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Quermass-interaction processes: conditions for stability

W. S. Kendall, M. N. M. van Lieshout, A. J. Baddeley
1999 Advances in Applied Probability  
Given a Poisson point process, on each point one places a grain, a (possibly random) compact convex set. Let Ξ be the union of all grains.  ...  We consider a class of random point and germ-grain processes, obtained using a rather natural weighting procedure.  ...  Part of WSK's work on this project was funded by the EU research grant ERB-CHRX-CT94-0449.  ... 
doi:10.1017/s0001867800009137 fatcat:rlziir7mjngspdt2bgj6xcmsti

Quermass-interaction processes: conditions for stability

W. S. Kendall, M. N. M. van Lieshout, A. J. Baddeley
1999 Advances in Applied Probability  
Given a Poisson point process, on each point one places a grain, a (possibly random) compact convex set. Let Ξ be the union of all grains.  ...  We consider a class of random point and germ-grain processes, obtained using a rather natural weighting procedure.  ...  Part of WSK's work on this project was funded by the EU research grant ERB-CHRX-CT94-0449.  ... 
doi:10.1239/aap/1029955137 fatcat:g7xywmz5g5eqvdb25vfp5i335a

Generation of 3D representative volume elements for heterogeneous materials: A review

Swantje Bargmann, Benjamin Klusemann, Jürgen Markmann, Jan Eike Schnabel, Konrad Schneider, Celal Soyarslan, Jana Wilmers
2018 Progress in Materials Science  
methods targeting simulation of the physical process(es) responsible for the microstructure formation and evolution, and (iii) geometrical methods concentrating solely on mimicking the morphology (ignoring  ...  the physical basis of the microstructure formation process).  ...  We gratefully acknowledge financial support from the German Research Foundation (DFG) via SFB 986 ''M 3 ", projects A5, B6, and B8.  ... 
doi:10.1016/j.pmatsci.2018.02.003 fatcat:aeie32pxmnfgdge2wmsnzadhvq

A Tractable Analysis of the Blind-spot Probability in Localization Networks under Correlated Blocking [article]

Sundar Aditya, Harpreet S. Dhillon, Andreas F. Molisch, Hatim Behairy
2018 arXiv   pre-print
In this paper, we analyze the blind spot probability of a typical target by using stochastic geometry to model the randomness in the obstacle and anchor locations.  ...  In localization applications, the line-of-sight between anchors and targets may be blocked by obstacles in the environment.  ...  were modeled as random line-segments using a germ-grain model.  ... 
arXiv:1801.08560v2 fatcat:nz7j4vorkvbfrmaf56b3ctmya4

Random Set Theory and Problems of Modeling

Noel Cressie, G. M. Laslett
1987 SIAM Review  
Collections of objects (the data) are assimilated to a random set (the model), whose parameters provide description and/or explanation.  ...  The purpose of this article is to show the potentials and limitations of a probabilistic and statistical approach.  ...  We would like to thank the referees for perceptive comments which led to substantial improvements in the paper.  ... 
doi:10.1137/1029111 fatcat:76f3wug35ff3bhwfspojpy22si

Analysis of femtocell coverage fraction and isolated probability using stochastic geometry

Huanle Zhang, Jian Liu, Yupeng Jia, Yulu Ma
2013 2013 IEEE Global Communications Conference (GLOBECOM)  
The randomness of the locations of femtocells brings us a lot of difficulties to analyze and compare.  ...  Then, we add restriction on the minimum distance between each femtocell base station and compare the performance of cases with and without restrictions.  ...  Then the associated Boolean model is the union: Ξ BM = i (x i + Ξ i ) (2) In Boolean model, points and RACs are also called germs and grains, respectively.  ... 
doi:10.1109/glocomw.2013.6855693 fatcat:tpceh3eagbaq5ctg4j326ditqa

Generalizing the Abbott–Firestone curve by two new surface descriptors

J. Schmähling, F.A. Hamprecht
2007 Wear  
By comparing measured and analytically calculated functions, one can estimate model parameters from the characterizing functions, which then serve as simplified surface descriptors.  ...  In surface characterization tasks, the material ratio function is one of the most important tools and the basis for many parameters defined in international standards.  ...  At each of these random points (also called germs), a 3D-object (called a grain) of random shape and rotation is placed 7 .  ... 
doi:10.1016/j.wear.2007.01.025 fatcat:o2xifxa5x5gt3jeemkirpjtbra

Stochastic geometry and random graphs for the analysis and design of wireless networks

M. Haenggi, J.G. Andrews, F. Baccelli, O. Dousse, M. Franceschetti
2009 IEEE Journal on Selected Areas in Communications  
Often, the location of the nodes in the network can be modeled as random, following for example a Poisson point process.  ...  In this case, different techniques based on stochastic geometry and the theory of random geometric graphs -including point process theory, percolation theory, and probabilistic combinatorics -have led  ...  ACKNOWLEDGEMENTS The first two authors would like to acknowledge the support of DARPA IPTO's IT-MANET program through grant W911NF-07-1-0028.  ... 
doi:10.1109/jsac.2009.090902 fatcat:kdjhybk26zbmzc3uljjcs2b6oa

Millimeter Wave Integrated Access and Backhaul in 5G: Performance Analysis and Design Insights [article]

Chiranjib Saha, Harpreet S. Dhillon
2019 arXiv   pre-print
In fact, this tight integration of access and backhaul is one of the key ways in which 5G millimeter wave (mm-wave) heterogeneous cellular networks (HetNets) differ from traditional settings where the  ...  Our analysis also shows that it is not possible to improve the user rate in an IAB setting by simply densifying the SBSs due to the bottleneck on the rate of wireless backhaul links between MBS and SBS  ...  On the contrary, the association cells have much regular shape (see Figs. 3(a) and 3(b)) if we consider spatial correlation of link states which is induced by the germ-grain model.  ... 
arXiv:1902.06300v2 fatcat:hghcliu7gvb3jhygj5xsqrao2a

The Star Gazer and the Flesh Eater: Elements of a Theory of Metahistory

David C Krakauer
2011 Cliodynamics  
Complexity The way we set about to explain regularity and randomness relates directly to the concept of complexity.  ...  A classification of traditional, disciplinary approaches to dynamics based on the contribution of regular and random processes.  ...  Both of these energetic, or thermodynamic, perspectives on historical trends towards hierarchy find variant forms in the study of Big History.  ... 
doi:10.21237/c7clio21207 fatcat:rtrftjr4ffgcnhv4vh6arzyvwi

A review of the analysis of multiple nucleation with diffusion controlled growth

Michael E. Hyde, Richard G. Compton
2003 Journal of Electroanalytical Chemistry  
A short historical background to the study of nucleation via potentiostatic current transient modelling is provided, followed by an outline of the major methods currently used, with some comments on their  ...  Finally, methods, including optical microscopy and SPM, used for studying directly the development of surfaces on which nucleation is occurring are described.  ...  One feature of the above models is that they allow estimation of the number of active sites and nucleation rate as a function of experimental conditions.  ... 
doi:10.1016/s0022-0728(03)00250-x fatcat:fl4ip5igeffjjaj3dccn7eqxra

Stochastic Geometry and Wireless Networks: Volume I Theory

François Baccelli
2009 Foundations and Trends® in Networking  
When the underlying random model is ergodic, the probabilistic analysis also provides a way of estimating spatial averages which often capture the key dependencies of the network performance characteristics  ...  This methodology consists in the computation of both time and space averages within a unified setting which inherently addresses the scalability issue in that it poses the problems in an infinite domain  ...  They also thank Paola Bermolen, Pierre Brémaud, Srikant Iyer, Mohamed Karray, Omid Mirsadeghi, Paul Muhlethaler Barbara Staehle and Patrick Thiran for their comments on various parts of the manuscript.  ... 
doi:10.1561/1300000006 fatcat:3f3rgmgmtncvbeief3wpdo2vd4

Clustering comparison of point processes with applications to random geometric models [article]

Bartłomiej Błaszczyszyn, D. Yogeshwaran
2014 arXiv   pre-print
We explain the relations between these tools and provide examples of point processes admitting them.  ...  Furthermore, we sketch some recent results obtained using the aforementioned comparison tools, regarding percolation and coverage properties of the Boolean model, the SINR model, subgraph counts in random  ...  Acknowledgements This paper is based on research supported in part by Israel Science Foundation 853/10, AFOSR FA8655-11-1-3039 and FP7-ICT-318493-STREP.  ... 
arXiv:1212.5285v2 fatcat:4wim5afjurdhjldgmajfmp35vi

Stochastic modelling, Bayesian inference, and new in vivo measurements elucidate the debated mtDNA bottleneck mechanism

Iain G Johnston, Joerg P Burgstaller, Vitezslav Havlicek, Thomas Kolbe, Thomas Rülicke, Gottfried Brem, Jo Poulton, Nick S Jones
2015 eLife  
Using approximate Bayesian computation and mouse data, we find most statistical support for a combination of binomial partitioning of mtDNAs at cell divisions and random mtDNA turnover, meaning that the  ...  New experimental measurements from a wild-derived mtDNA pairing in mice confirm the theoretical predictions of this model.  ...  consistent with the estimate of ⇠ 25 divisions between generations in the female mouse germ line [55] ).  ... 
doi:10.7554/elife.07464 pmid:26035426 pmcid:PMC4486817 fatcat:u5m4v35jj5gsjjdes7udb7xe5m

Emergent drumlins and their clones: from till dilatancy to flow instabilities

Chris D. Clark
2010 Journal of Glaciology  
The ubiquity and patterning of bedforms appears to be well explained by a naturally arising flow instability in the subglacial system, and which has been demonstrated by analytical and numerical modelling  ...  A problem for the instability theory is an apparent mismatch between predicted and observed sedimentological properties of bedforms.  ...  philosophies in the approach of the two camps.  ... 
doi:10.3189/002214311796406068 fatcat:qlhuqkwiwveihkcikqbgzvtikq
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