters are used as “tuning parameters” to satisfy additional design specificationsand performance limitations, and convex optimization is used to compute the solutions,which can be regarded as stationary points. This leads to new solutions in robust control,signal processing, power optimization, etc.

Future applications in aerospace and transportation, information technology, life scienceand technology, materials and processing, and robotics will require understanding of systemsthat are well beyond the level of complexity the current systems theory can handle. On theother hand, as computation, communication and sensing are getting increasingly inexpensive,massive opportunities for applying systems and control principles to new fields have emerged.These developments imply that the traditional systems theory will have to be expanded. Forexample, hybrid systems theory that would profit from stronger interaction with traditionaldiscrete mathematics and combinatorics. Also in order to cope with the increasing complexityin modeling, sensing and control, new mathematical paradigms are needed.

Dynamical systems and stochastic models

Mathematical modeling and simulation based on the theory of dynamical systems have fun-damental strategic value. The traditional numerical methods approximating such systems arewell understood and practically useful, provided the systems are very stable. If the systemsare less stable with large Lyapunov exponents the existing theory does not produce usefulresults. These less stable systems are, however, very important. They include, for example,the prediction of weather and climate change, and the systems of molecular dynamics.

Recent progress in the theory of finite dimensional maps and stochastic differential equa-tions provides the mathematical foundation on which a new and deeper understanding ofthe corresponding numerical methods can be built. These maps have in common that thestatistical time averages are independent of the initial conditions and that the orbits are socalled “strange attractors”. There are rigorous results showing that the probability distribu-tions in certain low-dimensional cases are stable under small random perturbations. Similarresults are expected to hold in more realistic settings such as molecular dynamics simula-tions, and the goal should be to give an explanation for the “unreasonable effectiveness” ofthese simulations. Areas of application are computations in inviscid fluids and astrophysics,and possible collaboration partners in government and industry are SMHI and Sandvik AB.

The importance of stochastic models has increased in the last decades. Random matrixtheory (RMT) is a source of new stochastic models, which arise in various contexts, e.g. inquantum physics, statistical mechanics, and statistical modeling in finance, signal processing,wireless communication and information theory. We have studied certain growth modelswith a deterministic part and an added stochastic noise. The models are closely related todirected polymers and optimal paths in a random environment, and in the scaling limits of

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these models RMT distributions appear. This is surprising since there is no random matrixin the model, which clearly indicates that distributions from RMT are natural limit laws.

Numerical methods for stochastic and partial differential equations

The basic modeling of continuum problems relies on ordinary and partial differential equa-tions. The faster computers make it possible to include fundamental micro-scale models inbetter computational modeling of continuum problems, using multi-scale methods.

For instance, material properties are described by microscopic physical principles, formu-lated as differential equations with very small time and spatial scales. However, computercalculations with such a microscopic model is limited to small domains and short times: asimple water molecule is described by Schodingers equation in a 39 dimensional space, incontrast to the macroscopic continuum elasticity properties for ice which are determined bythe less complex Navier’s equations in three space dimensions. There is a growing activ-ity, in which members at the proposed center participate, to determine, theoretically andcomputationally, more accurate macroscopic approximations of high dimensional microscopicformulations. An example is computations of phase transformations in material science, withthe goal to design new materials of interest to the industry. Such improved computationalmodels often use a combination of mathematical methods in stochastics and numerical anal-ysis. The mathematical theory of numerical methods for ordinary and partial differentialequations is highly developed, and many aspects of stochastic theory is also on good founda-tion. The combination of numerical methods and stochastic problems, however, is still in itsinfancy: fundamental practical and theoretical problems are open and have not been muchstudied. Many important problems of relevance to Swedish industry require competence indifferential equations and dynamical systems, numerical methods, and stochastic analysis.This will be amply provided by the proposed center.

2.4 Applications to key technologies

To identify our focus of research and to enhance collaboration between groups, a wide rangeof problems are proposed for which the combined expertise of the groups within CIAM canbe utilized to maximize synergy within the Center. Other project areas will be identifiedvia the dialogue with industry. The idea is to use competence from more than one researchgroup in each project. These problems may seem quite disjoint, but in mathematics com-mon structures are identified and brought out. In different combinations, analysis, discretemathematics and combinatorics, stochastics, systems theory, and computer science will pro-vide the conceptual frameworks, while numerical analysis and optimization will provide thealgorithms and quantative solutions.

Mathematics and information

Information, the fabric of modern society, gives rise to a multitude of mathematical problems,of both intrinsic mathematical interest and practical importance. An important long termstrategic contribution of the center will be to increase the number of people that can handlesuch problems in a competent manner. Either by solving the problem on their own, findingthe right person to talk to or simply by identifying it as a problem of real mathematicalcontent.

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An example of an application where several mathematical areas meet is Radio ResourceManagement (RRM) for cellular telephone carriers. By now a classical problem is allocationof frequencies for GSM telephone networks. New and future technologies will lead to inter-esting and challenging problems in discrete mathematics, combinatorics and optimization(integer programming). Cryptography has been mentioned above. The internet also providesmany challenging problems. Routing control in computer and inter-computer communicationlanes is similar to road traffic control.

Another example is broadcast encryption. In some applications the same digital infor-mation is sent from one source to multiple destinations. We might also want to restrict theset of receivers. A typical example of this situation would be a pay-per-use news servicedistributed over the internet or over a mobile phone system. The natural approach is toencrypt the information with a secret key known to all (legitimate) users. In most situationswe would expect the set of users to change dynamically, as new subscribers would arrivewhile present users might decide to discontinue their subscription. To prevent the latter typeof users from continuing to take advantage of the service without paying, the secret key usedfor encryption has to be changed periodically. How to distribute this new key only to the setof legitimate users in a secure and efficient way is a problem of great practical importancethat leads to interesting problems in cryptography and combinatorics. Note that we want todistribute the new key over the public medium, since sending it privately to each user woulduse up too much bandwidth in many applications. This problem has been partly studiedalready in collaboration with Ericsson. More efficient solutions would, however, be neededin many applications and it is a wide open question whether such schemes do exist.

Mathematics in high-resolution spectral estimation and image processing

The expertise in computational harmonic analysis represented by our research consortiumis of vital importance in addressing problems in, among other things, image processing andimage and video compression. Indeed, there is a patent pending in this area and a prototypehas been produced. Wavelet methods have shown to be very successful in image compressionand the compression standard JPEG2000 is based on such methods. In video there usually isa large correlation between the sequence of images. We have developed a method using thiscorrelation to obtain a very effective compression scheme for video sequences. In particular,this method would be suitable for video with relative little amount of movement, such asvideos from surveillance cameras and video conferencing.

Efficient nonlinear spectral estimation and image processing methods based on analyticinterpolation and filter banks have recently been developed by one of the groups in the consor-tium, and these can be applied to high-resolution spectral estimation and speech processing.According to Sony Ericsson Mobile Communications, a biometric for access control will be-come very important in future mobile terminals, as mobile phones (terminals) are shrinkingin size. Also, generating robust voice recognition/verification reference models with accuratepole-zero modeling of speech could improve the success rate of speech activated systems. Themore general approach taken in our approach would generate more sophisticated methodsfor tackling these questions.

Imaging and information in biology and and medicine

Medical data processing is an application area which interests the research consortium. Inparticular, recent results have been obtained in applications to tomography (attenuated

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Radon transforms). The corresponding numerics is presently being developed in collaborationwith Sidec, a company developing software for medical applications. Medical signals fromEEG measurements and the time frequency contents have been studies by wavelet tools incollaboration with a group at Karolinska Institutet. Methods have been developed (involvingwavelets and statistical tools) to discriminate between EEG signal from different classes ofpatients (e.g., diabetes/not diabetes).

The area of bioinformatics poses many fundamental mathematical problems, bound toenrich both mathematics itself and the biological applications. What is the principle behindthe codes discovered by gene sequenceing? How does one reconstruct evolutionary trees fromgenetic data? What are the mathematical models of interactions between protonomics andgenomics?

The use of optimization within medical applications is another area which has emergedrapidly over the last years. Medical equipment is today often highly sophisticated and theuse of mathematical models and optimization may enhance its performance significantly.An example is radiation therapy, where the objective is to cure cancer by radiation. Wehave presently a joint project with RaySearch Laboratories AB in this area. The radiationis given by a particle beam, which may be modulated so as to differentiate the intensity inthe body. The objective is to create a beam intensity which maximizes the damage to tumorcells and minimizes the damage to healthy tissue. It is a very time-consuming task to do thismanually, and it is also hard to take full advantage of the ability to modulate the beam, evenfor experts. An alternative is to pose the intensity modulation problem as an optimizationproblem. Thus, this problem typically becomes a large-scale optimization problem.

Spectral and inverse problems in engineering

Spectral properties of partial differential equations are of importance in many practicalapplications and concrete engineering problems.

The gaps in the continuous spectrum of Schrodinger operators describe prohibited en-ergies, and these gaps are used by specialists in solid state physics. Indeed physicists areinterested in new materials with prescribed gaps in the continuous spectrum at required en-ergies in order to construct semi-conductors. Usually this is achieved by using crystals whichhave a periodic structure. Crystals with an eigenstate inside a gap are used for producinglasers. The corresponding problems for Maxwell’s equations lead to a new very exciting areaof research concerning construction of photonic crystals, which definitely will be one of themain developments of future microelectronics. Acreo FiberLab is interested in this line ofresearch and wants to collaborate with us.

It has recently been discovered that there exist fairly effective solution methods for 1Dinverse problem for Schrodinger operators with a damping term. Solution of such a problemleads to new applications, such as the creation of new sound insulation materials. It alsocould be useful in creating materials providing an effective vibration isolation within theaudible frequency range.

Mathematics for industrial system design and control

An example of a problem that is not solved in its fundamentals is traction control for wheeledoff-road vehicles. How should the drive line components be designed in an optimal way? Howshould sensors be chosen and located? What should a model for design optimization looklike? How detailed should such a model be?

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Similar questions arise for the problem of designing the feedback control. To choose amodel of appropriate form and complexity is in general a task that demands considerablemathematical skill, and often also knowledge in signal processing. A common practice insimplifying dynamic models is to neglect some parameters which increase the order of themodel. It is an open fundamental issue of utmost theoretical importance how the complexityreduction should be done.

Our industrial partners include AssiDoman Cartonboard AB; Frovi, whose interest isin the modeling of the multi-ply paper manufacturing process for the purpose of simula-tion, optimization, and control and Volvo Construction Equipment AB, whose interest isthe modeling of the drive line of vehicles for the purpose of energy and pollution efficientcontrol. Moreover, ABB Robotics needs high-order non-linear kinematic and dynamic mod-els for control, supervision and design optimization. They need more efficient analytical andnumerical methods for real time execution of accurate models covering both the robots andtheir surroundings.

Stochastic models for specification-based software testing

It is of great economic benefit to automate the software testing process, and this is possiblewhen software requirements are formalised (for example by using logic). The problem thenarises how to design practical and efficient algorithms for testing. To solve this problem, twofundamental issues must be addressed: (i) coverage, test termination and reliability models,and (ii) efficient test case generation (TCG).

Under (i) we have developed a new model of probabilistic correctness that corrects manytechnical defects currently found in models of software reliability in the literature. Under(ii) we follow an approach to TCG taken in the literature known as the computationallearning paradigm. Our approach is deterministic, and has a mathematical foundation inapproximation theory. A substantial issue here for industrial application of the method isthe problem to generalise approximation methods from basic data types such as integer andfloat to structured (typically high-dimensional) data types (e.g. records, files, recursive datastructures) in a rigorous but effective way. We have had 10 Masters projects in softwaretesting with various companies including Ericsson, Motorola, OM Group and BEA Logic.This forms the basis for further collaboration.

Optimization of large scale and heterogeneous systems

The rapid development in communication and computing, and the emergence of new tech-nologies, inspire engineers to build increasingly complex systems consisting of a plethoraof different physical devices and data processing units. We see this manifested e.g. in theembedded control systems found in cars and airplanes, in the complex structure of mod-ern power distribution networks, in communication networks such as the Internet, and inmany other areas. The design and coordination of such systems generally involves massivecomputation with discrete as well as continuous variables, decentralized decision making,and proper coding and encryption of communication channels. As the performance of thesesystems is pushed it will be increasingly important to optimize the design. This will re-quire the combined expertise from areas such as optimization and systems theory, numericalmathematics, combinatorics and graph theory.

Practical optimization is a very complex process. First, the real problem has to be mod-eled mathematically, and then the optimization problem has to be solved. The resulting

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optimization problems are for many applications too large to be tractable for the currentlyavailable software. This can be overcome by using model reduction techniques to simplifythe model and/or by exploiting structure in individual problem classes to obtain efficientalgorithms. A characteristic for many applications is that efficient solvers only can be ob-tained by combining results from mathematical systems theory and numerical linear algebrawith optimization theory. The additional complexity that arises in problems where decisionmaking is decentralized, or where logical variables are mixed with continuous variables, cansometimes be handled by combining methods from combinatorics, graph theory and opti-mization. The composition of CIAM is in this sense ideal, since we possess complementarycompetence in these fields.

Shape optimization

An interesting and difficult application area, encountered by Saab Aerosystems in Linkoping,is shape optimization of aeronautical structures with respect to three disciplines, namely (i)structural analysis (stiffness and strength), (ii) fluid dynamics (air resistance and flow con-trol), and (iii) electro-magnetism (radar target signature). Optimization within each singleone of these disciplines is a difficult task in itself. When all three disciplines must be consid-ered simultaneously, it becomes a longterm challenge for a multidisciplinary research group.This problem area will be studied in collaboration with the KTH Computational Scienceand Engineering Center (KCSE).

2.5 Significance

The scientific project areas outlined above all lead to both fundamental progress withinmathematics and to new applications of mathematics to industrial problems. The researchof the Center will become recognized by the international mathematical community andwill also be of strategic importance to Swedish industry and to society in general. The fullpotential of the resource provided by mathematics is made available to Swedish industry toenhance its competitiveness. We will produce a new generation of industrial mathematicianswith a solid mathematical background coupled with knowledge, experience and interest inapplications. Indeed, the best young minds will receive a training which better emphasizesapplied problems and better prepares for future work in industry itself or for collaborativeprojects with industry. They will leave KTH for successful work outside academia. In fact,quite a few KTH mathematicians, both with a pure and applied background, have gone toindustry over the past years. We expect the demand for such graduates to increase.

2.6 Added value

The groups behind this proposals are individually very strong within their disciplines. To-gether they encompass a broad spectrum of competence, ranging from many branches of puremathematics to several applied disciplines. This program gives a unique opportunity to createa unified research program devoted to industrial and applied mathematics. It provides an ex-cellent framework for broadening our research focus, by launching interdisciplinary projectswhere we take full advantage of our joint competence. Something with this potential impactcould not be created by giving grants individually to the participating groups.

In the management plan (Enclosure 4) a program is described that ensures solid inter-disciplinary cooperation and industrial relevance.

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Enclosure 3: Strategic Relevance Center for Industrial and Applied Mathematics

3 The Strategic Relevance of the Center

The purpose of CIAM is to bring out the industrial potential inherent in mathematics.It is motivated by the fact that competitive product development is increasingly based onmathematical technology. This “mathematization” of technology is becoming more and moreimportant in a competitive world.

How CIAM will contribute to the future competitiveness of Sweden

Our vision is that the full potential of the resource provided by mathematics is made avail-able to Swedish industry. In this respect, an important contribution is the training of a cadreof versatile mathematicians, well-trained both in relevant branches of modern mathematicsand in its applications to industrial and real-world problems. These young people can be ex-pected to assume crucial roles in developing and securing Swedish economic capacity in thecoming decades. Another strategically important contribution is the creation of a new, effi-cient, and highly visible channel of contact and transfer of know-how between the academicmathematicians and the industrial and applied communities.

Competitiveness of Swedish industry requires a knowledge-based economy. Over the lastdecades, many of the available engineering techniques have become mathematically moresophisticated, due to the possibility of implementing more complicated algorithms with thehelp of computers. It is undoubtedly the case today that many engineers after graduationdo not have a sufficiently deep understanding of the algorithms and mathematics behindthe sophisticated computer based tools (s)he has learned and therefore is not in general ableto put them to truly innovative use. Following a trend that has been noticeable for sometime in the USA, some hi-tech companies now are eager to hire mathematicians, realizingthat mathematicians have great analytical ability and flexibility. However, for this strategyto be successful one needs well-educated mathematicians with both ability and interest inunderstanding industrial problems.

CIAM’s strategic relevance for Swedish industry

CIAM will serve as a resource for Swedish companies encountering difficult problems withsome mathematical content. A serious problem one encounters in any interaction betweenindustry and academia is that the two communities work with different time scales. Industryoften requires a result that can be quickly implemented in order to be interested in co-financing, especially in the present economic climate. Academia, on the other hand, wants togain scientific insight, needs to produce publications, and works on a much longer time scale.This conflict of interest often leads to reduced interest in further dialogue. To compoundthis problem, the two communities use different language, and to overcome this a concertedeffort is required. The purpose of CIAM is to bridge this gap.

The following success story can serve as a single example and illustrate how the Centercan contribute to a long-term perspective on research and development. At the end of the1990s, ABB had problems with their electric drives. Due to backlash in the gears, chaoticdynamics occurred, leading to wear and breakdown, and thus interruptions in production.Mathematicians are well familiar with the mechanisms behind this problem. In collaborationwith one of the groups behind this proposal, it was decided that a graduate student was tostudy the problem. ABB wanted a quick fix, but, since their part of the financing was only25%, they had to yield to our point of view: the work would have to take its time and result

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Enclosure 3: Strategic Relevance Center for Industrial and Applied Mathematics

in a PhD thesis. The implementation of the final results is now a regulator, with which eachrolling mill delivered by ABB is equipped. The new PhD was hired by ABB and developedABBs new concept of advanced solution for drives in the process industry. A goal of thecenter would be to replicate and expand on this type of collaboration.

CIAM’s strategic relevance for Swedish research capacity

In many cases there is no conflict between industrial relevance and research depth. Ourexperience is that the coupling between theory and application is usually beneficial for bothaspects. The theoretical knowledge gives insight into how to formulate and solve the problem,and the application gives new research challenges with respect to problems to consider, andhow they should be addressed.

In the proposed Center the collaboration between industry and applied mathematics willbe extended to include more of core mathematics. This will increase the talent pool exposedto industrial mathematics and couple applications closer to the mathematical education. Itwill also shorten the time between mathematical discoveries and their practical use.

Utilization of research results

Since the core activities of the Center will be research projects in cooperation with industrialpartners, the research results will primarily be utilized in the respective company. However,since mathematical structures are more general, secondary utilization toward other appli-cations are to be expected. The purpose of CIAM is also to educate a new generation ofmathematicians with a profound understanding and experience of applications of mathe-matics. Given a cadre of young well-educated industrial mathematicians, it is likely thatspin-off companies will emerge. Indeed, the partners in the consortium behind this proposalhave many patents between them, and several of our former PhDs, as well as some formerfaculty members, work in small high-tech companies like RaySearch Laboratories, CodingTechnologies, Optimization Partner, ComSol, etc.

Available support

We will build on and develop our extensive network with both industrial partners and Euro-pean research consortia, and on our experience and contacts from Competence Centers suchas the Parallel and Scientific Computing Institute (PSCI) sponsored by Vinnova. Some ofour present industrial contacts are described in Enclosure 2 (under Section 2.1). New con-tacts will be actively pursued as the Center gets established. The PSCI Competence Centeris directed by one of the co-applicant of this proposal (Bjorn Engquist) and is now in itstenth and last year. The enthusiasm from industry in terms of collaborative research anddevelopment, and financial support has been overwhelming. As a result PSCI was supportedfinancially by Vinnova to a larger extent than any other Competence Center.

We will build CIAM on the experience of PSCI, the scope of which will be expanded toencompass a much wider spectrum of mathematics. We also intend to establish strong linksto other centra at KTH and to many groups in the newly established School of EngineeringSciences. A case in point is KTH Computational Science and Engineering Center (KCSE),which can supply additional competence in some of the project areas listed in Enclosure 2.

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Enclosure 4: Organization Center for Industrial and Applied Mathematics

4 Organization and Management of the Center

4.1 Research groups

The Center for Industrial and Applied Mathematics (CIAM) will directly involve approxi-mately 20 professors from two departments at KTH, the Department of Mathematics and theDepartment of Numerical Analysis and Computer Science, as well as from the KTH Compu-tational Science and Engineering Center (KCSE). Others will participate on a project basis,as needed. More specifically, the core of CIAM will consist of following groups (group leadersin parenthesis)

• Analysis (Michael Benedicks)

• Discrete mathematics and combinatorics (Anders Bjorner)

• Numerical analysis (Bjorn Engquist)

• Optimization and Systems Theory (Anders Lindquist)

• Theoretical Computer Science (Johan Hastad)

Consequently, CIAM will consist of well-established experts in a wide area of applicable andapplied mathematics, each with a wide international network of collaborators. In Enclosure2 (Section 2.4) a wide range of problems are proposed for which the combined expertiseof the groups within CIAM can be utilized to maximize synergy within the Center. Theseproblem areas have been designed to require participation from more than one group, andthis will be reflected in the reference groups for each project. Other projects of this type willbe identified as we go along.

Fully developed, the CIAM will consist of some 40 scientists (many on a part-time basis)including PhD students and postdoctoral fellows. The Center will be housed on the centralKTH campus around ”Borggarden”, where presently the two departments are located.

4.2 Management structure

The management structure will reflect the fact that the purpose of CIAM is to create realsynergy over the breadth of expertise of the participants, thereby creating a significant addedvalue compared to giving grants individually to the participating researchers.

Chief officers of the Center

Director: Professor Anders LindquistDeputy Director: Professor Johan HastadDirector of Studies: Professor Anders ForsgrenIndustrial Coordinator: to be hired (50 % position)

The director of the Center will be Anders Lindquist, Professor of Optimization andSystems Theory and presently Head of the Department of Mathematics. He will step downfrom being head of the department, when and if the Center is approved, to concentratehis efforts on CIAM. Anders Lindquist has had long and extensive experience in leadingresearch organizations and consortia and has substantial international experience, see his CV

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in Enclosure 7. He has been involved in a large number of industrial and applied projects.He holds himself three patents and has been the advisor of several students with patents.

It is very important that the need for collaboration between the two participating de-partments, between applied and core mathematics, and with industrial partners, is clearlyreflected in the management structure. The deputy director, Johan Hastad, will be takenfrom the other participating department, the Department of Numerical Analysis and Com-puter Science. Also he has long experience of leadership. He is presently the director ofresearch and graduate education in the School of Computer Science. He is also the youngestamong the co-applicants, ensuring continuity of management in the long perspective.

The consortium behind this proposal consists of both pure and applied mathematicians.Anders Bjorner will be the new (part-time) director of the Mittag-Leffler Institute, a verywell known international institute for mathematics at Djursholm (ten minutes by car fromKTH), which attracts leading mathematicians from all over the world to its programs. Theseprograms are mostly in pure mathematics, but recently several applied program have beenarranged. Regardless of whether the ongoing program is pure or applied, the Mittag-LefflerInstitute will be be an important resource for CIAM through the link of Professor Bjorner.Indeed, an underlying idea of CIAM is the fact that the required mathematics needed inindustrial problems often comes from pure mathematics and that CIAM is needed as aninterface to communicate this knowledge.

Professor Anders Forsgren, who has extensive previous experience with leading programs,will be the Director of Studies (studierektor). He will be working with the regular KTHorganization to coordinate industrial and interdisciplinary contents in courses, and he willlead the CIAM international masters program.

To assist the director in initiating and maintaining contacts with industry, an IndustrialCoordinator will be hired on a part-time basis ( 50 %). The PSCI competence center hadsuch a person, who performed this task very skillfully, and he is a possible candidate for thisposition.

Boards and Committees

CIAM will have a Board (styrelse), chaired by an industrial representative, with equalrepresentation from industry and academia. The board will review the progress of the Centerand will approve the budget.

There will be an Executive Committee (ledningsgrupp) of researchers, that meets ona regular basis for strategic decision-making and to monitor progress. Each meeting willinclude regular presentations of projects, and each project will have a reference group witha member from at least two of the research groups. In addition, there will be regularlyscheduled half-day conferences, where new results are presented. There will also be regularpresentations to industrial partners.

CIAM will also have an International Advisory Board that will meet on a yearly orbiannual basis. A number of leading members of the scientific community have already agreedto serve on this board: Professor Martin Grotschel, Director of the DFG Research CenterMatheon ”Mathematics for Key Technologies”, Berlin; Professor Margaret Wright, CourantInstitute, NYU, former President of the Society for Industrial and Applied Mathematics(SIAM); Professor Rolf Jeltsch, ETH, Zurich, former President of the European Mathemat-ical Society; and Professor C. I. Byrnes, Dean of Engineering at Washington University St.Louis, who has an extensive experience with start-up companies based on new innovations.

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4.3 Activities organized by the Center

Postdoctoral program

The postdoctoral program will be an important part of CIAM and its projects. The post-doctoral fellows, who will take an integral part in the projects, will be recruited on a verycompetitive international basis. This will facilitate attracting a larger percentage of women,who are traditionally severely underrepresented in Swedish mathematics. Some collaborationwith the Mittag-Leffler Institute concerning postdocs is planned.

Industrial Math Clinic

The Center will organize an annual Industrial Math Clinic, bringing together engineers fromindustry with students at the Center and their academic mentors. The industry representa-tives will be invited to suggest problems and participate in the solution process. The mentorswill screen the pool of problems and also guide the students in their work. The work typ-ically results in a report or a computer program. This type of clinic has been successfullyconducted at some other international centers and universities.

Colloquium and Workshop Series

Together with the Department of Mathematics at Stockholm University and Institut Mittag-Leffler, the CIAM will launch a series of monthly colloquia in mathematics and its appli-cations, intended for a broad audience. The very best international lecturers will give pre-sentations describing progress in mathematics and, in particular, its applications. This willbecome an important part of the dissemination and outreach program, and a special effortwill be made to use this forum for attracting women to mathematics.

The Center will invite prominent lecturers to give short one-week courses on topics inapplied mathematics. A yearly workshop, organized by the students, will consist of studentpresentations, invited talks and panel discussions.

Ph.D. Program in Industrial and Applied Mathematics

Graduate students will have both an academic and an industrial advisor to ensure bothacademic standards and industrial relevance.

International Masters Program in Industrial and Applied Mathematics

As a spin-off of the interdisciplinary efforts of the research program at the Center, a mastersprogram in industrial and applied mathematics will be launched. This program will be usedeither by mathematics majors wanting more knowledge in how to apply their knowledge, orby students in more applied fields searching to strengthen their mathematical background.

Fostering networks

A central idea of the center is to foster networks between academia and industry. The Centerwill provide a forum where industrial scientists can share their knowledge and expertisewith interested mathematicians. On the other hand, it will provide expertise in a broadspectrum of mathematics that can be shared by industry. The ultimate goal is to see advancedmathematics being used to enhance the competitive edge of modern Swedish industry.

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Enclosure 5: Statement from KTH Center for Industrial and Applied Mathematics

5 Statement from the University

Engineering and mathematics have always been closely linked. The ability to make calcula-tions is a prerequisite for success in engineering. Thus mathematics is the most basic andgeneric of all sciences at a technical university. Mathematics forms the knowledge base ofall students, independently of discipline. It is thus important to closely link higher levelresearch in core mathematics, applied mathematics and engineering education in mathe-matics together. KTH has a successful Mathematics Department with leading internationalmathematicians and also a flow of mathematically talented students through undergradu-ate, graduate and PhD programmes. It is interesting to note that, in the trend towards newengineering courses aimed at new industrial fields such as biotechnology, media technology,financial analysis, design and architecture, mathematics is maintaining and increasing itsrole as the glue binding the different engineering programmes together.

Mathematics at KTH has succeeded in achieving impressive synergy between teaching alarge number of students in the first and second years and becoming a leading, internationalresearch institution. Among Swedish university maths departments, KTHs ranks highest.Much of the applied mathematics within a technical university is done within departmentscloser to the actual technical subject areas. By tradition, KTH has strong applied math-ematics within fluid mechanics, numerical analysis, bio-informatics, computer science andcontrol theory, to mention just a few. This makes the proposed centre an important hubfor true, cross-disciplinary activities with overlapping subject areas and the development ofbasic mathematics.

In 2005, KTH will be organised into nine Schools in order to create a more clearly struc-tured and flexible university for both in-house operations and external cooperation partners.While the organisation into schools will create the critical mass necessary for successful re-search within a given field of science or engineering, the formation of interdisciplinary meta-centres between schools will be essential in order to provide platforms for interdisciplinaryresearch at KTH.

By forming a Centre for Industrial and Applied Mathematics (CIAM), in which re-searchers from both core mathematics and applied mathematics collaborate with industry,it will be possible to create a bridge between a broad area of mathematics and industrialapplications. The research topics proposed by the centre are also perfectly aligned with theprofile areas of the KTH Development Plan of October 2003:http://www.kth.se/styrdokument/utvecklingsplan/2004/developingplan04.pdf .

The centre will be operated by a consortium of experts in analysis, discrete mathematicsand combinatorics, stochastics, numerics, optimization, systems theory, and computer sci-ence international leaders in their respective fields from two distinguished departments, tobring to the fore the applied and application aspects of modern mathematics. The researchprogramme is application-driven and will be carried out in collaboration with industrialpartners. Several members of this consortium are currently involved in on-going industrialprojects which can be used as a foundation to build on.

A centre of the size and scope proposed will offer excellent opportunities and openingsfor PhD studies, with a pool of capable supervisors. The range of research areas involvingmany active researchers ensures an attractive environment for students. Its size also makes itpossible for students to work in groups. The planned Master program will form an importantbridge between the existing civ. ing. programmes and the doctorate programmes. The centrewill thus broaden the scope of advanced mathematics courses at KTH.

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Enclosure 5: Statement from KTH Center for Industrial and Applied Mathematics

The proposed collaborative scheme has a very high probability of success. New areas ofapplied mathematics can be clearly identified that will contribute to scientific developmentwithin very different subject areas such as system biology, climate research, computationalmathematics and financial mathematics, but perhaps even more importantly it is clear thatnew such areas will emerge in the environment created by the centre. Through interactionwith other departments at KTH, the center is expected to provide considerable added valueto KTH.

KTH is prepared to allocate resources for a continued support of activities after a five-yearperiod. The support will not exceed 50 percent of the SSF Centre of Excellence funding.

The management of the centre will be very strong. It will, due to the character of thecentre, be more dispersed than the other KTH centres; consequently a strong in-house andexternal executive committee will be necessary. Prof. Lindquist, who is an internationallyleading scientist within his field, will lead this centre. In the field of optimization and controltheory, Prof. Lindquist is a frequent plenary speaker at major conferences. His professionalbackground at the Department of Mathematics with very strong ties to applied mathematicsat other KTH departments makes him very suitable to lead a centre where mathematics andapplied mathematics are intended to work together in a constructive manner. Over the yearshe has also demontrated considerable managerial skills, as head of department and leader ofseveral research programmes.

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Enclosure 6: Budget Plan Center for Industrial and Applied Mathematics

6 Budget Plan

2006 2007 2008 2009 2010 Total

Salaries

10 PhD students (80 %) 3072 3072 3600 3600 3600 169443 postdoctoral fellows 1728 1728 1934 1934 1934 9258Director (35%) 403 415 428 441 454 2141Industrial Coordinator (50%) 360 360 360 360 360 1800Secretary (50%) 220 227 233 240 248 1168Senior researchers, advisors and visitors 1000 1000 800 800 800 4400Total salaries 6783 6802 7355 7375 7396 35711

Running costs

Dissemination (math clinic, workshops, etc.) 500 500 350 300 300 1950Equipment, etc. 300 100 80 80 80 640Board 120 120 120 120 120 600Travel 300 300 300 300 300 1500Local costs (including office space) 1017 1020 1103 1106 1109 5347Total running costs 2237 2040 1953 1906 1909 10047

Overhead

HSG 1642 1609 1694 1689 1693 8328Moms 927 908 956 953 956 4700Total 2568 2518 2650 2643 2649 13028

TOTAL 11589 11360 11959 11924 11954 58786

Comments

1. Graduate students will work up to 20% as teaching assistants in the CIAM mastersprogram, and this part will be funded by KTH. This experience will be an integralpart of the training of the PhDs.

2. We expect to be able to hire several more PhD students as “industridoktorander” asindustrial projects are set up in collaboration with industry.

3. Concerning Director and Industrial Coordinator, see Enclosure 4.

Funding after the SSF-funded period

We expect to attract some EU funding as more established collaboration with industry isrealized. We also expect to obtain increased co-financing of doctoral students (industridok-torander) as CIAM is established on a firmer basis during the first five years. Together withthe continued support of up to 50% of the SSF Center of Excellence funding pledged byKTH (see Enclosure 5), we expect to be able to continue on approximately the same levelas before.

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