Stochastic Geometr,y Spatial Statistics, and their ... · also biologists, ecologists, engineers,...

Stochastic Geometry,

Spatial Statistics,

and their Applications

� SGSSA07 �

February 14-17, 2007Schloss Reisensburg, Günzburg, Germany

Contents

Welcome 5

Conference Information 6

Program 7

Wednesday, February 14, 2007 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Thursday, February 15, 2007 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Friday, February 16, 2007 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Saturday, February 17, 2007 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Abstracts 11

List of Participants 45

3

Dear colleagues,

we are happy to welcome you within the ancient walls of the medieval fortress Reisensburgnow hosting our Workshop on Stochastic Geometry, Spatial Statistics, and their Applications.Planned originally as a regional meeting of colleagues from Southern Germany, to the surpriseof the organisers the workshop soon drew the attention of a wider community and quickly grewto become an international conference with more than 60 participants from 12 countries all overthe world. Now it is an interdisciplinary forum bringing together not only mathematicians butalso biologists, ecologists, engineers, material scientists, medical doctors and physicists workingon similar problems from stochastic geometry and related �elds. We hope that these few daysat the Reisensburg will provide an inspiring framework for new contacts, an intensive exchangeof ideas, and starting new joint research projects.

As the organisers, we would like to thank you for coming and for your contributions creating thecomprehensive scienti�c program of this workshop. We are also very grateful for the �nancial sup-port of this workshop granted by Ulm University and the Faculty of Mathematics and Economicsthat allowed for reducing conference fees and o�ering travel grants to various participants. Formaking this possible, we owe special thanks to the President of Ulm University, Prof. Dr. KarlJoachim Ebeling, Managing Director Dieter Kaufmann, and Dean Prof. Dr. Frank Stehling.

Last but not least, the organisation of the workshop would not have been possible without thedevoted help of the secretary of the Institute of Stochastics, Mrs. Renate Jäger and our PhD stu-dents Stefanie Eckel, Frank Fleischer, Wolfgang Karcher, Sebastian Lück, Daniel Meschenmoser,Jonas Rumpf, Malte Spiess, Ralf Thiedmann, and Florian Voss who contributed substantially tothe preparation and realisation of this meeting.

We wish you a pleasant and informative stay at Schloss Reisensburg.

Günzburg, February 14th, 2007

Volker Schmidt, Evgeny Spodarev

5

Conference Information

The International Workshop on StochasticGeometry, Spatial Statistics and theirApplications from 14 to 17 February 2007 atSchloss Reisensburg (SGSSA07) is organizedby the Institute of Stochastics, Faculty ofMathematics and Economics of UlmUniversity.

Organisers Volker Schmidt, Evgeny SpodarevTopics Convex, integral and stochastic geometry,

spatial statistics, geometric point processes,random �elds, random measures, random tessellations,image processing, image analysis and their applications

Deadlines Registration: January 15, 2007Abstract submission: February 1, 2007

Contact [email protected] Web-Page http://www.mathematik.uni-ulm.de/SGSSA07

Accommodation: The conference fee of 220 e includes accommodation and full board, i. e.breakfast, lunch and dinner, starting with lunch on Wednesday, February 14, and ending withlunch on Saturday, February 17. Meals are served at the following times: Breakfast: 07.15 -09.00; Lunch: 12.00 - 14.00; Dinner: 18.00 - 20.00. Beverages have to be paid for individually.

Conference venue: Schloss Reisensburg is an International Congress Center of Ulm University,located in a medieval castle in the vicinity of Ulm (in Günzburg, a small town between Ulm andAugsburg). It provides comfortable apartments, conference rooms, and full internet access formore than 50 people. The castle has a WLAN with internet access available in the conferencerooms and in the lobby. Internet access via ethernet is possible in the bedrooms.

Travelling information: The nearest international airports are Munich and Stuttgart. Günzburgcan be easily reached by train from Munich, Ulm or Stuttgart. At the railway station one hasto take a taxi cab to get to the castle. Details can be found at the following web address:http://www.uni-ulm.de/reisensburg/

6

Program

Wednesday, February 14, 2007

11.00 - 12.00 Registration12.00 - 14.00 Lunch14.00 - 18.00 Talks

14.00 Luis M. Cruz-Orive:The pivotal formula (p. 13)

14.30 Tomasz Schreiber:Polygonal Markov �elds: simulation algorithms andapplications for image segmentation (p. 42)

15.00 Stephan Huckemann:Isometric Lie Group Actions on Riemannian Manifoldsand Principal Component Analysis (p. 22)

15.30 Co�ee Break

16.00 Lothar Heinrich:CLTs for Poisson hyperplane processes onnon-spherical expanding sampling domains (p. 20)

16.30 Claudia Lautensack:Random Laguerre Tessellations and Applicationsto Microstructures of Materials (p. 30)

17.00 Hendrik Schmidt:Networks and Stochastic Geometry - Models,Fitting, and Applications in Telecommunication (p. 41)

18.00 Dinner20.00 Get Together

7

8 PROGRAM

Thursday, February 15, 2007

09.00 - 12.00 Talks

09.00 Ilya Molchanov:Risk measures and random sets (p. 36)

09.30 Jürgen Kampf:Characterisation of convexity of random sets (p. 26)

10.00 Lars Michael Ho�mann:Mixed Measures of Convex Cylinders (p. 21)

10.30 Co�ee Break

11.00 Hans R. Künsch:Stochastic geometry and transport and�ow properties of porous media (p. 29)

11.30 Fred Hamprecht:Minkowski functionals in the analysisof surface microstructure (p. 19)

12.00 - 14.00 Lunch14.00 - 18.00 Talks

14.00 Elisabeth Kalko:Spatial statistics as a tool to assess seed dispersalby bats and distribution patterns of plants (p. 25)

14.30 Kris Vasudevan:Statistical Analysis of Spatial Point Patterns:Deep Seismic Re�ection Data (p. 43)

15.00 Stefanie Eckel:Analysis of the spatial correlations forrelative purchasing power in Baden-Württemberg (p. 15)

15.30 Co�ee Break

16.00 Aila Särkkä:Space-time growth-interaction models (p. 40)

16.30 Marian Kazda:Spatio-temporal evaluation of linear rootstructures - a challenge for the future (p. 27)

17.00 Pavel Grabarnik:Space-time modelling by Gibbs point process withhierarichical interactions: application to Ecology (p. 17)

18.00 Dinner

9

Friday, February 16, 2007

09.00 - 12.00 Talks

09.00 Peter Moerters:The double points of Brownian motion (p. 35)

09.30 Ste�en Winter:Fractal curvature measures (p. 44)

10.00 Daniel Meschenmoser:Estimation of the Mean Intrinsic Volumesof the Wiener Sausage (p. 34)

10.30 Co�ee Break

11.00 Torsten Mattfeldt:Statistical modelling of the patterns of planarsections of prostatic capillaries on thebasis of stationary Strauss hard-core processes (p. 32)

11.30 Sebastian Lück:A stochastic model for the reorganizationof keratin networks (p. 31)

12.00 - 14.00 Lunch14.00 - 18.00 Talks

14.00 Ingemar Kaj:Scaling properties of Poisson germ-grain models (p. 24)

14.30 Stella David:Asymptotic Goodness-of-Fit Tests for StationaryPoint Processes Based on the Integrated SquaredError of Product Density Estimators (p. 14)

15.00 Katja Ickstadt:Spatial point process modelling:Covariates and Computations (p. 23)

15.30 Co�ee Break

16.00 Carl Krill:Unraveling the mystery of the lognormal grain-sizedistribution induced by normal grain growth (p. 28)

16.30 Frank Fleischer:Simulation of typical Poisson-Voronoi-Cox-Voronoi cells with applications totelecommunication network modelling (p. 16)

17.00 Kai Matzutt:Construction of Random Laguerre Tessellations (p. 33)

18.00 Dinner

10 PROGRAM

Saturday, February 17, 2007

09.00 - 12.00 Talks

09.00 Joachim Ohser:Estimation of second order characteristics ofpoint �elds via frequency space (p. 37)

09.30 Ute Hahn:Scale invariant summary statistics for stationaryand inhomogeneous point processes (p. 18)

10.00 Zbyn¥k Pawlas:Variance estimators in marked point processes (p. 38)

10.30 Co�ee Break

11.00 Jonas Rumpf:Tropical Cyclone Risk Assessment Using a SpatialStochastic Model for Track Simulation (p. 39)

11.30 Viktor Benes:On an application of spatio-temporal point processes (p. 12)

12.00 - 14.00 Lunch

14.00 Departure

Abstracts

11

12 ABSTRACTS

Viktor Benes, Charles University Prague

On an application of spatio-temporal point processes

An introduction to spatio-temporal doubly stochastic point processes is presented towards anapplication in neurophysiology. It enables the description of overdispersion in a spike train modeldependent on the location of the recorded animal.

13

Luis M. Cruz-Orive, University of Cantabria

The pivotal formula

Cauchy's projection formula in R3 states that the surface area of a convex body equals four timesthe mean area of its orthogonal projection onto an isotropic plane. Recently a dual formula hasbeen published for an isotropic planar section (called a pivotal section) of a convex body througha �xed interior point (called a pivotal point): the surface area of the body equals four times themean area of the 'support set' of the section. The result is a special case of a more general resultvalid for an arbitrary bounded particle with piecewise smooth boundary. In general the surfacearea and the volume of the particle are proportional to corresponding mean functionals de�ned onthe pivotal section. The results are a consequence of a new representation of a motion invarianttest line in R3. The pivotal formula is chosen as a 'workhorse' to illustrate in an elementarymanner how stereological formulae may be developed using integral geometry and statistics.

The variance of the pivotal estimators is compared against those of the surfactor and the nucleator(namely the previously available estimators of surface area and volume, respectively) for a spherecontaining an eccentric pivotal point or nucleolus.

14 ABSTRACTS

Stella David, University of Augsburg

Asymptotic Goodness-of-Fit Tests for Stationary Point Processes Based on the Inte-

grated Squared Error of Product Density Estimators

The second-order properties of a stationary point process are determined by its product densityor - provided the process is isotropic - by its pair correlation function. In this talk we investigatekernel-type estimators for the product density and the pair correlation function and, in particular,the estimators' integrated squared error (ISE). In the setting of Brillinger-mixing point processesand Poisson cluster processes we present central limit theorems for the ISE of these estimators.Based on these CLTs we can construct asymptotic goodness-of-�t tests for the distribution of astationary point process.

15

Stefanie Eckel, Ulm University

Analysis of the spatial correlations for relative purchasing power in Baden-Württemberg

Joint work with W. Brachat-Schwarz, F. Fleischer, P. Grabarnik, V. Schmidt, and W. Walla

The relative purchasing power, i. e. the purchasing power per inhabitant is one of the keycharacteristics for businesses deciding on site selection. Apart from that it also plays a major rolein regional planning, pricing policy and market research. In this talk we investigate the spatialcorrelations for relative purchasing power with respect to the townships in Baden-Württemberg.In particular, changes in relative purchasing power are analysed for three di�erent time intervalsby means of distance dependent characteristics like the mark correlation function as well asSimpson indices and by tests on random labelling. It is shown that there are positive correlationsfor small distances between di�erent townships but that these positive correlations are becomingweaker over the years until they are almost non-existing. A conclusion from this loss of spatialcorrelations is that the relative purchasing power itself might also become more and more purelyrandom which means that the relative purchasing power in a township is less and less in�uencedby the relative purchasing power of townships nearby.

16 ABSTRACTS

Frank Fleischer, Ulm University

Simulation of typical Poisson-Voronoi-Cox-Voronoi cells with applications to telecom-

munication network modelling

Joint work with Catherine Gloaguen, Hendrik Schmidt, Volker Schmidt, and Florian Voss.

In this talk we consider a simulation algorithm for the typical cell of a Poisson-Voronoi-Cox-Voronoi tessellation (PVCVT). The generating point process for this Voronoi tessellation is givenby a stationary Cox point process whose random intensity measure is concentrated on the edgesof a Poisson-Voronoi tessellation. The algorithm is based on a Palm representation of Slivniaktype derived by an application of Neveu's exchange formula for jointly stationary point processes.The PVCVT can be used to model serving zones in telecommunication networks in the context ofthe Stochastic Subscriber Line Model developed by the Institute of Stochastics at Ulm Universityand France Télécom R&D, Paris. It is explained how to obtain e�cient estimators for related costfunctionals like shortest path lengths in two-level hierarchical models based on the simulation ofthe typical cell for a PVCVT. Thereby, earlier results for Poisson-line-Cox-Voronoi tessellationsare supplemented and extended.

17

Pavel Grabarnik, Russian Academy of Science

Space-time modelling by Gibbs point process with hierarichical interactions: application

to Ecology

Joint work with Aila Särkkä

We present a novel approach to modelling forest spatio-temporal data which has two ingredients:modelling the spatial structure of a forest stand by a Gibbs point process with hierarchicalinteractions (Högmander and Särkkä, 1999), and temporal modelling by Markov random �eldof life spans of individual trees. Rather than trying to �nd a full spatio-temporal model for thegrowth and mortality of trees, the tree pattern evolution is modelled by two stages.

At the �rst stage, we aim to quantify a tension of the competition process in terms of interactionsbetween trees within and between di�erent tree size classes by means of multitype Gibbs pointprocesses with hierarchical interactions. These processes consist of several type of points andallow to describe systems with nonsymmetric interaction and, therefore, are appropriate whenmodelling spatial structure of a forest stand since large trees a�ect small trees but not vice versa.We divide the trees into several size classes, which then form the hierarchical levels: the biggesttrees are not in�uenced by any other trees than the trees in the same size class. Trees in theother size classes, however, are in�uenced by the other trees in the same class as well as all thebigger trees. Relationships between trees within a hierarchical level (size class) are describedby symmetric interaction, while relationships between the levels (size classes) are described bynonsymmetric interaction.

At the second stage, we describe the tree pattern evolution, which is in our case due to themortality process, by a Markov random �eld model. The time dimension is included as a variablecharacterising the life span of a tree.

The approach is illustrated by the Temiryazevskaja dacha data set, collected on a pure, even aged,naturally established pine forest stand in Moscow region, consisting of locations and diametersof tree stems measured at 9 time points over 57 years.

References:

[1] Högmander, H. and Särkkä, A. 1999. Multitype spatial point patterns with hierarchicalinteractions. Biometrics 55, 1051-1058.

18 ABSTRACTS

Ute Hahn, University of Augsburg

Scale invariant summary statistics for stationary and inhomogeneous point processes

Second order statistics for stationary point processes in their traditional form are scale dependent.An example is Ripley's K-function, which gives the expected number of points in a ball aroundthe typical point, divided by the intensity λ of the process X, in terms of the reduced Palmexpectation this is written as K(r) := 1

λE!o(#X ∩ b(o, r)). The K-function of to two non

Poisson point processes that di�er only by a scale factor is di�erent. On the contrary, the K-function is invariant to uniform independent thinning, a fact that has been used by Baddeleyet al. (2000) for a generalization to inhomogeneous point processes that result from locationdependent thinning. Another way to analyse inhomogeneous point patterns is to assume thatthey result from a transformation of a homogeneous point process, as in Nielsen and Jensen(2004) and Fleischer et al. (2006), and to reconstruct the original process. Both methods arenot very appropriate in the case of an inhomogeneous pattern which consists of regions that looklocally like scaled versions of the same process. Suitable statistics are scale invariant, that is, theycoincide for point processes that can be transformed into each other by uniform scaling. We willtherefore introduce scale invariant renormalized variants of the known second order statistics.For example, a scale invariant version of the K function is given by K∗(r) := λK(rλ−1/d),which means that K∗(r) := E!

o(#X ∩ b(o, r/ d√

λ)). The renormalized second order statisticsgeneralize in a natural way to a form for inhomogeneous point processes obtained by localscaling. This is achieved by rede�ning the way inter-point distances are measured. Given theintensity function λ(x) of the process, the λ-scaled distance between two point u, v ∈ Rd shallbe de�ned as dλ(u, v) :=

∫[u,v] λ(x)1/ddx, where integration is along the segment u, v. This

includes rede�ning the ball bλ(x, r) as the set of all points with λ-scaled distance less than r to thecenter x. With this de�nition, the scale invariant K-function reads K∗(r) := E!

o(#X∩bλ(o, r)).It is not always clear which method is the best for a given inhomogeneous point pattern, sincemost often the genesis of the pattern can not be uniquely ascribed to a thinning, transformationor local scaling. We will discuss criteria that help to decide which statistics will give the bestcharacterization in this case.

References:

[1] Baddeley, A.J., Møller, J., Waagepetersen, R. (2000). Non- and semi-parametric estimationof interaction in inhomogeneous point patterns. Statistica Neerlandica, 54, 329�350.

[2] Fleischer, F., Beil, M., Kazda, M., and Schmidt, V. (2006). Analysis of spatial point patternsin microscopic and macroscopic biological image data. Pages 235�260 in Baddeley, A., Gregori,P., Mateu, J., Stoica, R., and Stoyan, D. (editors): Case Studies in Spatial Point Process

Modeling, volume 185 of Lecture Notes in Statistics, New York. Springer.

[3] Nielsen, L. S. and Jensen, E. B. V. (2004). Statistical inference for transformation inhomo-geneous point processes. Scandinavian Journal of Statistics, 31(1):131�142.

19

Fred Hamprecht, University of Heidelberg

Minkowski functionals in the analysis of surface microstructure

Joint work with Jochen Schmaehling

In the development and production of industrial parts, both the macroscopic shape and themicrostructure of the parts surface on a µm-scale strongly in�uence the parts properties. Forinstance, surfaces in frictional contact should be structured in a way to reduce the expected wearby optimizing its lubrication properties. Modern measurement techniques make it possible toacquire a complete three-dimensional height map of the surfaces. Although many proposals fora succinct description of such height maps have been made, these often lack a sound theoreticalbackground.

A simple but powerful approach is to use the Minkowski functionals of the excursion sets of thedata to characterize the surface structure. These functionals can be interpreted in di�erent waysdepending on the model used for the surface. Two models seem especially suited for technicalsurfaces: Gaussian random �elds for surfaces with no obvious structure, and Boolean grainmodels for surfaces consisting of smaller structuring elements, e. g. sintered materials. Thetalk presents a framework for the analysis of three-dimensional surface data using the Minkowskifunctionals. This approach allows for a stepwise data reduction: A complex data set is �rstreduced to three characterizing functions. By comparing measured and analytically calculatedfunctions, one can estimate model parameters from the characterizing functions, which thenserve as simpli�ed surface descriptors. The capabilities of the introduced methods are illustratedby means of simulations and comparison with experiments. Due to a new fast and accurateestimator for the characterizing functions, this technique is also suitable for time-critical taskslike the application in production automation.

20 ABSTRACTS

Lothar Heinrich, University of Augsburg

CLTs for Poisson hyperplane processes on non-spherical expanding sampling domains

It has been recently proved in [1] that the total number of vertices of convex polytopes induced bya stationary d�dimensional Poisson hyperplane process with intensity λ in a ball B% (centered atthe origin of Rd with unboundedly growing radius % ) is asymptotically normally distributed withvariance proportional to (λ %)2d−1 cd as % → ∞. In case the hyperplane process is additionallyisotropic the constant cd is explicitely known. In this talk we consider stationary and in particular

motion�invariant Poisson hyperplane processes in Rd subdividing an expanding sampling windowW% = % W , where W is a �xed compact body containing a ball Bε with ε > 0. We studythe dependence of cd on W . Two multivariate extensions of this CLT concerning the jointdistribution of numbers as well as of k−volumes of intersection k−�ats (for k = 0, 1, .., d − 1)in W% generalize results obtained in [1] for W = B1.

References:

[1] Heinrich, L., Schmidt, H., Schmidt, V. (2006) Central limit theorems for Poisson hyperplane

tessellations, Ann. Appl. Probab. 16, 919 - 950.

21

Lars Michael Ho�mann, Universität Karlsruhe (TH)

Mixed Measures of Convex Cylinders

Schneider and Weil obtained translative integral formulas for curvature measures of convex bodiesby introducing mixed measures of convex body. These results can be extended to arbitrary closedconvex sets since mixed measures are locally de�ned.

First, we will derive the special form of mixed measures of convex cylinders and adapt someformulas and results from to this setting. Then, we use these results to compute quermassdensities for (non-stationary Poisson) processes of convex cylinders and their Boolean modelsgeneralizing results by Davy and Fallert, respectively.

22 ABSTRACTS

Stephan Huckemann, Uni Göttingen

Isometric Lie Group Actions on Riemannian Manifolds and Principal Component Anal-

ysis

A general framework for principal component analysis (PCA) on quotient spaces that result froman isometric Lie group action on a Riemannian manifold is laid out. Such quotient spaces mayno longer carry a manifold structure, even more, they might be no longer Hausdor� spaces. Still,generalized geodesics and orthogonal projection on the quotient space as the key ingredients forPCA may be de�ned. Building on that an algorithmic method to perform PCA is developed. As atypical example where manifold and non-manifold quotients appear, this framework is applied toKendall's shape spaces and compared to the `classical' method of PCA by projecting to Euclideantangent space.

23

Katja Ickstadt, University of Dortmund

Spatial point process modelling: Covariates and Computations

Joint work with Sibylle Sturtz

Spatial epidemiology focusses on describing and modelling spatial data in dependence of covari-ates. Prominent examples are the CAR model (Besag et al., 1991), the conjugate Poisson�Gamma hierarchical model (Clayton and Kaldor, 1987), and clustering algorithms (e.g., Knorr-Held and Raÿer, 2000). Those classes of models assume data and covariates given at the samespatial resolution, whereas in real applications these are often measured at disparate scales. Theusual modelling approach aggregates both data and covariates to a common spatial scale leadingto the problem of the ecological fallacy.An alternative approach is based on the random �eld gen-eralization of Poisson�Gamma hierarchical models (Wolpert and Ickstadt, 1998), and includesdata and covariates on their original spatial resolutions. This approach was generalized by Bestet al. (2000) for applications in epidemiology and allows risk factors to be modelled multiplica-tively or additively leading to di�erent interpretations. We present the results of a big simulationstudy designed to analyze the behavior of these Poisson�Gamma hierarchical models under dif-ferent covariate scenarios, as well as a real data example. Compared to other spatial models, thesimulation study identi�es Poisson�Gamma random �eld models to be more �exible and easierto interpret for modelling di�erent spatial patterns with and without latent risk sources. Foradditively generated risks, multiplicative and additive modelling of covariates perform similar,whereas for multiplicatively generated data multiplicative modelling is favourable. Computationsare based on a Markov chain Monte Carlo scheme using the inverse Lévy measure algorithm(Wolpert and Ickstadt, 1998). The analyses are implemented in WinBUGS (Spiegelhalter et al.,2004). For linking R and WinBUGS, either the R-package R2WinBUGS (Sturtz et al., 2005) orthe BRUGS software (Thomas et al., 2006) may be employed.

References:

[1] Besag, J., York, J. and Mollié, A. (1991): Bayesian image restoration, with two applications inspatial statistics (with discussion), Annals of the Institute of Statistical Mathematics, 43, 1�59.[2] Best, N.G., Ickstadt, K. and Wolpert, R.L. (2000): Spatial Poisson regression for health andexposure data measured at disparate resolutions. Journal of the American Statistical Association,95, 1076�1088.[3] Clayton, D. and Kaldor, J. (1987): Empirical Bayes estimates of age-standardized relativerisks for use in disease mapping, Biometrics, 43, 671-681.[4] Knorr-Held, L. and Raÿer, G. (2000): Bayesian detection of clusters and discontinuities indisease maps, Biometrics, 56, 13�21.[5] Thomas, A., O'Hara, B., Ligges, U. and Sturtz, S. (2006): Making BUGS Open, R-News6/1, 12-17.[6] Wolpert, R.L. and Ickstadt, K. (1998): Poisson/gamma random �eld models for spatialstatistics, Biometrika, 85, 251�267.

24 ABSTRACTS

Ingemar Kaj, Uppsala University

Scaling properties of Poisson germ-grain models

We study properties of certain limiting random systems that arise by aggregation of sphericalgrains which are uniformly scattered according to a Poisson point process in d-dimensional space.The grains have random radius, independent and identically distributed, with a distribution whichis assumed to have a power law behavior either in zero or at in�nity. The resulting con�gurationsof mass suitably centered and normalized exhibit limit distributions under scaling, which areconveniently described in a random �elds setting.

25

Elisabeth Kalko, Ulm University & Smithsonian Tropical Research Institute

Spatial statistics as a tool to assess seed dispersal by bats and distribution patterns of

plants

Fruit-eating bats (Chiroptera) ful�l crucial ecosystem services as seed dispersers in tropical habi-tats for a wide range of plants including economically valuable trees such as the Karité (Vitellariaparadoxa) which forms the basis of nutritious cooking oil and shea butter and Cola cordifolia(Sterculiaceae) which produces edible fruits, valuable wood and bark that is used for medicinalpurposes. Furthermore, forest regrowth is fostered by pioneer plants, many of which are alsodispersed by bats such as Pepper plants (Piper sp.) in the Neotropics. To better understand theimpact bats have on the regeneration and distribution of plants requires a thorough understandingof their foraging behaviour, in particular the treatment and spatial distribution of seeds. Typi-cally, bats �y towards fruiting trees or shrubs and pick a ripe fruit in �ight. They do not processthose fruit in the fruiting tree, probably because of enhanced predator pressure, but �y away withit to a temporary dining roost. Small seeds are swallowed and are defecated mostly unharmedwithin 20-40 min either at the dining roost or during commutes. Large seeds are dropped at thefeeding roost. To assess the impact fruit-eating bats have on the distribution pattern and onrecruitment success of plants requires a detailed understanding of the whole dispersal process.As this is impossible to achieve by direct long-term observations, indirect approaches involvingspatial statistics are the method of choice to shed some more light into the dark. In my talk, Iwill be presenting examples where spatial statistics are being used a) to determine the associa-tion of feeding roosts of bats in relation to the distribution of trees, b) to assess and interpretpossible links between tree age classes with regard to human use (disturbed versus undisturbedareas) and c) to predict plant distributions in relation to spatial data gained from foraging batsby radiotracking. Ultimately, a better understanding of the dispersal process through analysisof spatial associations between bats and plants and in case of anthropogenic in�uence betweendistribution of plants in disturbed versus undisturbed areas is crucial for the development of ef-fective management strategies in order to maintain viable population of economically importantplants and to foster natural regeneration.

26 ABSTRACTS

Jürgen Kampf, Universität Karlsruhe (TH)

Characterisation of convexity of random sets

It was shown in [1] that the expected parallel volume of a planar random compact set is apolynomial, i� the set is almost surely convex. In this talk we will obtain a stronger version ofthis characterisation by a di�erent approach. In particular, we can then apply our results to anextension of the well-known Wills functional to general compact sets.

References:

[1] Hug, Last, Weil: Polynomial parallel volume, convexity and contact distributions of randomsets, Probab. Theory Relat. Fields 135, p.169-200, 2006

27

Marian Kazda, Ulm University

Spatio-temporal evaluation of linear root structures - a challenge for the future

Roots are functional plant parts for water and nutrient acquisition. Root distribution patternsdepend on site factors (water and nutrient availability, soil pH, aeration etc.) and also arespecies-speci�c. Interdisciplinary evaluation of root distribution on soil trench pro�les showed rootclustering, which di�ered according to species in intensity and the size of clusters (Fleischer et al.2006). Images of �ne roots obtained from minirhizotrons (transparent tubes in soil for periodicalendoscopic imaging) were evaluated by our group in terms of root production and mortality. Suchdata enable calculation of root turnover rates but very little is known about �ne root architecturein spatio-temporal terms. Thus, several thousands of sequential images available for tree species(Picea abies, Fagus sylvatica) as well as for the herbaceous Carex acutiformis can be used to studythe following questions: is the topology and structure of �ne roots branching species-speci�c?how do the architectural parameters depend upon soil properties? is the architecture changed inthe presence of mycorrhiza? are there temporal changes in the �ne root architecture? is therean interaction between root density parameters and root longevity?

Such information will substantially improve our understanding of functions connected to rootcharacteristics and acquisition of water and nutrients.

References:

[1] Frank Fleischer, Stefanie Eckel, Marian Kazda, Iris Schmid and Volker Schmidt, Point processmodelling of root distribution in pure stands of Fagus sylvatica and Picea abies, Canadian Journalof Forest Research, vol. 36(1), 2006, pp. 227-237.

28 ABSTRACTS

Carl Krill, Ulm University

Unraveling the mystery of the lognormal grain-size distribution induced by normal grain

growth

The latency period of infectious diseases, the daily value of the pollution standard index, thenumber of letters in spoken words: these are but a few of the many quantities known to followa lognormal distribution - a commonly encountered circumstance in the life and social sciences.Quite the opposite is true in the �eld of materials, however, in which most statistical parametersseem to be governed by a Gaussian distribution. Nevertheless, there does exist one well-knownmaterials phenomenon that is thought to be fundamentally lognormal in nature - namely, graingrowth - but to this day no one understands exactly why this happens to be the case. In fact,the most widely accepted theoretical model for grain growth entails a size distribution that iscompletely incompatible with the lognormal shape found in experiment. One possible explanationfor this discrepancy lies in the mean-�eld approximation inherent to analytic models for normalgrain growth: they ignore the existence of growth-induced correlations in the sizes of neighboringgrains in polycrystalline microstructures. We have attempted to quantify such nearest-neighborsize correlations via a combination of large-scale phase-�eld simulations of grain growth in 3Dand three-dimensional microstructural characterizations of real polycrystalline specimens by x-raymicrotomography. The results suggest that only part of the apparent lognormality of measuredgrain-size distributions can be attributed to the e�ect of size correlations. Paradoxically, this�nding raises the intriguing possibility that size distributions induced by grain growth aren'treally lognormal, after all!

29

Hans R. Künsch, ETH Zürich

Stochastic geometry and transport and �ow properties of porous media

In soil physics, the e�ect of geometric properties of the pore space on �ow and transport propertiesis still poorly understood. In particular, one would like to know which geometric properties ofthe pore space have a strong in�uence on the �ow properties. Recently, there has been a lotof progress in imaging technology allowing to map the pore space of some soils very accurately.Still, such images are costly and therefore for a systematic investigation of the relation betweengeometric characteristics and �ow properties it would be useful to be able to simulate quicklypore spaces with given geometric characteristics. I will brie�y report on a joint project with soilscientists from ETH Zurich and numerical analysts from TU Braunschweig where we have startedsuch an investigation. In particular, we have generated Boolean models with di�erent values ofthe speci�c Minkowski functionals and studied how this a�ects �ow properties. Unfortunately,the Boolean model is not able to generate samples that are visually close to real pore spaces, andit seems that for the prediction of �ow properties the Minkowski functionals must be combinedwith information on the pore size distribution.

30 ABSTRACTS

Claudia Lautensack, Fraunhofer Institut für Techno- und Wirtschaftsmathematik

Random Laguerre Tessellations and Applications to Microstructures of Materials

Random tessellations are classical models from stochastic geometry which are used in a wide rangeof application areas. The most well-known models are Voronoi and Johnson-Mehl (additivelyweighted Voronoi) tessellations. A huge number of results for moments as well as distributionsof their cell characteristics exists.

Laguerre (or power) tessellations are another type of weighted Voronoi tessellations which possessvery promising properties. This talk is concerned with geometrical properties of random Laguerretessellations. The focus is on tessellations generated by a homogeneous marked Poisson process.Formulas for some cell characteristics such as the intensity of vertices or the edge length densityare given.

As an example of application we discuss models for the microstructure of cellular materials basedon random Laguerre tessellations.

31

Sebastian Lück, Ulm University

A stochastic model for the reorganization of keratin networks

Joint work with Wolfgang Arendt, Michael Beil, Frank Fleischer, Stéphanie Portet and VolkerSchmidt

Keratin networks play a dominant role in protecting the integrity of biological cells when theyare exposed to mechanical stress and determine the elasticity of the cytoplasm. Changes ofnetwork morphology adjust the elastic properties of the cell and have e.g. been linked to themigration of cancer cells and metastasis. Network reorganization processes are, however, not wellunderstood and cannot be studied by current microscopy techniques. A mathematical model willbe presented that has been designed to study the e�ects of di�erent hypothetical reorganizationscenarios on network morphology by means of computer simulation. The model belongs to theclass of piecewise-deterministic Markov processes. Its state space is a hybrid type incorporating ageometric component describing the network as well as a function space modelling concentration�elds of soluble keratin in the cytoplasm. Di�usion of the soluble keratin in the cytoplasm hasbeen described by means of a partial di�erential equation with periodic boundary conditions.Existence and uniqueness of a solution have been ensured by functional analytical techniquesfrom the theory of bilinear forms.

The talk will focus on introducing the biological background and giving an overview of themathematical modelling concept. Some �rst simulation results will be presented.

32 ABSTRACTS

Torsten Mattfeldt, Ulm University

Statistical modelling of the patterns of planar sections of prostatic capillaries on the

basis of stationary Strauss hard-core processes

Joint work with Stefanie Eckel, Frank Fleischer, and Volker Schmidt

Blood capillaries in glandular tissues may be considered as biological realizations of stationary andisotropic �bre processes. The geometry of such �bre processes may be investigated stereologicallyfrom sections by an explorative approach, where the capillaries are characterized in terms of theirreduced pair correlation functions (Krasnoperov & Stoyan, 2004). This approach was recentlyapplied to multiple specimens of normal prostatic tissue and prostatic carcinomas using computer-intensive methods such as bootstrapping for statistical inference (Mattfeldt & Fleischer, 2005,2006; Mattfeldt et al., 2006).

In the present study, an attempt was made to go beyond the explorative approach and to char-acterize the same point patterns by means of a parametric model. For this purpose, the �exibleclass of Gibbs processes was considered. Speci�cally, stationary Strauss hard-core processes were�tted to the observed point patterns. The goodness of �t achieved by the model was checked bysimulations with the Markov chain Monte Carlo method using the Metropolis-Hastings algorithm.Model �tting and simulations were performed with the help of the spatstat package under R.In the tumour tissue, a highly signi�cant decrease of the interaction parameter of the Strausshard-core process could be found as compared to the normal prostatic tissue. This �nding isdiscussed in terms of a loss of the normal lobular architecture of the glands in the tumour tissue.

References:

[1] Krasnoperov, R.A. & Stoyan, D. (2004) Second-order stereology of spatial �bre systems. J.Microsc. 216, 156�164.

[2] Mattfeldt, T. & Fleischer, F. (2005) Bootstrap methods for statistical inference from stereo-logical estimates of volume fraction. J. Microsc. 218, 160�170.

[3] Mattfeldt, T. & Fleischer, F. (2006) Computer-intensive methods for statistical inferencefrom stereological data. Proc. Int. Conf. Spat. Statist. Stoch. Geom. (S4G), Prague. Ed. R.Lechnerova, I. Saxl V. Benes, 349�360.

[4] Mattfeldt, T. Eckel, S., Fleischer, F. & Schmidt, V. (2006) Statistical analysis of reducedpair correlation functions of capillaries in the prostate gland. J. Microsc. 223, 107�119.

33

Kai Matzutt, Bielefeld University

Construction of Random Laguerre Tessellations

A Laguerre tessellation (or tiling) in Euclidean space can be viewed as a deformed Voronoitessellation. A non trivial deformation is achieved by shifting the faces of the cells accordingto some 'relative weights' assigned to the generating points. I discuss a method to produce arandom Laguerre tessellation as a cluster process. The basic idea is to take the image of someappropriately marked Poisson point process under a certain mapping which guarantees all desiredproperties as a face-to-face tiling.

34 ABSTRACTS

Daniel Meschenmoser, Ulm University

Estimation of the Mean Intrinsic Volumes of the Wiener Sausage

Joint work with J. Rataj and E. Spodarev

The dilated path of the Brownian motion in Rd is called a Wiener sausage. This randomcompact set can be almost surely approximated (in the sense of Hausdor� metric) by a sequenceof polyconvex sets. In the two-dimensional case, the curvature measures of this approximationconverge weakly to the curvature measures of the Wiener sausage. Based on these convergenceresults, the mean intrinsic volumes of the Wiener sausage are computed numerically using MonteCarlo simulations. As functionals depending on the dilation radius, the estimators are comparedto known asymptotic results.

35

Peter Moerters, University of Bath

The double points of Brownian motion

It is well-known that in dimensions two and three a Brownian path has double points almostsurely. The set of double points is an interesting random fractal and I will review some results,old and new, and some open questions about the fractal geometry of this set.

36 ABSTRACTS

Ilya Molchanov, University of Bern

Risk measures and random sets

Risk measures are monotonic translation-covariant functions of random variables. The particularfamily of coherent risk measures satis�es further homogeneity and subadditivity properties. Thistalk surveys the basic facts concerning general and coherent risk measures and emphasises theirrelationships to random sets and the concept of depth-trimmed regions from the multivariatestatistics.

37

Joachim Ohser, University of Applied Sciences Darmstadt

Estimation of second order characteristics of point �elds via frequency space

In stochastic geometry the spectral analysis is mainly used for point processes, see Bartlett (1963,1964) for the theoretic foundations for one and two dimensional point processes and Renshaw(1983) and Mugglestone (1996) for applications to ecological data. More general approachescan be found in Daley & Vere-Jones (1988, Chapter 11) and Ripley (1981). Daley and Vere-Jones generalised Bartlett's theory to stationary random measures with an additional invarianceproperty. Ripley developed in the spectral analysis for general spatial random processes.

Since there are similarities between random sets and point processes, it is obvious to extent thespectral theory introduced in Koch et al. (2003) and Unverzagt (2005) to a random measureassociated with a stationary point process. We follow these approaches and derive a method ofestimating the pair correlation of a point process via frequency space. The presented estimatorinvolves a very natural smoothing technique basing on the mapping of the point sites to thepoint lattice associated with an digital image. It is shown that the estimator is asymptoticallyunbiased for decreasing lattice spacing.

38 ABSTRACTS

Zbyn¥k Pawlas, Charles University Prague

Variance estimators in marked point processes

We consider stationary marked point processes on the d-dimensional Euclidean space with one-dimensional mark space. Our aim is to study the statistical properties of estimators of the varianceof the typical mark variable. The standard sample variance can be substantially biased due tothe dependences among marks. The possibilities to reduce this bias are discussed. We proposean estimator based on U -statistics of second order. Theoretical computation and simulations forselected types of marked point process show that the sample variance has lower mean squarederror than the estimator based on U -statistics unless the spatial correlation is very strong.

39

Jonas Rumpf, Ulm University

Tropical Cyclone Risk Assessment Using a Spatial Stochastic Model for Track Simula-

tion

Joint work with Peter Höppe, Ernst Rauch, Volker Schmidt, and Helga Weindl

A method for assessing the risks of damages caused by tropical cyclone landfall is introduced:First, a model for the basin-wide Monte-Carlo-simulation of the tropical cyclone tracks is de-veloped and applied to data from the North Atlantic ocean basin. This model is based on aspatial random walk. Then, a large number of synthetic tracks is generated by means of animplementation of this model. This synthetic data is far more comprehensive than the availablehistorical data, while exhibiting the same basic characteristics, thereby creating a more soundbasis for the assessment of landfall risk than previously available, especially with regard to longterm risk.

40 ABSTRACTS

Aila Särkkä, Chalmers University Of Technology

Space-time growth-interaction models

Joint work with Eric Renshaw

Abstract: We suggest to use immigration-growth spatial interaction processes as models insituations, where both locations of points (e.g. trees) and measurements (e.g. diameter orheight) develop according to a space-time stochastic process. New immigrants arrive randomlyin time according to a Poisson process, have uniformly distributed locations on the study regionand are assigned (small) marks. In the successive small time intervals, each individual eitherdies naturally with some probability, or else it undergoes a deterministic incremental size change,which depends on an individual growth function and a spatial interaction function. We discusstwo growth functions (linear and logistic) and two interaction functions (symmetric and non-symmetric), and suggest to estimate the parameters of these models by the method of leastsquares. We have applied our approach to model growth of trees in a forest but the modelscould be useful in several other areas as well.

41

Hendrik Schmidt, France Telecom NSM/RD/RESA/NET

Networks and Stochastic Geometry - Models, Fitting, and Applications in Telecommu-

nication

Joint work with Frank Fleischer, Catherine Gloaguen, and Volker Schmidt

In recent years, spatial stochastic models have found widespread applications in network modelingand provide established methods to represent structural details of real data. The so-calledStochastic Subscriber Line Model (SSLM), developed in joint research by France Télécom R&Dand the Institute of Stochastics at Ulm University, constitutes an example of a comprehensivestochastic-geometric approach to model telecommunication access networks.

In this talk we introduce the SSLM along with the employed models of stochastic geometry, e. g.random tessellations used to represent the geometric structures of real infrastructure data. Inparticular, by proposing a statistical �tting procedure, we address the question how the connectionbetween these models and given data can be made. Moreover, we present an approach to costmeasurement based on random placement of point processes on underlying linear structures.

42 ABSTRACTS

Tomasz Schreiber, Nicolaus Copernicus University Torun

Polygonal Markov �elds: simulation algorithms and applications for image segmentation

Joint work with Marie-Colette van Lieshout

Polygonal Markov �elds, originally introduced by Arak and Surgailis, are continuum ensembles ofpolygonal contours in the plane, enjoying a number of interesting properties including consistency,isometry invariance, two-dimensional germ-Markov property and availability of exact formulae forvarious numeric characteristics. With their Gibbs-style construction the polygonal Markov �eldsshare many features with the two-dimensional Ising model and, more generally, with lattice-indexed Markov �elds. This seems to make them particularly well suited for image segmentationpurposes where in principle they should do the same work the lattice-indexed Markov �elds aredesigned for, while being completely free of lattice artifacts due to their continuum nature. Themajor obstacle for these applications has been so far the lack of e�cient simulation algorithms.The �rst Metropolis-Hastings sampler has been developed by Cli�ord and Nicholls. In this talk Iwill present a completely new simulation algorithm for polygonal �elds, introducing new movesof global nature aimed at obtaining good mixing rates and based on the so-called disagreementloops and dynamic representation of polygonal �elds. The algorithm has been developed by theauthor in cooperation with Marie-Colette van Lieshout and Rafal Kluszczynski and encouragingresults have been reported in test applications.

43

Kris Vasudevan, University of Calgary

Statistical Analysis of Spatial Point Patterns: Deep Seismic Re�ection Data

Joint work with S. Eckel, F. Fleischer, V. Schmidt and F.A. Cook

Spatial point patterns generated from bitmaps of images of processed re�ection seismic pro�lesare analyzed to quantify the re�ectivity patterns. The point process characteristics for twodi�erent regions of a deep seismic re�ection pro�le in northwestern Canada demonstrate thatin both cases the points are not randomly distributed and that the point pattern distributionis di�erent between the regions. The cluster e�ects for small point pair distances are strongerfor the region of data where there is strong sedimentary layering than for the region where thelayering is less distinct. As a result, it appears that future developments in point pattern analysismay provide a new tool for analysing spatial variations in re�ection data.

44 ABSTRACTS

Ste�en Winter, Universität Karlsruhe (TH)

Fractal curvature measures

Curvature measures are an important tool in geometry. Originally introduced for sets with positivereach, certain extensions to more general classes of sets are known. One way of extendingcurvature measures is to use approximations of F by its parallel sets

Fε = {x : dist(x, F ) ≤ ε}.

Following this approach, we introduce the notion of fractal curvature and fractal curvature

measure, respectively, for certain classes of fractal sets. For such sets some rescaling is necessaryin order to obtain limits.

For certain classes of self-similar sets, the existence of (averaged) fractal curvatures can beshown. They can be computed explicitly and are in a certain sense 'invariants' of the sets, whichmay help to distinguish and classify fractals. The corresponding fractal curvature measures canalso be characterized. The concept can be seen as a generalization of the well known Minkowskicontent and, as a special application, allows to 'localize' this notion. In particular, we will discusswhich of the usual properties of curvature measures remain valid for the fractal counterparts.

List of Participants

Felix Ballani

Institute of Computer ScienceFreie Universität BerlinArnimallee 314195 Berlin, [email protected]

Volker Baumstark

Institute for StochasticsUniversität Karlsruhe (TH)Englerstraÿe 276128 Karlsruhe, [email protected]

Viktor Benes

Department of Probability and Mathematical StatisticsCharles UniversitySokolovskà 83Praha 8, Czech RepublicViktor.Benes@m�.cuni.czTalk: On an application of spatio-temporal point processes (p. 12)

Luis Cruz-Orive

Department of Mathematics, Statistics and ComputationUniversity of CantabriaAvda. Los Castros, s/n39005 Santander, [email protected]: The pivotal formula (p. 13)

45

46 LIST OF PARTICIPANTS

Stella David

Chair of Stochastics and its ApplicationsUniversity of Augsburg86135 Augsburg, [email protected]: Asymptotic Goodness-of-Fit Tests for Stationary Point Processes Basedon the Integrated Squared Error of Product Density Estimators (p. 14)

Stefanie Eckel

Institute of StochasticsUlm UniversityHelmholtzstraÿe 2289081 Ulm, [email protected]: Analysis of the spatial correlations for relativepurchasing power in Baden-Württemberg (p. 15)

Frank Fleischer

Institute of StochasticsUlm UniversityHelmholtzstraÿe 1889081 Ulm, Germanyfrank.�[email protected]: Simulation of typical Poisson-Voronoi-Cox-Voronoi cells withapplications to telecommunication network modelling (p. 16)

Norbert Gäng

Institute of Systematic Botany and EcologyUlm UniversityAlbert Einstein Allee 4789081 Ulm, [email protected]

Catherine Gloaguen

France Telecom Paris38/40 rue du General Leclerc92794 Issy-Moulineaux Cedex 9, [email protected]

47

Pavel Grabarnik

Institute of Physico-Chemical and Biological Problems of Soil ScienceRussian Academy of Science142290 Pushchino, Moscow region, [email protected]: Space-time modelling by Gibbs point process withhierarichical interactions: application to Ecology (p. 17)

Ute Hahn

Chair of Stochastics and its ApplicationsUniversity of Augsburg86135 Augsburg, [email protected]: Scale invariant summary statistics for stationaryand inhomogeneous point processes (p. 18)

Fred Hamprecht

Interdisciplinary Center for Scienti�c Computing (IWR)University of HeidelbergIm Neuenheimer Feld 36869120 Heidelberg, [email protected]: Minkowski functionals in the analysis of surface microstructure (p. 19)

Kordula Heinen

Institute of Systematic Botany and EcologyUlm UniversityAlbert-Einstein-Allee 1189081 Ulm, [email protected]

Lothar Heinrich

Chair of Stochastics and its ApplicationsUniversity of Augsburg86135 Augsburg, [email protected]: CLTs for Poisson hyperplane processes onnon-spherical expanding sampling domains (p. 20)

Mario Hoerig

Universität Karlsruhe (TH)[email protected]


Lars Ho�mann

Institut für Algebra und GeometrieUniversität Karlsruhe (TH)Englerstraÿe 276131 Karlsruhe, Germanylars.ho�[email protected]: Mixed Measures of Convex Cylinders (p. 21)

Stephan Huckemann

Institute for Mathematical StochasticsUniversity of GöttingenMaschmühlenweg 8-1037073 Göttingen, [email protected]: Isometric Lie Group Actions on Riemannian Manifoldsand Principal Component Analysis (p. 22)

Daniel Hug

Mathematisches InstitutUniversity of FreiburgEckerstraÿe 179104 Freiburg, [email protected]

Katja Ickstadt

Fachbereich Statistik / Mathematische Statistik und biometrische AnwendungenUniversity of Dortmund44221 Dortmund, [email protected]: Spatial point process modelling: Covariates and Computations (p. 23)

Holger Janzer

Institute of Theoretical PhysicsUlm UniversityAlbert-Einstein-Allee 1189069 Ulm, [email protected]

Ingemar Kaj

Mathematical Statistics GroupUppsala UniversityÅngströmlaboratoriet, Lägerhyddsv. 175106 Uppsala, [email protected]: Scaling properties of Poisson germ-grain models (p. 24)

49

Elisabeth Kalko

Department of Experimental EcologyUlm UniversityAlbert-Einstein Allee 1189069 Ulm, GermanyPhone: 0049 (0)731 502 2660 or 2661Fax: 0049 (0)731 502 [email protected]: Spatial statistics as a tool to assess seed dispersalby bats and distribution patterns of plants (p. 25)

Jürgen Kampf

Institute for StochasticsUniversität Karlsruhe (TH)Englerstraÿe 276128 Karlsruhe, [email protected]: Characterisation of convexity of random sets (p. 26)

Wolfgang Karcher

Institute of StochasticsUlm UniversityHelmholtzstraÿe 1889081 Ulm, [email protected]

Marian Kazda

Institute of Systematic Botany and EcologyUlm UniversityAlbert-Einstein-Allee 1189081 Ulm, GermanyPhone: 0731-50-22702Fax: [email protected]: Spatio-temporal evaluation of linear root (p. 27)

Markus Kiderlen

Department of Mathematical SciencesUniversity of AarhusNy Munkegade, Bygning 15308000 Århus C, [email protected]


Valerie Klatte


Thomas Klein

Chair of Stochastics and its ApplicationsUniversity of Augsburg86135 Augsburg, [email protected]

Takis Konstantopoulos

School of Mathematical & Computer SciencesHeriot-Watt UniversityUK EH14 4AS Edinburgh, Scotland, [email protected]

Carl Krill

Institute of Micro and NanomaterialsUlm UniversityAlbert Einstein Allee 4789081 Ulm, [email protected]

Hans-Rudolf Kuensch

Seminar for StatisticsSwiss Federal Institute of Technology ZurichLeonhardstraÿe 278092 Zürich, [email protected]: Stochastic geometry and transport and �ow properties of porous media (p. 29)

Wei Lao


51

Günter Last


Claudia Lautensack

Department of Models and Algorithms in Image ProcessingUniversity of Applied Sciences DarmstadtFraunhofer Institut für Techno- und Wirtschaftsmathematik (ITWM)Fraunhofer-Platz 167663 Kaiserslautern, GermanyPhone: +49 (0)631/31600-4250Fax: +49 (0)631/[email protected]: Random Laguerre Tessellations and Applications to Microstructures of Materials (p. 30)

Werner Lehnert

Zentrum für Sonnenenergie und Wassersto�-Forschung (ZSW) Baden-WürttembergHelmholtzstraÿe 889081 Ulm, [email protected]

Sebastian Lück

Institute of StochasticsUlm UniversityHelmholtzstraÿe 1889081 Ulm, [email protected]: A stochastic model for the reorganization of keratin networks (p. 31)

Raphael Mainiero



Torsten Mattfeldt

Institute of PathologyUlm UniversityAlbert-Einstein-Allee 1189081 Ulm, [email protected]: Statistical modelling of the patterns of planar sections of prostatic capillarieson the basis of stationary Strauss hard-core processes (p. 32)

Kai Matzutt

Department of Mathematics (SFB701)Bielefeld UniversityPostfach 10013133501 Bielefeld, [email protected]: Construction of Random Laguerre Tessellations (p. 33)

Michael Mayer

Department of Mathematical Statistics and Actuarial ScienceUniversity of BernSidlerstr. 53012 Bern, [email protected]

Daniel Meschenmoser

Institute of StochasticsUlm UniversityHelmholtzstraÿe 1889081 Ulm, [email protected]: Estimation of the Mean Intrinsic Volumes of the Wiener Sausage (p. 34)

Peter Moerters

Department of Mathematical SciencesUniversity of BathClaverton DownBath BA2 7AY, [email protected]: The double points of Brownian motion (p. 35)

53

Ilya Molchanov

Department of Mathematical Statistics and Actuarial ScienceUniversity of BernSidlerstr. 53012 Bern, [email protected]: Risk measures and random sets (p. 36)

Frederic Morlot

France Telecom Paris38-40, rue du General Leclerc92794 Issy-les-Moulineaux Cedex 9, [email protected]

Werner Nagel

Institut für StochastikFriedrich-Schiller-University JenaErnst-Abbe-Platz 1-407743 Jena, [email protected]

Ilkka Norros

VTT FinlandTechnical Research Centre of FinlandP.O.Box 1000FIN-02044 , FinlandIlkka.Norros@vtt.�

Joachim Ohser

Fachbereich Mathematik und NaturwissenschaftenUniversity of Applied Sciences DarmstadtHaardtring 10064295 Darmstadt, [email protected]: Estimation of second order characteristics of point �elds via frequency space (p. 37)

Zbynek Pawlas

Department of Probability and Mathematical StatisticsCharles UniversitySokolovskà 83Praha 8, Czech [email protected]�.cuni.czTalk: Variance estimators in marked point processes (p. 38)


Daniel Piechowski


Michaela Prokesova

Thiele Centre for Applied Mathematics in Natural ScienceUniversity of AarhusNy Munkegade8000 Århus C, [email protected]

Johannes Renfordt


Susanne Rothbauer


Jonas Rumpf

Institute of StochasticsUlm UniversityHelmholtzstraÿe 1889081 Ulm, [email protected]: Tropical Cyclone Risk Assessment Using a SpatialStochastic Model for Track Simulation (p. 39)

Aila Särkkä

Department of Mathematical StatisticsGöteborg UniversityChalmers tvärgata 341296 Göteborg, [email protected]: Space-time growth-interaction models (p. 40)

55

Manfred Sauter


Katja Schladitz

Department of Models and Algorithms in Image ProcessingFraunhofer Institut für Techno- und Wirtschaftsmathematik (ITWM)Fraunhofer-Platz 167663 Kaiserslautern, [email protected]

Hendrik Schmidt

France Telecom Paris38-40, rue du General Leclerc92794 Issy-les-Moulineaux Cedex 9, FrancePhone: +33(0)[email protected]: Networks and Stochastic Geometry - Models, Fitting,and Applications in Telecommunication (p. 41)

Volker Schmidt


Tomasz Schreiber

Faculty of Mathematics and Computer ScienceNicolaus Copernicus University TorunChopina 12/1887-100 Torun, [email protected]: Polygonal Markov �elds: simulation algorithms andapplications for image segmentation (p. 42)

Malte Spiess



Evgeny Spodarev


Peter Straka


Tetyana Sych

Department of Models and Algorithms in Image ProcessingFraunhofer Institut für Techno- und Wirtschaftsmathematik (ITWM)Fraunhofer-Platz 167663 Kaiserslautern, [email protected]

Ralf Thiedmann


Kris Vasudevan

Department of Geology and GeophysicsUniversity of Calgary2500 University Drive NWT3B 4Y3 Calgary, Alberta, [email protected]: Statistical Analysis of Spatial Point Patterns: Deep Seismic Re�ection Data (p. 43)

Florian Voss

Institute of StochasticsUlm UniversityHelmholtzstraÿe 1889081 Ulm, Germany�[email protected]

57

Wolfgang Weil

Institute for Algebra and GeometryUniversität Karlsruhe (TH)Englerstraÿe 276128 Karlsruhe, [email protected]

Ste�en Winter

Institute for Algebra and GeometryUniversität Karlsruhe (TH)Englerstraÿe 276131 Karlsruhe, [email protected]: Fractal curvature measures (p. 44)

Stochastic Geometr,y Spatial Statistics, and their ... · also biologists, ecologists, engineers,...

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