This is the last letter I shall write as ECMI President.In January, Professor Helge Holden from the Norwe-gian University of Science and Technology, Trondheimwill take over this position for two years. Helge Holdenhas been a member of ECMI Council since 1996 and isinvolved in a number of other activities on a Europeanscale. He is currently Secretary of the European Mathe-matical Society and so perhaps we can look forward tomore coordination of pure and applied mathematics inEurope under his leadership?

The big event of this summer was the ICIAM 2003meeting in Sydney. A surprisingly large number of Eu-ropean mathematicians managed to make their way toAustralia and ECMI and our sort of mathematics waswell represented. Particularly interesting for me was theIndustry Day which was attended by a significant num-ber of Australia’s leading industrialists who both lis-tened to what academic mathematicians had to offer andtold us what they needed from us. Mathematicians ev-erywhere are finding stimulating problems in ever moreareas of application and there were sessions at ICIAMdevoted to subjects as diverse as sport, blood flow, reeffish, automotive brakes, cash management and maritimewarfare.

I hope that all ECMI members will participate in thenext ECMI Conference which will take place in Eind-hoven from June 21-25, 2004. The call for minisym-posia and papers is out and the closing date for submis-sions is January 30th and February 25th respectively.We are particularly keen to encourage talks and min-isymposia with a real industrial theme and also to getas many industrial scientists as possible to attend themeeting. There are more details later in this Newsletteror they can found on www.ecmi2004.tue.nl/.

In the last Newsletter I mentioned applications to theEU 6th Framework. I can already report one success;the Smith Institute submitted an application for a Spe-cial Support Action to the initiative on New and Emerg-ing Science and Technology (NEST) and has receivedfunding to organize four meetings on new areas forthe application of mathematics. The experience gainedin MACSInet helped to formulate this proposal and toidentify the possibility of mathematics being of use inthese new areas. The themes of the meetings will be:

the business environment, criminality in the social envi-ronment, visualization and simulation, complexity at themolecular level. More details about this initiative are in-cluded later on in this Newsletter and anyone interestedin taking part should contact the appropriate organiser.Although this is a small project by European standardsit is to be hoped that it will open some eyes in Brusselsto the uses of mathematics and that more exciting thingswill follow.

This Newsletter heralds a new scheme in which weinvite a ’guest editor’ to provide a section on a partic-ular theme. Our first guest editor is Professor OtmarScherzer from the University of Innsbruck and you canalready see that this idea enhances the scientific contentof the Newsletter. Please remember that we welcomecontributions so if you have a short article that you thinkwould be of interest to other ECMI members do send itin.

Finally I will sign off by wishing ECMI and all itsmembers great success in the years to come.

Hilary OckendonOxford

ockendon@maths.ox.ac.uk

3

This section has been compiled by professor OtmarScherzer as the first guest editor invited by ECMI Coun-cil.

Imaging

Otmar ScherzerDepartment of Computer Science

University InnsbruckA-6020 Innsbruck

Austria

Imagingis a rapidly growing area in applied sciences.It has an interdisciplinary character and has a wide areaof applications such as medicine, non–destructive eval-uation, astronomy, as well as many other industrial pro-cesses. The vividness of imaging is document by manyinternational conferences and workshops. To mentionjust a few events happening in the near future: The In-stitute for Pure and Applied Mathematics (IPAM) in LosAngeles is hosting a special semester on “Inverse Prob-lems: Computational Methods and Emerging Applica-tions”, which is organized by Heinz Engl (Linz), theformer ECMI President. The special semester includesseveral workshops, one of the focuses on imaging. Forfurther details see

www.ipam.ucla.edu/programs/invws1

Moreover, there is announced a SIAM Conference onImaging Science in Utah in May 2004. See

http://www.siam.org/meetings/is04/

Finally I would like to mention that just recently SIAMfounded an activity group.

The increasing demand on imaging is due to the changeof role of vision. Today vision is not by eyes only butextended for instance by ultrasound and x-ray tomogra-phy, impedance tomography (EIT), to name but a few.Areas of applications are of course medicine, non de-structive evaluation, industrial process tomography, as-tronomy, to name but a few. The resulting images ormovies can enhance understanding.

The relevance of the area of imaging for industry isbest documented by the title of a recent feature articlein Physics World by Robert West [1]

“In industry, seeing is believing”.

Mathematical modeling and reconstruction algo-rithms are key technologies in imaging. Advancedmathematical technology for imaging utilizes inverseproblems theory, image processing, visualization, com-puter vision and results from cognitive vision, statisticsand pattern recognition.

In this ECMI Newsletter we have collected some re-cent work on imaging to give an impression on mathe-matical tools in imaging and concrete areas of applica-tions.

References

[1] R. West, In industry, seeing is believingPhysicsWorld, June 2003.

4

The Imagers Group at UCLA

The Imagers Group

The image analysis and processing research group at theComputational and Applied Mathematics (CAM) groupin the Mathematics Department of UCLA, known asThe Imagers, is a successful model for initiating a novelprogram at the intersection of modern applied mathe-matics and the digital and information technologies.

The Imagers group was initiated about 8 years agoand was mainly led by Tony Chan and Stan Osher, twosenior faculty members of the Mathematics Departmentat UCLA. Luminita Vese, a new regular faculty mem-ber in Mathematics, is now another one of the leaders.It was formed initially as a research group meeting forstudents and faculty working in the general area of PDEimaging. It later evolved into a forum for a broader cam-pus group interested in imaging, with a regularly sched-uled seminar in image processing (currently run by S.Esedoglu and L. Vese). It also forms a basis for collab-orative research and joint proposals for external fund-ing. New students looking for research areas and thesistopics also find it a useful venue to get introduced toan active research area in the department. Current CAMfaculty members associated with the group include Mar-tin Burger, Doug Enright and Selim Esedoglu. Recent-ly joined new members are three senior faculty mem-bers in the mathematics department: Andrea Bertozzi(formerly at Duke University), Mark Green (Director ofthe Institute of Pure and Applied Mathematics, a NSF-funded national mathematics institute) and Eitan Tad-mor. It may be of interest to note that Mark is an al-gebraic geometer by training and became interested inmathematics image analysis through running IPAM’smany programs related to image processing. Currentlythere are more than ten Ph.D. graduate students and sev-eral postdoctoral fellows who constitute the new bloodof the Imagers Group.

During the past decade, there also have been nu-merous Imagers alumni. These include (in alphabeti-cal order), Peter Blomgren (CSU San Diego and for-merly at Stanford’s Mathematics Department), Li-TienCheng (UC San Diego), Jamylle Carter (Univ of Min-nesota), Ron Fedkiw (Stanford University), MyungjooKang (Seoul National Univ.) Sung-Ha Kang (Univ. ofKentucky), Richard Tsai (Princeton University), Jack-ie (Jianhong) Shen, (Univ of Minnesota), Bing Song(Univ. of Maryland), David Strong (Pepperdine Univer-sity), Hong-Kai Zhao (UC Irvine), and Hao-Min Zhou(Georgia Tech, formerly at Caltech). We also havea long term relationship with the applied mathematicsgroup at the Univ. Valencia, with frequent visits fromAntonio Marquina, Pep Mulet and Rosa Donat, as wellas with many other groups throughout the world.

The Imagers Group has been partly supported by theOffice of Naval Research (USA) and the National Sci-ences Foundation (USA), and recently also by the Na-tional Institute of Health (USA).

Many of the research activities and agendas present-ed here can be found at the homepage of the Imagers at:www.math.ucla.edu/˜imagers. The site of theCAM Re-portsalso contains most of the preprints of the ImagersGroup: www.math.ucla.edu/applied/cam/.

Research Areas and Tasks

The general research areas of the Imagers Group are inmathematical modelling and computational techniquesfor image analysis and processing, with connections tocomputer vision and computer graphics applications.

Traditional methods in image processing are most-ly based on Fourier or spectral analysis and stochas-tic models. These methodologies have been high-ly successful. Recently, there has been increased in-terest in a new and complementary approach, usingpartial differential equations (PDEs) and differential-geometric models and techniques. This approach of-fers a more systematic treatment of geometric featuresof images, such as shapes, contours, and curvatures, aswell as allowing the wealth of techniques developed forPDEs and Computational Fluid Dynamics (CFD) to bebrought to bear on image processing tasks.

Notable examples of such techniques are total vari-ation regularized image restoration methods and vari-ational level set methods for image segmentation andactive contours. Ideas from shock capturing can alsobe borrowed to handle compression of image data withsharp discontinuities (i.e. edges). All of these tech-niques were co-invented by members of the ImagersGroup.

These new variational PDE models also call fornew computational techniques to deal with their in-herent nonlinearities, anisotropy, singularities, and ill-conditioning. The Imagers Group is devoted to thedevelopment of novel algorithms and computationalschemes that efficiently take care of these issues by in-corporating more geometric, adaptive, multi-scale, andregularization ideas and tools.

Another challenge the Imagers Group faces is to com-bine effectively these PDE models with the statisticaland transform based models, in order to reap the advan-tages of each approach. With its broad research connec-tions to both latter groups, the Imagers Group is servingas a significant communication bridge in contemporarymathematical image analysis and processing.

The Imagers Group is also dedicated to applyingand extending all these novel models and computation-al schemes in modern image analysis and processingto other scientific areas including the imaging sciences

5

(e.g., astronomic or medical imaging), mathematical bi-ology, the material sciences, scientific visualization, anddata and pattern mining.

Part of UCLA’s Vision Initiative

What makes the Imagers Group more special is that itis embedded in a larger important initiative at UCLA- theVision Initiative, which is an emerging interdisci-plinary program across many departments and divisionsat UCLA.

The idea of the UCLA Vision Initiative is to bringtogether all scientists and researchers working on imag-ing, image analysis, graphics, computer vision, and hu-man vision, and to create a local integrated atmosphereto foster and enhance collaborations, and informationand knowledge sharing.

Beside the Imagers group, the Vision Initiative main-ly consists of theCenter of Image and Vision Scienceled by Professors Alan Yuille, Song-Chun Zhu, andYing-Nian Wu in the Statistics Department, theUCLABrain Mapping Centerin the Department of Neurolo-gy, the Laboratory on Neuro-Imaging led by Art Togaand Paul Thompson, theVision Science Groupin theDepartment of Psychology, theGroup of Computer Vi-sion in Medicinein the Department of Radiology, andtheComputer Vision Groupled by Stefano Soatto in theComputer Science Department.

The Vision Initiative is intended to make significantcontributions to the advancement of the image and vi-sion sciences, through its systematic way of integrat-ing the information and digital technologies with the lifesciences.

The Imagers Group represents the mathematical coreof the Vision Initiative. On the one hand, with itsmany existing mathematical models and computing al-gorithms developed throughout the years, the ImagersGroup provides mathematical as well as computation-al solutions to many challenging research tasks of theother more applied divisions in the Vision Initiative. Inreturn, the Imagers Group is also a beneficiary of theother programs in that there exists a constant incomingflow of new and interesting problems that demand andinspire novel ideas in mathematical modelling and com-putation.

For example, in a recent collaboration between theImagers group and the Neuro-Imaging group, ideas indifferential geometry have been successfully applied tothe mapping of the brain. Another example is the devel-opment of new variational image processing models asinspired by human vision research.

Case Examples

Active Contours Without Edges

Images are the 2-D projections of the 3-D world withvarious objects. To identify and extract the 2-D regionsassociated to those objects is the challenging task ofim-age segmentation, with broad applications in vision andimage analysis.

Denote byu0 an observed 2-D image on a domainΩ.Segmentation is to identify an edge setΓ which leadsto a complete partition ofΩ : Ω \ Γ = ∪N

i=1Ωi, witheach connected componentΩi corresponding to a singleobject.

Active contour is a popular segmentation approach,of which a candidate edge contour evolves under theguidance of image gradients till it rests along the realedge. It however fails for many astronomic or medicalimages due to lack of sharp gradients.

T. Chan and L. Vese’s novel model-active contourswithout edges, formulated independent of the gradientinformation, is to minimizeE(c+, c−, Γ):∫

i(Γ)|u0(x)− c+|2dx +

∫

e(Γ)|u0(x)− c−|2dx + ν|Γ|,

whereν > 0, andi(Γ) ande(Γ) denote the interior andexterior ofΓ, and|Γ| its length.

In S. Osher and J. Sethian’s level-set formulation,Γis embedded as the zero level setφ = 0 of a Lips-chitz functionφ, andφ > 0 andφ < 0 define theinterior and exterior. Then the Euler-Lagrange equationfor E[c1, c2,Γ|u0] under the level-set formulation canbe shown to be

φt = δ(φ)[νdiv

( ∇φ

|∇φ|)− |u0 − c+|2 + |u0 − c−|2

],

where once the current best estimation of the edge setΓ = φ = 0 is given, both mean fieldsc± can beexplicitly computed, andδ denotes the Dirac delta func-tion.

This two-phase model can be naturally extended tomulti-phase ones by cleverly using multiple level setsand the four-color problem. These models are close-ly related to Mumford-Shah’s segmentation model. T.Chan and L. Vese have studied the level-set computa-tional methods for all these extended models. L. Veseand S. Osher have used the total variation minimizationas well for active contours.

Bayesian/Variational Image Inpainting

Inpainting is an artistic synonym forimage interpola-tion. Digital inpainting based on high order PDEs wasfirst successfully developed in the breakthrough workof Masnou, Morel, and Bertalmio, Sapiro, Caselles,

6

Ballester, and was shown there to have broad applica-tions in dis-occlusion, super-resolution, and error con-cealment in wireless transfers.

The approach that the Imagers Group has taken forinpainting is mainly variational and geometric, and pro-foundly rooted in the Bayesian or Helmholtz principlein vision research.

Let u denote an ideal complete image on a 2-D do-main Ω, andu0 the observednoisy or blurry portionof u on a sub-domainD. The goal of inpainting is torecoveru on the entire image domainΩ as faithfullyas possible from the available datau0 on D. Follow-ing the Bayesian framework, a general variational in-painting model is to minimize an energy in the form ofE[u|u0, D] = E[u0|u,D] + E[u], where the first termis call thedata generative model, and the second, theimage prior model.

Image acquisition is often modelled byu0

∣∣D

=(Ku + n)D, whereK is a blurring kernel, andn an ad-ditive Gaussian white noise field. Then the data modelis explicitly given byE[u0|u,D] = λ

∫D(Ku−u0)2dx.

The prior modelE[u] is thus more critical for good in-painting.

To complete missing edges to their first order geome-try, Chan and Shen first proposed to apply the BV imageprior model of Rudin, Osher, Fatemi, which leads to theminimization of

Etv[u|u0, D] = α

∫

Ω|Du|+ λ

∫

D(Ku−

u0)2dx.By employing the object-boundary imagemodel, Esedoglu and Shen proposed to minimize theMumford-Shah inpainting energyEms[u,Γ|u0, D]:

α

∫

Ω\Γ|∇u|2dx + β|Γ|+ λ

∫

D(Ku− u0)2dx.

Chan, Esedoglu, Kang, and Esedoglu have also showedthe essential role of high order geometry in image in-painting, and the above two models both have been gen-eralized to include the curvature information and yieldbetter inpainting outputs. Inspired by these models,high order nonlinear geometric PDE inpainting modelshave also been developed.

Dynamic Visibility and the Level Set Method

This problem is quite easy to state: Given a collection ofclosed surfaces representing objects in space, determinequickly the regions (in space or on the surfaces) thatare visible to an observer or observers. This questionis crucial to applications in fields including rendering,visualization, etching and solving certain inverse prob-lems. In a 3D virtual reality environment, knowing thevisible region speeds up the rendering by enabling us

to skip occluded regions. We outline here work doneby R. Tsai, P. Burchard, L.-T. Cheng, S. Osher and G.Sapiro on this problem. They represent the family of(possibly moving) occluders implicitly as the zero lev-el set of a single function of (x,y,z,t), defined on a grid.Next, this function is replaced by the signed distancefunction to the boundary. This can be done by using theoptimal fast algorithm of Tsitsiklis. Then, for a givenvantage point a, they develop a simple, easily paralleliz-able, multiresolution algorithm of optimal complexityto compute the dynamic visibility function, which de-pends on a (or several a’s) and the occluders. All the ad-vantages of the level set formulation, such as topologychange and easily quantified geometry are evident. Re-cently, Tsai and Cheng have extended this to(1)optimalpath planning through obstacles to maximize visibility,(2)rapidly reconstruct visible surfaces from a discreteset of observations and (3) forged a link with Hamilton-Jacobi equations.

Image decomposition models into cartoon and tex-ture

A new image processing task has been introduced by Y.Meyer: to decompose a given initial imagef into thesumu + v, whereu is a cartoon (simplified) part off ,while v is an oscillatory part of zero mean, representingtexture+noise. For instance, D. Mumford and J. Shah’smodel, and the total variation minimization model of L.Rudin, S. Osher and E. Fatemi give decompositions off : Ω → R into a cartoon partu ∈ BV (Ω) (or in asubset ofBV (Ω)), andv := f − u ∈ L2(Ω), repre-senting noise. Y. Meyer proposes the use of general-ized functions and weaker norms to model the oscilla-tory componentv (such as the dual space toW 1,1(Ω)),instead of using square integrable functions, such rep-resentations being more sensitive to model texture. D.Mumford and B. Gidas also suggest that texture, noise,or clutter cannot be modeled as locally integrable func-tions, but must be generalized functions. However, inpractice, it is not possible to directly solve the modelproposed by Y. Meyer.

L. Vese and S. Osher have recently proposed a firstpractical model for such task, imposing that thev com-ponent belongs toW−1,p(Ω), p ≥ 1 (note that forp = 2, we recover the spaceH−1(Ω)). They minimizeF (u,~g):

|u|BV (Ω) + λ‖f − (u + div~g)‖2L2(Ω) + µ‖~g‖Lp(Ω), (1)

wherev = div~g, with ~g = (g1, g2) ∈ Lp(Ω)2, and|u|BV (Ω) denotes the total variation ofu. This mod-el has been applied to denoising, “cartoon” and textureseparation, texture segmentation.

Inspired from this work, other models have been pro-posed for image decomposition into cartoon + texture.

7

S. Osher, A. Solé and L. Vese proposed another ap-proach, modeling thev component as a generalizedfunction inH−1(Ω): the model is

infu

F (u) = |u|BV (Ω) + λ‖∇4−1(f − u)‖2L2(Ω).

This minimization leads to a fourth order PDE in theunknownu, and it has been applied to denoising, de-blurring, and decomposition.

In the context of wavelets and energy minimization,we refer to very recent work by I. Daubechies and G.Teschke, and by J.-L. Starck, M. Elad and D.L. Donoho.In the context of energy minimization and duality, werefer to the work by J.-F. Aujol, G. Aubert, L. Blanc-Féraud and A. Chambolle. An application of the imagedecomposition model (1) to image inpainting has beenproposed by M. Bertalmio, L. Vese, G. Sapiro and S.Osher.

An example of astronomical imaging:detection of arcs

In astronomical data sometimesgravitational lensingcan be observed. Light emitted by galaxies far behinda cluster, the so called background galaxies, is bendedthrough the cluster’s high mass. In the images thesegalaxies appear as arcs grouped around the cluster’scenter. Fig. 1 shows astronomical image data contain-ing such arcs. Near the image center one can see twobright galaxies which are rather close together. Thecenter of the galaxy cluster is approximately in betweenthese galaxies.

The aim of our work has been to develop an algorithmfor (semi)-automatical detection of arcs. Our softwarecomprises of four subsequent steps:

1. Scaling the image intensity to enhance the arcs’ in-tensity. This is necessary, since in the original datathe signal to noise ratio of arcs is extremely low.

2. Filtering by anisotropic diffusion to remove noiseand to enhance arcs.

3. Segmentation based on edge detection.

4. Selection of elongated thin objects.

Figure 1: Astronomical image showing a cluster ofgalaxies (about in the middle of the image) and arcsgrouped around the center.

The results of our software are shown in Fig. 2. We test-ed our algorithm on several images. Besides the knownarcs we found a series of reasonable candidates with ouralgorithm.In astronomy information on arcs is relevant

8

Figure 2: Detected arcs. We assign candidates of arcsa probability (red – almost certain that it is an arc, yel-low – high probability, green – middle probability, stilla reasonable candidate).

• to study the mass of the galaxy clusters and itsdistribution, especially to detect and analyze darkmatter.

• to investigate the far back galaxies enhanced bythis lensing effect.

This work was done in cooperation with SabineSchindler from the Institute of Astrophysics, Innsbruck.It was supported by the Tiroler Zukunftsstiftung.

The algorithm is described in detail in

F.Lenzen, S.Schindler, O.Scherzer,"Automatic detection of arcs and arclets formed bygravitational lensing",Preprint Series of the Department of Computer Science,University of Innsbruck, Vol. 11, July 2003

Electrical Impedance Imaging in thehalf space: Visualizing obstacles byelectrostatic measurements on a plane

Birgit SchappelFachbereich Mathematik & Informatik,Johannes-Gutenberg-Universität Mainz,

55099 Mainz, Germany

For a nonnegative scalar conductivity coefficientσ theelectrostatic potentialu inside a domainΩ ⊂ R3 fulfillsthe elliptic partial differential equation

div(σ gradu) = 0. (2)

If a current densityf 6= 0 is induced on the boundaryΓof Ω we obtain a nontrivial solution of (2) which fulfillsthe Neumann boundary condition

σ∂u

∂ν= f on Γ. (3)

The aim of electrical impedance imaging is the recon-struction and visualization of the conductivity coeffi-cientσ from the knowledge of the Neumann dataf andthe associated Dirichlet datag = u|Γ onΓ.In the current project to be described here we restrictourselves to the following situation: LetΩ be the upperhalf spaceR3

+, D a union of domains withD ⊂ Ω andΩ \D connected. Then the function

σ(x) =

κ(x), x ∈ D

1, x ∈ Ω \D(4)

with ε ≤ κ(x) ≤ 1 − ε, ε > 0, x ∈ D, models the sit-uation of a homogeneous body with inclusions of lowerconductivity. (The case of inclusions with higher con-ductivity can be handled similarly.) Our aim is the vi-sualization of the inclusionsD by extending a methoddue to Brühl [1] for bounded domainsΩ to the halfspace (see also [2]). Considering an unbounded domainis of special interest in various applications: E.g. inGeophysics EIT is used as an additional examinationmethod for the detection of cavities and for the predic-tion of seismic activities. When using EIT for mam-mography as it is for example done by Siemens AG ina corporation with Trans Scan Medical Inc, a currentdensity is induced in the breast through a sensor of fewsquare centimeters and the corresponding potential ismeasured. Of course the body of the patient is boundedbut in comparison with the sensor so large that the mod-el of an unbounded domain seems to be appropriate.The basic idea of our imaging technique is as follows:Let Λ denote the Neumann-Dirichlet-Operator for thedifferential operator from (2) withσ as in (4) and letΛ1

denote the Neumann-Dirichlet-Operator for the Laplace

9

Operator inΩ. These operators map the given Neumannboundary values to the Dirichlet boundary values of thesolutionu of (2) and (3). Then we are able to give atheoretical characterization of the range of the opera-tor (Λ − Λ1)1/2. Using this we can show that the traceof a functiongz, which is essentially the fundamentalsolution of the Laplace equation reflected at the planeR2×0, belongs toR((Λ−Λ1)1/2), if and only if z isa point lying in the inclusionD. Using the so calledPicard criterion and the eigenvalues and eigenvectorsof Λ − Λ1 this can be tested numerically. Since wecan only induce a finite numberm of input currentsfk,k = 1, . . . , m, we have to solve an Eigenvalue-Problemfor anm×m-matrix, which is extremely cheap.For the visualization we apply this test for all points ofan equidistant grid covering that part ofΩ which is ofinterest. The binary output of our test is used to markpoints which are tested positive, i.e. which should be-long toD. In this way we obtained the reconstructionsfor the 2D-case shown in Figures 1 and 2.

Figure 3: Upper: data without noise. Lower: data with0.1% noise.

Figure 4: Reconstruction of an inclusion off from themeasurement area from data without noise.

The quality of our reconstructions obtained by thismethod depends on the depth of the inclusions, their lo-cation relative to the measurement area and - of course- on the amount of noise in the data. This needs to befurther investigated.

References

[1] M. BRÜHL Explicit characterization of inclu-sions in electrical impedance tomographySIAMJ.Math.Anal.,Vol.32, No.6 (2001), pp 1327–1341.

[2] B. SCHAPPEL Electrical Impedance Tomographyin the half space: Locating Obstacles by electrostat-ic measurements on a plane;Proceedings of the 3rdWorld Congress on Industrial Process Tomography.

10

Digital Inpainting

Harald GrossauerDepartment of Computer Science

University Innsbruck, A-6020 Innsbruck, Austria

“Inpainting” is to restaurate missing or damaged partsof an image. It can also be used for “airbrushing” toremove unwanted image details. “Digital Inpainting”refers to inpainting of digitized images with computersupport. Ideally the user would only mark the region tobe replaced or repaired and the computer would do therestauration automatically. Unfortunately it is not thateasy. Human observers interpret a picture, they recog-nize objects, and they have a certain expectation aboutthe contents. So even if a significant part of an object ishidden, humans still may have a reasonably good imag-ination of the complete data.

Models

To implement inpainting algorithms one has to developa model taking care of the typical image structure. Mostof the information in an image can be classified into twocategories: geometry and texture, see e.g. [1]. An oftenused model for image geometry is that of BV-functions.Ideally a purely geometric image would consist of dis-joint sets of constant intensity. Here the important in-formation on the sets are their shapes, i.e., the edges ofthe image. Physiological experiments have shown thatmany of the impression a human gains from an imageis related to edges. Several inpainting algorithms havebeen implemented based on geometric partial differen-tial equations and are trying to continue edges in a “nat-ural” way: elastica energy minimization [2], Navier–Stokes equations [3], curvature driven diffusion [4], theMumford–Shah–Euler inpainting [5], to name only afew. Beside edge information the human visual systemis also sensitive to texture. It is usually modeled as aMarkov random field [6] or as a highly oscillatory func-tion [7]. In general texture is more difficult to handlethan geometry.

Ginzburg–Landau

We propose a geometric inpainting algorithm based onthe Ginzburg–Landau equation. This model was intro-duced in 1950 to describe superconductors near theircritical temperature. They derived an expression for thethermodynamic potential, similar to:

E(u,∇u) =∫

Ω|∇u|2 + α|u|2 + β|u|4

α andβ are chosen to form a symmetric double wellpotential. Any functionu minimizing this functional

necessarily has to fulfill the following partial differentialequation

(∂u

∂t=

)∆u +

1ε2

(1− |u|2) u = 0

which has been rescaled to contain only a single param-eterε. The Ginzburg–Landau equation has some favor-able properties for image processing applications. Forinstance it has a tendency to connect discontinuities byminimal surface interfaces. So given an image with amissing or unwanted domainΩ our code finds a solutionof the Ginzburg–Landau equation, where the availableparts of the image are prescribed as Dirichlet boundarycondition. More details and information can be foundin [8].

References

[1] J.-F. Aujol et.al.,Image Decomposition Applicationto SAR Images, Scale Space Methods in Comput-er Vision, Lecture Notes in Computer Science 2695,Springer

[2] S. Masnou,Disocclusion: A Variational ApproachUsing Level Lines, IEEE Transactions on Signal Pro-cessing, 11(2), February 2002, p.68–76

[3] M. Bertalmio, A. Bertozzi, G. Sapiro,Navier–Stokes, Fluid Dynamics, and Image and Video In-painting, IEEE CVPR 2001, Hawaii, USA, Decem-ber 2001

[4] T. Chan, J. Shen,Non–Texture Inpainting byCurvature–Driven Diffusions (CDD), Journal of Vi-sual Communication and Image Representation ,12(4), 2001, p.436–449

[5] S. Esedoglu, J. Shen,Digital Inpainting Based onthe Mumford–Shah–Euler Image Model, EuropeanJournal of Applied Mathematics, 13, pp. 353-370,2002

[6] R. Paget, I. D. Longstaff,Texture synthesis via anonparametric Markov random field, Proceedings ofDICTA-95, Vol. 1, (Brisbane, Australia), pp. 547–552

[7] Y. Meyer,Oscillating Patterns in Image Processingand Nonlinear Evolution Equations, AMS Universi-ty Lecture Series, Vol. 22, 2002

[8] H. Grossauer, O. Scherzer,Using the ComplexGinzburg–Landau Equation for Digital Inpaintingin 2D and 3D, Scale Space Methods in ComputerVision, Lecture Notes in Computer Science 2695,Springer

11

Figure 5: PDE inpainting of Michelangelo’s “Holy Family”. In the result(right picture) two regions have been high-lighted that exhibit a particular challenge for PDE based geometry inpainting algorithms, namely high contrast edges.Texture synthesis is not practical since the inpainting domain is surrounded by lots of differently textured areas.

Figure 6: An example which is not well suited for PDE inpainting. The texture synthesis algorithm achieves very goodresults(right picture)but PDE based inpainting algorithms clearly fail for large sized domains surrounded by stronglytextured areas(middle picture). The PDE inpainting was finished after a few minutes, whereas the texture synthesistook more than 10 hours to complete!

Figure 7: A combined approach. The main work is done using PDE inpainting, texture (waves, grass and even noise) isadded later on in a texture synthesizing pass. Removal of such large objects is a difficult task, especially if they coverseveral distinct areas (grass, trees, water, houses).

12

48th European Study Group "Mathe-matics with the Industry" (48th ESGI)

First announcement

The 48th European Study Group "Mathematics with theIndustry" (48th ESGI) will be held at the Delft Universi-ty of Technology in Delft, the Netherlands from March15th until 19th, 2004.Place: Delft Institute for Applied Mathematics (DIAM)EEMCS Building, Mekelweg 4 Delft, the NetherlandsTime: 15- 19 March 2004Organization: H.X. Lin (DIAM), C. Kraaikamp (DI-AM), C.W. Oosterlee (DIAM).For more information, we refer to our website:http://ta.twi.tudelft.nl/swiJOIN US TO TACKLE PROBLEMS FROM IN-DUSTRY ! The study group brings together aca-demic mathematicians and industrial commercialcompanies. Selected problems will be present-ed that mathematicians try to solve. At theend of the meeting the results will be presented.

49th European Study Group with In-dustry

Oxford, 29 March - 2 April 2004,

The study groups will return to their roots when OCI-AM hosts the 49th European Study Group with Indus-try in Oxford from 29 March to 2 April 2004. Somefunding will be available via MACSI-net to support par-ticipants from outside the UK. Further details and ap-plication procedures will appear on the OCIAM webpages at http://www.maths.ox.ac.uk/ociam/ in January.

ESGI50 in Helsinki 24-28.5.2004

The 50th European Study Group "Mathematics with In-dustry" will be held in Helsinki Finland May 24-28,2004. The event is organised by CSC, the Finnish ITcenter for science. People in companies with interestingmathematical modelling problems and mathematicians

interested in spending a busy week solving them are en-couraged to contact us!See our website: http://www.csc.fi/esgi50or contact esgi50@csc.fi for further details.

The International Conference "InverseProblems: Modeling and Simulation"

June 07-12, 2004, Fethiye, Turkey

The First Announcement

The International Conference "Inverse Problems: Mod-eling and Simulation" will be held during June 07-12,2004, in the historic city of Fethiye, on the Mediter-ranean Sea, in Turkey. The main aim of the Conferenceis to promote unity through diversity and to encourageworldwide interest in the theory and applications of in-verse problems. Our forum is going to bring togeth-er leading scientists from many different countries andmany speciality applications. The proposed Internation-al Conference will be under the auspices of such interna-tional journals as Inverse Problems, Inverse Problems inEngineering, Inverse and Ill-Posed Problems, and Com-putational Methods in Applied Mathematics. The orga-nizers of the Conference, in particular the Fethiye Mu-nicipality, will work to put together an excellent scien-tific program with social programs consisting of tours tohistoric places and boat rides. We welcome you to theInternational Conference "Inverse Problems: Modelingand Simulation".CHAIRS:Heinz W. Engl (Radon Institute for Computational andApplied Mathematics, Austria)Alemdar Hasanov (Hasanoglu) (Kocaeli University,Turkey)Sergey Kabanikhin (Sobolev Institute of Mathematics,Russia)Preliminary list of members of the INTERNATIONALPROGRAM COMMITTEE (further members to be con-firmed):M. Bektemesov (Almaty, Kazakhstan)M. Burger (UCLA)A. Iserles (Cambridge, UK)V. Isakov (Wichita State, USA)A. Jaoua (Tunis)R. Kress (Goettingen, Germany)M.M. Lavrentiev (Novosibirsk, Russia)Li Ta-Tsien (Fudan, Shanghai)V.G. Romanov (Novosibirsk, Russia)M. Pidcock (Oxford Brookes, UK)G. Uhlmann (Univ. of Washingon, USA)V.V. Vasin (Ekaterinburg, Russia)

13

M.Yamamoto (Tokyo, Japan)J. Zou (Chinese Univ. of Hongkong. China)

Main topics:

• inverse problems in geophysical sciences;

• inverse problems in underwater acoustics;

• inverse problems in signal and image processing;

• wavelets and inverse problems;

• inverse scattering problems;

• links between optimization and inverse problems;

• Monte-Carlo formulation of inverse problems;

• control problems and inverse problems;

• inverse problems in fluid dynamics;

• inverse problems in potential theory;

• determination of physical and mechanical proper-ties of media;

• numerical simulation and analysis of inverse andill-posed problems;

• regularization of ill-posed problems.

Deadlines:

Proposal of Special Sessions December 31, 2003Abstracts January 31, 2004

Abstracts:

The abstracts of the Conference, consisting of the alllectures (one LaTex page), will be published. All par-ticipants will obtain copies during the Conference. Ab-stracts are due by January 31, 2004 and should be sentto both of the following email addresses:nikolaus@indmath.uni-linz.ac.at, oznur@kou.edu.tr

Visas:

Visas are not required for participants coming from anycountry.

Hotel Accomodations

A large number of rooms will be reserved in variousclose hotels throughout Ovacik town, Oludeniz-Fethiye(www.oludeniz.org), one of the historical places of theMediterranian Sea Region. The hotel rooms will be re-served at specially discounted rates, and all the hotels

are within 5 to 15 min. walking distance of each oth-er. The prices (between 300-600USD for a week) willinclude breakfast and dinner.All the hotels are 50 km from the international airport atDalaman.Participants, as well as accompanying persons, need topay an additional USD 100 to the account of the confer-ence for lunch, which will be served during the confer-ence (meetings), and for transportation to/from hotels/palace of Culture.Due to the expenses involved all participants includingspeakers are required to pay the registration fee.

Registration Fee:

Received by by byDec31,2003

Jan31,2004

Mar31,2004

Nonstudent USD 150 USD 175 USD 200Student USD 75 USD 100 USD 100

Banktransfer:

Pamukbank, Izmit Branch, Izmit-Kocaeli, TURKEYAccount No: 442-23867234 Account Name: Interna-tional Workshop In the bank transfer please show yourname, surname and the name of hotel you have chosenand keep the receipt.

Social Programs

Social Programs consist of Opening and Closing Cere-monies, Cocktail Party, Banquet and visits to historicalplaces plus boat tours. There is no fee for registeredparticipants.

Transportation

The hotels are 50 minutes from the international airportat Dalaman. Representatives of the hotels will meet par-ticipants at the Information Service of the airport. AConference bus service will provide transportation onJune 07, 2004, from the international airport at Antalya.

Contact Address

A. Hasanov (Hasanoglu)Kocaeli University,Applied Mathematical Sciences Research Center,Ataturk Bulvari, 41300 Izmit, Kocaeli, Turkeyahasanov@kou.edu.trcc: oznur@kou.edu.tr

14

15

ECMI modelling week 2004

The 17th ECMI modelling week was held at the Univer-sity of Bristol, from 22nd to 31st of August 2003. About40 students from across Europe came together to receivean intense ten-day training in mathematical modellingapplied to industry. Scientists working in industry wereinvited to present problems, and the students divided in-to multi-national teams to tried to solve them. The EC-MI modelling week is Europe’s leading workshop forteaching industrial mathematics. It is also a fun socialevent where many life-long friends are made! Here arephotos sent by the students. The organiser of the work-shop was Eddie Wilson. For more information pleasecontact RE.Wilson@bristol.ac.uk.

16

Mathematics for Industry in Denmark:The ESGI47 and Mathematics for In-dustry Workshop, August 2003

The 47th European Study Group with Industry and itsembedded Mathematics for Industry Workshop tookplace in Denmark from August 24 until August 29. Themeeting was hosted by the University of Southern Den-mark in a picturesque area of Southern Jutland, close toGraasten.The meeting brought together about 65 participants,among whom were professional mathematicians, en-gineers, physicists, and industrial participants. Themeeting was a truly international one, with delegatesfrom many European countries and from overseas. Thisyear, the meeting organisation was rest on the Sønder-borg team: Professor Roderick Melnik (Chairman), DrFrands Voss (Managing Director), and Associate Pro-fessor Morten Willatzen, with substantial help givenby other members of the Organising Committee: As-sociate Professor Poul Hjorth, Associate Professor JensGravesen (both DTU), and Professor Henrik G. Petersen(Maersk Institute, SDU). Participants came from 4 ma-jor Danish Universities, as well as from the UK, Nor-way, Italy, Czech Republic, Turkey, China, Germany,Latvia, Canada, the United States, and Finland. Theycame to Denmark for 5 productive days of collaborativework.Five challenging projects were presented by leading in-dustrial companies:

• Stall Prediction Model, presented by Ulrik Ullumfrom Grundfos;

• Mathematical Analysis of the Dynamic Flow Char-acteristic in a Damping Nozzle for a PressureTransmitter, presented by Jes Vogler from DanfossIndustrial Control;

• Determination of Distances from a 2D Picture, pre-sented by Martin Valvik from Unisensor;

• Model to Check Distance to Catalog Curve, pre-sented by Ulrik Ullum from Grundfos; and

• Trigger Algorithm for Ultrasonic Flow Metering,presented by Lars Ploug-Sørensen from DanfossFlow Division.

The meeting featured also the Mathematics for Indus-try Workshop on Tuesday afternoon with three distin-guished international speakers. Professor H.T. Banksof North Carolina State University (USA) talked aboutComputational Methods for Estimation in the Presenceof Uncertainty. He shared with participants his experi-ence in solving industrial problems and provided a num-

17

ber of interesting examples from the Industrial Mathe-matics Program at North Carolina State University. Pro-fessor M. Cross of the University of Greenwich (UK)talked about Computational Modelling of Industrial Op-erations Involving Multi-Physics and Multi-Scale Pro-cesses. His presentation included examples of modelsfor granular flows in hoppers, alloy segregation dur-ing solidification, metals extrusion and heap leaching ofores. Professor M. Brokate of the Technical Universityof Munich (Germany) presented his talk on Mathemati-cal Models of Hysteresis. The talk included a series ofinteresting examples related to control of engineeringsystems with hysteresis.After a brainstorming session on Monday afternoon,participants were working hard in groups led by themoderators of the projects. This year project modera-tors were Poul Hjorth, Jens Gravesen (both TechnicalUniversity of Denmark), Peter Howell (University ofOxford), Hemant Kamath and Morten Willatzen (bothUniversity of Southern Denmark). Project presentationsummaries were given on Wednesday evening with anumber of useful suggestions coming from the audi-ence. By Friday it was clear that the ESGI47 was areal success with excellent progress made on each ofthe projects. Final presentations showed that each studygroup developed their models and provided an excellentbasis to complete the projects.After hard work, the Study Group participants visitedthe Graasten Chapel and the Royal Castle in the South-ern Jutland.

This report was sent byRoderick MelnikUniversity of Southern DenmarkE-mail: rmelnik@mci.sdu.dk

The 45th European Study Group Math-ematics with Industry in Leiden

Last February the 45th European Study Group Mathe-matics with Industry was held at the University of Lei-den in The Netherlands. It was the fifth time a Dutchstudy group was organised. As one of the organisers Iwant to give you a short impression of the week. Forthe week approximately fifty participants, mainly fromThe Netherlands but also quite a few from the UK, cameto Leiden to make a start on solving the problems pre-sented by the five companies. The participants workedvery enthusiastic and very hard, and made nice progresstowards solving the problems. The problems were quitedivers and to give you an idea of this, I will give a briefdescription of every problem. For more detailed de-scriptions seewww.math.leidenuniv.nl/~swi .

In due time the proceedings can also be found there.KLM: Forecasting the performance and flexibility ofa flight schedule.KLM flies to over 150 destinations with 97 aircraft.Four times a year, a new flight schedule is developedaimed principally at maximising the number of seatswhich can be sold. The schedule design takes into ac-count operational feasibility to some extent, but con-centrates on the commercial aspects such as expecteddemand per destination and the number of transfer con-nections at Schiphol.

Each day during operation, many adaptations are madeto this schedule to minimise delays caused by for exam-ple problems with the aircraft or weather. If it is knownthat an aircraft will arrive at Schiphol Airport with a de-lay, they try to assign its next flight to another aircraftso that that flight can still leave on time. Usually, a cou-ple of other adaptations are needed to have all flightsfit again. Some schedules prove more flexible and ro-bust than others in coping with delays. KLM wantedto know if a simple fast method could be found to testthe performance and flexibility of a given flight sched-ule when incorporating the adaptations that are made tothe schedule during operation. So far they had been do-ing simulations with real data and they wanted to knowwhether this could be reduced or avoided.RIVO: Modelling the expanding Pacific Oyster pop-ulation in the Eastern Scheldt.Pacific oysters, native to Japan, were introduced into theEastern Scheldt Estuary in The Netherlands after the se-vere winter of 1962/63 diminished the stock of Euro-pean flat oysters. At that time, it was believed that thePacific Oyster could not breed at such latitudes. How-ever, during the hot summer of 1976, the first settlingof larvae was observed on dike foots and jetties afterwhich importation of the Pacific Oyster was immediate-ly halted. In 1982, a second larvae outburst permanentlyestablished the wild Pacific oysters in the waters of theEastern Scheldt and the population has been growingrapidly ever since.

The Pacific oyster represents a serious environmentalproblem in the Eastern Scheldt due to lack of naturalpredators and because they compete with other speciessuch as cockles, mussels and cultivated oysters for spaceand food. One of the tasks for the study group was tostudy whether a mathematical model of the oyster pop-ulation could predict the spreading of the oyster popu-lation and even give a suggestion to how the populationgrowth can be brought under control.PHILIPS: The behaviour of a droplet of polymer so-lution in an ink-jet printer.Light-emitting polymer displays are a new, interestingflat display principle. The active material is a verythin layer of semi-conducting polymer. To make a

18

full colour display red, green and blue polymer so-lutions must be positioned in pixels of the order of66 × 200 micron. Philips is currently trying to adaptink-jet technology to position these small drops of poly-mer solution effectively.

The polymers involved in this process have a high-molecular weight which causes the droplet formationfrom the ink-jet to be highly non-Newtonian; this is un-like the behaviour of normal inks. Philips wanted thestudy group to model the visco-elastic behaviour of thejetted polymer solution to enable them to obtain infor-mation about the velocity and droplet formation of thepolymer liquid.Dutch Forensic Institute (NFI): Probability modelsfor tool marks and shoe prints.When a tool has been used to commit a crime (such asusing a screwdriver to open a door during a burglary)the tool leaves certain marks which are unique to thatparticular tool. The question when handling a case incourt is of course whether a tool of a suspect could haveleft these traces. A similar question can also be askedfor shoe prints found at a crime scene. These questionscan be answered by comparing the traces to test tracesof the tool or shoe of the suspect. The position of certainlines, curves, dents or more distinguishing marks on thetool or shoe help tomatchthe trace left at a crime scene.However, so far, a good subjective judgment couldn’t bemade. The study group was asked to design a probabil-ity model that gives the probability that the trace foundat a scene of crime was made by the tool or shoe of acertain suspect.National Carillon Museum: How to optimise thehanging of carillon bells and wires in a tower.A carillon consists of around 20 to 45 bells hung in atower. The bells are played using a keyboard situat-ed below and a wire connects each bell clapper to itsrelevant key on the keyboard. The oldest and simplestwire-connection system is the ‘broek-system’ connect-ing three wires to the ‘broekring’: one from the clapper,one from the key and one from a fixed point on the wall.

To construct a carillon such that all the designingproperties are satisfied, and that all the bells sound asthey should is incredibly difficult. The carillon-builderattempts to place the bells in a geometrically balancedway, but it is hard to prevent all the wires from touchingor to make every key and bell play equally well. Theproblem posed by the museum was to come up with anmethod to position the bells and wires in a tower in anoptimal way.

The companies also participated very enthusiasti-cally in the study group which lead to great interactionsand nice results. And, they were very pleased withthe work carried out during the study group. I want to

thank all the participants and my co-organisers, NickOvenden and Derk Pik, it was a great week !

The next Dutch study group will be held at theTechnical University of Delft in the week of 15-19March 2004. I hope to see you there !

Vivi RottschäferLeiden University.

19

Joint European Project "MathematicsCurricula for Technological Develop-ment"

European Commission, Directorate-General Educationand Culture, through European Training Foundation,Tempus Department has approved the realization of theproject JEP 17017-02 starting on October 1, 2003.The central aim of this project is introduction of "Math-ematics for Industry" master curricula at the Departmentof Mathematics and Informatics at Faculty of NaturalSciences and Mathematics, University of Novi Sad, Ser-bia and Montengro. The Programme is aimed to pro-vide graduates in mathematics and other closely relatedfields with a broad knowledge and experience needed towork successfully as mathematicians in industry. TheProgramme will be made in accordance with EuropeanConsortium for Mathematics in Industry (ECMI) rulesand structure, taking into account specific needs of tran-sition economy of Serbia and Montengro.The project will have two phases. The First Phase willbe preparatory phase lasting one year and it would bedevoted to formulation of the curriculum at The Depart-ment of Mathematics and Informatics in Novi Sad.The Phase Two of the project will be actual introduc-tion and realisation of the Programme. Teaching pro-cess with lectures and exercises will take place next twoyears. Large number of activities in practical training inmathematical modelling is planned within the projectactivities: Modelling Weeks at academic partners in-stitutions, Industrial Mathematics Days in Serbia andMontenegro, seminars, workshops and intensive cours-es on relevant subject will be organised. Mobility ofboth students and teachers (in both directions) is one ofthe main goals. At the same time evaluation and mon-itoring process by experts and ECMI Board start as apart of continuous effort on this project and later on, asusual with ECMI centres.The Consortium which will realize this project consistsof academic and nonacademic partners. The Contract-ing Institution is Dresden University of Technology andProf. Dr. Martin Weber will act as the grantholder ofthe project. The coordinating and beneficiary institutionis University of Novi Sad, Department of Mathematicsand Informatics. ECMI nodes, Lappeenranta Universi-ty of Technology (contact Prof. Dr. Matti Helio) and

University of Milan (contact Prof. Dr. Luca Pavarino)will be academic partners. Non-academic partners atthe project are Belgrade Stock Exchange and Chamberof Commerce of Vojvodina. They will provide exper-tise in designing courses and connections with indus-try. Two individual experts who will help in realisationof the project activities are prof. Wojciech Okrasinskifrom University of Zielona Gora and Prof. dr MichaelOberguggenberger, Head of Department of EngineeringMathematics, Geometry and Computer Science, Uni-versität Innsbruck, Austria.

Department of Mathematics and Informatics is the oneof the leading mathematical institutions in Serbia andMontengro. Research and education in the areas ofMathematics and Computer Science are main activitiesof the Department. High quality degree programmesin Mathematics and Computer Science are offered atboth undergraduate and graduate level. The reform ofundergraduate programmes towards European standardswas done last year at the maximum level permitted bythe current laws in FRY. Research activity covers manytopics in mathematics and computer science. By theseactivities and by the results obtained in the last threedecades, the Department has become not only the lead-ing research centre for mathematical sciences in FRY,but also one of the most prominent mathematical insti-tutions in this part of Europe. The Faculty consists of37 professors, 10 assistants with master’s degree and 15teaching assistants. Up to 2000 there was 1310 gradu-ates in mathematics and computer science, 18 special-ists, 95 masters and 88 PhD thesis defended.

The result of the project will be introduction and reali-sation of the new curriculum of Mathematics in Indus-try at the Department of Mathematics and Informaticsat University of Novi Sad. The curricula will be definedand put into being during the project producing the firstgraduates during its duration. The mobility betweenpartner institutions will be established. The Universityof Novi Sad will be ready to join the ECMI Education-al System as a Teaching Centre. Graduates from thisProgramme will be mathematicians with vast interdisci-plinary experience and oriented to real world problemsable to join companies after the completion of studies.

Spreading the positive impact of this project withinnon-academic community in FRY will be challeng-ing. Working closely by non-academic partners on thisproject and using the experience of EU partners and theindividual experts we hope to succed in this difficulttask.

Dr. Nataa Krejic, Dr. Marko Nedeljkov, Dr. Andre-ja Tepavcevic, University of Novi Sad, Department ofMathematics and Informatics

20

New and Emerging Themes in Industri-al and Applied Mathematics (NETIAM)

The Smith Institute is coordinating a project for actionin support of the European Commission’s programmein New and Emerging Science and Technology (NEST)under Framework 6. The project will concentrate onNew and Emerging Themes in Industrial and AppliedMathematics (NETIAM), and bring the Smith Institutetogether with Fraunhofer-ITWM in Germany, the Tech-nical University of Eindhoven in The Netherlands, theUniversity of Firenze in Italy and Ventspils UniversityCollege in Latvia.NETIAM will use mathematical frameworks to identi-fy ground-breaking research directions in four themes:modelling the business environment, modelling crimi-nality in the social environment, visualization and sim-ulation of materials, and complexity at the molecularlevel. Technology Translators from the Smith Institutewill facilitate Thematic Workshops hosted by its fourNETIAM partners around Europe, and then a PlenaryWorkshop will consolidate the findings into a form thatwill enable new research consortia to be taken forward.The project will start in February 2004 and last 16months. For further information, contact Melvin Brownat the Smith Institute (melvin@smithinst.co.uk).The Smith Institute is an intermediate institution basedin the UK which specialises in industrial mathematicsand system engineering. It works closely with academ-ic departments in 30 UK universities and this is its firstforay into the wider European arena. The Smith In-stitute manages the Faraday Partnership for IndustrialMathematics which was launched in 2000 with assis-tance from the Department of Trade and Industry andthe Engineering and Physical Sciences Research Coun-cil. Faraday Partnerships promote industrial competi-tiveness, through improved collaboration between in-dustry and the science base for the purposes of re-search, development and technology transfer. Moredetails about the Institute and this programme can befound on http://www.smithinst.ac.uk/.

Some cracking ideas on egg incubation

Adapted from a report prepared by:Carina Edwards, Nick Ovenden, Vivi Rottschäfer.

Introduction

This problem was posed by Bristol Zoological Gardensand investigated during the 46th European Study Groupwith Industry 2003 at the University of Bristol. BristolZoo looks after rare and endangered species of birds,one of which is the African penguin, and the Zoo is in-terested in finding efficient ways of breeding them incaptivity. One of the strategies used is the removal ofeggs from the nest just after they are laid. If eggs aretaken away from the mother, then she will usually laymore. The eggs that are taken away from the penguinsthen need to be incubated artificially. There are artificialincubation machines in use which attempt to replicatethe conditions of natural incubation. The overall goal isthus to ensure that artificial incubation is as successfulas natural incubation so that one may breed the speciesas rapidly as possible.Three factors are thought to be important for the suc-cessful incubation of eggs:

1. Temperature: this must be kept close to the birds’own temperature of37 C.

2. Humidity: a successfully hatched egg will typical-ly lose 15%-17% of its mass through vapour lossduring the incubation period.

3. Motion: it is necessary for an egg to be rotatedfrom time to time. It is not precisely known whybirds do this (there are several theories), but hatch-ing does not occur unless the eggs are subject tosome kind of occasional turning.

One of the questions we tried to answer is whether allof these factors are (equally) important for incubation.In particular, we examined the issue of why eggs needto be turned.The main questions we formulated and tried to answerduring the study group were the following:

21

• Why do birds rotate their eggs ?Since there were several theories given in the liter-ature for this, it was the most difficult but also themost important question to answer.

• Does thermal convection play a role during incu-bation ?

• What are the properties of the flow inside the shellfollowing the rotation of the egg ?

In this article, we attempt to provide at least partial an-swers to all of these questions.

Stage 1 turning model: assumptions

The model is formulated for the first stage of develop-ment, which is when turning is most crucial. By fo-cussing on this period of development several simplify-ing assumptions can be made.

1. The egg is aclosed system. The eggshell struc-ture consists of the cuticle, the true shell, an out-er membrane and a fluid-loaded inner membrane.The fluid-loaded inner membrane initially preventsgaseous exchange with the outside world and clos-es the system. All water vapour loss in the firststage of development can be attributed to loss-es from this inner membrane. After a few days,the inner membrane loses enough fluid to becomeporous, enabling gaseous exchange and respira-tion; this is assumed to occur after the first stageof development.

2. The embryo lies just inside the yolk sac attachedto the membrane. It is less dense than the materialforming the yolk and is assumed to be physicallysmall during the first stage of development. Thebuoyancy force of the embryo is assumed to act ata point and returns the embryo to the top of theegg. The slight density stratification of the yolkmay contribute to this process but is not modelledseparately.

3. The albumen is aviscoelasticfluid. The rotationof the egg by the penguin happens over a shortenough timescale that it is assumed to be impul-sive. Thus, the albumen can be expected to un-dergo rigid body rotation. The relaxation of theembryo back to its rest position at the top of theegg happens over a much longer timescale, duringwhich the albumen flows as a viscous liquid. Theflow is driven by the buoyancy force of the embryowithin the yolk, and additionally the buoyancy ofthe yolk within the albumen.

4. Where certain physical properties of the albumenand yolk have been difficult to ascertain (suchas diffusivity constants), the respective values forpure water have been used.

Fluid dynamics of the egg: what is the reasonfor turning?

It would appear that penguins turn their eggs through asignificant angle at intervals of approximately 20 min-utes. The hypothesis for this behaviour is that the pen-guin is redistributing either heat or nutrients within theegg.

Is convection important?

As penguins sit on top of their eggs, the system is con-vectively stable (as heat rises!) and we can concludethat heat transport through the egg is a diffusive pro-cess. This can be further confirmed by evaluating theRayleigh number, which quantifies the relative sizes ofthe viscous and thermal buoyancy effects. Assumingthat any convection present will occur in the albumenannulus surrounding the yolk the buoyancy force is ofO(ραg∆T ) per unit volume whereρ ∼ 103 kgm−3

is the albumen density,α ∼ 10−4 K−1 is the coef-ficient of thermal expansion (taken for pure water at20oC), g = 10ms−2 is the gravitational accelerationand ∆T is the temperature difference between shelland yolk. In comparison, the viscous forces are ofO(µU/δ2) for flow speedO(U) per unit volume, whereµ ∼ 5 × 10−2 kgm−1s−1 is the viscosity of the thick-er albumen, andδ is the albumen thickness. TakingU = 2πR/t with t = δ2/κ, whereR ∼ 2 × 10−2mis the radius of the egg andκ is the thermal diffusivity,gives the Rayleigh number as

Ra =α∆Tgδ4

2πRνκ. (5)

The thermal conductivity of the albumen is estimated tobe similar to that of water,k ∼ 0.5W m−1 K−1, withspecific heat capacityCp ∼ 3 × 103 J kg−1 K−1 (alsotaken to be equal to that of pure water). Thus the thermaldiffusivity is estimated to beκ ∼ 1/6 × 10−6 m2 s−1.From these values, we find that for a given temperaturedifference∆T

Ra ∼ ∆T.

As the critical Rayleigh number is ofO(1000), even ifthe penguin were to heat the egg from below, it wouldbe unable to generate enough heat to set up convectioncurrents. A similar result is obtainable for both the thinalbumen layer (treated as a separate entity) and the yolk,leading to the conclusion that convection is negligibleeverywhere inside the egg.

22

Thermal diffusion

The timescale for thermal diffusion is given byτD =R2/κ. Using the estimates forR andκ given above, wefind

τD ∼ 102 − 103 s.

As the penguin rotates its eggs at intervals of 20 minuteswe can take the egg rotation time scale asτR ∼ 103 s.If the penguin needed to turn the egg to maintain a uni-form temperature throughout the egg, then we wouldexpect to seeτD À τR. However, it would seem thatthis is not the case, and so temperature control is notthe reason for turning. Our conclusion is backed up byexperience from artificial incubators, where eggs muststill be turned even though the temperature is uniformthroughout.

Molecular diffusion

The albumen surrounding the embryo contains anti-bacterial chemicals, growth hormones and nutrients.It is essential that the embryo is continually suppliedwith these. However, when we consider the timescaleof molecular diffusionτM = R2/D, where D ∼10−9 m2s−1 is the molecular diffusivity (assumed to beequal to that for pure water), we find

τM ∼ 105 s.

As τM À τR this indicates that one (if not the only)purpose of turning must be to provide the embryo withfresh nutrients contained within the albumen.

Yolk settling

To justify the assumption that the yolk acts as a solidbody within the egg with the buoyancy force acting ata point, it is necessary to check that there is no signif-icant settling effect over the relevant timescales. Theyolk consists of roughly a7% suspension of fat particles(colloids) [1], which will diffuse and settle under theirown weight. The relevant timescale for the settling canbe calculated by treating the colloids as spheres fallingfreely under gravity in a viscous fluid. We can then ap-ply Stoke’s law to get the terminal velocity as

VS =29

∆ρga2

µyolk,

where∆ρ is the density difference between the fat par-ticles and the rest of the yolk,a is the size of the col-loid particles (diameter) andµyolk is the mean viscos-ity of the yolk. Given the values∆ρ ∼ 10 kgm−3,a ∼ 10−5 m and µyolk ∼ 4 × 10−1 kgm−1s−1 (400times that of water) from [1], we find that

VS ∼ 10−7 − 10−8 ms−1.

Using this velocity as an idea of how fast the particlesmove under gravity, it clearly would take a yolk of ra-dius 10−2m about three days to settle. Therefore, theassumption of treating the yolk as a solid body appearsto be very reasonable.

Two-dimensional egg relaxation model (afterturning)

Neglecting the full three-dimensionality of the egg, wefirst examine the mixing imposed through the action of abuoyant yolk and embryo after an impulsive solid bodyrotation through some angle.All starred variables defined below are dimension-al quantities whereas all other variables are non-dimensional. We define a typical length scale to be theradius of the yolka∗, and the gap width (albumen thick-ness) when yolk and shell are concentric is given byδ∗.Non-dimensionalising all lengths bya∗ gives a gap as-pect ratio of

h0 = δ∗2πa∗ .

Defining a Reynolds number based on a typical flowvelocity u∗, yolk radiusa∗ and mean albumen viscos-ity ν∗, lubrication theory applies if the gap aspect ratioh0 ¿ 1 and if thereduced Reynolds number

h20Re ¿ 1;

in our model both these conditions shall be assumed tobe satisfied.The densities of embryo, yolk and albumen are given asρ∗E , ρ∗Y andρ∗A respectively. Furthermore, we take

ρ∗E 6 ρ∗Y 6 ρ∗A, (6)

leading to the viscous flow being driven by buoyancyforces. Subsequently assuming that pressure, buoyantand viscous forces all balance, we require

∆ρ∗g∗(a∗)2 ∼ P ∗a∗, (7)

µ∗u∗

(δ∗)2∼ P ∗

a∗, (8)

where∆ρ∗ = ρ∗A − ρ∗Y is the typical density differ-ence,g∗ is gravitational acceleration andP ∗ is the typ-ical pressure generated. Combining these expressionsleads to the condition that

(δ∗)2∆ρ∗g∗

µ∗u∗∼ 1. (9)

Substituting the values obtained from [1] leads to atypical flow velocity in the albumenu∗ of 10−4ms−1.Therefore, a typical timescale for the restoring flow af-ter rotation isa∗/u∗ ∼ 102s.A detailed model has been constructed to describe themotion of the yolk and embryo after an impulsive turn

23

and this can be found in the full version of this report[2]. However we already have enough information toexplain how the turning of the egg allows the embryoaccess to more nutrients and thus improve its chancesof survival.

The role of shearing in improving diffusion ofnutrients and waste products

Figure 8: How a shearing flow can help to diffuse wasteand nutrients

Here we attempt to explain why the turning of the eggand subsequent spinning of the yolk by the lighter em-bryo improves access to nutrients and disperses wasteeffectively. The left-hand diagram of figure 8 showsthe inside of an egg with the embryo resting at thetop. We assume the radius of the yolk isa∗ ∼ 10−2mand that the width of the surrounding albumen layer isδ∗ ∼ 10−3m. After some time at rest, the embryo ex-pends the nutrients in the neighbouring albumen, leav-ing a strip (marked in black) of albumen that has becomefull of waste products and devoid of nutrients. Assum-ing this strip to be of sizeδ∗ × δ∗ and the moleculardiffusion coefficient to beD ∼ 10−9m2s−1 (as givenin section ) then the time taken for this strip to diffuseaway will be of the order

τ ∼ δ∗2

D∼ 103 s.

The following two diagrams in figure 8, show what hap-pens to this strip when the egg is turned. Following animpulsive rotation about some angle, the lighter embryothen forces the yolk to spin round until the embryo isback at the top of the egg. Given anO(1) turning angle,it is clear that the shearing flow in the albumenstretchesthe length of the strip by a factora∗/δ∗ ∼ 10. Similar-ly, the width of the stripw∗ reduces by the same factor10−1, leading to a strip now only of widthw ∼ 10−4m.The timescale of the diffusion process is proportional tow2, meaning that the stretched strip only takes

τ ∼ w2

D∼ 10 s

to diffuse. Hence, the embryo’s access to nutrients isgreatly increased by occasional turning.

Conclusions

An examination of the egg turning from a fluid dy-namics perspective appears to suggest that the reasonfor turning is to enable mixing in the albumen. Thismixing provides the embryo with important nutrients,anti-bacterial agents and disperses waste in the earlystages of incubation. Turning of the egg does not seemto be required for uniform heating, an argument borneout not only by our calculations but from practicalexperience with artificial incubators.

This article has been adapted from a more detailed re-port which will be published in the final report of the46th European Study Group with Industry which washeld in Bristol in 2003. This report is not yet publishedbut it will soon be available on the Smith Institute web-site www.smithinst.ac.uk.

References

[1] Romanoff A.L.& Romanoff A.J.S., The AvianEgg, J.Wiley and Sons Inc.New York, 1949.

[2] 46th European Study Group with Industry Report.

24

Fundamental Natural Frequencyof a Fluid-Loaded Plate

Robert Piché, Antti Suutala and Veijo IkonenInstitute of Mathematics

Tampere University of TechnologyPOB 553, FIN-33101 Tampere, Finland

Introduction

Finland’s first ”Study Group”-style event, held atTampere University of Technology on Oct 21–252002, attracted 25 participants. The four indus-trial problems and their solutions are available athttp://math.tut.fi/workshop02/. The following is a sum-mary of one of the solutions.The engineers at Wärtsilä Diesel want to know the res-onance frequencies of their engines in order to avoidharmful resonances. In order to better understand thevibration of metal vessels that contain diesel oil, thecompany built a test rig (Figure 2) and did FEM compu-tations. They found that these computations are too ex-pensive and time-consuming for designers, so we wereasked to find simple “back of the envelope” approximateformulas for natural frequencies.In this report we concentrate on the vibrations of thelarge plate at the base of the test vessel. The plate di-mensions areL = 1490 mm byM= 1322 mm, its thick-ness iss = 10 mm, and its mass density isρsteel= 7850kg m−3. The fuel oil density isρoil =912 kg m−3 andits depthh varies from 0 to 1000 mm.

Figure 2: Vibration test vessel

The problem is similar to the vibrating element den-sitometer studied by Ellis Cumberbatch and coworkersin Claremont College’s industrial mathematics clinics[Mathematical Modelling, E. Cumberbatch & A. Fitt,eds, Cambridge Univ. Press, 2001]. Their solution useddifferential equations, ours is based on variational meth-ods.

Variational formulation

A vibrating system’s fundamental vibration frequencycan be specified by the Rayleigh-Ritz principle

ω21 = min

u

V (u)T (u)

,

whereV (u) is the amplitude of the potential energy,ω2T (u) is the amplitude of kinetic energy, and mini-mization is over admissible nonzero shape functionsu.

The kinetic energy of the base plate is

ω2Tplate=12

M∫

0

L∫

0

sρplatew2 dx dy

and its potential energy isVplate. The kinetic energy ofthe side plates is neglected, but their potential energyamplitude, modelled as elastic supports at the boundaryof the base plate, is denotedVsides.The oil is modelled as an incompressible fluid. The ki-netic energy amplitude of the oil above the base plateis

ω2Toil =12

h∫

0

M∫

0

L∫

0

sρoil |∇φ|2 dx dy dz,

whereφ. is the velocity potential.

Rayeigh’s method

A good approximation to the fundamental frequencycan be obtained by assuming a reasonable mode shape.We assume the base plate’s mode shape to be

w(x, y) = sin(πx

L

)sin

(πy

M

).

The velocity potential is assumed to be of the form

φ(x, y, z) = w(x, y)Z(z)

The velocity potential function satisfies Laplace’s equa-tion∇2φ = 0, which gives

w,xx +w,yy

w+

Z ′′

Z= 0.

The usual separation of variables argument leads to

Z = a cosh(βz) + b sinh(βz),

whereβ2 = π2

L2 + π2

M2 . The coefficientsa and b aredetermined by the boundary conditionsφ,x (x, y, 0) =w(x, y) (for displacement continuity at the bottom ofthe oil) andφ(x, y, h) = 0 (for zero pressure at the topsurface), yielding

Z =sinh (β(h− z))

β cosh(βh).

Substituting these assumed mode shapes into the energyintegrals gives the following approximation for the baseplate’s fundamental frequency:

ω1(h) ≈ ω1(0)√1 +

ρoil tanh(βh)

ρsteelsβ

(10)

This simple formula, withω1(0) set to the measuredvalue, agrees remarkably well with the measured andFEM-computed values provided by Wärtsilä:

25

oildepth

fundamental frequency (Hz)

(mm) measuredFEM formula (10)0 35.2 36.5 35.2200 23.3 25.0 20.1500 18.4 18.8 16.8900 16.2 15.4 16.4 ECMI Certificates

The ECMI Educational Committee awards ECMI cer-tificates to the following candidates:Oliver Faulhaber (Kaiserslautern),Lutz Justen (Kaiserslautern),Benjamin Seibold (Kaiserslautern).

Oliver Faulhaber was a student in the study programme"Economathematics". He spent one term at the Nation-al University of Singapore (NUS) from June to Decem-ber 2001 and participated in the ECMI-Modelling Week2002 in Kaiserslautern. Oliver Faulhaber performeda project under the guidance of Professor Korn in co-operation with the Commerzbank, Frankfurt. This workresulted in a thesis entitled "Analytic Methods for Pric-ing Double Barrier Options in the Presence of Stochas-tic Volatility" . He works now at the insurance companyMannheimer Versicherungen in Mannheim, Germany,where he is involved in the development of new prod-ucts.

Abstract of the thesis:

While there exist closed-form solutions for vanilla op-tions in the presence of stochastic volatility for nearly adecade, practitioners still depend on numerical methods– in particular The Finite Difference and Monte Carlomethods – in the case of double barrier options. It wasonly recently that Lipton proposed (semi-)analytical so-lutions for this special class of path- dependent options.Although he presents two different approaches to derivethese solutions, he restricts himself in both cases to aless general model, namely one where the correlationand the interest rate differential are assumed to be ze-ro. Naturally the question arises, if these methods arestill applicable for the general stochastic volatility mod-el without these restrictions. In this paper we show thatsuch a generalization fails for both methods. We will ex-plain why this is the case and discuss the consequencesof our results.

26

Lutz Justen was a student in the study programme"Technomathematics". He spent one term for projectwork at Oxford University, UK, from April to Septem-ber 2000 and participated in the ECMI-Modelling Week2002 in Kaiserslautern. Lutz Justen performed aproject under the guidance of Professor Neunzert inco-operation with the Fraunhofer Institute of Industri-al Mathematics, Kaiserslautern. This work resulted ina thesis entitled "An Inverse Heat Conduction Problemwith Unknown Initial Condition" . He is now PhD stu-dent at the University of Bremen.

Abstract of the thesis:

In glass manufacturing and metal casting, exact knowl-edge of the temperature distribution inside a body isnecessary to predict large thermal stresses and possiblecracks. Since direct measurements inside the body areoften difficult or even impossible, we describe a way ofrecovering the initial temperature distribution and hencethe temperature for all times from partial boundary mea-surements. We prove the ill-posedness of the problem inthe sense that small measurement errors may cause largedeviations in the solution. Furthermore we show back-ward uniqueness for a large class of boundary sets. Un-der certain smoothness assumptions on the true solutionwe give a stability estimate using a mollification methodoriginally applied to the Sideways Heat Equation. Weemploy efficient numerical regularization methods suchas Tikhonov regularization and the Conjugate Gradientmethod and do some numerical tests

Benjamin Seibold was a student in the study programme"Technomathematics". He spent one term at the Univer-sity of Berkeley, USA, from September 2000 to June2001 and participated in the ECMI-Modelling Week2002 in Kaiserslautern. Benjamin Seibold performeda project under the guidance of Professor Neunzert inco-operation with the Fraunhofer Institute of Industri-al Mathematics, Kaiserslautern. This work resulted in

a thesis entitled "Optimal Prediction in Molecular Dy-namics". He is now PhD student in Kaiserslautern.

Abstract of the thesis:

Optimal prediction is a method to approximate the av-erage solution of a large system of ordinary differen-tial equations by a smaller system. In this thesis weshow how optimal prediction can be applied in the fieldof molecular dynamics in order to reduce the numberof particles. We apply optimal prediction to a modelproblem describing a surface coating process and showhow asymptotic methods can be used to approximatethe original system by a smaller system. We considerthe reduction of computational effort and analyze - an-alytically and by numerical experiments - under whichconditions the optimal prediction system is a valid ap-proximation to the original system.

27

The International Workshop on theStudy Program Technomathematics

held from September 11 - 13, 2003, at the TechnicalUniversity Dresden1 was a contribution of the Depart-ment of Mathematics to the festivities celebrated thisyear at the Technische Universitaet Dresden on occa-sion of its175th anniversary.

Its foundation as aHigher Technical Education Institutetook place in 1828.In 1851 the institute was upgraded to theRoyal Saxo-nian Technical School, later the name was changed in-to Technische Hochschule Dresdenand reached its finaldesignationTechnische Universitaet Dresdenin 1961.

In 1993 the Technical University had incorporated vari-ous other institutions of teaching and research, especial-ly the Academy of Forestry, College of Traffic Scienceand the Medical Academy as well as the Teacher’s Col-lege.Now the Technical University Dresden also offers pro-grams in humanities and social sciences as well as ineconomics, linguistics and other subjects. The total ofcurrently about 30000 students is roughly evenly splitbetween these new subjects and the traditional disci-plines such as engineering, science, forestry and infor-matics.The curriculum of mathematics at the TU Dresden hasalways required a minor in an engineering or sciencesubject.

Since more than ten years the department offers the fol-lowing study programs

MathematicsTechnomathematicsEconomathematicsTeaching of Mathematics.

Moreover, the Department of Mathematics is responsi-ble for the mathematical education in all other facultiesof the university.

The graduates of the department have never encountereddifficulties in finding suitable employment throughoutGermany and Europe. It is hoped that this source ofhighly qualified graduates will also bring forward theregional industry.

Similar challenges need to be met in other central andeast European regions. This applies in particular to thecountries joining the European Union in 2004.In this sense the conference was also a contribution tothe development of acommon educational infrastruc-ture for a successful economical European integration,based on innovated technologies. This idea was sup-ported and pointed out by many participants of the con-ference.

Representatives from 27 universities and technical uni-versities from Germany, Austria, Czech Republic, Esto-nia, Hungaria, Latvia, Lithuania, Poland, Russian Fed-eration, Serbia and Montenegro and Ukraina took partin the workshop. The workshop continued the traditionof similar conferences that were organized by the Uni-versities of Kaiserslautern (Germany) in 1990, and Linz(Austria) in 1992.

Some of the current changes at East-European universi-ties are similar to the transition the Technical Universi-ty Dresden underwent a decade ago in connection withthe reunification of Germany. Future developments willcertainly occur within a common European framework.

Surface modeling for filling gaps

It is important that researchers and educators activelyparticipate in shaping the new systems of higher edu-cation in Europe. Otherwise educational reforms mightbe determined by shortterm political pressure or eco-nomical trends. Therefore, we must strive to exchangeour experiences, define our goals and realize appropri-ate structures on a European level. This kind of col-laboration and harmonization is particularly promisingin the field of Technomathematics. It is well known thatmost of universities represented at the conference have a

1. The aims of the workshop are spelled out e.g. in the ECMINewsletter (no.33, March 2003).

28

long tradition in Applied Mathematics and very well es-tablished scientific relations with German, Austrian andother central European universities. Now is the time toextend this cooperation also to common study programswhich facilitate fruitful exchanges of students and sci-entific staff.Another aspect is the interaction between science andeconomics, in general, and between mathematics,engineering sciences and computer science, in partic-ular. Hence in designing curricula there have to beincorporated many facettes, namely

Mathematical foundationsEngineering sciencesInformation technologyMathematical modelingIndustrial activities.

The last two items and their interplay are of central im-portance for Technomathematics and therefore figuredprominently at the workshop.At the workshop the following plenary lectures weregiven by

H. NEUNZERT (Universitaet Kaiserslautern,Fraunhofer-Institut fuer Techno- und Wirtschafts-mathematik)Technomathematics – Failure or Success?

A. NEUBAUER (Johannes Kepler Universitaet Linz)Industrial Collaborations of the Industrial MathematicsInstitute in Linz

W. MACHT (Advanced Micro Devises Inc. Dresden)Statistical Yield Analysis in Semiconductor Industry

A. GILG (Siemens Muenchen)Mathematics in theElectronics Industry: Challenge and Demand

M. HOLZNER (AUDI AG, Ingolstadt)Virtual Design in Automotive Development

M. H ILDEN (Robert Bosch GmbH Stuttgart)Hydraulic Simulations for Active Safety in Cars – Fieldof Work of a Technomathematician at the Robert BoschGmbH

O. VOGEL, A. GRIEWANK (TU Dresden),K.-H. ENGEMANN (Hurth Modul Chemnitz)Manufacturing of Optimized Hypoid Bevel Gears –Modelling and Solving an Inverse Problem

All participants got pertinent information and ideas tomotivate and structure the study of Technomathematics.

The participants of the workshop discussed and adoptedthe

Position Paper Concerning the Study ProgramTechnomathematics

which summarizespast experiences,definesthe min-imum standard,suggestsquality measures andgives

guidelines for the establishment of technomathematicscourses.The final version of this position paper will be publishedin one of the next issues of the ECMI Newsletter.

There was also consent that a common web-siteof the participating universities will be prepared bythe Department of Mathematics at the TU Dresden.This web-site (http://www.math.tu-dresden.de/Techno-Mathematik/techno2003) will present the posters exhib-ited at the workshop.

Although the ECMI was not explicitly involved into theworkshop, its presence has been appearent by severalcolleagues well known in ECMI, e.g. H. Neunzert, A.Neubauer, W. Okrasinski, and others. Moreover, the ed-itorial board kindly agreed to publish the abstracts ofsome lectures given at the workshop in next issues ofthe ECMI Newsletter.

The participants visited the modern gas fired powerplant in Dresden, had a guided tour around the centerof the new-born Dresden and enjoyed the city and itsenvirons.

The workshop was sponsered by

the German Academic Exchange Service (DAAD),

Gesellschaft von Freunden und Foerderern der TUDresden e.V.,

Technische Universitaet Dresden.

G.F. Baer, V. Nollau, M.R. Weber(Dept. of Mathematics, TU Dresden)

29

Nomination

Prof . Heinz W. Engl (Linz, Austria) has been elect-ed Full Member of the Austrian Academy of Sciences.

The Wacker Prize

The Hansjörg Wacker Memorial Prize 2004 will beawarded at the ECMI 2004 Conference which will takeplace at Eindhoven, The Netherlands from June 21-252004. All ECMI Institutional Members are invited tosubmit eligible papers for this prize. Entries should bein the form of a mathematical thesis at the masters’ lev-el written at the Institution on an industrial subject. Thework must have been completed after March 2002. Thewinner will be invited to attend the ECMI 2004 meeting(all expenses paid) to present his/her project there andto receive the prize of 1500 euro.

Submission of Entries

Four copies of the thesis should be sent to the ad-dress below to arrive by December 31 2003. The entryshould be accompanied by a letter from a member ofthe academic staff at the Institution which summarisesthe mathematical and industrial relevance of the work.It should also state if the thesis is part of the assessmentfor a degree or other qualification.Entries should be sent toProfessor Dr Andreas NeubauerInstitut für IndustriemathematikJohannes Kepler Universität LinzA-4040 LinzAustriaThe envelope should be clearly marked WACKERPRIZE.

30

ENBIS, European Network for Businessand Industrial Statistics

In August, 1999, a group of statisticians and statisticalpractitioners met in Linkoping, Sweden to discuss thedesirability and possibility for creating a European so-ciety for industrial and applied statistics. The need forsuch a society was grounded in the following:- Many statistical practitioners work in professional en-vironments where they are rather isolated from interac-tions and stimulation from likeminded professionals- Statistics is vital for the economic and technical de-velopment and improved competitiveness of EuropeanIndustryA subsequent communication among European Statis-ticians showed support for the idea of creating such asociety taking advantage of the internet to make this alow budget, low effort operation that could be launchedwithout delay.In December, 2000 a founding conference was held inAmsterdam, and the name ENBIS (European Networkfor Business and Industrial Statistics) was adopted asthe name for the society. The mission of ENBIS wasagreed to be:- Foster and facilitate the application and understandingof statistical methods to the benefit of European busi-ness and Industry- Provide a forum for the dynamic exchange of ideasand facilitate networking among statistical practitioners(a statistical practitioner is any person using statisticalmethods whether formally trained or not),- Nurture interactions and professional development ofstatistical practioners regionally and internationally.ENBIS has adopted the subsequent points as its vision:- To promote the widespread use of sound science driv-en, applied statistical methods in European business andindustry,- That membership consists primarily of statistical prac-titioners from business and industry,- To emphasize multidisciplinary problem solving in-volving statistics- To facilitate the rapid transfer of statistical methodsand related technologies to and from business and in-dustry,- To link academic teaching and research in statisticswith industrial and business practice,

- To facilitate and sponsor continuing professional de-velopment,- To keep its membership up to date in the field of statis-tics and related technologies,- To seek collaborative agreements with related organi-zations.In January, 2002 an EC funded project PRO-ENBISwas established under the GROWTH programme. PRO-ENBIS has aims similar to those of ENBIS and someENBIS activities are partly sponsored by that pro-gramme.ENBIS is a web-based society with membership free ofcharge. Although less than three years old, the networkhas already more than 800 members, primarily from Eu-ropean countries. In some countries a national branch ofENBIS has been formed to stimulate local interaction.Membership interactions are primarily via the internetthrough the monthly newsletter and through participa-tion in interest groups (working groups). Currentlythere are eight interest groups covering themes suchas design of experiments, data mining, general statis-tical modeling, reliability and safety, process model-ing and control, quality improvement, statistical con-sultancy and measurement uncertainty. A further inter-est group on statistics in pharmaceutical industry (non-clinical) is on its way.Besides annual conferences of ENBIS, various work-shops are organized by the interest groups, and ENBISparticipates actively in conferences organized by relatedorganizations. Thus, ENBIS is collaborating with EC-MI in organizing the 2004 conference in Eindhoven.For more information about ENBIS, visit the web-sitehttp://www.enbis.orgPoul Thyregod, President of ENBIS

31