Stochastic Geometry Wiley Series In Prob Abiland Mathematical Statistics Pdf
References
- Abbe, E. (1879). Über Blutkörperzählung. Jena Z. Med. Naturwiss. 13 (Neue Serie), 98– 105.
- Abellanas, M., Bajuelos, A., Hernández, G., Hurtado, F., Matos, I., and Palop, B. (2006). Good illumination of minimum range. arXiv:cs/0606013v1 [cs.CG].
- Abellanas, M., Bajuelos, A., and Matos, I. (2007a). Some problems related to good illumination. In O. Gervasi and M. Gavrilova, eds, Computational Science and its Application —ICCSA 2007, Lecture Notes in Computer Science 4705, pp. 1– 14. Springer-Verlag, Berlin.
- Abellanas, M., Bajuelos, A., and Matos, I. (2007b). Variations of good illumination. In Proceedings of XII Spanish Workshop on Computational Geometry, pp. 265– 72, Valladolid, Spain.
- Abellanas, M., Bajuelos, A. L., Hernádez, G., Matos, I., and Palop, B. (2009). The embracing Voronoi diagram and closest embracing number. J. Math. Sci. 161, 909– 18.
- Aboav, D. A. (1970). The arrangement of grains in a polycrystal. Metallography 3, 383– 90.
- Aboav, D. A. (1980). The arrangement of cells in a net. Metallography 13, 43– 58.
- Aboav, D. A. (1991). The stereology of the intergranular surface of a metal. Acta Stereol. 10, 43– 54.
- Aboav, D. A. (1992). The topology of a polycrystal in three dimensions. Mater. Sci. Forum 94–6, 275– 80.
- Adler, F. R. (1996). A model of self-thinning through local competition. Proc. Natl. Acad. Sci. USA 93, 9980– 4.
- Adler, P. M., Mourzenko, V. V., Thovert, J.-F., and Bogdanov, I. (2005). Study of single and multiphase flow in fractured porous media, using a percolation approach. In B. Faybishenko, P. A. Witherspoon, and J. Gale, eds, Dynamics of Fluids and Transport in Fractured Rock, Geophysical Monograph Series 162, pp. 33– 41. Amer Geophysical Union, Washington, D. C.
- Adler, P. M. and Thovert, J.-F. (1999). Fractures and Fracture Networks. Kluwer Academic Publishers, Dordrecht.
- Adler, R. J. (1981). The Geometry of Random Fields. John Wiley & Sons, Ltd, Chichester.
- Adler, R. J. (2000). On excursion sets, tube formulas and maxima of random fields. Ann. Appl. Probab. 10, 1– 74.
- Adler, R. J., Samorodnitsky, G., and Taylor, J. E. (2010). Excursion sets of three classes of stable random fields. Adv. Appl. Prob. 42, 293– 318.
- Adler, R. J. and Taylor, J. E. (2007). Random Fields and Geometry. Springer-Verlag, New York.
- Adler, R. J. and Taylor, J. E. (2011). Topological Complexity of Smooth Random Functions. École d'Été de Probabilités de Saint-Flour XXXIX-2009. Lecture Notes in Mathematics 2019. Springer-Verlag, New York.
- Albert, R. and Barabási, A.-L. (2002). Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47– 97.
- Albert, R., Jeong, H., and Barabási, A.-L. (1999). Diameter of the World-Wide Web. Nature 401, 130– 1.
- Albert, R., Jeong, H., and Barabási, A.-L. (2000). Error and attack tolerance of complex networks. Nature 406, 378– 82.
- Aldous, D. (1989). Probability Approximations via the Poisson Clumping Heuristic. Springer-Verlag, New York.
- Aldous, D. J. and Kendall, W. S. (2008). Short-length routes in low-cost networks via Poisson line patterns. Adv. Appl. Prob. 40, 1– 21.
- Aldous, D. J. and Shun, J. (2010). Connected spatial networks over random points and a route-length statistic. Statist. Sci. 25, 275– 88.
- Aletti, G., Bongiorno, E. G., and Capasso, V. (2009). Statistical aspects of fuzzy monotone set-valued stochastic processes. Application to birth-and-growth processes. Fuzzy Sets and Systems 160, 3140– 51.
- Aletti, G., Bongiorno, E. G., and Capasso, V. (2011). Integration in a dynamical stochastic geometric framework. ESAIM Probab. Stat. 15, 402– 16.
- Alinchenko, M. G., Anikeenko, A. V., Medvedev, N. N., Voloshin, V. P., Mezei, M., and Jedlovszky, P. (2004). Morphology of voids in molecular systems. A Voronoi-Delaunay analysis of a simulated DMPC membrane. J. Phys. Chem. B 108, 19056– 67.
- Alishahi, K. and Sharifitabar, M. (2008). Volume degeneracy of the typical cell and the chord length distribution for Poisson–Voronoi tessellations in high dimensions. Adv. Appl. Prob. 40, 919– 38.
- Allard, D. and Fraley, C. (1997). Nonparametric maximum likelihood estimation of features in spatial point processes using Voronoï tessellation. J. Amer. Statist. Assoc. 92, 1485– 93.
- Altendorf, H. and Jeulin, D. (2009). 3D directional mathematical morphology for analysis of fiber orientations. Image Anal. Stereol. 28, 143– 53.
- Ambartzumian, R. V. (1966). On an equation for stationary point processes (in Russian). Dokl. Akad. Nauk Armjanskoi SSR 42, 141– 7.
- Ambartzumian, R. V. (1973). On random fields of segments and random mosaics in the plane (in Russian). Teor. Veroyatn. Prim. 18, 515– 26. Corrections: 19,600.
- Ambartzumian, R. V. (1974a). Convex polygons and random tessellations. In E. F. Harding and D. G. Kendall, eds, Stochastic Geometry, pp. 176– 91. John Wiley & Sons, Ltd, London.
- Ambartzumian, R. V. (1974b). The solution to the Buffon–Sylvester problem in R3 . Z. Wahrscheinlichkeitsth. verw. Geb. 27, 53– 74.
- Ambartzumian, R. V. (1977). Stochastic geometry from the standpoint of integral geometry. Adv. Appl. Prob. 9, 792– 823.
- Ambartzumian, R. V. (1981). Stereology of random planar segment processes. Rend. Sem. Mat. Torino 39, 147– 59.
- Ambartzumian, R. V. (1982). Combinatorial Integral Geometry. John Wiley & Sons, Ltd, Chichester.
- Ambartzumian, R. V. (1990). Factorization Calculus and Geometric Probability. Cambridge University Press, Cambridge.
- Ambartzumian, R. V. and Ohanian, V. K. (1975). Homogeneous and isotropic fibre fields in the plane (in Russian). Izv. AN Armen. SSR Ser. Math. 10, 509– 28.
- Ambrosio, L., Capasso, V., and Villa, E. (2009). On the approximation of mean densities of random closed sets. Bernoulli 15, 1222– 42.
- Andersen, P. K., Borgan, Ø., Gill, R. D., and Keiding, N. (1993). Statistical Models Based on Counting Processes. Springer-Verlag, New York.
- Anderssen, R. S. and Jakeman, A. J. (1975a). Abel-type integral equations in stereology. J. Microsc. 105, 121– 53.
- Anderssen, R. S. and Jakeman, A. J. (1975b). Product integration for functionals of particle size distributions. Utilitas Math. 8, 111– 26.
- Andersson, J., Häggström, O., and Månsson, M. (2006). The volume fraction of a non-overlapping germ–grain model. Electron. Commun. Probab. 11, 78– 88.
- Andrade, P. N. and Fortes, M. A. (1988). Distribution of cell volumes in a Voronoi partition. Phil. Mag. 58, 671– 4.
- Ang, Q. W., Baddeley, A., and Nair, G. (2012). Geometrically corrected second order analysis of events on a linear network, with applications to ecology and criminology. Scand. J. Statist. 39, 591– 617.
- Antoniadis, A., Fan, J., and Gijbels, I. (2001). A wavelet method for unfolding sphere size distributions. Can. J. Statist. 29, 251– 68.
- Arak, T., Clifford, P., and Surgailis, D. (1993). Point-based polygonal models for random graphs. Adv. Appl. Prob. 25, 348– 72.
- Arak, T. and Surgailis, D. (1989). Markov fields with polygonal realizations. Probab. Theory Related Fields 80, 543– 79.
- Arbeiter, E. and Zähle, M. (1994). Geometric measures for random mosaics in spherical spaces. Stoch. Stoch. Rep. 46, 63– 77.
- Armitage, P. (1949). An overlapp problem arising in particle counting. Biometrika 36, 257– 66.
- Armitage, P., Berry, G., and Matthews, J. N. S. (2002). Statistical Methods in Medical Research. Blackwell, Malden, MA., 4th edition.
- Arns, C. H., Knackstedt, M. A., and Mecke, K. R. (2002). Characterising the morphology of disordered materials. In K. R. Mecke and D. Stoyan, eds, Morphology of Condensed Matter. Physics and Geometry of Spatially Complex Systems, Lecture Notes in Physics 600, pp. 37– 74. Springer-Verlag, Berlin.
- Arns, C. H., Mecke, J., Mecke, K., and Stoyan, D. (2005). Second-order analysis by variograms for curvature measures of two-phase structures. Eur. Phys. J. B 47, 397– 409.
- Artstein, Z. (1984a). Convergence of sums of random sets. In R. V. Ambartzumian and W. Weil, eds, Stochastic Geometry, Geometric Statistics, Stereology, Teubner-Texte zur Mathematik 65, pp. 34– 42. B. G. Teubner Verlagsgesellschaft, Leipzig.
- Artstein, Z. (1984b). Limit laws for multifunctions applied to an optimization problem. In G. Salinetti, ed., Multifunctions and Integrands, Stochastic Analysis, Approximation and Optimization, Lecture Notes in Math. 1091, pp. 66– 79. Springer-Verlag, Berlin.
- Artstein, Z. and Vitale, R. A. (1975). A strong law of large numbers for random compact sets. Ann. Prob. 3, 879– 82.
- Asano, A., Miyagawa, M., and Fujio, M. (2003). Morphological texture analysis using optimization of structuring elements. In T. Asano, R. Klette, and C. Ronse, eds, Geometry, Morphology, and Computational Imaging, Lecture Notes in Computer Science 2616, pp. 141– 52. Springer-Verlag, Berlin.
- Aste, T. (1999). The shell map: the structure of froths through a dynamical map. In J. F. Sadoc and N. Rivier, eds, Foams and Emulsions, pp. 497– 510. Kluwer Academic Publishers, Dordrecht.
- Aste, T., Saadatfar, M., Sakellariou, A., and Senden, T. J. (2004). Investigating the geometrical structure of disordered sphere packings. Physica A 339, 16– 23.
- Aste, T., Saadatfar, M., and Senden, T. J. (2005). Geometrical structure of disordered sphere packings. Phys. Rev. E 71, 061302.
- Aste, T., Szeto, K. Y., and Tam, W. Y. (1996). Statistical properties and shell analysis in random cellular structures. Phys. Rev. E 54, 5482– 92.
- Aste, T. and Weaire, D. (2008). The Pursuit of Perfect Packing. Taylor & Francis, New York, 2nd edition.
- Åström, J. A., Mäkinen, J. P., Alava, M. J., and Timonen, J. (2000). Elasticity of Poissonian fiber networks. Phys. Rev. E 61, 5550– 6.
- Athreya, K. B. and Lahiri, S. N. (2010). Measure Theory and Probability Theory. Springer-Verlag, New York.
- Aubin, J.-P. (1999). Mutational and Morphological Analysis. Tools for Shape Evolution and Morphogenesis. Birkhäuser, Boston.
- Aubin, J.-P. and Frankowska, H. (1990). Set-Valued Analysis. Birkhäuser-Verlag, Basel, Boston.
- Aumann, R. J. (1965). Integrals of set-valued functions. J. Math. Anal. Appl. 12, 1– 12.
- Aurenhammer, F. (1991). Voronoi diagrams–a fundamental geometric data structure. ACM Computing Surveys 23, 345– 405.
- Averkov, G. and Bianchi, G. (2009). Confirmation of Matheron's conjecture on the covariogram of a planar convex body. J. Eur. Math. Soc. 11, 1187– 1202.
- Avrami, M. (1939). Kinetics of phase change I. J. Chem. Phys 7, 1103– 12.
- Ayala, G., Ferrandiz, J., and Montes, F. (1991). Random set and coverage measure. Adv. Appl. Prob. 23, 972– 4.
- Baccelli, F. and Błaszczyszyn, B. (2009a). Stochastic geometry and wireless networks I: Theory. Foundations and Trends in Networking 3, 249– 449.
- Baccelli, F. and Błaszczyszyn, B. (2009b). Stochastic geometry and wireless networks II: Applications. Foundations and Trends in Networking 4, 1– 312.
- Baccelli, F. and Brémaud, P. (2003). Elements of Queueing Theory: Palm Martingale Calculus and Stochastic Recurrences. Springer-Verlag, Berlin.
- Baccelli, F., Gloaguen, C., and Zuyev, S. (2000). Superposition of planar Voronoi tessellations. Stochastic Models 16, 69– 98.
- Baccelli, F., Klein, M., Lebourges, M., and Zuyev, S. (1997). Stochastic geometry and architecture of communication networks. Telecommunication Systems 7, 209– 27.
- Baccelli, F. and Zuyev, S. (1997). Stochastic geometry models of mobile communication networks. In J. H. Dshalaow, ed., Frontiers of Queuing Theory: Models and Applications in Science and Engineering, pp. 227– 43. CRC Press, Boca Raton.
- Bach, G. (1959). Über die Größ enverteilung von Kugelschnitten in durchsichtigen Schnitten endlicher Dicke. Z. wiss. Mikrosk. 64, 265– 86.
- Bach, G. (1965). Über die Bestimmung von charakteristischen Größ en einer Kugelverteilung aus der unvollständigen Verteilung der Schnittkreise. Metrika 9, 228– 33.
- Bach, G. (1967). Kugelgrößenverteilung und Verteilung der Schnittkreise; ihre wechselseitigen Beziehungen und Verfahren zur Bestimmung der einen aus den anderen. In E. R. Weibel and H. Elias, eds, Quantitative Methods in Morphology, pp. 23– 45. Springer-Verlag, Berlin.
- Bach, G. (1976). Über die Auswertung von Schnittflächenverteilungen. Biometrical J. 18, 407– 12.
- Baddeley, A. J. (1980). Absolute curvatures in integral geometry. Proc. Camb. Phil. Soc. 88, 45– 58.
- Baddeley, A. J. (1984). Stochastic geometry and image analysis. CWI Newsletter (Centrum voor Wiskunde en Informatica, Amsterdam) September 1984, pp. 2– 20.
- Baddeley, A. J. (2010). Modeling strategies. In A. E. Gelfand, P. J. Diggle, M. Fuentes, and P. Guttorp, eds, Handbook of Spatial Statistics, pp. 339– 69. CRC Press, Boca Raton.
- Baddeley, A. J. and Averback, P. (1983). Stereology of tubular structures. J. Microsc. 131, 323– 40.
- Baddeley, A. J. and Cruz-Orive, L. M. (1995). The Rao–Blackwell theorem in stereology and some counterexamples. Adv. Appl. Prob 27, 2– 19.
- Baddeley, A. J. and Dereudre, D. (2013). Variational estimators for the parameters of Gibbs point processes models. Bernoulli. Forthcoming.
- Baddeley, A. J. and Gill, R. D. (1997). Kaplan–Meier estimators of distance distributions for spatial point processes. Ann. Statist. 25, 263– 92.
- Baddeley, A. J., Gundersen, H. J. G., and Cruz-Orive, L. M. (1986). Estimation of surface area from vertical sections. J. Microsc. 142, 259– 76.
- Baddeley, A. J. and Jensen, E. B. V. (2005). Stereology for Statisticians. Chapman & Hall, Boca Raton.
- Baddeley, A. J. and Møller, J. (1989). Nearest-neighbour Markov point processes and random sets. Int. Statist. Rev. 57, 89– 121.
- Baddeley, A. J. and Nair, G. (2012). Fast approximation of the intensity of Gibbs point processes. Electron. J. Statist. 6, 1155– 69.
- Baddeley, A. J. and Silverman, B. W. (1984). A cautionary example for the use of second order methods for analyzing point patterns. Biometrics 40, 1089– 94.
- Baddeley, A. J., van Lieshout, M. N. M., and Møller, J. (1996). Markov properties of cluster processes. Adv. Appl. Prob. 28, 346– 55.
- Baecher, G. B. (1983). Statistical analysis of rock mass fracturing. Math. Geol. 15, 329– 48.
- Balberg, I., Anderson, C. H., Alexander, S., and Wagner, N. (1984). Excluded volume and its relation to the onset of percolation. Phys. Rev. B 30, 3933– 43.
- Ballani, F. (2006a). On modelling of refractory castables by marked Gibbs and Gibbsian-like processes. In A. Baddeley, P. Gregori, J. M. Mahiques, and D. Stoyan, eds, Case Studies in Spatial Point Process Modeling, Lecture Notes in Statistics 185, pp. 153– 67. Springer-Verlag, New York.
- Ballani, F. (2006b). On second-order characteristics of germ–grain models with convex grains. Mathematika 53, 255– 85.
- Ballani, F. (2011). Multiple-point hit distribution functions and vague convergence of related measures. Math. Nachr. 284, 938– 47.
- Ballani, F., Daley, D. J., and Stoyan, D. (2006). Modelling the microstructure of concrete with spherical grains. Comp. Mat. Sci. 35, 399– 407.
- Ballani, F., Kabluchko, Z., and Schlather, M. (2012). Random marked sets. Adv. Appl. Prob. 44, 603– 16.
- Ballani, F. and van de Boogaart, K. G. (2013). Weighted Poisson cells as models for random convex polytopes. Methodol. Comput. Appl. Probab. Forthcoming.
- Balslev, I., Døring, K., and Eriksen, R. D. (2000). Weighted central moments in pattern recognition. Pattern Recogn. Lett. 21, 381– 4.
- Bandemer, H. and Näther, W. (1992). Fuzzy Data Analysis. Kluwer Academic Publishers, Dordrecht.
- Barabási, A.-L. and Albert, R. (1999). Emergence of scaling in random networks. Science 286, 509– 12.
- Barber, P. R., Vojnovic, B., Ameer-Beg, S. M., Hodgkiss, R. J., Tozer, G. M., and Wilson, J. (2003). Semi-automated software for the three-dimensional delineation of complex vascular networks. J. Microsc. 211, 54– 62.
- Bargieł, M. (2008). Geometrical properties of simulated packings of spherocylinders. In M. Bubak, G. D. van Albada, J. Dongarra, and P. M. A. Sloot, eds, Computational Science –ICCS 2008. Part II, Lecture Notes in Computer Science 5102, pp. 126– 35. Springer-Verlag, Berlin.
- Barrat, A. and Weigt, M. (2000). On the properties of small-world network models. Eur. Phys. J. B 13, 547– 60.
- Bartlett, M. S. (1954). Processus stochastiques ponctuels. Ann. Inst. H. Poincaré 14, 35– 60.
- Bartlett, M. S. (1975). The Statistical Analysis of Spatial Pattern. Chapman & Hall, London.
- Baumstark, V. and Last, G. (2007). Some distributional results for Poisson–Voronoi tessellations. Adv. Appl. Prob. 39, 16– 40.
- Baumstark, V. and Last, G. (2009). Gamma distributions for stationary Poisson flat processes. Adv. Appl. Prob. 41, 911– 39.
- Beer, G. (1993). Topologies on Closed and Closed Convex Sets. Kluwer Academic Publishers, Dordrecht.
- Beneš, V. (1994). On second-order formulas in anisotropic stereology. Adv. Appl. Prob. 27, 326– 43.
- Beneš, V., Chadœuf, J., and Ohser, J. (1994). Estimation of intensity in anisotropic fibre processes. Math. Nachr. 169, 5– 17.
- Beneš, V., Jiruše, M., and Slámová, M. (1997). Stereological unfolding of the trivariate size-shape-orientation distribution of spheroidal particles with application. Acta Materialia 45, 1105– 13.
- Beneš, V. and Krejčíř,, P. (1997). Decomposition in stereological unfolding problems. Kybernetika 33, 245– 58.
- Beneš, V. and Rataj, J. (2004). Stochastic Geometry: Selected Topics. Kluwer Academic Publishers, Boston.
- Beneš, V. and Gokhale, A. M. (2000). Planar anisotropy revisited. Kybernetika 36, 149– 64.
- Bennett, M. R. and Robinson, J. (1990). Probabilistic secretion of quanta from nerve terminals at synaptic sites on muscle cells: nonuniformity, autoinhibition and the binomial hypothesis. Proc. Roy. Soc. Lond. Ser. B 239, 329– 58.
- Beresteanu, A., Molchanov, I., and Molinari, F. (2011). Partial identification using random set theory. J. Econometrics 166, 17– 32.
- Berg, C. (1969). Corps convexes et potentials sphériques. Mat.-Fys. Medd. 37,6.
- Berg, C., Christensen, J. P. R., and Ressel, P. (1984). Harmonic Analysis on Semigroups. Springer-Verlag, Berlin.
- Berkowitz, B. and Adler, P. M. (1998). Stereological analysis of fracture network structure in geological formations. J. Geophys. Res. 103, 15339– 60.
- Bernal, J. D. (1960). Geometry of the structure of monatomic liquids. Nature 185, 68– 70.
- Bernardeau, F. and van de Weygaert, R. (1996). A new method for accurate estimation of velocity field statistics. Mon. Not. R. Astron. Soc. 279, 693– 711.
- Berryman, J. G. (1987). Relationship between specific surface area and spatial correlation functions for anisotropic porous media. J. Math. Phys. 28, 244– 5.
- Besag, J. (1975). Statistical analysis of non-lattice data. The Statistician 24, 179– 95.
- Besag, J. (1978). Some methods of statistical analysis for spatial data. Bull. Int. Statist. Inst. 47, 77– 92.
- Besag, J. and Diggle, P. J. (1977). Simple Monte Carlo tests for spatial pattern. Appl. Statist. 26, 327– 33.
- Bezrukov, A., Bargieł, M., and Stoyan, D. (2002). Statistical analysis of simulated random packings of spheres. Part. Part. Syst. Charact. 19, 111– 18.
- Bezrukov, A. and Stoyan, D. (2006). Simulation and statistical analysis of random packings of ellipsoids. Part. Part. Syst. Charact. 23, 388– 98.
- Bianchi, G. (2005). Matheron's conjecture for the covariogram problem. J. London Math. Soc. 71, 203– 20.
- Bianchi, G. (2009). The covariogram determines three-dimensional convex polytopes. Adv. Math. 220, 1771– 1808.
- Biggins, J. D. (1977). Martingale convergence in the branching random walk. J. Appl. Prob. 14, 25– 37.
- Billera, L. J. and Diaconis, P. (2001). A geometric interpretation of the Metropolis–Hastings algorithm. Statist. Sci. 16, 335– 9.
- Billingsley, P. (1995). Probability and Measure. John Wiley & Sons, Inc., New York, 3rd edition.
- Bindrich, U. and Stoyan, D. (1991). Stereology for pores in wheat bread: statistical analyses for the Boolean model by serial sections. J. Microcs. 162, 231– 9.
- Biswal, B., Øren, P.-E., Held, R. J., Bakke, S., and Hilfer, R. (2009). Modeling of multiscale porous media. Image Anal. Stereol. 28, 23– 34.
- Blackwell, P. G. and Møller, J. (2003). Bayesian analysis of deformed tessellation models. Adv. Appl. Prob. 35, 4– 26.
- Błaszczyszyn, B., Rau, C., and Schmidt, V. (1999). Bounds for clump size characteristics in the Boolean model. Adv. Appl. Prob. 31, 910– 28.
- Błaszczyszyn, B. and Schott, R. (2003). Approximate decomposition of some modulated-Poisson Voronoi tessellations. Adv. Appl. Prob. 35, 847– 62.
- Błaszczyszyn, B. and Schott, R. (2005). Approximations of functionals of some modulated-Poisson Voronoi tessellations with applications to modeling of communication networks. Japan J. Indust. Appl. Math. 22, 179– 204.
- Blödner, R., Mühlig, P., and Nagel, W. (1984). The comparison by simulation of solutions of Wicksell's corpuscle problem. J. Microsc. 135, 61– 74.
- Bodziony, J. (1965). On certain indices characterizing the geometric structure of rocks. Bull. Acad. Polon. Science Ser. Science. Technol. 13, 469– 75.
- Bogachev, V. I. (2007). Measure Theory, Volume I and II. Springer-Verlag, New York.
- Böhm, S. and Schmidt, V. (2003). Palm representation and approximation of the covariance of random closed sets. Adv. Appl. Prob. 35, 295– 302.
- Boissonnat, J.-D. and Yvinec, M. (1998). Algorithmic Geometry. Cambridge University Press, Cambridge.
- Bollobás, B., Janson, S., and Riordan, O. (2007). The phase transition in inhomogeneous random graphs. Random Structures Algorithms 31, 3– 122.
- Bollobás, B. and Riordan, O. (2004). The diameter of a scale-free random graph. Combinatorica 24, 5– 34.
- Bollobás, B. and Riordan, O. (2006). Percolation. Cambridge University Press, New York.
- Bollobás, B., Riordan, O., Spencer, J., and Tusnády, G. (2001). The degree sequence of a scale-free random graph process. Random Structures Algorithms 18, 279– 90.
- Bollobás, B. and Riordan, O. M. (2003). Mathematical results on scale-free random graphs. In S. Bornholdt and H. G. Schuster, eds, Handbook of Graphs and Networks: From the Genome to the Internet, pp. 1– 34. Wiley-VCH, Berlin.
- Boots, B. N. (1982). The arrangements of cells in "random" networks. Metallography 15, 53– 62.
- Boots, B. N. (1984). Comments on "Aboav's rule" for the arrangement of cells in a network. Metallography 17, 411– 18.
- Boots, B. N. (1987). Voronoi (Thiessen) Polygons. Geo Books, Norwich.
- Bosan, S., Kareco, T., Ruehlmann, D., Chen, K. Y. M., and Walley, K. R. (2003). Three-dimensional capillary geometry in gut tissue. Microsc. Res. Tech. 61, 428– 37.
- Brakke, K. A. (1986a). Statistics of random plane Voronoi tessellations. Technical report, Department of Mathematical Sciences, Susquehanna University, Selinsgrove.
- Brakke, K. A. (1986b). Statistics of three dimensional random Voronoi tessellations. Technical report, Department of Mathematical Sciences, Susquehanna University, Selinsgrove.
- Brémaud, P. (1981). Point Processes and Queues: Martingale Dynamics. Springer-Verlag, New York.
- Bretheau, T. and Jeulin, D. (1989). Caractéristiques morphologiques des constituants et comportement à la limite élastique d'un matériau biphasé fe/ag. Revue Phys. Appl. 24, 861– 9.
- Brillinger, D. R. (1975). Statistical inferences for stationary point processes. In M. Puri, ed., Stochastic Processes and Related Topics, pp. 55– 9. Academic Press, New York.
- Brillinger, D. R. (1978). Comparative aspects to the study of ordinary time series and point processes. In P. R. Krishnaiah, ed., Developments in Statistics, Volume I, pp. 227– 320. Academic Press, New York.
- Brix, A. (1999). Generalized gamma measures and shot-noise Cox processes. Adv. Appl. Prob. 31, 929– 53.
- Brix, A. and Kendall, W. S. (2002). Simulation of cluster point processes without edge effects. Adv. Appl. Prob. 34, 267– 80.
- Brodatzki, U. and Mecke, K. R. (2001). Morphological model for colloidal suspensions. arXiv:cond-mat/0112009v1 [cond-mat.soft].
- S. Brooks, A. Gelman, G. L. Jones, and X.-L. Meng, eds (2011). Handbook of Markov Chain Monte Carlo. CRC, Boca Raton.
- Brumberger, H. and Goodisman, J. (1983). Voronoi cells: An interesting and potentially useful cell model for interpreting the small-angle scattering of catalysts. J. Appl. Cryst. 16, 83– 8.
- Burger, C. and Ruland, W. (2001). Analysis of chord-length distributions. Acta Cryst. A 57, 482– 91.
- Burridge, J., Cowan, R., and Ma, I. (2013). Full-and-half Gilbert tessellations with rectangular cells. Adv. Appl. Prob. 45, 1– 19.
- Buryachenko, V. A. (2007). Micromechanics of Heterogeneous Materials. Springer-Verlag, New York.
- Cahn, J. W. (1956). The kinetics of grain boundary nucleated reactions. Acta Metallurgica 4, 449– 59.
- Cahn, J. W. (1967). The significance of average mean curvature and its determination by quantitative metallography. Trans. AIME 239, 610– 6.
- Cahn, J. W. and Nutting, J. (1959). Transmission quantitative metallography. Trans. AIME 215, 526– 8.
- Cai, Y. and Kendall, W. S. (2002). Perfect simulation for correlated Poisson random variables conditioned to be positive. Statist. Comput. 12, 229– 43.
- Calka, P. (2003a). An explicit expression for the distribution of the number of sides of the typical Poisson–Voronoi cell. Adv. Appl. Prob. 35, 863– 70.
- Calka, P. (2003b). Precise formulae for the distributions of the principal geometric characteristics of the typical cells of a two-dimensional Poisson–Voronoi tessellation and a Poisson line process. Adv. Appl. Prob. 35, 551– 62.
- Calka, P. (2010). Tessellations. In W. S. Kendall and I. Molchanov, eds, New Perspectives in Stochastic Geometry, pp. 145– 69. Oxford University Press, Oxford.
- Calka, P., Michel, J., and Paroux, K. (2009). Refined convergence for the Boolean model. Adv. Appl. Prob. 41, 940– 57.
- Campbell, N. R. (1909). The study of discontinuous phenomena. Proc. Camb. Phil. Soc. 15, 117– 36.
- Capasso, V., ed. (2003). Mathematical Modelling for Polymer Processing: Polymerization, Crystallization, Manufacturing. Mathematics in Industry 2. Springer-Verlag, Berlin.
- Capasso, V. and Micheletti, A. (2006). Stochastic geometry and related statistical problems in biomedicine. In A. Quarteroni, L. Formaggia, and A. Veneziani, eds, Complex Systems in Biomedicine, pp. 35– 69. Springer-Verlag, Milan.
- Capasso, V., Micheletti, A., and Morale, D. (2008). Stochastic geometric models, and related statistical issues in tumour-induced angiogenesis. Math. Biosci. 214, 20– 31.
- Čapek, P., Hejtmánek, V., Brabec, L., Zikánová, A., and Kočiřík, M. (2009). Stochastic reconstruction of particulate media using simulated annealing: improving pore connectivity. Trans. Porous Med. 76, 179– 98.
- Capiński, M. and Kopp, E. (2004). Measure, Integral and Probability. Springer-Verlag, London, 2nd edition.
- Car, P. and Parrinello, M. (1988). Structural, dynamical and electronic properties of amorphous silicon: anab initio molecular-dynamic study. Phys. Rev. Lett. 60, 204– 7.
- Caravenna, F., den Hollander, F., and Pétrélis, N. (2011). Lectures on random polymers. Report 2011-07, Mathematisch Instituut, Universiteit Leiden.
- Cascos, I. (2007). Depth functions based on a number of observations of a random vector. Statistic and Econometric Series 2007, Departamento de Estadística, Universidad Carlos III De Madrid. Working paper 07-29.
- Cascos, I. (2010). Data depth: Multivariate statistics and geometry. In W. S. Kendall and I. Molchanov, eds, New Perspectives in Stochastic Geometry, pp. 398– 432. Oxford University Press, Oxford.
- Cascos, I. and Molchanov, I. (2003). A stochastic order for random vectors and random sets based on the Aumann expectation. Statist. Probab. Lett. 63, 295– 305.
- Čebašek, V., Eržen, I., Vyhnal, A., Janáček, J., Ribarič, S., and Kubínová, L. (2010). The estimation error of skeletal muscle capillary supply is significantly reduced by 3D method. Microvascular Res. 79, 40– 6.
- Chadœuf, J., Bacro, J. N., Thébaud, G., and Labonne, G. (2008). Testing the boolean hypothesis in the non-convex case when a bounded grain can be assumed. Environmetrics 19, 123– 36.
- Chadœuf, J., Goulard, M., and Garcia-Sanchez, L. (1996). Modeling soil surface roughness by Boolean random functions. Microsc. Mircoanal. Microstruct. 7, 557– 63.
- Chadœuf, J., Senoussi, R., and Yao, J. F. (2000). Parametric estimation of a Boolean segment process with stochastic restoration estimation. J. Comput. Graph. Statist. 9, 390– 402.
- Chan, M. Y., Chen, D., Chin, F. Y. L., and Wang, C. A. (2004). Construction of the nearest neighbor embracing graph of a point set. In T. Hagerup and J. Katajainen, eds, Algorithm Theory —SWAT 2004, Lecture Notes in Computer Science 3111, pp. 150– 60. Springer-Verlag, Berlin.
- Chan, M. Y., Chen, D. Z., Chin, F. Y. L., and Wang, C. A. (2006). Construction of the nearest neighbor embracing graph of a point set. J. Comb. Optim. 11, 435– 43.
- Chen, A. (2008). Fast and efficient restricted Delaunay triangulation in random geometric graphs. Internet Math. 5, 195– 210.
- Chen, F. and Kelly, P. (1992). Algorithms for generating and segmenting morphologically smooth binary images. In Proceedings of the 26th Conference on Information Sciences and Systems, pp. 902– 6. Princeton University, Princeton.
- Chiu, S. N. (1994). Mean-value formulae for the neighbourhood of the typical cell of a random tessellation. Adv. Appl. Prob. 26, 565– 76.
- Chiu, S. N. (1995a). Aboav–Weaire's and Lewis–Rivier's law—a review. Mater. Char. 34, 149– 65.
- Chiu, S. N. (1995b). A comment on Rivier's maximum entropy method of statistical crystallography. J. Phys. A: Math. Gen. 28, 607– 15.
- Chiu, S. N. (1995c). Limit theorems for the time of completion of Johnson–Mehl tessellations. Adv. Appl. Prob. 27, 889– 910.
- Chiu, S. N. (1997). A central limit theorem for linear Kolmogorov's birth–growth models. Stoch. Process. Appl. 66, 97– 106.
- Chiu, S. N. (2003). Spatial point pattern analysis by using Voronoi diagrams and Delaunay tessellations —a comparative study. Biometrical J. 45, 367– 76.
- Chiu, S. N. (2007). Correction to Koen's critical values in testing spatial randomness. J. Statist. Comput. Simul. 77, 1001– 4.
- Chiu, S. N. (2010). Approximate and parametric bootstrap tests for two Poisson variates. J. Statist. Comput. Simul. 80, 263– 71.
- Chiu, S. N. and Lee, H. Y. (2002). A regularity condition and strong limit theorems for linear birth–growth processes. Math. Nachr. 241, 21– 7.
- Chiu, S. N. and Liu, K. I. (2013). Stationarity tests for spatial point processes using discrepancies Biometrics. Forthcoming.
- Chiu, S. N. and Molchanov, I. S. (2003). A new graph related to the directions of nearest neighbours in a point process. Adv. Appl. Prob. 35, 47– 55.
- Chiu, S. N., Molchanov, I. S., and Quine, M. P. (2003). Maximum likelihood estimation for germination–growth processes with application to neurotransmitters data. J. Statist. Comput. Simul. 73, 725– 32.
- Chiu, S. N. and Quine, M. P. (1997). Central limit theory for the number of seeds in a growth model in Rd with inhomogeneous Poisson arrivals. Ann. Appl. Probab. 7, 802– 14.
- Chiu, S. N. and Quine, M. P. (2001). Central limit theorem for germination–growth models in Rd with non-Poisson locations. Adv. Appl. Prob. 33, 751– 5.
- Chiu, S. N., Quine, M. P., and Stewart, M. (2000). Nonparametric and parametric estimation for a linear germination–growth model. Biometrics 56, 755– 60.
- Chiu, S. N. and Stoyan, D. (1998). Estimators of distance distributions for spatial patterns. Stat. Neerl. 52, 239– 46.
- Chiu, S. N., van de Weygaert, R., and Stoyan, D. (1996). The sectional Poisson–Voronoi tessellation is not a Voronoi tessellation. Adv. Appl. Prob 28, 356– 76.
- Chiu, S. N. and Wang, L. (2009). Homogeneity tests for several Poisson populations. Comput. Statist. Data Anal. 53, 4266– 78.
- Chiu, S. N. and Yin, C. C. (2000). The time of completion of a linear birth–growth model. Adv. Appl. Prob. 32, 620– 7.
- Chiu, S. S. and Larson, R. C. (2009). Bertrand's paradox revisited: more lessons about the ambiguous word, random. J. Ind. Syst. Eng. 3, 1– 26.
- Choquet, G. (1953/1954). Theory of capacities. Ann. Inst. Fourier V, 131– 295.
- Chubynsky, M. V. and Thorpe, M. F. (2001). Self-organization and rigidity in network glasses. Curr. Opin. Solid State Mater. Sci. 5, 525– 32.
- Chung, F. and Lu, L. (2001). The diameter of sparse random graphs. Adv. Appl. Math. 26, 257– 79.
- Chung, F. and Lu, L. (2003). The average distance in a random graph with given expected degrees. Internet Math. 1, 91– 114.
- Ciccariello, S. (1995). Integral expressions of the derivatives of the small-angle scattering correlation function. J. Math. Phys. 36, 219– 46.
- Ciccariello, S. (2009). The correlation functions of plane polygons. J. Math. Phys. 50, 103527.
- Ciccariello, S. (2010). The isotropic correlation function of planar figures: the triangle case. J. Phys.: Conf. Ser. 247, 012014.
- Clausius, R. (1857). Über Art der Bewegung, welche wir Wärme nennen. Ann. Phys. (Berlin) 100, 353– 80.
- Clausius, R. (1858). Über die mittlere Länge der Wege, welche bei der Molecularbewegung gasförmiger Körper von den einzelnen Molecülen zurückgelegt werden; nebst einigen anderen Bemerkungen über die mechanischen Wärmetheorie. Ann. Phys. (Berlin) 181, 239– 58.
- Coeurjolly, J.-F., Dereudre, D., Drouilhet, R., and Lavancier, F. (2012). Takacs–Fiksel method for stationary marked Gibbs point processes. Scand. J. Statist. 39, 416– 43.
- Coleman, R. (1981). Size determination of transparent spheres in an opaque specimen from a slice. J. Microsc. 123, 343– 5.
- Coleman, R. (1982). The sizes of spheres from profiles in a thin slice. I: Opaque spheres. Biometrical J. 24, 273– 86.
- Coleman, R. (1983). The sizes of spheres from profiles in a thin slice. II: Transparent spheres. Biometrical J. 25, 745– 56.
- Coleman, R. (1989). Random sections of a sphere. Canad. J. Statist. 17, 27– 39.
- Coles, P. and Jones, B. (1991). A lognormal model for the cosmological mass distribution. Mon. Not. R. Astr. Soc. 248, 1– 13.
- Collins, R. (1968). A geometrical sum rule for two dimensional fluid correlation functions. J. Phys. C 1, 1461– 72.
- Comas, C., Mehtätalo, L., and Miina, J. (2013). Analysing space-time tree interdependence based on individual tree growth functions. Stoch. Env. Res. Risk A. Forthcoming. DOI: 10.1007/s00477-013-0704-3.
- Corte, H. and Kallmes, O. J. (1962). Statistical geometry of a fibrous network. In F. Bolam, ed., The Formation and Structure of Paper, MCI Accession Number 28440, pp. 13– 46. Technical Section of the British Paper and Board Makers' Association, London.
- Coster, M., Arnould, X., Chermant, J. L., Moataz, A. E., and Chartier, T. (2005). A microstructural model by space tessellation for a sintered ceramic: Cerine. Image Anal. Stereol. 24, 105– 16.
- Cowan, R. (1978). The use of the ergodic theorems in random geometry. Suppl. Adv. Appl. Prob. 10, 47– 57.
- Cowan, R. (1979). Homogeneous line-segment processes. Math. Proc. Camb. Phil. Soc. 86, 481– 9.
- Cowan, R. (1980). Properties of ergodic random mosaic processes. Math. Nachr. 97, 89– 102.
- Cowan, R. (2006). A more comprehensive complementary theorem for the analysis of Poisson point processes. Adv. Appl. Prob. 38, 581– 601.
- Cowan, R. (2010). New classes of random tessellations arising from iterative division of cells. Adv. Appl. Prob. 42, 26– 47.
- Cowan, R., Chiu, S. N., and Holst, L. (1995). A limit theorem for the replication time of a DNA molecule. J. Appl. Prob. 32, 296– 303.
- Cowan, R., Quine, M., and Zuyev, S. (2003). Decomposition of gamma-distributed domains constructed from Poisson point processes. Adv. Appl. Prob. 35, 56– 69.
- Cox, D. R. (1955). Some statistical models connected with series of events. J. Roy. Statist. Soc. B 17, 129– 64.
- Cox, D. R. and Isham, V. (1980). Point Processes. Chapman & Hall, London.
- Cox, D. R. and Isham, V. (1988). A simple spatial-temporal model of rainfall. Proc. Roy. Soc. London A 415, 317– 28.
- Cox, D. R. and Lewis, P. A. W. (1966). The Statistical Analysis of Series of Events. Methuen, London and John Wiley & Sons, Inc., New York.
- Crain, I. K. (1976). Statistical analysis of geotectonics. In D. F. Merriam, ed., Random Processes in Geology, pp. 3– 15. Springer-Verlag, Berlin.
- Crain, I. K. and Miles, R. E. (1976). Monte Carlo estimates of the distribution of the random polygons determined by random lines in a plane. J. Statist. Comput. Simul. 4, 293– 325.
- Cressie, N. (1993). Statistics for Spatial Data. John Wiley & Sons, Inc., New York, revised edition.
- Cressie, N. and Hulting, F. L. (1992). A spatial statistical analysis of tumor growth. J. Amer. Statist. Assoc. 87, 272– 83.
- Cressie, N. and Laslett, G. M. (1987). Random set theory and problems of modelling. SIAM Rev. 29, 557– 74.
- Cressie, N. and Wikle, C. K. (2011). Statistics for Spatio-Temporal Data. John Wiley & Sons, Inc., Hoboken, New Jersey.
- Crofton, M. W. (1885). Probability. In Encyclopaedia Britannica. IX edition.
- Crompton, J. N. G., Waghorne, R. M., and Brook, G. B. (1966). The estimation of size distribution and density of precipitates from electron micrographs of thin foils. Brit. J. Appl. Phys 17, 1301– 5.
- Cruz-Orive, L. M. (1976). Particle size-shape distributions: the general spheroid problem. I. J. Microsc. 107, 235– 53.
- Cruz-Orive, L. M. (1978). Particle size-shape distributions: the general spheroid problem. II. J. Microsc. 112, 153– 67.
- Cruz-Orive, L. M., Hoppeler, H., Mathieu, O., and Weibel, E. R. (1985). Stereological analysis of anisotropic structures using directional statistics. Appl. Statist. 34, 14– 32.
- Daley, D. J. and Last, G. (2005). Descending chains, the lilypond model, and the mutual-nearest-neighbour matching. Adv. Appl. Prob. 37, 604– 28.
- Daley, D. J., Mallows, C. L., and Shepp, L. A. (2000). A one-dimensional Poisson growth model with non-overlapping intervals. Stoch. Process. Appl. 90, 223– 41.
- Daley, D. J., Stoyan, H., and Stoyan, D. (1999). The volume fraction of a Poisson germ model with maximally non-overlapping spherical grains. Adv. Appl. Prob. 31, 610– 24.
- Daley, D. J. and Vere-Jones, D. (1988). An Introduction to the Theory of Point Processes. Springer-Verlag, New York.
- Daley, D. J. and Vere-Jones, D. (2003). An Introduction to the Theory of Point Processes. Volume I: Elementary Theory and Methods. Springer-Verlag, New York, 2nd edition.
- Daley, D. J. and Vere-Jones, D. (2008). An Introduction to the Theory of Point Processes. Volume II: General Theory and Structure. Springer-Verlag, New York, 2nd edition.
- Davidson, R. (1974a). Construction of line-processes: second-order properties. In E. F. Harding and D. G. Kendall, eds, Stochastic Geometry, pp. 55– 75. John Wiley & Sons, Ltd, London.
- Davidson, R. (1974b). Line-processes, roads and fibres. In E. F. Harding and D. G. Kendall, eds, Stochastic Geometry, pp. 248– 51. John Wiley & Sons, Ltd, London.
- Davidson, R. (1974c). Stochastic processes of flats and exchangeability. In E. F. Harding and D. G. Kendall, eds, Stochastic Geometry, pp. 13– 45. John Wiley & Sons, Ltd, London.
- Davison, A. C. and Hinkley, D. V. (1997). Bootstrap Methods and their Application. Cambridge University Press, Cambridge.
- de Berg, M., Cheong, O., van Kreveld, M., and Overmars, M. (2008). Computational Geometry: Algorithms and Applications. Springer-Verlag, New York, 3rd edition.
- de Gennes, P.-G. (1979). Scaling Concepts in Polymer Physics. Cornell University Press, Ithaca.
- Debye, P., Anderson, H. R., and Brumberger, H. (1957). Scattering by an inhomogeneous solid. II. The correlation function and its application. J. Appl. Phys. 28, 679– 83.
- DeHoff, R. T. (1965). The estimation of particle distributions from simple counting measurements made on random plane sections. Trans. AIME 233, 25– 9.
- DeHoff, R. T. (1967). The quantitative estimation of mean surface curvature. Trans. AIME 239, 617– 21.
- DeHoff, R. T. (1968). Curvature and topological properties of interconnected phases. In R. T. DeHoff and F. N. Rhines, eds, Quantitative Microscopy, pp. 291– 324. McGraw-Hill, New York.
- Deijfen, M. (2003). Asymptotic shape in a continuum growth model. Adv. Appl. Prob. 35, 303– 18.
- Deijfen, M. (2009). Stationary random graphs with prescribed iid degrees on a spatial Poisson process. Electron. Commun. Probab. 14, 81– 9.
- Deijfen, M., Häggström, O., and Holroyd, A. E. (2012). Percolation in invariant Poisson graphs with i.i.d. degrees. Ark. Mat. 50, 41– 58.
- Delaney, G. W., Di Matteo, T., and Aste, T. (2010). Combining tomographic imaging and DEM simulations to investigate the structure of experimental sphere packings. Soft Matter 6, 2992– 3006.
- Delesse, M. A. (1847). Procede mecanique pour determiner la composition des roches. C. R. Acad. Sci. (Paris) 25, 544– 5.
- Delfiner, P. (1972). A generalization of the concept of size. J. Microsc. 95, 203– 16.
- Demichel, Y., Estrade, A., Kratz, M., and Samorodnitsky, G. (2011). How fast can the chord length distribution function decay? Adv. Appl. Prob. 43, 504– 23.
- den Hollander, F. (2009). Random Polymers. Lecture Notes in Mathematics 1974. Springer-Verlag, Berlin.
- Deng, M. and Dodson, C. T. J. (1994). Paper: an Engineered Stochastic Structure. Tappi Press, Atlanta.
- Dereudre, D., Drouilhet, R., and Georgii, H.-O. (2012). Existence of Gibbsian point processes with geometry-dependent interactions. Probab. Theory Related Fields 153, 643– 70.
- Dereudre, D. and Lavancier, F. (2009). Campbell equilibrium equation and pseudo-likelihood estimation for non-hereditary Gibbs point processes. Bernoulli 15, 1368– 96.
- Dereudre, D. and Lavancier, F. (2011). Practical simulation and estimation for Gibbs Delaunay–Voronoi tessellations with geometric hardcore interaction. Comput. Statist. Data Anal. 55, 498– 519.
- Diggle, P. J. (1979). On parameter estimation and goodness-of-fit testing for spatial point-patterns. Biometrics 35, 87– 101.
- Diggle, P. J. (1981). Binary mosaics and the spatial pattern of heather. Biometrics 37, 531– 9.
- Diggle, P. J. (1983). Statistical Analysis of Spatial Point Patterns. Academic Press, London.
- Diggle, P. J. (2003). Statistical Analysis of Spatial Point Patterns. Edward Arnold, London, 2nd edition.
- Diggle, P. J. (2007). Spatio-temporal point processes: methods and applications. In B. Finkenstädt, L. Held, and V. Isham, eds, Statistical Methods for Spatio-Temporal Systems, pp. 1– 45. Chapman & Hall/CRC, Boca Rota.
- Diggle, P. J., Fiksel, T., Grabarnik, P., Ogata, Y., Stoyan, D., and Tanemura, M. (1994). On parameter estimation for pairwise interaction processes. Int. Statist. Rev. 62, 99– 117.
- Diggle, P. J., Gates, D. J., and Stibbard, A. (1987). A non-parametric estimator for pairwise-interaction point processes. Biometrika 74, 763– 70.
- Diggle, P. J. and Gratton, R. J. (1984). Monte Carlo methods of inference for implicit statistical models (with discussion). J. Roy. Statist. Soc. B 46, 193– 227.
- Diggle, P. J. and Milne, R. K. (1983). Bivariate Cox processes: Some models for bivariate spatial point-patterns. J. Roy. Statist. Soc. B 45, 11– 21.
- Diggle, P. J. and ter Braak, C. J. F. (1982). Point sampling of binary mosaics in ecology. In B. Ranneby, ed., Statistics in Theory and Practice. Essays in Honour of Bertil Matérn, pp. 107– 22. Swedish University of Agricultural Sciences, Umea.
- Dillard, T., N'guyen, F., Maire, E., Salvo, L., Forest, S., Bienvenu, Y., Bartout, J.-D., Croset, M., Dendievel, R., and Cloetens, P. (2005). 3D quantitative image analysis of open-cell nickel foams under tension and compression loading using X-ray microtomography. Philos. Mag. 85, 2147– 75.
- Dirichlet, G. L. (1850). Über die Reduction der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen. J. Reine und Angew. Math. 40, 209– 27.
- Dodson, C. T. J. and Sampson, W. W. (1999). Spatial statistics of stochastic fiber networks. J. Stat. Phys. 96, 447– 58.
- Döge, G. (2001). Perfect simulation for random sequential adsorption of d-dimensional spheres with random radii. J. Statist. Comput. Simul. 69, 141– 56.
- Doležal, F. (1982). The use of stereology for the evaluation of crack patterns in agricultural soils. In I. Saxl, ed., Proceedings of the Colloquium on Mathematical Morphology, Stereology and Image Analysis, 14–16 September 1982, Prague, pp. 305– 7. Akademia, Prague.
- Dominguez, M. and Torres, L. (1997). Analysis and synthesis of textures through the inference of Boolean functions. Signal Processing 59, 1– 16.
- Donev, A., Torquato, S., and Stillinger, F. H. (2005). Neighbor list collision-driven molecular dynamics simulation for nonspherical hard particles. I. Algorithmic details. J. Comput. Phys. 202, 737– 64.
- Dorogovtsev, S. N. and Mendes, J. F. F. (2002). Evolution of networks. Adv. in Phys. 51, 1079– 187.
- Dousse, O., Franceschetti, M., Macris, N., Meester, R., and Thiran, P. (2006). Percolation in the signal to interference ratio graph. J. Appl. Prob. 43, 552– 62.
- Douven, I., Decock, L., Dietz, R., and Égré, P. (2013). Vagueness: a conceptual spaces approach. J. Philos. Logic 42, 137– 60.
- Dozzi, M., Merzbach, E., and Schmidt, V. (2001). Limit theorems for sums of random fuzzy sets. J. Math. Anal. Appl. 259, 554– 65.
- Drees, H. and Reiss, R.-D. (1992). Tail behaviour in Wicksell's corpuscle problem. In Galambos, J. and I. Katai, eds, Probability and Applications, pp. 205– 20. Kluwer Academic Publishers, Dortrecht.
- Du, Q., Faber, V., and Gunzburger, M. (1999). Centroidal Voronoi tessellations: Applications and algorithms. SIAM Rev. 41, 637– 76.
- D. Dubois and H. Prade, eds (2000). Fundamentals of Fuzzy Sets. Handbooks of Fuzzy Sets Series 7. Kluwer Academic Publishers, Dordrecht.
- Durrett, R. (2007). Random Graph Dynamics. Cambridge University Press, Cambridge.
- Durrett, R. (2010). Probability. Theory and Examples. Cambridge University Press, Cambridge, 4th edition.
- Duvalian, A. V. (1971). A method for the approximate determination of the variance of dihedral angles in alloys (in Russian). Zavod. Lab. 37, 939– 41.
- Edelsbrunner, H. (1987). Algorithms in Combinatorial Geometry. Springer-Verlag, Berlin.
- Eggemann, N. and Noble, S. D. (2011). The clustering coefficient of a scale-free random graph. Discrete Appl. Math. 159, 953– 65.
- El-Azab, A., Deng, J., and Tang, M. (2007). Statistical characterization of dislocation ensembles. Philos. Mag. 87, 1201– 23.
- Elsner, A., Wagner, A., Aste, T., Hermann, H., and Stoyan, D. (2009). Specific surface area and volume fraction of the cherry-pit model with packed pits. J. Phys. Chem. B 113, 7780– 4.
- Emery, X., Kracht, W., Egaña, Á., and Garrido, F. (2012). Using two-point set statistics to estimate the diameter distribution in Boolean models with circular grains. Math. Geosci. 44, 805– 22.
- Erdós, P. and Rényi, A. (1959). On random graphs I. Publ. Math. Debrecen 6, 290– 7.
- Erdós, P. and Rényi, A. (1960). On the evolution of random graphs. Publ. Math. Inst. Hungar. Acad. Sci. 5, 17– 61.
- Estrade, A., Iribarren, I., and Kratz, M. (2012). Chord-length distribution functions and Rice formulae. Application to random media. Extremes 15, 333– 52.
- Evans, J. W. (1993). Random and cooperative sequential adsorption. Rev. Modern Phys. 65, 1281– 1329.
- Exner, H. E. (2004). Stereology and 3D microscopy: Useful alternatives or competitors in the quantitative analysis of microstructures? Image Anal. Stereol. 23, 73– 82.
- Fairclough, A. R. N. and Davies, G. A. (1990). Poisson line processes in 2 space to simulate the structure of porous media: methods of generation, statistics and applications. Chem. Eng. Comm. 2, 23– 48.
- Falconer, K. J. (1990). Fractal Geometry. Mathematical Foundations and Applications. John Wiley & Sons, Inc., New York.
- Federer, H. (1959). Curvature measures. Trans. Amer. Math. Soc. 93, 418– 91.
- Fellous, A., Granara, J., and Krickeberg, K. (1978). Statistics of stationary oriented line Poisson processes in the plane. In R. E. Miles and J. Serra, eds, Geometrical Probability and Biological Structures: Buffon's 200th Anniversary, Lecture Notes in Biomathematics 23, pp. 295– 9. Springe-Verlag, Berlin.
- Fienberg, S. E. (2010a). Introduction to papers on the modeling and analysis of network data. Ann. Appl. Statist. 4, 1– 4.
- Fienberg, S. E. (2010b). Introduction to papers on the modeling and analysis of network data II. Ann. Appl. Statist. 4, 533– 4.
- Finney, J. L. (1975). Volume occupation, environment and accessibility in proteins. The problem of the protein surface. J. Mol. Biol. 96, 721– 32.
- Finney, J. L. (1979). A procedure for the construction of Voronoi polyhedra. J. Comput. Phys. 32, 137– 43.
- Fischer, R. A. and Miles, R. E. (1973). The role of spatial pattern in the competition between crop plants and weeds: A theoretical analysis. Math. Biosci. 18, 335– 50.
- Fisher, N. I., Lewis, T., and Embleton, B. J. J. (1987). Statistical Analysis of Spherical Data. Cambridge University Press, Cambridge.
- Flaxman, A. D., Frieze, A. M., and Vera, J. (2006). A geometric preferential attachment model of networks. Internet Math. 3, 187– 205.
- Flaxman, A. D., Frieze, A. M., and Vera, J. (2007). A geometric preferential attachment model of networks II. Internet Math. 4, 87– 112.
- Fleischer, F., Eckel, S., Schmidt, I., Schmidt, V., and Kazda, M. (2006). Point process modelling of root distribution in pure stands of Fagus sylvatica and Picea abies . Can. J. Forest Res. 36, 227– 37.
- Fleischer, F., Gloaguen, C., Schmidt, V., and Voss, F. (2009). Simulation of the typical Poisson–Voronoi–Cox–Voronoi cell. J. Statist. Comput. Simul. 79, 939– 57.
- Fletcher, N. D. and Evans, A. N. (2005). Texture segmentation using area morphology local granulometries. In C. Ronse, L. Najman, and E. Decencière, eds, Mathematical Morphology: 40 Years On, Computational Imaging and Vision 30, pp. 367– 76. Springer-Verlag, Dordrecht.
- Flory, P. J. (1953). Principles of Polymer Chemistry. Cornell University Press, Ithaca.
- Flory, P. J. (1969). Statistical Mechanics of Chain Molecules. John Wiley & Sons, Inc., New York.
- Flory, P. J. (1976). Statistical thermodynamics of random networks. Proc. R. Soc. London A 351, 351– 80.
- Flynn, D. C., Nulton, J. D., Salamon, P., Frey, T. G., Rabinovitch, A., Sun, M. G., and Baljon, A. R. C. (2009). A stereological unfolding method for the study of the mitochondrial network. Image Anal. Stereol. 28, 11– 22.
- Fortune, S. (1992). Voronoi diagrams and Delaunay triangulations. In D.-Z. Du and F. K. Wang, eds, Computing in Euclidean Geometry, pp. 193– 233. World Scientific, Singapore.
- Foxall, R. and Baddeley, A. (2002). Nonparametric measures of association between a spatial point process and a random set, with geological applications. J. Roy. Statist. Soc. C 51, 165– 82.
- Franceschetti, M. and Meester, R. (2008). Random Networks for Communication. Cambridge University Press, Cambridge.
- Franken, P., König, D., Arndt, U., and Schmidt, V. (1981). Queues and Point Processes. Akademie-Verlag, Berlin and John Wiley & Sons, Ltd, Chichester.
- Franklin, J. N. (1977). Some stereological principles in morphometric cytology. SIAM J. Appl. Math. 33, 267– 78.
- Franklin, J. N. (1981). Confidence intervals for stereological estimators with infinite variance. SIAM J. Appl. Math. 40, 179– 90.
- Frenkel, D. and Smit, B. (2002). Understanding Molecular Simulation: From Algorithms to Applications. Academic Press, San Diego, 2nd edition.
- Freudenthal, A. (1950). The Inelastic Behavior of Engineering Materials and Structures. John Wiley & Sons, Inc., New York.
- Frieden, B. R. (1983). Probability, Statistical Optics and Data testing. Springer-Verlag, New York.
- Frisch, H. L. and Stillinger, F. H. (1963). Contribution to the statistical geometric basis of radiation scattering. J. Chem. Phys. 38, 2200– 7.
- Fu, K.-a. and Zhang, L.-x. (2008). Strong limit theorems for random sets and fuzzy random sets with slowly varying weights. Inform. Sci. 178, 2648– 60.
- Fullman, R. L. (1953). Measurement of particle sizes in opaque bodies. J. Metals 5, 447– 52.
- Galbraith, R. F. (2005). Statistics for Fission Track Analysis. Chapman & Hall/CRC, Boca Rota.
- Gärdenfors, P. (2000). Conceptual Spaces: The Geometry of Thought. MIT Press, Cambridge, MA.
- Gardner, R. J., Kiderlen, M., and Milanfar, P. (2006). Convergence of algorithms for reconstructing convex bodies and directional measures. Ann. Statist. 34, 1331– 74.
- Gates, D. J. and Westcott, M. (1986). Clustering estimates in spatial point processes with stable potentials. Ann. Inst. Statist. Math. 38, 123– 35.
- Gavrikov, V. L., Grabarnik, P. Y., and Stoyan, D. (1993). Trunk-top relations in a Siberian pine forest. Biometrical J. 35, 487– 98.
- Gavrilova, M. L., ed. (2008). Generalized Voronoi Diagram: A Geometry-Based Approach to Computational Intelligence. Studies in Computational Intelligence 158. Springer-Verlag, Berlin.
- Gelfand, A. E., Diggle, P. J., Fuentes, M., and Guttorp, P., eds (2010). Handbook of Spatial Statistics. CRC, Boca Raton.
- Gentle, J. E. (2003). Random Number Generation and Monte Carlo Methods. Springer-Verlag, New York, 2nd edition.
- George, E. I. (1987). Sampling random polygons. J. Appl. Prob. 24, 557– 73.
- Georgii, H.-O. (1976). Canonical and grand canonical Gibbs states for continuum systems. Comm. Math. Phys. 48, 31– 51.
- Georgii, H.-O. (1988). Gibbs Measures and Phase Transition. de Gruyter, Berlin.
- Georgii, H.-O. (2000). Phase transition and percolation in Gibbsian particle models. In K. R. Mecke and D. Stoyan, eds, Statistical Physics and Spatial Statistics: the Art of Analyzing and Modeling Spatial Structures and Pattern Formation, Lecture Notes in Physics 554, pp. 267– 94. Springer-Verlag, Berlin.
- Georgii, H.-O., Häggström, O., and Maes, C. (2001). The random geometry of equilibrium phases. In C. Domb and J. Lebowitz, eds, Phase Transitions and Critical Phenomena, pp. 1– 142. Academic Press, London.
- Geyer, C. J. (1992). Practical Markov chain Monte Carlo (with discussion). Statist. Sci. 7, 473– 511.
- Ghorbani, M. (2012). Cauchy cluster process. Metrika. Forthcoming. DOI: 10.1007/s00184-012-0411-y.
- Giger, H. (1967). Ermittlung der mittleren Maßzahlen von Partikeln eines Körpersystems durch Messungen auf dem Rand eines Schnittbereiches. Z. angew. Math. Phys. 18, 883– 8.
- Giger, H. and Riedwyl, H. (1970). Bestimmung der Größ enverteilung von Kugeln aus Schnittkreisradien. Biometrisch Z. 12, 156– 68.
- Gilbert, E. N. (1959). Random graphs. Ann. Math. Statist. 30, 1141– 4.
- Gilbert, E. N. (1961). Random plane networks. J. SIAM 9, 533– 43.
- Gilbert, E. N. (1962). Random subdivisions of space into crystals. Ann. Math. Statist. 33, 958– 72.
- Gilbert, E. N. (1967). Random plane networks and needle-shaped crystals. In B. Noble, ed., Applications of Undergraduate Mathematics in Engineering, chapter 16. Macmillan, New York.
- Gill, R. D. (1994). Lectures on survival analysis. In P. Bernard, ed., Lectures on Probability Theory: Ecole d'Eté de Probabilités de Saint-Flour XXII-1992, Lecture Notes in Mathematics 1581, pp. 115– 241. Springer-Verlag, Berlin.
- Gille, W. (1988). The chord length distribution on parallelepipeds with their limiting cases. Exp. Technik Phys. 36, 197– 208.
- Gille, W. (2002). The set covariance of a dead leaves model. Adv. Appl. Prob. 34, 11– 20.
- Gille, W. (2011). Scattering properties and structure functions of Boolean models. Comput. Struct. 89, 2309– 15.
- Gille, W. (2014). Particles, Puzzles and Scattering Patterns –Mysteries of Small-Angle Scattering. Forthcoming.
- Girling, A. J. (1982). Approximate variances associated with random configurations of hard spheres. J. Appl. Prob. 19, 588– 96.
- Glagolev, A. A. (1933). On the geometrical methods of quantitative mineralogic analysis of rocks. Trans. Inst. Econ. Min. Moscow 59, 1– 47.
- Glatter, O. (1979). The interpretation of real-space information from small-angle scattering experiments. J. Appl. Cryst. 12, 166– 75.
- Gloaguen, C., Fleischer, F., Schmidt, H., and Schmidt, V. (2006). Fitting of stochastic telecommunication network models, via distance measures and Monte Carlo tests. Telecommunication Systems 31, 353– 77.
- Glötzl, E. (1980). Lokale Energien und Potentiale für Punktprozesse. Math. Nachr. 96, 196– 206.
- Glötzl, E. (1981). Time-reversible and Gibbsian point processes I. Markovian spatial birth and death processes on a general phase space. Math. Nachr. 102, 217– 22.
- Gneiting, T. and Guttorp, P. (2010). Continuous parameter stochastic process theory. In A. E. Gelfand, P. J. Diggle, M. Fuentes, and P. Guttorp, eds, Handbook of Spatial Statistics, pp. 17– 28. CRC Press, Boca Raton.
- Gokhale, A. M. (1990). Unbiased estimation of curve length in 3-D using vertical slices. J. Microsc. 159, 133– 41.
- Gokhale, A. M. (1992). Estimation of length density Lv from vertical slices of unknown thickness. J. Microsc. 167, 1– 8.
- Gokhale, A. M. (1993). Utility of the horizontal slice for stereological characterization of lineal features. J. Microsc. 170, 3– 8.
- Gokhale, A. M., Tewari, A., and Garmestani, H. (2005). Constraints on microstructural two-point correlation functions. Scripta Materialia 53, 989– 93.
- Goulard, M., Chadœuf, J., and Bertuzzi, P. (1994). Random Boolean functions: non-parametric estimation of the intensity. Application to soil surface roughnessy. Statistics 25, 123– 36.
- Goutsias, J. and Batman, S. (2000). Morphological methods for biomedical image analysis. In Sonka, M. and Fitzpatrick, J. M., eds, Handbook of Medical Imaging. Volume 2: Medical Image Processing and Analysis, pp. 175– 272. SPIE Press, Bellingham, Washington.
- Goutsias, J. and Heijmans, H. J. A. M., eds (2000). Mathematical Morphology. IOS Press, Amsterdam.
- Goutsias, J., Mahler, R. P. S., and Nguyen, H. T. (1997). Random Sets: Theory and Applications. Springer-Verlag, New York.
- Goutsias, J. and Sivakumar, K. (1998). A multiresolution morphological approach to stochastic image modeling. CWI Quarterly 11, 347– 69.
- Grabarnik, P., Pagès, L., and Bengough, A. G. (1998). Geometrical properties of simulated maize root systems: consequences for length density and intersection density. Plant Soil 200, 157– 67.
- Grandell, J. (1976). Doubly Stochastic Poisson Processes. Lecture Notes in Mathematics 529. Springer-Verlag, Berlin.
- Grandell, J. (1981). Some recent developments of theory and application of Cox processes. In B. Bereanu, S. Grigorescu, M. Iosifescu, and T. Postelnicu, eds, Sixth Conf. Prob. Theory, Brasov 1979, pp. 288– 9. Bucuresti.
- Gray, N. H., Anderson, J. B., Devine, J. D., and Kwasnik, J. M. (1976). Topological properties of random crack networks. Math. Geol 8, 617– 26.
- Greco, A., Jeulin, D., and Serra, J. (1979). The use of the texture analyser to study sinter structure: application to the morphology of calcium ferrites encountered in basic sinters of rich iron ores. J. Microsc. 116, 199– 211.
- Greeley, R. (1987). Planetary Landscapes. Allen & Unwin, Boston.
- Greig-Smith, P. (1952). The use of random and contiguous quadrats in the study of the structure of plant communities. Ann. Bot. 16, 293– 316.
- Greig-Smith, P. (1983). Quantitative Plant Ecology. Blackwell, Oxford, 3rd edition.
- Grimmett, G. (1999). Percolation. Grundlehren der mathematischen Wissenschaften 321. Springer-Verlag, Berlin, 2nd edition.
- Groos, J. and Kopp-Schneider, A. (2006). Application of a color-shift model with heterogeneous growth to a rat hepatocarcinogenesis experiment. Math. Biosci. 202, 248– 68.
- Groos, J. and Kopp-Schneider, A. (2010). Application of a two-phenotype color-shift model with heterogeneous growth to a rat hepatocarcinogenesis experiment. Math. Biosci. 224, 95– 100.
- Gruber, P. M. and Wills, J. M. (1993). Handbook of Convex Geometry. Elsevier Science, Amsterdam.
- Gu, M. G. and Zhu, H.-T. (2001). Maximum likelihood estimation for spatial models by Markov chain Monte Carlo stochastic approximation. J. Roy. Statist. Soc. B 63, 339– 55.
- Guan, Y. (2008). A KPSS test for stationarity for spatial point processes. Biometrics 64, 800– 6.
- Guderlei, R., Klenk, S., Mayer, J., Schmidt, V., and Spodarev, E. (2007). Algorithms for the computation of the Minkowski functionals of deterministic and random polyconvex sets. Image Vision Comput. 25, 464– 74.
- Guibas, L. J. and Stolfi, J. (1988). Ruler, compass and computer: the design and analysis of geometric algorithms. In Earnshaw, R., ed., Theoretical Foundation of Computer Graphics and CAD, pp. 111– 65. Springer-Verlag, Berlin.
- Guinier, A. and Fournet, G. (1995). Small-angle Scattering of X-rays. John Wiley & Sons, Inc., New York.
- Gundersen, H. J. G. (1979). Estimation of tubule or cylinder L V , S V , and V V on thick sections. J. Microsc. 117, 333– 46.
- Gut, A. (2013). Probability: A Graduate Course. Springer Science + Business Media, New York, 2nd edition.
- Guttorp, P. (2007). Discussion of 'modern statistics for spatial point processes' by J. Møller and R. P. Waagepetersen. Scand. J. Statist. 34, 692– 3.
- Guttorp, P. and Thorarinsdottir, T. L. (2012). What happened to discrete chaos, the Quenouille process, and the sharp Markov property? Some history of stochastic point processes. Int. Stat. Rev. 80, 253– 68.
- Haas, A., Matheron, G., and Serra, J. (1967). Morphologie mathematique et granulometries en place I, II. Ann. Mines 11, 736– 53; 12, 767–82.
- Hadwiger, H. (1957). Vorlesungen über Inhalt, Oberfläche und Isoperimetrie. Springer-Verlag, Berlin.
- Hadwiger, H. and Giger, H. (1968). Über Treffzahlwahrscheinlichkeiten im Eikörperfeld. Z. Wahrscheinlichkeitsth. verw. Geb. 10, 329– 34.
- Häggström, O. and Meester, R. (1996). Nearest neighbor and hard sphere models in continuum percolation. Random Structures Algorithms 9, 295– 315.
- Hahn, U. (1995). On the precision of some estimators of the number of cells per unit area in planar tessellations. Unpublished manuscript.
- Hahn, U. and Lorz, U. (1994a). On the precision of some stereological estimators of the spatial Poisson–Voronoi tessellation. Acta Stereol. 13, 245– 50.
- Hahn, U. and Lorz, U. (1994b). Stereological analysis of the spatial Poisson–Voronoi tessellation. J. Microsc. 175, 176– 85.
- Hahn, U., Micheletti, A., Pohlink, R., Stoyan, D., and Wendrock, H. (1999). Stereological analysis and modelling of gradient structures. J. Microsc. 195, 113– 24.
- Hall, P. (1985a). Distribution of size, structure and number of vacant regions in a high-intensity mosaic. Z. Wahrscheinlichkeitsth. verw. Geb. 70, 237– 61.
- Hall, P. (1985b). On continuum percolation. Ann. Probab. 13, 1250– 66.
- Hall, P. (1988). Introduction to the Theory of Coverage Processes. John Wiley & Sons, Inc., New York.
- Hall, P. and Smith, R. L. (1988). The kernel method for unfolding sphere distributions. J. Comput. Phys. 74, 409– 21.
- Hall, P. and Ziegel, J. (2011). Distribution estimators and confidence intervals for stereological volumes. Biometrika 98, 417– 31.
- Hamilton, W. D. (1971). Geometry for the selfish herd. J. Theor. Biol. 31, 295– 311.
- Hanisch, K.-H. (1981). On classes of random sets and point processes. Serdica 7, 160– 7.
- Hanisch, K.-H. (1982). On inversion formulae for n-fold Palm distributions of point processes in LCS-spaces. Math. Nachr. 106, 171– 9.
- Hanisch, K.-H. (1983). On stereological estimation of second-order characteristics and of hard-core distances of systems of sphere-centres. Biometrical J. 25, 731– 43.
- Hanisch, K.-H. (1984a). On Palm and second-order quantities of point processes and germ–grain models. Technical Report Wissenschaftl. Sitzungen Stochastik WSS-01/84, Akademie der Wissenschaften der DDR, Berlin.
- Hanisch, K.-H. (1984b). Scattering analysis of point processes and random measures. Math. Nachr. 117, 235– 45.
- Hanisch, K.-H. (1984c). Some remarks on estimators of the distribution function of nearest-neighbour distance in stationary spatial point-patterns. Math. Operationsf. Statist., ser. Statistics 15, 409– 12.
- Hanisch, K.-H. (1985). On the second order analysis of stationary and isotropic fibre processes by line-intercept methods. In W. Nagel, ed., Geobild '85: Workshop on Geometrical Problems of Image Processing, Georgenthal (GDR), January 14–18, 1985: Proceedings, pp. 141– 6. Wissenschaftliche Beiträge der Friedrich-Schiller-Universität Jena.
- Hanisch, K.-H., Klimanek, P., and Stoyan, D. (1985). Stereological analysis of dislocation arrangements in crystals from TEM images. Cryst. Res. Technol. 20, 921– 30.
- Hanisch, K.-H. and Stoyan, D. (1980). Stereological estimation of the radial distribution function of centres of spheres. J. Microsc. 122, 131– 41.
- Hansen, J.-P. and McDonald, I. R. (2006). Theory of Simple Liquids. Academic Press, London, 3rd edition.
- Hansen, M. B., Baddeley, A. J., and Gill, R. D. (1999). First contact distribution for spatial patterns: regularity and estimation. Adv. Appl. Prob. 31, 15– 33.
- Hansen, M. B., Gill, R. D., and Baddeley, A. (1996). Kaplan–Meier type estimators for linear contact distributions. Scand. J. Statist 23, 129– 55.
- Harker, D. and Parker, E. R. (1945). Grain shape and grain growth. Trans. Amer. Soc. Metals 34, 156– 73.
- Hasegawa, M. and Tanemura, M. (1976). On the pattern of space division by territories. Ann. Inst. Math. 28, 509– 19.
- Hasegawa, M. and Tanemura, M. (1980). Spatial patterns of territories. In Recent Developments in Statistical Inference and Data Analysis, pp. 73– 8. North-Holland, Amsterdam.
- Hasegawa, M., Tanemura, M., and Takiguchi, S. (1981). Spatial patterns in ecology. In Int. Roundtable Congress 50th Anniversary Jap. Statist. Soc. 1981, pp. 146– 61. Japan Statist. Soc.
- Hayen, A. and Quine, M. P. (2000a). Calculating the proportion of triangles in a Poisson–Voronoi tessellation of the plane. J. Statist. Comput. Simul. 32, 67– 74.
- Hayen, A. and Quine, M. P. (2000b). The proportion of triangles in a Poisson–Voronoi tessellation of the plane. Adv. Appl. Prob. 32, 67– 74.
- Hazlett, R. D. (1997). Statistical characterization and stochastic modeling of pore networks in relation to fluid flow. Math. Geol. 29, 801– 22.
- Heijmans, H. J. A. M. (1994). Morphological Image Operators. Academic Press, Boston, MA.
- Heinrich, L. (1992a). Mixing properties of Gibbsian point processes and asymptotic normality of Takacs–Fiksel estimates. Preprint 92-051, Universität Bielefeld.
- Heinrich, L. (1992b). On existence and mixing properties of germ–grain models. Statistics 23, 271– 86.
- Heinrich, L. (1993). Asymptotic properties of minimum contrast estimators for parameters of Boolean models. Metrika 31, 349– 60.
- Heinrich, L. (1998). Contact and chord length distribution of a stationary Voronoi tessellation. Adv. Appl. Prob. 30, 603– 18.
- Heinrich, L. (2005). Large deviations of the empirical volume fraction for stationary Poisson grain models. Ann. Appl. Probab. 15, 392– 420.
- Heinrich, L. and Molchanov, I. (1994). Some limit theorems for extremal and union shot noise processes. Math. Nachr 168, 139– 59.
- Heinrich, L. and Muche, L. (2008). Second-order properties of the point process of nodes in a stationary Voronoi tessellation. Math. Nachr. 281, 350– 75. (Erratum: 2010, vol. 283, pp. 1674–6).
- Heinrich, L. and Schmidt, V. (1985). Normal convergence of multidimensional shot noise and rates of their convergence. Adv. Appl. Prob. 17, 709– 30.
- Heinrich, L. and Schüle, E. (1995). Generation of the typical cell of a non-Poissonian Johnson–Mehl tessellation. Stochastic Models 11, 541– 60.
- Heinrich, L. and Spiess, M. (2009). Berry–Esseen bounds and Cramér-type large deviations for the volume distribution of Poisson cylinder processes. Lith. Math. J. 49, 381– 98.
- Heinrich, L. and Werner, M. (2000). Kernel estimation of the diameter distribution in Boolean models with spherical grains. J. Nonparametr. Stat. 12, 147– 76.
- Heinrich, P., Stoica, R. S., and Tran, V. C. (2012). Level sets estimation and Vorob'ev expectation of random compact sets. Spatial Statistics 2, 47– 61.
- Heinzer, S., Krucker, T., Stampanoni, M., Abela, R., Meyer, E. P., Schuler, A., Schneider, P., and Müller, R. (2006). Hierarchical microimaging for multiscale analysis of large vascular networks. NeuroImage 32, 626– 36.
- Hermann, H. (1991). Stochastic Models of Heterogeneous Materials. Materials Science Forum 78. Trans Tech Publications Inc., Zürich.
- Hermann, H. (1998). Transformation kinetics in partially crystallized amorphous alloys –a theoretical approach. Europhys. Lett. 41, 245– 50.
- Hermann, H., Elsner, A., Hecker, M., and Stoyan, D. (2005). Computer simulated dense-random packing models as approach to the structure of porous low-k dielectrics. Microelec. Eng. 81, 535– 43.
- Hermann, H., Elsner, A., and Stoyan, D. (2013). Surface area and volume fraction of random open-pore systems. Submitted.
- Hermann, H., Wendrock, H., and Stoyan, D. (1989). Cell-area distributions of planar Voronoi mosaics. Metallography 23, 189– 200.
- Hernandez, G., Leon, R., Salinas, L., and Dimnet, E. (2012). A fragmentation model with neighborhood interaction. Appl. Math. Model. 36, 1694– 702.
- Hestroffer, D., Berthier, J., Descamps, P., Tanga, P., Cellino, A., Lattanzi, M., Di Martino, M., and Zappala, V. (2002). Asteroid (216) Kleopatra. Test of the radar-derived shape model. Astron. Astrophys. 392, 729– 33.
- Heveling, M. and Last, G. (2005). Characterization of Palm measures via bijective point-shifts. Ann. Probab. 33, 1698– 1715.
- Heveling, M. and Last, G. (2006). Existence, uniqueness, and algorithmic computation of general lilypond systems. Random Structures Algorithms 29, 338– 50.
- Heveling, M. and Reitzner, M. (2009). Poisson–Voronoi approximation. Ann. Appl. Probab. 19, 719– 36.
- Hilfer, R. (1991). Geometric and dielectric characterization of porous media. Phys. Rev. B 44, 60– 75.
- Hilfer, R. (2000). Local porosity theory and stochastic reconstruction for porous media. In K. R. Mecke and D. Stoyan, eds, Statistical Physics and Spatial Statistics: the Art of Analyzing and Modeling Spatial Structures and Pattern Formation, Lecture Notes in Physics 554, pp. 203– 41. Springer-Verlag, Berlin.
- Hilhorst, H. J. (2006). Planar Voronoi cells: the violation of Aboav's law explained. J. Phys. A: Math. Gen. 39, 7227– 43.
- Hilhorst, H. J. (2007). New Monte Carlo method for planar Poisson–Voronoi cells. J. Phys. A: Math. Gen. 40, 2615– 38.
- Hilhorst, H. J. (2008). Statistical properties of planar Voronoi tessellations. Eur. Phys. J. B 64, 437– 41.
- Hill, B. J., Kendall, W. S., and Thönnes, E. (2012). Fibre-generated point processes and fields of orientations. Ann. Appl. Statist. 6, 994– 1020.
- Hilliard, J. E. (1962). Specification and measurement of microstructural anisotropy. Trans. Metall. Soc. Amer. Inst. Met. Eng. 224, 1201– 11.
- Hilliard, J. E. (1967). Determination of structural anisotropy. In Elias, H., ed., Stereology: Proceedings of the Second International Congress for Stereology, Chicago, 1967, pp. 219– 27. Springer-Verlag, Berlin.
- Hilliard, J. E. and Lawson, L. R. (2003). Stereology and Stochastic Geometry. Kluwer Academic Publishers, Dordrecht.
- Hinde, A. L. and Miles, R. E. (1980). Monte Carlo estimates of the distributions of the random polygons of the Voronoi tessellation with respect to a Poisson process. J. Statist. Comput. Simul. 10, 205– 23.
- Hjelle, Ø. and Dæhlen, M. (2006). Triangulations and Applications. Springer-Verlag, Berlin.
- Ho, L. P. and Chiu, S. N. (2006). Testing the complete spatial randomness by Diggle's test without an arbitrary upper limit. J. Statist. Comput. Simul. 76, 585– 91.
- Ho, L. P. and Chiu, S. N. (2009). Using weight functions in spatial point pattern analysis with application to plant ecology data. Comm. Statist. Simulation Comput 38, 269– 87.
- Hodder, I. and Orton, C. (1976). Spatial Analysis in Archaeology. Cambridge University Press, Cambridge.
- Hoffmann, L. M. (2007). Intersection densities of nonstationary Poisson processes of hypersurfaces. Adv. Appl. Prob. 39, 307– 17.
- Holroyd, A. E. and Peres, Y. (2005). Extra heads and invariant allocations. Ann. Probab. 33, 31– 52.
- Honda, H. (1983). Geometric models for cells in tissues. Int. Rev. Cytology 81, 191– 248.
- Horálek, V. (1988). A note on the time-non-homogeneous Johnson–Mehl tessellation. Adv. Appl. Prob. 20, 684– 5.
- Horálek, V. (1990). ASTM grain-size model and related random tessellation models. Mater. Char. 25, 263– 84.
- Horgan, G. W. and Young, I. M. (2000). An empirical stochastic model for the geometry of two-dimensional crack growth in soil (with Discussion). Geoderma 96, 263– 76.
- Hörig, M. and Redenbach, C. (2012). The maximum volume hard subset model for Poisson processes: simulation aspects. J. Statist. Comput. Simul. 82, 107– 21.
- Hosemann, R. and Bagchi, S. N. (1962). Direct Analysis of Diffraction by Matter. North Holland, Amsterdam.
- Howard, V. and Reed, M. G. (2005). Unbiased Stereology: Three-dimensional Measurement in Microscopy. Garland Science/BIOS Scientific Publishers, New York, 2nd edition.
- Huang, F. and Ogata, Y. (2001). Comparison of two methods for calculating the partition functions of various spatial statistical models. Aust. N.Z. J. Stat. 43, 47– 65.
- Huber, M. (2011). Spatial point processes. In Brooks, S., Gelman, A., Jones, G. L., and Meng, X.-L., eds, Handbook of Markov Chain Monte Carlo, pp. 227– 52. CRC Press, Boca Raton.
- Hug, D., Last, G., and Weil, W. (2002a). Generalized contact distributions of inhomogeneous Boolean models. Adv. Appl. Prob. 34, 21– 47.
- Hug, D., Last, G., and Weil, W. (2002b). A survey on contact distributions. In K. R. Mecke and D. Stoyan, eds, Morphology of Condensed Matter. Physics and Geometry of Spatially Complex Systems, Lecture Notes in Physics 600, pp. 317– 57. Springer-Verlag, Berlin.
- Hug, D., Last, G., and Weil, W. (2006). Polynomial parallel volume, convexity and contact distributions of random sets. Probab. Theory Related Fields 135, 169– 200.
- Hug, D. and Schneider, R. (2010). Large faces in Poisson hyperplane mosaics. Ann. Probab. 38, 1320– 44.
- Hughes, B. D. (1996). Random Walks and Random Environments. Volume 2: Random Environments. Oxford University Press, New York.
- Hunt, A. G. (2005). Percolation Theory for Flow in Porous Media. Lecture Notes in Physics 674. Springer-Verlag, Berlin.
- Icke, V. and van de Weygaert, R. (1987). Fragmenting the universe I. Astron. Astrophys. 184, 16– 32.
- Illian, J., Penttinen, A., Stoyan, H., and Stoyan, D. (2008). Statistical Analysis and Modelling of Spatial Point Patterns. John Wiley & Sons, Ltd, Chichester.
- Isokawa, Y. (2000). Poisson–Voronoi tessellations in three-dimensional hyperbolic space. Adv. Appl. Prob. 32, 648– 62.
- Ivanoff, G. (1982). Central limit theorems for point processes. Stoch. Process. Appl. 12, 171– 86.
- Jacobsen, M. (2006). Point Process Theory and Applications: Marked Point and Piecewise Deterministic Processes. Birkhäuser, Boston.
- Jacod, J. and Joathon, P. (1971). Use of random genetic models in the study of sedimentary processes. J. Assoc. Math. Geol. 3, 265– 79.
- Jakeman, A. J. and Schaeffer, R. L. (1978). On the properties of product integration estimators for linear functionals of particle size distributions. Utilitas Math. 14, 117– 28.
- Jalilian, A., Guan, Y., and Waagepetersen, R. (2013). Decomposition of variance for spatial Cox processes. Scand. J. Statist. 40, 119– 37.
- Jammalamadaka, S. R. and SenGupta, A. (2001). Topics in Circular Statistics. World Scientific, Singapore.
- Janáček, J. and Kubínová, L. (2010). Variances of length and surface area estimates by spatial grids: preliminary study. Image Anal. Stereol. 29, 45– 52.
- Jankowski, H. and Stanberry, L. (2010). Expectations of random sets and their boundaries using oriented distance functions. J. Math. Imaging Vis. 36, 291– 303.
- Jankowski, H. and Stanberry, L. (2012). Confidence regions for means of random sets using oriented distance functions. Scand. J. Statist. 39, 340– 57.
- Janson, S. (1986). Random coverings in several dimensions. Acta Math. 156, 83– 118.
- Janson, S. and Kallenberg, O. (1981). Maximizing the intersection density of fibre processes. J. Appl. Prob. 18, 820– 8.
- Janson, S., Łuczak, T., and Ruciński, A. (2000). Random Graphs. John Wiley & Sons, Inc., New York.
- Jensen, E. B. (1984). A design-based proof of Wicksell's integral equation. J. Microsc. 136, 345– 8.
- Jensen, E. B., Baddeley, A. J., Gundersen, H. J. G., and Sundberg, R. (1985). Recent trends in stereology. Int. Statist. Rev. 53, 99– 108.
- Jensen, E. B., Kieû, K., and Gundersen, H. J. G. (1990a). On the stereological estimation of reduced moment measures. Ann. Inst. Statist. Math. 42, 445– 61.
- Jensen, E. B., Kieû, K., and Gundersen, H. J. G. (1990b). Second-order stereology. Acta Stereol. 9, 15– 35.
- Jensen, E. B. V. (1998). Local Stereology. World Scientific, Singapore.
- Jeulin, D. (1987). Anisotropic rough surface modelling by random morphological functions. Acta Stereol. 6, 183– 9.
- Jeulin, D. (1994). Random structure models for composite media and fracture statistics. In K. Z. Markov, ed., Advances in Mathematical Modelling of Composite Materials, pp. 239– 89. World Scientific, Singapore.
- D. Jeulin, ed. (1997). Advances in Theory and Applications of Random Sets. World Scientific, Singapore.
- Jeulin, D. (2000). Random texture models for material structures. Statist. Comput. 10, 121– 32.
- Jeulin, D. (2002). Modelling random media. Image Anal. Stereol. 21 (Suppl 1), S31– 40.
- Jeulin, D. (2012). Multi scale random sets: from morphology to effective behaviour. In M. Günther, A. Bartel, M. Brunk, S. Schöps, and M. Striebel, eds, Progress in Industrial Mathematics at ECMI 2010, Mathemataics in Industry 17, pp. 381– 93. Springer-Verlag, Berlin.
- Jeulin, D., Monnaie, P., and Péronnet, F. (2001). Gypsum morphological analysis and modeling. Cement Concrete Comp. 23, 299– 311.
- Jeulin, D. and Moreaud, M. (2007). Percolation of random cylinder aggregates. Image Anal. Stereol. 26, 121– 7.
- Jiao, Y., Stillinger, F. H., and Torquato, S. (2007). Modeling heterogeneous materials via two-point correlation functions: Basic principles. Phys. Rev. E 76, 031110.
- Jiao, Y., Stillinger, F. H., and Torquato, S. (2009). A superior descriptor of random textures and its predictive capacity. Proc. Natl. Acad. Sci. 106, 17634– 9.
- Jiao, Y., Stillinger, F. H., and Torquato, S. (2010). Geometrical ambiguity of pair statistics. II. Heterogeneous media. Phys. Rev. E 82, 011106.
- Jiao, Y. and Torquato, S. (2011). Maximally random jammed packings of Platonic solids: Hyperuniform long-range correlations and isostaticity. Phys. Rev. E 84, 041309.
- Jodrey, W. S. and Tory, E. M. (1979). Simulation of random packing of spheres. Simulation 32, 1– 12.
- Johnson, W. A. and Mehl, R. F. (1939). Reaction kinetics in processes of nucleation and growth. Trans. AIME 135, 416– 58.
- Jolivet, E. (1986). Parametric estimation of the covariance density for a stationary point process on Rd . Stoch. Process. Appl. 22, 111– 19.
- Jongbloed, G. (1991). Non-parametric approach to Wicksell's corpuscle problem. Master's thesis, Faculty of Mathematics and Computer Science, Delft University of Technology.
- Jónsdóttir, K. Ý., Schmiegel, J., and Jensen, E. B. V. (2008). Lévy-based growth models. Bernoulli 14, 62– 90.
- Ju, L., Du, Q., and Gunzburger, M. (2002). Probabilistic methods for centroidal Voronoi tessellations and their parallel implementations. Parallel Comput. 28, 1477– 500.
- Kadashevich, I., Schneider, H.-J., and Stoyan, D. (2005). Statistical modeling of the geometrical structure of the system of artificial air pores in autoclaved aerated concrete. Cement Concrete Res. 35, 1495– 502.
- Kadashevich, I. and Stoyan, D. (2010). Simulation of brittle fracture of autoclaved aerated concrete. Comput. Concrete 7, 39– 51.
- Kallenberg, O. (1976a). On the structure of stationary flat processes I. Z. Wahrscheinlichkeitsth. verw. Geb. 37, 157– 74.
- Kallenberg, O. (1976b). Random Measures. Akademie-Verlag, Berlin.
- Kallenberg, O. (1977). A counterexample to R. Davidson's conjecture on line processes. Math. Proc. Camb. Phil. Soc. 82, 301– 7.
- Kallenberg, O. (1980). On the structure of stationary flat processes II. Z. Wahrscheinlichkeitsth. verw. Geb. 52, 127– 47.
- Kallenberg, O. (1981). On the structure of stationary flat processes III. Z. Wahrscheinlichkeitsth. verw. Geb. 56, 239– 53.
- Kallenberg, O. (1983a). Random Measures. Akademie-Verlag, Berlin and Academic Press, London, 3rd edition.
- Kallenberg, O. (1983b). The invariance problem for stationary line and flat processes. In E. B. Jensen and H. J. G. Gundersen, eds, Second International Workshop on Stereology and Stochastic Geometry, pp. 105– 14. Memoirs No. 6. Institute of Mathematics, Department of Theoretical Statistics, University of Aarhus.
- Kallenberg, O. (1986). Random Measures. Akademie-Verlag, Berlin and Academic Press, London, 4th edition.
- Kallenberg, O. (2002). Foundations of Modern Probability. Springer-Verlag, New York, 2nd edition.
- Kallmes, O. and Corte, H. (1960). The structure of paper. I: The statistical geometry of an ideal two dimensional fiber network. Tappi J. 43, 737– 52. (Erratum: 1961, vol. 44, p. 448).
- Kalmykov, A. E. and Shepilov, M. P. (2000). Analytical solution to the equation for pair correlation function of particles formed in the course of phase separation in a glass. Glass Phys. Chem. 26, 143– 7.
- Kanatani, K. I. (1984). Stereological determination of structural anisotropy. Int. J. Eng. Sci. 22, 531– 46.
- Kanaun, S. K. and Levin, V. M. (1994). Effective field method in mechanics of matrix composite materials. In K. Z. Markov, ed., Advances in Mathematical Modelling of Composite Materials, pp. 1– 58. World Scientific, Singapore.
- Kanit, T., Forest, S., Galliet, I., Mounoury, V., and Jeulin, D. (2003). Determination of the size of the representative volume element for random composites: statistical and numerical approach. Int. J. Solids. Structures 40, 3647– 79.
- Kärkkäinen, S., Miettinen, A., Turpeinen, T., Nyblom, J., Pötschke, P., and Timonen, J. (2012). A stochastic shape and orientation model for fibres with an application to carbon nanotubes. Image Anal. Stereol. 31, 17– 26.
- Kärkkäinen, S., Penttinen, A., Ushakov, N. G., and Ushakova, A. P. (2001). Estimation of orientation characteristic of fibrous material. Adv. Appl. Prob. 33, 559– 75.
- Karr, A. F. (1978). Derived random measures. Stoch. Process. Appl. 8, 159– 69.
- Karr, A. F. (1984). Combined non-parametric inference and state estimation for mixed Poisson processes. Z. Wahrscheinlichkeitsth. verw. Geb. 66, 81– 96.
- Karr, A. F. (1986). Point Processes and Their Statistical Inference. Marcel Dekker, New York.
- Karr, A. F. (1991). Point Processes and Their Statistical Inference. Marcel Dekker, New York, 2nd edition.
- Kautz, M., Berger, U., Stoyan, D., Vogt, J., Khan, N. I., Diele, K., Saint-Paul, U., Triet, T., and Nam, V. N. (2011). Desynchronizing effects of lightning strike disturbances on cyclic forest dynamics in mangrove plantations. Aquat. Bot. 95, 173– 81.
- Keiding, N., Jensen, S. T., and Ranek, L. (1972). Maximum-likelihood estimation of the size distribution of linear cell nuclei from the observed distribution in a plane section. Biometrics 28, 813– 30.
- Kellerer, A. M. (1983). On the number of clumps resulting from the overlap of randomly placed figures in a plane. J. Appl. Prob. 20, 126– 35.
- Kendall, D. G. (1974). Foundations of a theory of random sets. In E. F. Harding and D. G. Kendall, eds, Stochastic Geometry, pp. 322– 76. John Wiley & Sons, Ltd, London.
- Kendall, D. G. (1983). The shape of Poisson Delaunay triangles. In M. C. Demetrescu and M. Iosifescu, eds, Studies in Probability and Related Topics in Honour of Octav Onicescu, pp. 321– 30. Nagard, Montreal.
- Kendall, D. G., Barden, D., Carne, T. K., and Le, H. (1999). Shape and Shape Theory. John Wiley & Sons, Ltd, Chichester.
- Kendall, M. G. and Moran, P. A. P. (1963). Geometrical Probability. Griffin, London.
- Kendall, W. S. (2011). Geodesics and flows in a Poissonian city. Ann. Appl. Probab. 21, 801– 42.
- Kendall, W. S. and Le, H. (2010). Statistical shape theory. In W. S. Kendall and I. Molchanov, eds, New Perspectives in Stochastic Geometry, pp. 348– 73. Oxford University Press, Oxford.
- Kendall, W. S. and Mecke, J. (1987). The range of the mean-value quantities of planar tessellations. J. Appl. Prob. 24, 411– 21.
- W. S. Kendall and I. Molchanov, eds (2010). New Perspectives in Stochastic Geometry. Oxford University Press, Oxford.
- Kendall, W. S. and Møller, J. (2000). Perfect simulation using dominating processes on ordered spaces, with application to locally stable point processes. Adv. Appl. Prob. 32, 844– 65.
- Kendall, W. S. and Thönnes, E. (1999). Perfect simulation in stochastic geometry. Pattern Recognition 32, 1569– 86.
- Kendall, W. S., van Lieshout, M. N. M., and Baddeley, A. J. (1999). Quermass-interaction processes: conditions for stability. Adv. Appl. Prob. 31, 315– 42.
- Kessler, M. A. and Werner, B. T. (2003). Self-organisation of sorted patterned ground. Science 299, 380– 3.
- Khintchin, A. Y. (1955). Mathematical Methods in the Theory of Queueing (in Russian). Trudy Matematicheskogo Instituta imeni V. A. Steklova 49, Akad. Nauk, U.S.S.R. (English translation by D. M. Andrews and M. H. Quenouille in 1969, published by Griffin).
- Khmaladze, E. and Toronjadze, N. (2001). On the almost sure coverage property of Voronoi tessellation: the R1 case. Adv. Appl. Prob. 33, 756– 64.
- Kiang, T. (1966). Random fragmentation in 2 and 3 dimensions. Z. Astrophys. 64, 433– 9.
- Kiderlen, M. (2001). Non-parametric estimation of the directional distribution of stationary line and fibre processes. Adv. Appl. Prob. 33, 6– 24.
- Kiderlen, M. (2008). Estimation of the mean normal measure from flat sections. Adv. Appl. Prob. 40, 31– 48.
- Kiderlen, M. and Jensen, E. B. V. (2003). Estimation of the directional measure of planar random sets by digitization. Adv. Appl. Prob. 35, 583– 602.
- Kiderlen, M. and Pfrang, A. (2005). Algorithms to estimate the rose of directions of a spatial fibre system. J. Microsc. 219, 50– 60.
- Kiderlen, M. and Rataj, J. (2006). On infinitesimal increase of volumes of morphological transforms. Mathematika 53, 103– 27.
- Kingman, J. F. C. (1969). Random secants of a convex body. J. Appl. Prob. 6, 660– 72.
- Kingman, J. F. C. (1977). Remarks on the spatial distribution of a reproducing population. J. Appl. Prob. 14, 577– 83.
- Kingman, J. F. C. (1993). Poisson Processes. Oxford Studies in Probability 3. Oxford University Press, Oxford.
- Kingman, J. F. C. (2006). Poisson processes revisited. Probab. Math. Statist. 26, 77– 95.
- Kishore, V., Santhanam, M. S., and Amritkar, R. E. (2011). Extreme events on complex networks. Phys. Rev. Lett. 106, 188701.
- Kishore, V., Santhanam, M. S., and Amritkar, R. E. (2012). Extreme events and event size fluctuations in biased random walks on networks. Phys. Rev. E 85, 056120.
- Klain, D. A. (1995). A short proof of Hadwiger's characterization theorem. Mathematika 42, 329– 39.
- Klain, D. A. and Rota, G.-C. (1997). Introduction to Geometric Probability. Cambridge University Press, Cambridge.
- Klenk, S., Schmidt, V., and Spodarev, E. (2006). A new algorithmic approach to the computation of Minkowski functionals of germ–grain models. Comput. Geom. 34, 127– 48.
- Klette, R. and Rosenfeld, A. (2004). Digital Geometry: Geometrical Methods for Digital Picture Analysis. Morgan Kaufmann, San Francisco.
- Klier, G. (1969). Mathematisch-statistische Untersuchungen zur Verteilung der Bäume im Bestand. Wiss. Z. TU Dresden 18, 1061– 5.
- Kloeden, P. E. and Lorenz, T. (2011). Stochastic morphological evolution equations. J. Differential Equations 251, 2950– 79.
- Koch, R. A., Pfeiffer, L., and Stammler, L. (1983). Der Basalt von Stolpen in der Lausitz. Deutscher Verlag für Grundstoffindustrie, Leipzig.
- Kohutek, I. and Saxl, I. (1993). Properties of the Voronoi tessellation corresponding to the generalized planar Gauss-Poisson process. Acta Stereol. 12, 155– 60.
- Kolmogorov, A. N. (1933). Grundbegriffe der Wahrscheinlichkeitsrechnung Ergebnisse der Mathematik. Springer-Verlag, Berlin.
- Kolmogorov, A. N. (1937). Statistical theory of crystallization of metals. Bull. Acad. Sci. USSR Mat. Ser. 1, 355– 9.
- Kopp-Schneider, A., Portier, C., and Bannasch, P. (1998). A model for hepatocarcinogenesis treating phenotypical changes in focal hepatocellular lesions as epigenetic events. Math. Biosci. 148, 181– 204.
- Koschitzki, S. (1980). Some stereological problems for random discs in R3 . Math. Operationsf. Statist., Ser. Statistics 11, 75– 83.
- Kovalenko, I. N. (1997). A proof of a conjecture of D.G. Kendall concerning shapes of random polygons of large area. Cybernet. Systems Anal. 33, 461– 7.
- Kovalenko, I. N. (1998). An extension of a conjecture of D.G. Kendall concerning shapes of random large polygons to Poisson Voronoï cells. In P. Engel and H. Syta, eds, Voronoï Impact on Modern Science, Book I, Volume 21 of Proceedings of the Institute of Mathematics of the National Academy of Sciences of Ukraine, pp. 266– 74. Institute of Mathematics, Kyiv.
- Kovalenko, I. N. (1999). A simplified proof of a conjecture of D.G. Kendall concerning shapes of random polygons. J. Appl. Math. Stochastic Anal. 12, 301– 10.
- Krasnoperov, R. A. and Gerasimov, A. N. (2003). Determination of size distribution of elliptical microvessels from size distribution measurement of their section profiles. Exp. Biol. Med. 228, 84– 92.
- Krasnoperov, R. A. and Stoyan, D. (2006). Spatial correlation analysis of isotropic microvessels: methodology and application to thyroid capillaries. Ann. Biomed. Eng. 34, 810– 22.
- Krätschmer, V. (2006). Integrals of random fuzzy sets. Test 15, 433– 69.
- Kraynik, A. M., Reinelt, D. A., and van Swol, F. (2003). Structure of random monodisperse foam. Phys. Rev. E 67, 031403.
- Krebs, C. J. (1999). Ecological Methodology. Addison Wesley Longman, Menlo Park, CA.
- Krickeberg, K. (1972). The Cox process. Instituto Nazionale di Alta Matematicam Symposia Matematica 9, 151– 67.
- Krickeberg, K. (1974). Moments of point processes. In E. F. Harding and D. G. Kendall, eds, Stochastic Geometry, pp. 89– 113. John Wiley & Sons, Ltd, London.
- Krickeberg, K. (1982). Processus Ponctuels en Statistique. In P. L. Hennequin, ed., Ecole d'Ete de Probabilities de Saint-Flour X 1980, Lecture Notes in Mathematics 929, pp. 205– 313. Springer-Verlag, Berlin.
- Kroese, D. P., Taimre, T., and Botev, Z. I. (2011). Handbook of Monte Carlo Methods. John Wiley & Sons, Inc., Hoboken, New Jersey.
- Kruse, R. and Meyer, K. D. (1987). Statistics with Vague Data. D. Reidel Publishing, Dortrecht.
- Kumar, S., Kurtz, S. K., Banavar, J. R., and Sharma, M. G. (1992). Properties of a three-dimensional Poisson–Voronoi tessellation: a Monte Carlo study. J. Stat. Phys. 67, 523– 52.
- Kumar, S. and Singh, R. N. (1995). Thermal conductivity of polycrystalline material. J. Amer. Ceram. Soc. 78, 728– 36.
- Kuo, W., Kim, K. O., and Kim, T. (2006). Modeling and analyzing yield, burn-in and reliability for semiconductor manufacturing: overview. In H. Pham, ed., Springer Handbook of Engineering Statistics, chapter 9, pp. 153– 69. Springer-Verlag, London.
- Kutoyants, Y. A. (1998). Statistical Inference for Spatial Poisson Processes. Lecture Notes in Statistics 134. Springer-Verlag, New York.
- Land, S. and Wilkison, M. H. F. (2009). Comparison of spatial pattern spectra. In M. H. F. Wilkinson and J. B. T. M. Roerdink, eds, Mathematical Morphology and Its Application to Signal and Image Processing, Lecture Notes in Computer Science 5720, pp. 92– 103. Springer-Verlag, Berlin.
- Lantuéjoul, C. (1978a). Computation of the histograms of the number of edges and neighbours of cells in a tessellation. In R. E. Miles and J. Serra, eds, Geometrical Probability and Biological Structures: Buffon's 200th Anniversary, Lecture Notes in Biomathematics 23, pp. 323– 9. Springer-Verlag, Berlin.
- Lantuéjoul, C. (1978b). La squelettisation et son application aux mesures topologiques des mosaïques polycristallines. Thèse de Docteur-Ingénieur, École des Mines de Paris.
- Lantuéjoul, C. (2002). Geostatistical Simulation: Models and Algorithms. Springer-Verlag, Berlin.
- Laslett, G. M. (1982a). Censoring and edge effects in areal and line transect sampling of rock joint traces. Math. Geol. 14, 125– 49.
- Laslett, G. M. (1982b). The survival curve under monotone density constraints with application to two-dimensional line segment processes. Biometrika 69, 153– 60.
- Laslett, G. M., Kendall, W. S., Gleadow, A. J. W., and Duddy, I. R. (1982). Bias in measurement of fission track length distributions. Nuclear Tracks 6, 79– 85.
- Last, G. (2006). Stationary partitions and Palm probabilities. Adv. Appl. Prob. 38, 602– 20.
- Last, G. (2010). Modern random measures: Palm theory and related models. In W. S. Kendall and I. Molchanov, eds, New Perspectives in Stochastic Geometry, pp. 77– 110. Oxford University Press, Oxford.
- Last, G. and Brandt, A. (1995). Marked Point Processes on the Real Line: The Dynamic Approach. Springer-Verlag, New York.
- Last, G. and Holtmann, M. (1999). On the empty space function of some germ–grain models. Pattern Recognition 32, 1587– 600.
- Last, G. and Penrose, M. D. (2013). Percolation and limit theory for the Poisson lilypond model. Random Structures Algorithms 42, 226– 49.
- Last, G. and Schassberger, R. (1996). A flow conservation law for surface processes. Adv. Appl. Prob. 28, 13– 28.
- Last, G. and Schassberger, R. (1998). On the distribution of the spherical contact vector of stationary germ–grain models. Adv. Appl. Prob. 30, 36– 52.
- Last, G. and Schassberger, R. (2000). On stationary stochastic flows and Palm probabilities of surface processes. Ann. Appl. Probab. 10, 463– 92.
- Last, G. and Schassberger, R. (2001). On the second derivative of the spherical contact distribution function of smooth grain models. Probab. Theory Related Fields 121, 49– 72.
- Last, G. and Szekli, R. (2011). Comparisons and asymptotics for empty space hazard functions of germ–grain models. Adv. Appl. Prob. 43, 943– 62.
- Lauschmann, H. and Mrkvička, T. (2009). Perimeter in material images: Comparison of continuous representation and global stereological estimation methods. Mater. Char. 60, 1133– 8.
- Lautensack, C. (2007). Random Laguerre Tessellations. PhD thesis, Universität Karlsruhe (TH), Germany.
- Lautensack, C. (2008). Fitting three-dimensional Laguerre tessellations to foam structures. J. Appl. Stat. 35, 985– 95.
- Lautensack, C., Giertzsch, M., Godehardt, M., and Schladitz, K. (2008). Modelling a ceramic foam using locally adaptable morphology. J. Microsc. 230, 396– 404.
- Lautensack, C. and Sych, T. (2006). 3D image analysis of open foams using random tessellations. Image Anal. Stereol. 25, 87– 93.
- Lautensack, C. and Zuyev, S. (2008). Random Laguerre tessellations. Adv. Appl. Prob. 40, 630– 50.
- Leistritz, L. and Zähle, M. (1992). Topological mean value relations for random cell complexes. Math. Nachr. 155, 57– 72.
- León, C. A., Massé, J.-C., and Rivest, L.-P. (2006). A statistical model for random rotations. J. Multivariate Anal. 97, 412– 30.
- Levitz, P. and Tchoubar, D. (1992). Disordered porous solids: from chord distributions to small angle scattering. Journal de Physique I 2, 771– 90.
- Lewis, F. T. (1931). A comparison between the mosaic of polygons in a film of artifical emulsion and in cucumber epidermis and human amnion. Anat. Rec. 50, 235– 65.
- Lewis, F. T. (1946). The shape of cells as a mathematical problem. Amer. Scientist 34, 359– 69.
- Lewis, H. D., Walthers, K. L., and Johnson, K. A. (1973). Particle size distributions by area analysis: Modifications of the Saltykov method. Metallography 6, 93– 101.
- Lewis, P. A. W. and Shedler, G. S. (1979). Simulation of non-homogeneous Poisson processes by thinning. Naval Res. Logist. Quart. 26, 403– 13.
- Li, D. S., Tschopp, M. A., Khaleel, M., and Sun, X. (2012). Comparison of reconstructed spatial microstructure images using different statistical descriptors. Comput. Mat. Sci. 51, 437– 44.
- Li, S., Ogura, Y., and Kreinovich, V. (2002). Limit Theorems and Application of Set-valued and Fuzzy Set-valued Random Variables. Kluwer Academic Publishers, Dordrecht.
- Liemant, A., Matthes, K., and Wakolbinger, A. (1988). Equilibrium Distributions of Branching Processes. Mathematical Research 42. Akademie-Verlag, Berlin.
- Likeš, J. (1963). On the problem of particle number and size determination in opaque bodies. Acta Tech. Acad. Sci. Hung. 42, 325– 41.
- Lindgren, G. and Rychlik, I. (1991). Slepian models and regression approximations in crossing and extreme value theory. Int. Statist. Rev. 59, 195– 225.
- Lipskij, J. N., Nikonov, V. A., Skobeleva, T. I., and Kazimirov, D. A. (1977). Catalogue of the Craters of the Mars and Statistics of the Craters of the Mars, Mercury and Moon. Acad. Sciences USSR, Geol. Inst., Moscow. (The analysis is based on: Shaded relief map of Mars, 1:25000000. U. S. Geol. Survey 1972).
- Liu, G., Yu, H., and Li, W. (1994). Efficient and unbiased evaluation of size and topology of space-filling grains. Acta Stereol. 13, 281– 6.
- Lochmann, K., Anikeenko, A., Elsner, A., Medvedev, N., and Stoyan, D. (2006). Statistical verification of crystallization in hard sphere packings under densification. Eur. Phys. J. B 53, 67– 76.
- Loosmore, N. B. and Ford, E. D. (2006). Statistical inference using the G or K point pattern spatial statistics. Ecology 87, 1925– 31.
- Lord, G. W. and Willis, T. F. (1951). Calculation of air bubble distribution from results of a Rosiwal traverse of aerated concrete. ASTM Bull. 56, 177– 87.
- Lorenz, C. D. and Ziff, R. M. (2001). Precise determination of the critical percolation threshold for the three-dimensional "Swiss cheese" model using a growth algorithm. J. Chem. Phys. 114, 3659– 61.
- Lorenz, T. (2010). Mutational Analysis. A Joint Framework for Cauchy Problems in and beyond Vector Spaces. Lecture Notes in Mathematics 1996. Springer-Verlag, Berlin.
- Lorz, U. (1990). Cell-area distributions of planar sections of spatial Voronoi mosaics. Mater. Char. 3, 297– 311.
- Lorz, U. (1995). Statistics for the spatial Poisson–Voronoi tessellation. In D. M. Titterington, ed., Complex Stochastic Systems and Engineering, pp. 141– 53. Clarendon Press, Oxford.
- Lorz, U. and Hahn, U. (1993). Geometric characteristics of spatial Voronoi tessellations and planar sections. Preprint 93-05, TU Bergakademie Freiberg.
- Lotwick, H. W. (1984). Some models for multitype spatial point processes, with remarks on analysing multitype patterns. J. Appl. Prob. 21, 575– 82.
- Lotwick, H. W. and Silverman, B. W. (1981). Convergence of spatial birth-and-death processes. Math. Proc. Camb. Phil. Soc 90, 155– 65.
- Louis, A. K., Riplinger, M., Spiess, M., and Spodarev, E. (2011). Inversion algorithms for the spherical Radon and cosine transform. Inverse Problems 27, 035015.
- Lowry, M. I. and Miller, C. T. (1995). Pore-scale modeling of nonwetting-phase residual in porous media. Water Resour. Res. 31, 455– 73.
- Lu, B. and Torquato, S. (1992). Lineal-path function for random heterogeneous materials. Phys. Rev. A 45, 922– 9.
- Lück, S., Fichtl, A., Sailer, M., Joos, H., Brenner, R. E., Walther, P., and Schmidt, V. (2013). Statistical analysis of the intermediate filament network in cells of mesenchymal lineage by greyvalue-oriented image segmentation. Comput. Stat. 28, 139– 60.
- Lück, S., Sailer, M., Schmidt, V., and Walther, P. (2010). Three-dimensional analysis of intermediate filament networks using sem tomography. J. Microsc. 239, 1– 16.
- Lücke, T. and Tittel, R. (1993). An improved description of non woven materials by an assembly of straight lines. Chem. Biochem. Eng. Q. 7, 169– 75.
- Mack, C. (1954). The expected number of clumps formed when convex laminae or bodies are placed at random and with random orientation on a plane area. Proc. Camb. Phil. Soc. 50, 581– 5.
- Mack, C. (1956). On clumps formed when convex laminae or bodies are placed at random in two or three dimensions. Proc. Camb. Phil. Soc. 52, 246– 50.
- Macosko, C. W. and Miller, D. R. (1991). Calculation of average molecular properties during nonlinear, living copolymerization. Makromol. Chem. 192, 377– 404.
- Mahin, W. K., Hanson, K., and Morris, J. W. (1980). Comparative analysis of the cellular and Johnson–Mehl microstructures through computer simulation. Acta Metallurgica 28, 443– 53.
- Maier, R., Mayer, J., and Schmidt, V. (2004). Distributional properties of the typical cell of stationary iterated tessellations. Math. Methods Oper. Res. 59, 287– 302.
- Maier, R. and Schmidt, V. (2003). Stationary iterated tessellations. Adv. Appl. Prob. 35, 337– 53.
- Malin, M. C., Edgett, K. S., Posiolova, L. V., McColley, S. M., and Dobrea, E. Z. N. (2006). Present-day impact cratering rate and contemporary gully activity on Mars. Science 314, 1573– 7.
- Malinowski, M. T. and Michta, M. (2010). Stochastic set differential equations. Nonlinear Anal. 72, 1247– 56.
- Månsson, M. and Rudemo, M. (2002). Random patterns of nonoverlapping convex grains. Adv. Appl. Prob. 34, 718– 38.
- Manwart, C., Torquato, S., and Hilfer, R. (2000). Stochastic reconstruction of sandstones. Phys. Rev. E 62, 893– 9.
- Marchant, J. C. and Dillon, P. L. P. (1961). Correlation between random-dot samples and the photographic emulsion. J. Opt. Soc. Amer. 51, 641– 4.
- Marcus, A. (1972). Some point process models of lunar and planetary surfaces. In P. A. W. Lewis, ed., Stochastic Point Processes: Statistical Analysis, Theory, and Applications, pp. 682– 99. John Wiley & Sons, Inc., New York.
- Mardia, K. V., Edwards, R., and Puri, M. L. (1977). Analysis of central place theory. Bull. Int. Statist. Inst. 47, 93– 110.
- Mardia, K. V. and Jupp, P. E. (2000). Directional Statistics. John Wiley & Sons, Ltd, Chichester.
- Marriott, F. H. C. (1971). Buffon's problem for non-random directions. Biometrics 27, 233.
- Martínez, V. J., Arnalte-Mur, P., Saar, E., de la Cruz, P., Pons-Borderia, M. J., Paredes, S., Fernadez-Soto, A., and Tempel, E. (2009). Reliability of the detection of the baryon acoustic peak. Astrophys. J. 696, L93– 7. (Erratum: 2009, vol. 703, p. L184).
- Martínez, V. J. and Saar, E. (2002). Statistics of the Galaxy Distribution. Chapman & Hall/CRC, Boca Raton.
- Mase, S. (1985). On the possible form of size distributions for Gibbsian processes of mutually non-intersecting discs. J. Appl. Prob. 23, 646– 59.
- Mase, S. (1990). Mean characteristics of Gibbsian point processes. Ann. Inst. Statist. Math. 42, 203– 20.
- Mase, S. (1992). Uniform LAN condition of planar Gibbsian point processes and optimality of maximum-likelihood estimators of soft-core potential functions. Probab. Theory Related Fields 92, 51– 67.
- Mase, S. (1995). Stereological estimation of particle size distributions. Adv. Appl. Prob 27, 350– 66.
- Matérn, B. (1960). Spatial Variation. Meddelanden fran Statens Skogsforskningsinstitut 49, 1– 144. See also Matérn (1986).
- Matérn, B. (1971). Doubly stochastic Poisson processes in the plane. In G. Patil, ed., Statistical Ecology, Volume 1, pp. 195– 213. Pennsylvania State University Press, University Park.
- Matérn, B. (1986). Spatial Variation. Lecture Notes in Statistics 36. Springer-Verlag, Berlin.
- Matheron, G. (1967). Elements pour une theorie des mileux poreux. Masson, Paris.
- Matheron, G. (1971). The Theory of Regionalized Variables and its Applications. École national supérieure des mines, Paris.
- Matheron, G. (1975). Random Sets and Integral Geometry. John Wiley & Sons, Inc., New York.
- Matheron, G. (1978). La formule de Steiner pour les erosions. J. Appl. Prob. 15, 126– 35.
- Matheron, G. (1989). Estimating and Choosing. Springer-Verlag, Berlin.
- Mathieu, O., Cruz-Orive, L. M., Hoppeler, H., and Weibel, E. R. (1983). Estimating length density and quantifying anisotropy in skeletal muscle capillaries. J. Microsc. 131, 131– 46.
- Matos, I. (2009). Limited Range Coverage Problems. PhD thesis, Departamento de Matemática, Universidade de Aveiro, Portugal.
- Matoušek, J. and Nešetřil, J. (2008). Invitation to Discrete Mathematics. Oxford University Press, Oxford.
- Mattfeldt, T. and Mall, G. (1984). Estimation of length and surface of anisotropic capillaries. J. Microsc. 135, 181– 90.
- Mattfeldt, T. and Stoyan, D. (2000). Improved estimation of the pair correlation function of random sets. J. Microsc. 200, 158– 73.
- Matthes, K. (1963). Stationäre zufällige Punktfolgen. Jahresbericht Deutsche Math. Verein. 66, 66– 79.
- Matthes, K., Kerstan, J., and Mecke, J. (1978). Infinitely Divisible Point Processes. John Wiley & Sons, Ltd, Chichester.
- Matthes, K., Warmuth, W., and Mecke, J. (1979). Bemerkungen zu einer Arbeit von Nguyen Xuan Xanh und Hans Zessin. Math. Nachr. 88, 117– 27.
- Mayer, J. (2004). A time-optimal algorithm for the estimation of contact distribution functions of random sets. Image Anal. Stereol. 23, 177– 83.
- McLachlan, G. J. and Krishnan, T. (2008). The EM Algorithm and Extensions. John Wiley & Sons, Inc., New York, 2nd edition.
- Mecke, J. (1967). Stationäre zufällige Maße auf lokalkompakten Abelschen Gruppen. Z. Wahrscheinlichkeitsth. verw. Geb. 9, 36– 58.
- Mecke, J. (1968). Eine charakteristische Eigenschaft der doppelt stochastischen Poissonschen Prozesse. Z. Wahrscheinlichkeitsth. verw. Geb. 11, 74– 81.
- Mecke, J. (1972). Zufällige Maße auf lokalkompakten Hausdorffschen Räumen. Beiträge zur Analysis 3, 7– 30.
- Mecke, J. (1975). Invarianzeigenschaften allgemeiner Palmscher Maße. Math. Nachr. 65, 335– 44.
- Mecke, J. (1979). An explicit description of Kallenberg's lattice-type point process. Math. Nachr. 89, 185– 95.
- Mecke, J. (1980). Palm methods for stationary random mosaics. In Ambartzumian, R. V., ed., Combinatorial Principles in Stochastic Geometry, pp. 124– 32. Armenian Academy of Sciences Publ., Erevan.
- Mecke, J. (1981a). Formulas for stationary planar fibre processes III –Intersection with fibre systems. Math. Operationsf. Statist., Ser. Statistics 12, 201– 10.
- Mecke, J. (1981b). Stereological formulas for manifold processes. Prob. Math. Statist. 2, 31– 5.
- Mecke, J. (1983). Inequalities for intersection densities of superpositions of stationary Poisson hyperplane processes. In E. B. Jensen and H. J. G. Gundersen, eds, Second International Workshop on Stereology and Stochastic Geometry, pp. 115– 24. Memoirs No. 6. Institute of Mathematics, Department of Theoretical Statistics, University of Aarhus.
- Mecke, J. (1984a). Isoperimetric properties of stationary random mosaics. Math. Nachr. 117, 75– 82.
- Mecke, J. (1984b). Parametric representation of mean values for stationary random mosaics. Math. Operationsf. Statist., Ser. Statistics 15, 437– 42.
- Mecke, J. (1984c). Random tessellations generated by hyperplanes. In R. V. Ambartzumian and W. Weil, eds, Stochastic Geometry, Geometric Statistics, Stereology, Teubner-Texte zur Mathematik 65, pp. 104– 9. B. G. Teubner Verlagsgesellschaft, Leipzig.
- Mecke, J. (1986). On some inequalities for Poisson networks. Math. Nachr. 128, 81– 6.
- Mecke, J. (1988a). An extremal property of random flats. J. Microsc. 151, 205– 9.
- Mecke, J. (1988b). Random r-flats meeting a ball. Arch. Math. 51, 378– 84.
- Mecke, J. (1991). On the intersection density of flat processes. Math. Nachr. 151, 69– 74.
- Mecke, J. (1995). Inequalities for the anisotropic Poisson polytope. Adv. Appl. Prob 27, 56– 62.
- Mecke, J. (1999). On the relationship between the 0-cell and the typical cell of a stationary random tessellation. Pattern Recognition 32, 1645– 8.
- Mecke, J. (2010). Inhomogeneous random planar tessellations generated by lines. J. Contemp. Math. Anal., Armen. 45, 357– 67.
- Mecke, J. and Muche, L. (1995). The Poisson Voronoi tessellation, I: A basic identity. Math. Nachr. 176, 199– 208.
- Mecke, J. and Nagel, W. (1980). Stationäre räumliche Faserprozesse und ihre Schnittzahlrosen. Elektron. Informationsverarb. Kyb. 16, 475– 83.
- Mecke, J., Nagel, W., and Weiss, V. (2008). A global construction of homogeneous random planar tessellations that are stable under iteration. Stochastics 80, 51– 67.
- Mecke, J., Schneider, R., Stoyan, D., and Weil, W. (1990). Stochastische Geometrie. Birkhäuser, Basel.
- Mecke, J. and Stoyan, D. (1980a). Formulas for stationary planar fibre processes I —general theory. Math. Operationsf. Statist., Ser. Statistics 12, 267– 79.
- Mecke, J. and Stoyan, D. (1980b). Stereological problems for spherical particles. Math. Nachr. 96, 311– 17.
- Mecke, J. and Stoyan, D. (2001). The specific connectivity number of random networks. Adv. Appl. Prob. 33, 576– 85.
- Mecke, J. and Thomas, C. (1986). On an extreme value problem for flat processes. Stochastic Models 2, 273– 80.
- Mecke, K. (1994). Integralgeometrie in der Statistischen Physik: Perkolation, komplexe Flüssigkeiten und die Struktur des Universums. Reihe Physik 25. Verlag Harry Deutsch, Frankfurt.
- Mecke, K. R. (1996). Morphological characterization of patterns in reaction-diffusion systems. Phys. Rev. E 53, 4794– 800.
- Mecke, K. R. (2000). Additivity, convexity, and beyond: applications of Minkowski Functionals in statistical physics. In K. R. Mecke and D. Stoyan, eds, Statistical Physics and Spatial Statistics: the Art of Analyzing and Modeling Spatial Structures and Pattern Formation, Lecture Notes in Physics 554, pp. 111– 84. Springer-Verlag, Berlin.
- Mecke, K. R. and Seyfried, A. (2002). Strong dependence of percolation thresholds on polydispersity. Europhys. Lett. 58, 28– 34.
- Mecke, K. R. and Wagner, H. (1991). Euler characteristic and related measures for random geometric sets. J. Stat. Phys. 64, 843– 50.
- Medvedev, N. N. (2000). The Voronoi–Delaunay Method for Non-crystal Structures (in Russian). SB Russian Academy of Sciences, Novosibirsk.
- Medvedev, N. N., Voloshin, V. P., Luchnikov, V. A., and Gavrilova, M. L. (2006). An algorithm for three-dimensional Voronoi S-network. J. Comput. Chem. 27, 1676– 92.
- Meester, R. and Roy, R. (1994). Uniqueness of unbounded occupied and vacant components in Boolean models. Ann. Appl. Probab 4, 933– 51.
- Meester, R. and Roy, R. (1996). Continuum Percolation. Cambridge University Press, Cambridge.
- Meester, R., Roy, R., and Sarkar, A. (1994). Nonuniversality and continuity of the critical covered volume fraction in continuum percolation. J. Stat. Phys. 75, 123– 34.
- Meijering, J. L. (1953). Interface area, edge length and number of vertices in crystal aggregates with random nucleation. Philips Res. Rep. 8, 270– 90.
- Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953). Equation of state calculations by fast computing machines. J. Chem. Phys. 21, 1087– 92.
- Michalke, W., Lang, M., Kreitmeier, S., and Göritz, D. (2001). Simulations on the number of entanglements of a polymer network using knot theory. Phys. Rev. E 64, 6300– 7.
- Michel, J. and Paroux, K. (2003). Local convergence of the Boolean shell model towards the thick Poisson hyperplane process in the Euclidean space. Adv. Appl. Prob. 35, 354– 61.
- Michel, J. and Paroux, K. (2007). Empirical polygon simulation and central limit theorems for the homogenous Poisson line process. Methodol. Comput. Appl. Probab. 9, 541– 56.
- Michell, J. (1767). An inquiry into the probable parallax, and magnitude, of the fixed stars, from the quantity of light which they afford us, and the particular circumstances of their situation. Phil. Trans. R. Soc. London 57, 234– 64.
- Miles, R. E. (1964a). Random polygons determined by random lines in a plane. Proc. Nat. Acad. Sci. (USA) 52, 901– 7.
- Miles, R. E. (1964b). Random polygons determined by random lines in a plane, II. Proc. Nat. Acad. Sci. (USA) 52, 1157– 60.
- Miles, R. E. (1970). On the homogeneous planar Poisson point process. Math. Biosci. 6, 85– 127.
- Miles, R. E. (1971a). Poisson flats in Euclidean spaces. Part II: Homogeneous Poisson flats and the complementary theorem. Adv. Appl. Prob. 3, 1– 43.
- Miles, R. E. (1971b). Random points, sets and tessellations on the surface of a sphere. Sankhyā A 33, 145– 74.
- Miles, R. E. (1972a). Multi-dimensional perspectives on stereology. J. Microsc. 95, 181– 95.
- Miles, R. E. (1972b). The random division of space. Suppl. Adv. Appl. Prob. 4, 243– 66.
- Miles, R. E. (1973). The various aggregates of random polygons determined by random lines in a plane. Adv. Math. 10, 256– 90.
- Miles, R. E. (1974a). A synopsis of 'Poisson Flats in Euclidean Spaces'. In E. F. Harding and D. G. Kendall, eds, Stochastic Geometry, pp. 202– 27. John Wiley & Sons, Ltd, London.
- Miles, R. E. (1974b). On the elimination of edge-effects in planar sampling. In E. F. Harding and D. G. Kendall, eds, Stochastic Geometry, pp. 228– 47. John Wiley & Sons, Ltd, London.
- Miles, R. E. (1976). Estimating aggregate and overall characteristics from thick sections by transmission microscopy. J. Microsc. 107, 227– 33.
- Miles, R. E. (1983). Stereology for embedded aggregates of not necessarily convex particles. In E. B. Jensen and H. J. G. Gundersen, eds, Second International Workshop on Stereology and Stochastic Geometry, pp. 127– 47. Memoirs No. 6. Institute of Mathematics, Department of Theoretical Statistics, University of Aarhus.
- Miles, R. E. (1984). A comprehensive set of stereological formulae for embedded aggregates of not-necessarily-convex particles. J. Microsc. 134, 127– 36.
- Miles, R. E. (1985). A comprehensive set of stereological formulae for embedded aggregates of not-necessarily-convex particles. J. Microsc 138, 115– 25.
- Miles, R. E. (1986). Spatial tessellations and their stereology. In S. Ishizaka, ed., Science on Form: Proceedings of the First International Symposium for Science on Form, pp. 147– 55. KTK Scientific Publishers, Tokyo.
- Miles, R. E. (1987). Dihedral angle distributions. Acta Stereol. 6, 19– 24.
- Miles, R. E. (1995). A heuristic proof of a long-standing conjecture of D. G. Kendall concerning the shapes of certain large random polygons. Adv. Appl. Prob 27, 397– 417.
- Miles, R. E. and Maillardet, R. J. (1982). The basis structures of Voronoi and generalized Voronoi polygons. J. Appl. Prob. 19A, 97– 112.
- Milne, R. K. and Westcott, M. (1972). Further results for Gauss-Poisson processes. Adv. Appl. Prob. 4, 151– 76.
- Minlos, R. A. (1968). Lectures on statistical physics. Usp. Mat. Nauk 23, 133– 90.
- Molchanov, I. S. (1992). Handling with spatial censored observations in statistics of Boolean models of random sets. Biometrical J. 34, 617– 31.
- Molchanov, I. S. (1993). Limit Theorems for Unions of Random Sets. Lecture Notes in Mathematics 1561. Springer-Verlag, Berlin.
- Molchanov, I. S. (1994). On statistical analysis of Boolean models with non-random grains. Scand. J. Statist. 21, 73– 82.
- Molchanov, I. S. (1996). A limit theorem for scaled vacancies of the Boolean model. Stoch. Stoch. Rep. 58, 45– 65.
- Molchanov, I. S. (1997). Statistics of the Boolean Model for Practitioners and Mathematicians. John Wiley & Sons, Inc., New York.
- Molchanov, I. S. (2005). Theory of Random Sets. Springer-Verlag, London.
- Molchanov, I. S. and Chiu, S. N. (2000). Smoothing techniques and estimation methods for nonstationary boolean models with applications to coverage. Biometrika 87, 265– 83.
- Molchanov, I. S. and Stoyan, D. (1994). Asymptotic properties of estimators for parameters of the Boolean model. Adv. Appl. Prob. 26, 301– 23.
- Molchanov, I. S. and Stoyan, D. (1995). Statistics of compact sets and random polygons. Stochastic Models 12, 199– 214.
- Molchanov, I. S., Stoyan, D., and Fyodorov, K. (1993). Directional analysis of planar fibre networks: application to cardboard microstructure. J. Microsc. 172, 257– 61.
- Molek, H., Pohlmann, S., Reuter, F., and Stoyan, D. (1981). Entwicklung eines komplexen Durchtrennungsgrades von Gesteinsverbänden mit Hilfe stereologischer Methoden. Neue Bergbautechnik 11, 221– 4.
- Møller, J. (1989). Random tessellations in Rd . Adv. Appl. Prob. 24, 37– 73.
- Møller, J. (1992). Random Johnson–Mehl tessellations. Adv. Appl. Prob. 24, 814– 44.
- Møller, J. (1994). Lectures on Random Voronoi Tessellations. Lecture Notes in Statistics 87. Springer-Verlag, Berlin.
- Møller, J. (1995). Generation of Johnson–Mehl crystals and comparative analysis of models for random nucleation. Adv. Appl. Prob. 27, 367– 83.
- Møller, J. (1999). Markov chain Monte Carlo and spatial point processes. In O. E. Barndorff-Nielsen, W. S. Kendall, and M. N. M. van Lieshout, eds, Stochastic Geometry: Likelihood and Computation, pp. 141– 72. Chapman & Hall/CRC, Boca Raton.
- Møller, J. (2001). A review of perfect simulation in stochastic geometry. In I. V. Basawa, C. C. Heyde, and R. L. Taylor, eds, Selected Proceedings of the Symposium on Inference for Stochastic Processes, IMS Lecture Notes Monograph Series 37, pp. 333– 56. Institute of Mathematical Statistics, Beachwood, Ohio.
- Møller, J. and Helisová, K. (2010). Likelihood inference for unions of interacting discs. Scand. J. Statist. 37, 365– 81.
- Møller, J., Huber, M. L., and Wolpert, R. L. (2010). Perfect simulation and moment properties for the Matérn type III process. Stoch. Process. Appl. 120, 2142– 58.
- Møller, J. and Stoyan, D. (2014). Stochastic geometry and random tessellations. In R. van de Weygaert, G. Vegter, V. Icke, and J. Ritzerveld, eds, Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings. Forthcoming.
- Møller, J., Syversveen, R. A., and Waagepetersen, R. P. (1998). Log Gaussian Cox processes. Scand. J. Statist. 25, 451– 82.
- Møller, J. and Waagepetersen, R. P. (2004). Statistical Inference and Simulation for Spatial Point Processes. Chapman & Hall/CRC, Boca Raton.
- Møller, J. and Zuyev, S. (1996). Gamma-type results and other related properties of Poisson processes. Adv. Appl. Prob. 28, 662– 73.
- Möller, O. (1989). A fast statistical procedure solving Wicksell's corpuscle problem. Elektron. Informationsverarb. Kyb. 25, 581– 5.
- Mollison, D. (1977). Spatial contact models for ecological and epidemic spread (with discussion). J. Roy. Statist. Soc. B 39, 283– 326.
- Molloy, M. and Reed, B. (1995). A critical point for random graphs with a given degree sequence. Random Structures Algorithms 6, 161– 79.
- Moran, P. A. P. (1972). The probabilistic basis of stereology. Supp. Adv. Appl. Prob. 4, 69– 91.
- Moran, P. A. P. (1976). Another quasi-Poisson planar point process. Probab. Theory Related Fields 33, 269– 72.
- Morgan, F. (2009). Geometric Measure Theory. A Beginner's Guide. Academic Press, Burlington, MA, 4th edition.
- Mörters, P. (2010). Random fractals. In W. S. Kendall and I. Molchanov, eds, New Perspectives in Stochastic Geometry, pp. 275– 304. Oxford University Press, Oxford.
- Morton, R. R. A. (1966). The expected number and angle of intersection between random curves in a plane. J. Appl. Prob. 3, 559– 62.
- Mouton, P. R. (2011). Unbiased Stereology: a Concise Guide. Johns Hopkins University Press, Baltimore.
- Mrkvička, T. and Mattfeldt, T. (2011). Testing histological images of mammary tissues on compatibility with the Boolean model of random sets. Image Anal. Stereol. 30, 11– 18.
- Mrkvička, T. and Rataj, J. (2008). On the estimation of intrinsic volume densities of stationary random closed sets. Stoch. Process. Appl. 118, 213– 31.
- Muche, L. (1993). An incomplete Voronoi tessellation. Appl. Mathematicae 22, 45– 53.
- Muche, L. (1996a). Distributional properties of the three-dimensional Poisson Delaunay cell. J. Stat. Phys. 84, 147– 67.
- Muche, L. (1996b). The Poisson–Voronoi tessellation II. Edge length distribution functions. Math. Nachr. 178, 271– 83.
- Muche, L. (1998). The Poisson Voronoi tessellation III. Miles' formula. Math. Nachr. 191, 247– 67.
- Muche, L. (2005). The Poisson–Voronoi tessellation: relationships for edges. Adv. Appl. Prob. 37, 279– 96.
- Muche, L. (2010). Contact and chord length distribution functions of the Poisson–Voronoi tessellation in high dimensions. Adv. Appl. Prob. 42, 48– 68.
- Muche, L. and Ballani, F. (2011). The second volume moment of the typical cell and higher moments of edge lengths of the spatial Poisson–Voronoi tessellation. Monatsh. Math. 163, 71– 80.
- Muche, L. and Stoyan, D. (1992). Contact and chord length distributions of the Poisson–Voronoi tessellation. J. Appl. Prob. 29, 467– 71.
- Müller, A. and Stoyan, D. (2002). Comparison Methods for Stochastic Models and Risks. John Wiley & Sons, Ltd, Chichester.
- Myles, J. P., Flenley, E. C., Fieller, N. R. J., Alkinson, H. V., and Jones, H. (1995). Statistical tests for clustering of second phases in composite materials. Philos. Mag. 72, 515– 28.
- Nagel, W. (1983). Dünne Schnitte von stationären räumlichen Faserprozessen. Math. Operationsf. Statist., Ser. Statistics 14, 569– 76.
- Nagel, W. (2010). Stereology. In W. S. Kendall and I. Molchanov, eds, New Perspectives in Stochastic Geometry, pp. 451– 75. Oxford University Press, Oxford.
- Nagel, W. and Weiss, V. (2003). Limits of sequences of stationary planar tessellations. Adv. Appl. Prob. 35, 123– 38.
- Nagel, W. and Weiss, V. (2004). Crack STIT tessellations –existence and uniqueness of tessellations that are stable with respect to iterations. Isvest. Nac. Akad. Nauk Armenii (Mat.) 39, 84– 114.
- Nagel, W. and Weiss, V. (2005). Crack STIT tessellations: characterization of stationary random tessellations stable with respect to iteration. Adv. Appl. Prob. 37, 859– 83.
- Nagel, W. and Weiss, V. (2006). STIT tessellations in the plane. Rend. Circ. Mat. Palermo (2) Suppl. 77, 441– 58.
- Nagel, W. and Weiss, V. (2008). Mean values for homogeneous STIT tessellations in 3D. Image Anal. Stereol. 27, 29– 37.
- Nemat-Nasser, S. and Hori, M. (1999). Micromechanics: Overall Properties of Heterogeneous Materials. Elsevier, Amsterdam, 2nd revised edition.
- Newman, M. E. J. (2003). The structure and function of complex networks. SIAM Review 45, 167– 256.
- Newman, M. E. J., Watts, D. J., and Barabási, A. L. (2006). The Structure and Dynamics of Networks. Princeton University Press, Princeton, New Jersey.
- Neyman, J. and Scott, E. L. (1958). Statistical approach to problems of cosmology. J. Roy. Statist. Soc. B 20, 1– 43.
- Neyman, J. and Scott, E. L. (1972). Processes of clustering and applications. In P. A. W. Lewis, ed., Stochastic Point Processes: Statistical Analysis, Theory and Applications, pp. 646– 81. John Wiley & Sons, Inc., New York.
- Nguyen, H. T. (2005). Fuzzy and random sets. Fuzzy Sets and Systems 156, 349– 56.
- Nguyen, H. T. (2006). An Introduction to Random Sets. Chapman & Hall/CRC, Boca Raton.
- Nguyen, H. T. and Wu, B. (2006). Fundamentals of Statistics with Fuzzy Data. Studies in Fuzziness and Soft Computing 198. Springer-Verlag, New York.
- Nguyen, X. X. (1979). Ergodic theorems for subadditive spatial processes. Probab. Theory Related Fields 48, 159– 76.
- Nguyen, X. X. and Zessin, H. (1979a). Ergodic theorems for spatial processes. Probab. Theory Related Fields 48, 133– 58.
- Nguyen, X. X. and Zessin, H. (1979b). Integral and differential characterizations of Gibbs processes. Math. Nachr. 88, 105– 15.
- Nicholson, W. L. (1970). Estimation of linear properties of particle size distributions. Biometrika 57, 273– 97.
- Nicholson, W. L. (1976). Estimation of linear functionals by maximum likelihood. J. Microsc. 107, 323– 36.
- Nicholson, W. L. (1978). Application of statistical methods in quantitative microscopy. J. Microsc. 113, 223– 336.
- Niskanen, K., Kajanto, I., and Pakarinen, P. (1998). Paper structure. In K. J. Niskanen, ed., Paper Physics, Papermaking Science and Technology Series 16, pp. 14– 53. Fapet Oy, Helsinki.
- Norberg, T. (1984). Convergence and existence of random set functions. Ann. Prob. 12, 726– 32.
- Norberg, T. (1989). Existence theorems for measures on continuous posets, with applications to random set theory. Math. Scand. 64, 15– 51.
- Norberg, T. (1992a). An ordered random set coupling. Theory Probab. Appl. 37, 161– 3.
- Norberg, T. (1992b). On the existence of ordered couplings of random sets–with applications. Isr. J. Math. 77, 241– 64.
- Norros, I. and Reittu, H. (2006). On a conditionally Poissonian graph process. Adv. Appl. Prob. 38, 59– 75.
- Nott, D. J. and Rydén, T. (1999). Pairwise likelihood methods for inference in image models. Biometrika 86, 661– 76.
- Nott, D. J. and Wilson, R. J. (1996). Size distributions for excursion sets. In D. Jeulin, ed., Advances in Theory and Applications of Random Sets, pp. 176– 96. World Scientific, Singapore.
- Nott, D. J. and Wilson, R. J. (1997). Parameter estimation for excursion set texture models. Signal Processing 63, 199– 210.
- Nuske, R. S., Sprauer, S., and Saborowski, J. (2009). Adapting the pair-correlation function for analysing the spatial distribution of canopy gaps. Forest Ecol. Manag. 259, 107– 16.
- Nutting, P. G. (1913). On the absorption of light in heterogeneous media. London, Edinb. & Dublin Philos. Mag. Ser. 6 26, 423– 6.
- Nychka, D. (1983a). Smooth non-parametric estimates of particle size distributions. Acta Stereol. 2, 25– 8.
- Nychka, D. (1983b). Solving integral equations with noisy data: An application of smoothing splines in pathology. In K. W. Heiner, R. S. Sacher, and J. W. Wilkinson, eds, Computer Science and Statistics: Proceedings of the 14th Symposium on the Interface, pp. 157– 63. Springer-Verlag, New York.
- Nychka, D., Wahba, G., Goldfarb, S., and Pugh, T. (1984). Cross-validated spline methods for the estimation of three-dimensional tumor-size distributions from observations on two-dimensional cross-sections. J. Amer. Statist. Assoc. 79, 832– 46.
- Ogata, Y. (1981). On Lewis' simulation method for point processes. IEEE Trans. Inf. Theor. IT-27, 23– 31.
- Ogata, Y. and Tanemura, M. (1981). Estimation of interaction potentials of spatial point-patterns through the maximum-likelihood procedure. Ann. Inst. Statist. Math. 33, 315– 38.
- Ogata, Y. and Tanemura, M. (1984). Likelihood analysis of spatial point-patterns. J. Roy. Statist. Soc. B 46, 496– 518.
- Ogawa, T. and Tanemura, M. (1974). Geometrical considerations on hard-core problems. Progress Theor. Phys. 51, 399– 417.
- Ohanian, V. K. (1973). On random Markovian colouring of the plane with two colours (in Russian). Dokl. Akad. Nauk. Armenian SSR 58, 193– 8.
- Ohanian, V. K. (1978). Combinatorial principles in stochastic geometry of random segment processes. In R. V. Ambartzumian, ed., Combinatorial Principles in Stochastic Geometry, pp. 81– 106. Publ. Akad. Sci. Armen. SSR.
- Ohser, J. (1980). On statistical analysis of the Boolean model. Elektron. Inf.-Verarb. Kyb. 16, 651– 53.
- Ohser, J. (1981). A remark on the estimation of the rose of directions of fibre processes. Math. Operationsf. Statist., Ser. Statistics 12, 581– 5.
- Ohser, J. (1983). On estimators for the reduced second-moment measure of point processes. Math. Operationsf. Statist., Ser. Statistics 14, 63– 71.
- Ohser, J. and Lorz, U. (1994). Quantitative Gefügeanalyse. Theoretische Grundlagen und Anwendungen. Freiberger Forschungshefte B276. Deutscher Verlag für Grundstoffindustrie, Leipzig.
- Ohser, J. and Mücklich, F. (1995). Stereology for some classes of polyhedrons. Adv. Appl. Prob. 27, 384– 96.
- Ohser, J. and Mücklich, F. (2000). Statistical Analysis of Microstructures in Materials Science. John Wiley & Sons, Ltd, Chichester.
- Ohser, J. and Schladitz, K. (2009). 3D Images of Material Structures. Processing and Analysis. Wiley-VCH, Weinheim.
- Ohser, J. and Stoyan, D. (1980). Zur Beschreibung gewisser zufälliger Muster in der Geologie. Z. angew. Geol. 26, 209– 12.
- Ohser, J. and Stoyan, D. (1981). On the second-order and orientation analysis of planar stationary point processes. Biometrical J. 23, 523– 33.
- Ohser, J. and Tscherny, H. (1988). Grundlagen der quantitativen Gefügeanalyse. Freiberger Forschungshefte B264. Deutscher Verlag für Grundstoffindustrie, Leipzig.
- Okabe, A., Boots, B., Sugihara, K., and Chiu, S. N. (2000). Spatial Tessellations –Concepts and Applications of Voronoi Diagrams. John Wiley & Sons, Ltd, Chichester, 2nd edition.
- Okabe, A. and Sugihara, K. (2012). Spatial Analysis Along Networks: Statistical and Computataional Methods. John Wiley & Sons, Inc., New York.
- Olsbo, V. (2007). On the correlation between the volumes of the typical Poisson–Voronoi cell and the typical Stienen sphere. Adv. Appl. Prob. 39, 883– 92.
- Ong, M. S., Kuang, Y. C., and Ooi, M. P.-L. (2012). Statistical measures of two dimensional point set uniformity. Comput. Statist. Data Anal. 56, 2159– 81.
- Øren, P.-E. and Bakke, S. (2002). Process based reconstruction of sandstones and prediction of transport properties. Trans. Porous Med. 46, 311– 43.
- Øren, P.-E. and Bakke, S. (2003). Reconstruction of Berea sandstone and pore-scale modelling of wettability effects. J. Petrol. Sci. Eng. 39, 177– 99.
- Ornstein, L. S. and Zernike, F. (1914). Accidental deviations of density and opalescence at the critical point of a single substance. Proc. R. Neth. Acad. Arts Sci. 17, 793– 806.
- Osher, S. and Fedkiw, R. (2003). Level Set Methods and Dynamic Implicit Surfaces. Springer-Verlag, New York.
- Oualkacha, K. and Rivest, L.-P. (2009). A new statistical model for random unit vectors. J. Multivariate Anal. 100, 70– 80.
- Overby, D. R. and Johnson, M. (2005). Studies on depth-of-field effects in microscopy supported by numerical simulations. J. Microsc. 220, 176– 89.
- Palm, C. (1943). Intensitätsschwankungen im Fernsprechverkehr. Ericsson Technics 44, 1– 189.
- Pelikan, K., Saxl, I., and Ponížil, P. (1994). Germ–grain model of short-fibre composites. In L. Wojnar, ed., Stermath'94 Proc. 4th Int. Conf. Stereology and Image Analysis in Materials Science, pp. 389– 96. Fotobit-Design, Krakow.
- Penrose, M. (2003). Random Geometric Graphs. Oxford Studies in Probability 5. Oxford University Press, Oxford.
- Penrose, M. D. (1997). The longest edge of the random minimal spanning tree. Ann. Appl. Probab. 7, 340– 61.
- Penrose, M. D. (2007). Laws of large numbers in stochastic geometry with statistical applications. Bernoulli 13, 1124– 50.
- Penrose, M. D. and Wade, A. R. (2010). Random directed and on-line networks. In W. S. Kendall and I. Molchanov, eds, New Perspectives in Stochastic Geometry, pp. 248– 74. Oxford University Press, Oxford.
- Penttinen, A. (1984). Modelling interactions in spatial point-patterns: parameter estimation by the maximum-likelihood method. Jyväskyla Studies in Computer Science, Economics and Statistics 7, Jyväskyla.
- Penttinen, A. and Niemi, A. (2007). On statistical inference for the random set generated Cox process with set-marking. Biometrical J. 49, 197– 213.
- Penttinen, A. and Stoyan, D. (1989). Statistical analysis for a class of line segment processes. Scand. J. Statist. 16, 153– 61.
- Penttinen, A., Stoyan, D., and Henttonen, H. M. (1992). Marked point processes in forest statistics. Forest Sci. 38, 806– 24.
- Peshkin, M. A., Strandburg, K. J., and Rivier, N. (1991). Entropic predictions for cellular networks. Phys. Rev. Lett. 7, 1803– 6.
- Peyrega, C., Jeulin, D., Delisée, C., and Malvestio, J. (2009). 3D morphological modelling of a random fibrous network. Imaga Anal. Stereol. 28, 129– 41.
- Picard, N. and Bar-Hen, A. (2000). Estimation of the envelope of a point set with loose boundaries. Appl. Math. Lett. 13, 13– 8.
- Pielou, E. C. (1977). Mathematical Ecology. John Wiley & Sons, Inc., New York.
- Piterbarg, V. I. (1996). Asymptotic Methods in the Theory of Gaussian Processes and Fields. Translation of Mathematical Monographs 148. American Mathematical Society, Providence, RI.
- Pohlmann, S., Mecke, J., and Stoyan, D. (1981). Stereological formulas for stationary surface processes. Math. Operationsf. Statist., Ser. Statistics 12, 429– 40.
- Pollard, D. (2002). A User's Guide to Measure Theoretic Probability. Cambridge University Press, Cambridge.
- Pólya, G. (1918). Zahlentheoretisches und Wahrscheinlichkeitstheoretisches über die Sichtweite im Walde. Arch. Math. Phys. 27, 135– 42.
- Poole, D. C., Batra, S., Mathieu-Costello, O., and Rakusan, K. (1992). Capillary geometrical changes with fiber shortening in rat myocardium. Circ. Res. 70, 697– 706.
- Porod, G. (1951). Die Röntgenkleinwinkelstreuung von dichtgepackten kolloiden Systemen I. Kolloid Zeitschrift 124, 83– 114.
- Porod, G. (1952). Die Röntgenkleinwinkelstreuung von dichtgepackten kolloiden Systemen II. Kolloid Zeitschrift 125, 51– 7.
- Pothuaud, L., Porion, P., Lespessailles, E., Benhamou, C. L., and Levitz, P. (2000). A new method for three-dimensional skeleton graph analysis of porous media: application to trabecular bone microarchitecture. J. Microsc. 199, 149– 61.
- Poupon, A. (2004). Voronoi and Voronoi-related tessellations in studies of protein structure and interaction. Curr. Opin. Struct. Biol. 2, 233– 41.
- Prager, S. (1969). Improved variational bounds on some bulk properties of a two-phase medium. J. Chem. Phys. 50, 4305– 12.
- Preparata, J. P. and Shamos, M. I. (1985). Computational Geometry, An Introduction. Springer-Verlag, New York.
- Preston, C. J. (1974). Gibbs States on Countable Sets. Cambridge University Press, Cambridge.
- Preston, C. J. (1976). Random Fields. Lecture Notes in Mathematics 534. Springer-Verlag, Berlin.
- Preston, C. J. (1977). Spatial birth-and-death processes. Bull. Int. Statist. Inst. 46, 371– 91.
- Priolo, A., Jaeger, H. M., Dammers, A. J., and Radelaar, S. (1992). Conductance of two-dimensional disordered Voronoi networks. Phys. Rev. B 46, 14889– 92.
- Prokešová, M. (2003). Bayesian MCMC estimation of the rose of directions. Kybernetika 39, 701– 17.
- Provatas, N., Haataja, M., Asikainen, J., Majaniemi, S., Alava, M., and Ala-Nissila, T. (2000). Fiber deposition models in two and three spatial dimensions. Colloids Surfaces A: Physicochem. Eng. Aspects 165, 209– 29.
- Quine, M. P. and Robinson, J. (1992). Estimation for a linear growth model. Statist. Prob. Lett. 15, 293– 7.
- Quine, M. P. and Watson, D. F. (1984). Radial simulation of n-dimensional Poisson processes. J. Appl. Prob. 21, 548– 57.
- Quintanilla, J. A. and Ziff, R. M. (2007). Asymmetry in the percolation thresholds of fully penetrable disks with two different radii. Phys. Rev. E 76, 051115.
- Radecke, W. (1980). Some mean value relations on stationary random mosaics in the space. Math. Nachr. 97, 203– 10.
- Rahman, A. (1966). Liquid structure and self-diffusion. J. Chem. Phys. 45, 2584– 92.
- Räisänen, V. I., Heyden, S., Gustafsson, P.-J., Alava, M. J., and Niskanen, K. J. (1997). Simulation of the effect of a reinforcement fiber on network mechanics. Nordic Pulp Paper Res. J. 12, 162– 6.
- Rancoita, P. M. V., Giusti, A., and Micheletti, A. (2011). Intensity estimation of stationary fibre processes from digital images with a learned detector. Image Anal. Stereol. 30, 167– 78.
- Rao, M. M. (1993). Conditional Measures and Applications. Marcel Dekker, New York.
- Rasson, J. P. and Hermans, M. (1988). On a connection between Davidson's entropy and a test of randomness for point and line process in the plane. Atti Accad. Peloritana Pericolanti, Cl. Sci, Fis. Mat. Nat. 65, 337– 46.
- Rataj, J. (1993). Random distances and edge-correction. Statistics 24, 377– 85.
- Rataj, J. (1996). Estimation of oriented direction distirbution of a planar body. Adv. Appl. Prob. 28, 394– 404.
- Rataj, J. and Saxl, I. (1989). Analysis of planar anisotropy by means of the Steiner compact. J. Appl. Prob. 26, 490– 502.
- Rathbun, S. L. (1996). Estimation of Poisson intensity using partially observed concomitant variables. Biometrics 52, 226– 42.
- Rathie, P. N. (1992). On the volume of the typical Poisson-Delaunay cell. J. Appl. Prob. 29, 740– 4.
- Rau, C. and Chiu, S. N. (2011). Grain rotations and distortions in the asymptotic variance of vacancy of the Boolean model. J. Math. Anal. Appl. 384, 647– 57.
- Redenbach, C. (2009a). Microstructure models for cellular materials. Comput. Mat. Sci. 44, 1397– 407.
- Redenbach, C. (2009b). Modelling foam structures using random tessellations. In V. Capasso, G. Aletti, and A. Micheletti, eds, Stereology and Image Analysis: ECS10 –10th European Congress of ISS, The MIRIAM Project Series 4. Societa Editrice Esculapio–Progetto Leonardo, Bologna.
- Redenbach, C. (2011). On the dilated facets of a Poisson-Voronoi tessellation. Image Anal. Stereol. 30, 31– 8.
- Redenbach, C., Shklyar, I., and Andrä, H. (2012). Laguerre tessellations for elastic stiffness simulations of closed foams with strongly varying cell sizes. Int. J. Eng. Sci. 50, 70– 8.
- Reiss, R.-D. (1993). A Course on Point Processes. Springer-Verlag, Berlin.
- Reitzner, M. (2010). Random polytopes. In W. S. Kendall and I. Molchanov, eds, New Perspectives in Stochastic Geometry, pp. 45– 76. Oxford University Press, Oxford.
- Reitzner, M., Spodarev, E., and Zaporozhets, D. (2012). Set reconstruction by Voronoi cells. Adv. Appl. Prob. 44, 938– 53.
- Rényi, A. (1967). Remarks on the Poisson process. Studia Sci. Math. Hung. 2, 119– 23.
- Rhines, F. N. (1986). Microstructology. Behaviour and Microstructure of Materials. Dr. Riederer-Verlag, Stuttgart.
- Rice, S. O. (1944, 1945). Mathematical analysis of random noise. Bell Syst. Tech. J. 23, 282– 332; 24, 45–146.
- Richards, F. M. (1974). The interpretation of protein structures: total volume, group volume distributions and packing density. J. Mol. Biol. 82, 1– 14.
- Richeson, D. S. (2008). Euler's Gem. The Polyhedron Formula and the Birth of Topology. Princeton University Press, Princeton, New Jersey.
- Ripley, B. D. (1976). The second-order analysis of stationary point processes. J. Appl. Prob. 13, 255– 66.
- Ripley, B. D. (1977). Modelling spatial patterns (with discussion). J. Roy. Statist. Soc. B 39, 172– 212.
- Ripley, B. D. (1979). Test of 'randomness' for spatial point-patterns. J. Roy. Statist. Soc. B 41, 368– 74.
- Ripley, B. D. (1981). Spatial Statistics. John Wiley & Sons, Inc., New York. (Reprinted in 2004.)
- Ripley, B. D. (1982). Edge effects in spatial stochastic processes. In B. Ranneby, ed., Statistics in Theory and Practice. Essays in Honour of Bertil Matérn, pp. 242– 62. Swedish University of Agricultural Sciences, Umea.
- Ripley, B. D. (1988). Statistical Inference for Spatial Processes. Cambridge University Press, Cambridge.
- Ripley, B. D. and Silverman, B. W. (1978). Quick tests for spatial interaction. Biometrika 65, 641– 2.
- Rivier, N. and Lissowski, A. (1982). On the correlation between sizes and shapes of cells in epithelial mosaics. J. Phys. A: Math. Gen. 15, L143– 8.
- Robbins, H. E. (1944). On the measure of a random set I. Ann. Math. Statist. 15, 70– 4.
- Robbins, H. E. (1945). On the measure of a random set II. Ann. Math. Statist. 16, 342– 7.
- Robins, V. (2002). Computational topology for point data: Betti numbers of α-shapes. In K. R. Mecke and D. Stoyan, eds, Morphology of Condensed Matter. Physics and Geometry of Spatially Complex Systems, Lecture Notes in Physics 600, pp. 261– 74. Springer-Verlag, Berlin.
- Rodrigez-Itube, I., Cox, D. R., and Isham, V. (1987). Some models for rainfall based on stochastic point processes. Proc. Roy. Soc. London A 410, 269– 88.
- Rodrigez-Itube, I., Cox, D. R., and Isham, V. (1988). A point process model for rainfall: further developments. Proc. Roy. Soc. London A 417, 283– 98.
- Rosenthal, J. S. (2006). A First Look at Rigorous Probability Theory. World Scientific, Singapore, 2nd edition.
- Rosiwal, A. (1898). Über geometrische Gesteinsanalysen. Ein einfacher Weg zur ziffernmäßigen Feststellung des Quantitatsverhältnisses der Mineralbestandteile gemengter Gesteine. Verh. K. K. Geol. Reichsanst. 5/6, 143– 75.
- Rother, W. and Zähle, M. (1990). A short proof of a principal kinematic formula and extensions. Trans. Amer. Math. Soc. 321, 547– 58.
- Rother, W. and Zähle, M. (1992). Absolute curvature measures, II. Geom. Dedicata 41, 229– 40.
- Royall, C. P., Dzubiella, J., Schmidt, M., and van Blöaderen, A. (2007). Nonequilibrium sedimentation of colloids on the particle scale. Phys. Rev. Lett. 98, 188304.
- Ruelle, D. (1969). Statistical Mechanics. John Wiley & Sons, Inc., New York.
- Ruelle, D. (1970). Superstable interaction in classical mechanics. Commun. Math. Phys. 18, 127– 59.
- Rychlik, I. and Lindgren, G. (1993). CROSSREG A technique for first passage and wave density analysis. Probab. Engrg. Inform. Sci. 7, 125– 48.
- Rysz, J. and Wiencek, K. (1980). Stereology of spherical carbide particles in steels. Arch. Nauki o Materialach I, 151– 68.
- Sahimi, M. (2003). Heterogeneous Materials I: Linear Transport and Optical Properties. Springer-Verlag, New York.
- Salinetti, G. and Wets, R. J.-B. (1986). On the convergence in distribution of measurable multifunctions (random sets), normal integrands, stochastic processes and stochastic infima. Math. Oper. Res. 11, 385– 419.
- Saltykov, S. A. (1945). Stereometric Metallography (in Russian). State Publishing House for Metals Sciences, Moscow.
- Saltykov, S. A. (1950). Introduction to Sterometric Metallography (in Russian). Publishing House of Academy of Science of Armenian SSR, Erevan.
- Saltykov, S. A. (1974). Stereometrische Metallographie. Deutscher Verlag für Grundstoffindustrie, Leipzig.
- Sampson, W. W. (2001). The structural characterisation of fibre networks in papermaking processes —a review. In C. F. Baker, ed., The Science of Papermaking. Transactions of the 12th Fundamental Research Symposium, pp. 1205– 88. FRC The Pulp & Paper Fundamental Research Society.
- Sampson, W. W. (2004). A model for fibre contact in planar random fibre networks. J. Mater. Sci. 39, 2775– 81.
- Sandau, K. (1993). An estimation procedure for the joint distribution of spatial direction and thickness of flat bodies using vertical sections. Part I: Theoretical considerations. Biometrical J. 35, 649– 60.
- Sandau, K. and Vogel, H.-J. (1993). An estimation procedure for the joint distribution of spatial direction and thickness of flat bodies using vertical sections. Part II: An application in soil micromorphology. Biometrical J. 35, 661– 75.
- Santaló, L. (1976). Integral Geometry and Geometric Probability. Addison-Wesley, Reading, MA.
- Santaló, L. (1980). Random lines and tessellations in a plane. Stochastica 4, 3– 13.
- Santaló, L. (1984). Mixed random mosaics. Math. Nachr. 117, 129– 33.
- Savary, L., Jeulin, D., and Thorel, A. (1999). Morphological analysis of carbon-polymer composite materials from thick sections. Acta Stereol. 18, 297– 303.
- Saxl, I. (1989). Stereology of Objects with Internal Structure. Academia, Prague.
- Saxl, I. and Ponížil, P. (2001). Grain size estimation: w–s diagram. Mater. Char. 46, 113– 18.
- Saxl, I. and Ponížil, P. (2002). Bernoulli cluster field: Voronoi tessellations. Appl. Math. 47, 157– 67.
- Saxl, I., Ponížil, P., and Sülleiova, K. (2003). Stereology and simulation of heterogeneous crystalline media. Int. J. Mater. Prod. Tech. 18, 1– 25.
- Schaap, W. E. and van de Weygaert, R. (2000). Continuous fields and discrete samples. Reconstruction through Delaunay tessellations. Astron. Astrophys. 363, L29– 32.
- Schack-Kirchner, H., Wilpert, K. V., and Hildebrand, E. E. (2000). The spatial distribution of soil hyphae in structured spruce-forest soils. Plant Soil 224, 195– 205.
- Scheidegger, A. E. (1979). Beziehungen zwischen Orientierungsstruktur der Tallagen und der Kluftstellungen in Österreich. Mitt. Österr. Geograph. Ges. 121, 187– 95.
- Scheike, T. H. (1994). Anisotropic growth of Voronoi cells. Adv. Appl. Prob. 26, 43– 53.
- Schlather, M. (1999). Introduction to positive definite functions and to unconditional simulation of random fields. Technical Report ST 99-10, Lancaster University.
- Schlather, M. (2000). A formula for the edge length distribution function of the Poisson Voronoi tessellation. Math. Nachr. 214, 113– 9.
- Schlather, M. (2001a). On the second-order characteristics of marked point processes. Bernoulli 7, 99– 117.
- Schlather, M. (2001b). Simulation and analysis of random fields. R News 1, 10– 20.
- Schlather, M. and Stoyan, D. (1997). The covariance of the Steinen model. In D. Jeulin, ed., Advances in Theory and Applications of Random Sets, pp. 157– 74. World Scientific, Singapore.
- Schmidt, V. (1985). Poisson bounds for moments of shot noise processes. Statistics 16, 253– 62.
- Schmidt, V. and Spodarev, E. (2005). Joint estimators for the specific intrinsic volumes of stationary random sets. Stoch. Process. Appl. 115, 959– 81.
- Schmitt, M. (1991). Estimation of the density in a stationary Boolean model. J. Appl. Prob. 28, 702– 8.
- Schneider, R. (1979a). Bestimmung konvexer Körper durch Krümmungsmasse. Comment. Math. Helvet. 54, 42– 60.
- Schneider, R. (1979b). Boundary structure and curvature of convex bodies. In J. Tolke and J. M. Wills, eds, Contributions to Geometry. Proc. Geometrie-Symp. Siegen 1978, pp. 13– 59. Birkhäuser, Basel.
- Schneider, R. (1980). Parallelmengen mit Vielfachheit und Steiner-Formeln. Geom. Ded. 9, 111– 27.
- Schneider, R. (1987). Geometric inequalities for Poisson processes of convex bodies and cylinders. Result Math. 11, 165– 85.
- Schneider, R. (1993). Convex Bodies: The Brunn–Minkowski Theory. Encyclopedia of Mathematics and Its Applications 44. Cambridge University Press, Cambridge.
- Schneider, R. and Weil, W. (1992). Integralgeometrie. B. G. Teubner, Stuttgart.
- Schneider, R. and Weil, W. (2000). Stochastische Geometrie. B. G. Teubner, Stuttgart.
- Schneider, R. and Weil, W. (2008). Stochastic and Integral Geometry. Springer-Verlag, Berlin.
- Schneider, R. and Weil, W. (2010). Classical stochastic geometry. In W. S. Kendall and I. Molchanov, eds, New Perspectives in Stochastic Geometry, pp. 1– 42. Oxford University Press, Oxford.
- Schreiber, T. (2010). Limit theorems in stochstic geometry. In W. S. Kendall and I. Molchanov, eds, New Perspectives in Stochastic Geometry, pp. 111– 44. Oxford University Press, Oxford.
- Schulz, G. E. W., Schwan, L. O., and Franke, P. (1993). The mean normalized Euler characteristic of a simultaneously starting and growing 2D Voronoi tessellation with Poisson distributed nuclei. J. Mater. Sci. 28, 2076– 714.
- F. Schüth, K. S. W. Sing, and J. Weitkamp, eds (2002). Handbook of Porous Solids. Wiley-VCH, Weinheim.
- Schwandtke, A. (1985). Distributional analysis of dihedral angles in single-phase polycrystalline structures –comments on a paper by J. Rys and A. Kasprzyk. Metalurgie i Odlewnictwo 11, 171– 82.
- Schwandtke, A. (1988). Second-order quantities for stationary weighted fibre processes. Math. Nachr. 139, 321– 34.
- Schwandtke, A., Ohser, J., and Stoyan, D. (1987). Improved estimation in planar sampling. Acta Stereol. 6, 325– 34.
- Schwandtke, A., Stoyan, D., and Schmidt, V. (1988). Some remarks on the stereological estimation of particle characteristics. Acta Stereol. 7, 143– 53.
- Schwertel, J. and Stamm, H. (1997). Analysis and modelling of tessellations by means of image analysis methods. J. Microsc. 186, 198– 209.
- Scott, G. D. (1960). Packing of spheres. Nature 188, 908– 9.
- Serra, J. (1975). Anisotropy fast characterization. Fascicules de morphologie mathématique appliquée 8. École de Mines de Paris, Fontainebleau.
- Serra, J. (1982). Image Analysis and Mathematical Morphology. Academic Press, London.
- Serra, J. (1987). Boolean random functions. Acta Stereol. 6, 325– 30.
- Serra, J. (1988). Image Analysis and Mathematical Morphology. Volume 2. Academic Press, London.
- Serra, J. (1989). Boolean random functions. J. Microsc. 156, 41– 63.
- Serra, J. (2009). The random spread model. In M. Passare, ed., Complex Analysis and Digital Geometry: Proceedings from the Kiselmanfest 2006, pp. 283– 310. Uppsala Universitet.
- Shannon, C. E. (1949). Communication in the presence of noise. Proc. IRE 37, 10– 21.
- Shepilov, M. P., Kalmykov, A. E., and Sycheva, G. A. (2006). Ordering effects in spatial arrangement of particles in phase separated sodium borosilicate glass. Phys. Chem. Glass. Eur. J. Glass Sci. Technol. B 47, 339– 43.
- Sherman, M. (2011). Spatial Statistics and Spatio-Temporal Data: Covariance Functions and Directional Properties. John Wiley & Sons, Ltd, Chichester.
- Shimatani, I. K. (2010). Spatially explicit neutral models for population genetics and community ecology: Extensions of the Neyman–Scott clustering process. Theor. Popul. Biol. 77, 32– 41.
- Shimatani, K. (2002). Point processes for fine-scale spatial genetics and molecular ecology. Biometrical J. 44, 325– 52.
- Sibson, R. (1980). The Dirichlet tessellation as an aid in data analysis. Scand. J. Statist. 7, 14– 20.
- Sibson, R. (1981). A brief description of natural neighbour interpolation. In V. Barnett, ed., Interpreting Multivariate Data, pp. 21– 36. John Wiley & Sons, Ltd, Chichester.
- Sigman, K. (1995). Stationary Marked Point Processes: An Intuitive Approach. Chapman & Hall, New York.
- Silverman, B. W., Jones, M. C., Wilson, J. D., and Nychka, D. W. (1990). A smoothed EM approach to indirect estimation problems, with particular reference to stereology and emission tomography. J. Roy. Statist. Soc. B 52, 271– 324.
- Singh, H., Gokhale, A. M., Mao, Y., and Spowart, J. E. (2006). Computer simulations of realistic microstructures of discontinuously reinforced aluminum alloy (DRA) composites. Acta Materialia 54, 2131– 43.
- Sivakumar, K. and Goutsias, J. (1997a). Discrete morphological size distributions and densities: estimation techniques and applications. J. Electron. Imaging 6, 31– 53.
- Sivakumar, K. and Goutsias, J. (1997b). Morphologically constrained discrete random sets. In D. Jeulin, ed., Advances in Theory and Applications of Random Sets, pp. 49– 66. World Scientific, Singapore.
- Sivakumar, K. and Goutsias, J. (1997c). On the discretization of morphological operators. J. Vis. Commun. Image R. 8, 39– 49.
- Sivakumar, K. and Goutsias, J. (1999). Morphologically constrained GRFs: Applications to texture synthesis and analysis. IEEE Trans. Pattern Anal. Mach. Intell. 21, 99– 113.
- Skare, Ø., Møller, J., and Jensen, E. B. V. (2007). Bayesian analysis of spatial point processes in the neighbourhood of Voronoi networks. Statist. Comput. 17, 369– 79.
- SKM95 = Stoyan, Kendall and Mecke (1995).
- Small, C. G. (1996). The Statistical Theory of Shape. Springer-Verlag, New York.
- Smalley, I. J. (1966). Contraction crack networks in basalt flows. Geol. Mag. 103, 110– 4.
- Smith, C. and Guttman, L. (1953). Measurement of internal boundaries in three-dimensional structures by random sectioning. Trans. AIME 197, 81– 7.
- Snethlage, M., Martínez, V. J., Stoyan, D., and Saar, E. (2002). Point field models for the galaxy point pattern: Modelling the singularity of the two-point correlation function. Astron. Astrophys. 388, 758– 65.
- Snyder, D. L. (1975). Random Point Processes. John Wiley & Sons, Inc., New York.
- Snyder, D. L. and Miller, M. I. (1991). Random Point Processes in Time and Space. Springer-Verlag, New York, 2nd edition.
- Soille, P. (1999). Morphological Image Analysis. Springer-Verlag, Berlin.
- Soille, P. (2003). Morphological Image Analysis: Principle and Applications. Springer-Verlag, Berlin, 2nd edition.
- Sok, R. M., Knackstedt, M. A., Sheppard, A. P., Pinczewski, W. V., Lindquist, W. B., Venkatarangan, A., and Paterson, L. (2002). Direct and stochastic generation of network models from tomographic images: Effect of topology on residual saturations. Trans. Porous Med. 46, 345– 71.
- Solomon, H. (1978). Geometric Probability. SIAM, Philadephia.
- Solomonoff, R. and Rapoport, A. (1951). Connectivity of random nets. Bull. Math. Biophys. 13, 107– 17.
- Song, C., Wang, P., and Makse, H. A. (2008). A phase diagram for jammed matter. Nature 453, 629– 32.
- Sonntag, U., Stoyan, D., and Hermann, H. (1981). Random set models in the interpretation of small-angle scattering data. Phys. Stat. Sol. (a) 68, 281– 8.
- Spektor, A. G. (1950). Analysis of distribution of spherical particles in non-transparent structures. Zavod. Lab. 16, 173– 7.
- Spiess, M. and Spodarev, E. (2011). Anisotropic Poisson processes of cylinders. Methodol. Comput. Appl. Probab. 13, 801– 19.
- Srinivasan, S. K. (1974). Stochastic Point Processes and Their Applications. Hafner Press, New York.
- Srinivasan, S. K. and Vijayakumar, A., eds (2003a). Point Prcesses and Product Densities. Narosa, New Delhi.
- Srinivasan, S. K. and Vijayakumar, A., eds (2003b). Stochastic Point Processes. Narosa, New Delhi.
- Stachurski, Z. H. (2011). On structure and properties of amorphous materials. Materials 4, 1564– 98.
- Stapper, C. H., McLaren, A., and Dreckmann, M. (1980). Yield model for productivity optimization of VLSI memory chips with redundancy and partially good product. IBM J. Res. Dev. 24, 398– 409.
- Stephan, H. (1975). Allocortex. Handbuch der mikroskopischen Anatomie des Menschen, Band IV, Nervensystem, Teil 9. Springer-Verlag, Berlin.
- Sterio, D. G. (1984). The unbiased estimation of numbers and sizes of arbitrary particles using the disector. J. Microsc. 134, 127– 36.
- Stiny, J. (1929). Technische Gesteinskunde für Bauingenieure, Kulturtechniker, Land-und Forstwirte. Springer-Verlag, Wien, 2nd edition.
- Stoica, R. S., Martínez, V. J., Mateu, J., and Saar, E. (2005). Detection of cosmic filaments using the Candy model. Astron. Astrophys. 434, 423– 32.
- Stoica, R. S., Martínez, V. J., and Saar, E. (2010). Filaments in observed and mock galaxy catalogues. Astron. Astrophys. 510, A38.
- Stoyan, D. (1979a). Interrupted point processes. Biometrical J. 21, 607– 10.
- Stoyan, D. (1979b). On the accuracy of lineal analysis. Biometrical J. 21, 439– 49.
- Stoyan, D. (1979c). Proof of some fundamental formulas of stereology for non-Poisson grain models. Math. Operationsf. Statist., Ser. Optimization 10, 573– 81.
- Stoyan, D. (1981). On the second-order analysis of stationary planar fibre processes. Math. Nachr. 102, 189– 99.
- Stoyan, D. (1982). Stereological formulae for size distributions through marked point processes. Prob. Math. Statist. 2, 161– 6.
- Stoyan, D. (1983). Inequalities and bounds for variances of point processes and fibre processes. Math. Operationsf. Statist., Ser. Statistics 14, 409– 19.
- Stoyan, D. (1984a). Estimating the volume density from thin sections. Biometrical J. 27, 427– 30.
- Stoyan, D. (1984b). Further stereological formulae for spatial fibre processes. Math. Operationsf. Statist., Ser. Statistics 15, 421– 8.
- Stoyan, D. (1984c). On correlations of marked point processes. Math. Nachr. 116, 197– 207.
- Stoyan, D. (1984d). Weighted fibres and surfaces in stereology. In R. V. Ambartzumian and W. Weil, eds, Stochastic Geometry, Geometric Statistics, Stereology, Teubner-Texte zur Mathematik 65, pp. 188– 96. B. G. Teubner Verlagsgesellschaft, Leipzig.
- Stoyan, D. (1985a). Practicable methods for the determination of the pair correlation function of fibre processes. In W. Nagel, ed., Geobild '85: Workshop on Geometrical Problems of Image Processing, Georgenthal (GDR), January 14– 18, 1985: Proceedings, pp. 131–40. Wissenschaftliche Beiträge der Friedrich-Schiller-Universität Jena.
- Stoyan, D. (1985b). Stereological determination of orientations, second-order quantities and correlations for random fibre systems. Biom J. 27, 411– 25.
- Stoyan, D. (1986). On generalized planar tessellations. Math. Nachr. 128, 215– 9.
- Stoyan, D. (1987). Statistical analysis of spatial point processes: a soft-core model and cross-correlation of marks. Biometrical J. 29, 971– 80.
- Stoyan, D. (1988). Thinnings of point processes and their use in the statistical analysis of a settlement pattern with deserted villages. Statistics 19, 45– 56.
- Stoyan, D. (1989). Statistical inference for a Gibbs point process of mutually non-intersecting discs. Biometrical J. 31, 153– 61.
- Stoyan, D. (1990a). Stereological formulae for a random system of non-overlapping spheres. Statistics 21, 131– 6.
- Stoyan, D. (1990b). Stereology and stochastic geometry. Int. Statist. Rev. 58, 227– 42.
- Stoyan, D. (1991). Describing the anisotropy of marked planar point processes. Statistics 22, 449– 62.
- Stoyan, D. (1993). A spatial statistical analysis of a work of art: did Hans Arp make a "truly random" collage? Statistics 24, 71– 80.
- Stoyan, D. (1994). Caution with "fractal" point-patterns! Statistics 25, 267– 70.
- Stoyan, D. (1998). Random sets: Models and statistics. Int. Statist. Rev. 66, 1– 27.
- Stoyan, D. and Beneš, V. (1991). Anisotropy analysis for particle systems. J. Microsc. 164, 159– 68.
- Stoyan, D., Davtyan, A., and Turetayev, D. (2002). Shape statistics for random domains and particles. In K. R. Mecke and D. Stoyan, eds, Morphology of Condensed Matter. Physics and Geometry of Spatially Complex Systems, Lecture Notes in Physics 66, pp. 299– 316. Springer-Verlag, Berlin.
- Stoyan, D. and Gerlach, W. (1987). Stereological determination of curvature distributions of spatial fibre systems. J. Microsc. 148, 297– 305.
- Stoyan, D. and Gloaguen, R. (2011). Nucleation and growth of geological faults. Nonlin. Processes Geophys. 18, 529– 36.
- Stoyan, D. and Grabarnik, P. (1991). Second-order characteristics for stochastic structures connected with Gibbs point processes. Math. Nachr. 151, 95– 100.
- Stoyan, D., Kendall, W. S., and Mecke, J. (1995). Stochastic Geometry and its Applications. John Wiley & Sons, Ltd, Chichester, 2nd edition. (Reprinted in 2008.)
- Stoyan, D. and Mecke, J. (1983a). Stochastische Geometrie. Akademie-Verlag, Berlin.
- Stoyan, D. and Mecke, J. (1983b). Stochastische Geometrie Eine Einführung. Akademie-Verlag, Berlin.
- Stoyan, D., Mecke, J., and Pohlmann, S. (1980). Formulas for stationary planar fibre processes II —Partially oriented fibre systems. Math. Operationsf. Statist., Ser. Statistics 11, 281– 6.
- Stoyan, D. and Mecke, K. (2005). The Boolean model: from Matheron till today. In M. Bilodeau, F. Meyer, and M. Schmitt, eds, Space, Structure and Randomness, Lecture Notes in Statistics 183, pp. 151– 81. Springer-Verlag, New York.
- Stoyan, D. and Molchanov, I. S. (1997). Set-valued means of random particles. J. Math. Imaging Vis. 7, 111– 21.
- Stoyan, D. and Ohser, J. (1982). Correlations between planar random structures (with an ecological example). Biometrical J. 24, 631– 47.
- Stoyan, D. and Ohser, J. (1984). Cross-correlation measure of weighted random measures and their estimation. Teor. Verojatn. Primen. 29, 338– 47.
- Stoyan, D. and Penttinen, A. (2000). Recent applications of point process methods in forestry statistics. Statist. Sci. 15, 61– 78.
- Stoyan, D. and Schlather, M. (2000). Random sequential adsorption: relationship to dead leaves and characterization of variability. J. Stat. Phys. 100, 969– 79.
- Stoyan, D. and Steyer, H.-L. (1979). Zur Genauigkeit der Linearanalyse. Neue Hütte 24, 303– 7.
- Stoyan, D. and Stoyan, H. (1980a). Gedanken zur Entstehung der Säulenformen bei Basalten. Z. Geol. Wiss. 8, 1529– 37.
- Stoyan, D. and Stoyan, H. (1980b). On some partial orderings of random closed sets. Math. Operationsf. Statist., Ser. Optimization 11, 145– 54.
- Stoyan, D. and Stoyan, H. (1983). Über eine Methode zur Quantifierung von Korrelationen zwischen geologischen Liniensystemen. Z. angew. Geologie 29, 512– 17.
- Stoyan, D. and Stoyan, H. (1985). On one of Matérn's hard-core point process models. Math. Nachr. 122, 205– 14.
- Stoyan, D. and Stoyan, H. (1986). Simple stochastic models for the analysis of dislocation distributions. Phys. Status Solidi A 97, 163– 72.
- Stoyan, D. and Stoyan, H. (1994). Fractals, Random Shapes and Point Fields. John Wiley & Sons, Ltd, Chichester.
- Stoyan, D. and Stoyan, H. (1996). Estimating pair-correlation functions of planar cluster processes. Biometrical J. 38, 259– 71.
- Stoyan, D. and Stoyan, H. (2000). Improving ratio estimators of second order point process characteristics. Scand. J. Statist. 27, 641– 56.
- Stoyan, D., Stoyan, H., Tscheschel, A., and Mattfeldt, T. (2001). On the estimation of distance distribution functions for point processes and random sets. Image Anal. Stereol. 20, 65– 9.
- Stoyan, D., von Wolfersdorf, L., and Ohser, J. (1990). Stereological problems for spherical particles–second-order theory. Math. Nachr. 146, 33– 46.
- Stoyan, D., Wagner, A., Hermann, H., and Elsner, A. (2011). Statistical characterization of the pore space of random systems of hard spheres. J. Non-Cryst. Solids 357, 1508– 15.
- Streit, R. L. (2010). Poisson Point Processes: Imaging, Tracking and Sensing. Springer-Verlag, New York.
- Stroeven, M., Askes, H., and Sluys, L. J. (2004). Numerical determination of representative volumes for granular materials. Comput. Methods Appl. Mech. Engrg. 193, 3221– 38.
- Stroeven, P. (2000). A stereological approach to roughness of fracture surfaces and tortuosity of transport paths in concrete. Cement Concrete Comp. 22, 331– 41.
- Stroeven, P., Le, N. L. B., Sluys, L. J., and He, H. (2012). Porosimetry by random node structuring in virtual concrete. Image Anal. Stereol. 31, 79– 87.
- Sukiasian, G. S. (1978). Random triangles on the plane (in Russian). Akad. Nauk Armjan. SSR Dokl. 66, 150– 5.
- Sukiasian, G. S. (1980). Processes of chords on lines intersecting random circle fields on a plane (in Russian). Akad. Nauk Armyan. SSR Dokl. 70, 297– 300.
- Sukiasian, G. S. (1982). Random sections of polyhedra (in Russian). Dokl. Akad. Nauk SSSR 263, 809– 12.
- Sukiasian, G. S. (1987). Randomizable point systems. Acta Appl. Math. 9, 83– 95.
- Sulanke, R. (1961). Die Verteilung der Sehnenlängen an ebenen und räumlichen Figuren. Math. Nachr. 23, 51– 74.
- Suwa, N., Takahashi, T., Saito, K., and Sawai, T. (1976). Morphometrical method to estimate the parameters of distribution functions assumed for spherical bodies from measurements on a random section. Tohoku J. Exp. Med. 118, 101– 18.
- Szekli, R. (1995). Stochastic Ordering and Dependence in Applied Probability. Lecture Notes in Statistics 97. Springer-Verlag, New York.
- Talbot, J., Tarjus, G., van Tassel, P. R., and Viot, P. (2000). From car parking to protein adsorption: an overview of sequential adsorption processes. Colloids Surfaces A: Physicochem. Eng. Aspects 165, 287– 324.
- Talukdar, M. S., Torsaeter, O., and Ioannidis, M. A. (2002). Stochastic reconstruction of particulate media from two-dimensional images. J. Colloid Interface Sci. 248, 419– 28.
- Talukdar, M. S., Torsaeter, O., Ioannidis, M. A., and Howard, J. J. (2002a). Stochastic reconstruction, 3D characterization and network modeling of chalk. J. Petrol. Sci. Eng. 35, 1– 21.
- Talukdar, M. S., Torsaeter, O., Ioannidis, M. A., and Howard, J. J. (2002b). Stochastic reconstruction of chalk from 2D images. Trans. Porous Med. 48, 101– 23.
- Tanaka, U., Ogata, Y., and Stoyan, D. (2008). Parameter estimation and model selection for Neyman-Scott point processes. Biometrical J. 50, 43– 57.
- Tanemura, M. (1988). Random packing and random tessellation in relation to the dimension of space. J. Microsc. 151, 247– 55.
- Tanner, J. C. (1983a). Polygons formed by random lines in a plane: some further results. J. Appl. Prob. 20, 778– 87.
- Tanner, J. C. (1983b). The proportion of quadrilaterals formed by random lines in a plane. J. Appl. Prob. 20, 400– 4.
- Taylor, C. C. (1983). A new method for unfolding sphere-size distributions. J. Microsc. 132, 57– 66.
- Teichmann, J., Ballani, F., and van den Boogaart, K. G. (2013). Generalizations of Matérn's hard-core point processes. Spatial Statistics 3, 33– 53.
- Thäle, C. and Weiss, V. (2010). New mean values for homogeneous spatial tessellations that are stable under iteration. Image Anal. Stereol. 29, 143– 57.
- Thall, P. F. (1983). A theorem on regular infinitely divisible Cox processes. Stoch. Process. Appl. 16, 205– 10.
- Thiedmann, R., Hartnig, C., Manke, I., Schmidt, V., and Lehnert, W. (2009). Local structural characteristics of pore space in GDLs of PEM fuel cells based on geometric 3D graphs. J. Electrochem. Soc. 156, B1339–47.
- Thiedmann, R., Spettl, A., Stenzel, O., Zeibig, T., Hindson, J. C., Saghi, Z., Greenham, N. C., Midgley, P. A., and Schmidt, V. (2012). Networks of nanoparticles in organic-inorganic composites: algorithmic extraction and statistical analysis. Image Anal. Stereol. 31, 27– 42.
- Thiessen, A. H. and Alter, J. C. (1911). Climatological data for July, 1911. District No. 11, Great Basin. Monthly Weather Review 39, 1082– 4.
- Thomas, C. (1984). Extremum properties of the intersection densities of stationary Poisson hyperplane processes. Math. Operationsf. Statist., Ser. Statistics 15, 443– 50.
- Thompson, E. (1930). Quantitative microscopic analysis. J. Geol. 38, 193– 222.
- Thönnes, E. (2001). The conditional Boolean model revisited. Markov Process. Related Fields 7, 77– 96.
- Thorisson, H. (2000). Coupling, Stationarity, and Regeneration. Springer-Verlag, New York.
- Thovert, J.-F. and Adler, P. M. (2004). Trace analysis for fracture networks of any convex shape. Geophys. Res. Lett. 31, L22502.
- Thovert, J.-F. and Adler, P. M. (2011). Grain reconstruction of porous media: Application to a Bentheim sandstone. Phys. Rev. E 83, 056116.
- Thovert, J.-F., Yousefian, F., Spanne, P., Jacquin, C. G., and Adler, P. M. (2001). Grain reconstruction of porous media: Application to a low-porosity Fontainebleau sandstone. Phys. Rev. E 63, 061307.
- Tong, C. S., Choy, S. K., Chiu, S. N., Zhao, Z. Z., and Liang, Z. T. (2008). Characterization of shapes for use in classification of starch grains images. Microsc. Res. Tech. 71, 651– 8.
- Torquato, S. (1991). Random heterogeneous media: Microstructure and improved bounds on effective properties. Appl. Mech. Rev. 44, 37– 76.
- Torquato, S. (2002). Random Heterogeneous Materials: Microstructure and Macroscopic Properties. Springer-Verlag, New York.
- Torquato, S. (2006). Necessary conditions on realizable two-point correlation functions of random media. Ind. Eng. Chem. Res. 45, 6923– 8.
- Torquato, S. (2010). Optimal design of heterogeneous materials. Annu. Rev. Mater. Res. 40, 101– 29.
- Torquato, S. (2012). Effect of dimensionality on the continuum percolation of overlapping hyperspheres and hypercubes. J. Chem. Phys. 136, 054106.
- Torquato, S. and Lu, B. (1993). Chord-length distribution function for two-phase random media. Phys. Rev. E 47, 2950– 3.
- Torquato, S. and Stillinger, F. H. (2010). Jammed hard-particle packings: From Kepler to Bernal and beyond. Rev. Mod. Phys. 82, 2633– 72.
- Tscheschel, A. and Chiu, S. N. (2008). Quasi-plus sampling edge correction for spatial point patterns. Comput. Statist. Data Anal. 52, 5287– 95.
- Tscheschel, A. and Stoyan, D. (2003). On the estimation variance for the specific Euler-–Poincaré characteristic of random networks. J. Microsc. 211, 80– 8.
- Tscheschel, A. and Stoyan, D. (2006). Statistical reconstruction of random point patterns. Comput. Statist. Data Anal. 51, 859– 71.
- Underwood, E. E. (1970). Quantitative Stereology. Addison-Wesley, Reading, MA.
- Underwood, E. E. (1976). Appendix Basic Stereology. In Proc Fourth Int. Cong. for Stereology 1975, pp. 509– 13. National Bureau of Standards Special Publ. 431. NBS, Washington, DC.
- van Dalen, G., Nootenboom, P., van Vliet, L. J., Voortman, L., and Esveld, E. (2007). 3D imaging, analysis and modelling of porous cereal products using X-ray microtomography. Image Anal. Sterol. 26, 169– 77.
- van de Laan, M. J. (1995). Efficiency of the NPMLE in the line-segment problem. Scand. J. Statist. 23, 527– 50.
- van de Weygaert, R. (1994). Fragmenting the universe III. The construction and statistics of 3-D Voronoi tessellations. Astron. Astrophys. 283, 361– 406.
- van de Weygaert, R. (2007). Voronoi tessellations and the cosmic web: spatial patterns and clustering across the universe. In C. M. Gold, ed., 4th International Symposium on Voronoi Diagrams in Science and Engineering, pp. 230– 9. IEEE Computer Society, Los Alamitos, CA.
- van de Weygaert, R. and Icke, V. (1989). Fragmenting the universe II. Voronoi vertices as Abell clusters. Astron. Astrophys. 213, 1– 9.
- R. van de Weygaert, G. Vegter, J. Ritzerveld, and V. Icke, eds (2014). Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings. Forthcoming.
- van der Hofstad, R. (2010a). Percolation and random graphs. In W. S. Kendall and I. Molchanov, eds, New Perspectives in Stochastic Geometry, pp. 173– 247. Oxford University Press, Oxford.
- van der Hofstad, R. (2010b). Random Graphs and Complex Networks. http://www.win.tue.nl/ rhofstad/NotesRGCN2010.pdf.
- van Es, B. (1991). Aspects of Nonparametric Density Estimation. CWI Tracts 77, Centrum voor Wiskunde en Informatica, Amsterdam.
- van Es, B. and Hoogendoorn, A. W. (1990). Kernel estimation in Wicksell's corpuscle problem. Biometrika 77, 139– 45.
- van Lieshout, M. N. M. (1995). Stochastic Geometry Models in Image Analysis and Spatial Statistics. CWI Tracts 108, Centrum voor Wiskunde en Informatica, Amsterdam.
- van Lieshout, M. N. M. (1999). Size-biased random closed sets. Pattern Recognition 32, 1631– 44.
- van Lieshout, M. N. M. (2000). Markov Point Processes and Their Applications. Imperial College Press, London.
- van Lieshout, M. N. M. (2006). Maximum likelihood estimation for random sequential adsorption. Adv. Appl. Prob. 38, 889– 98.
- van Lieshout, M. N. M. (2012). An introduction to planar random tessellation models. Spatial Statistics 1, 40– 9.
- van Lieshout, M. N. M. and Baddeley, A. J. (1996). A non-parametric measure of spatial interaction in point patterns. Statist. Neerl. 50, 344– 61.
- van Lieshout, M. N. M. and Stoica, R. S. (2003). The Candy model: properties and inference. Stat. Neerl. 57, 177– 206.
- van Zwet, E. W. (2004). Laslett's line segment problem. Bernoulli 10, 377– 96.
- Vanderbei, R. P. and Shepp, L. A. (1988). A probabilistic model for the time to unravel a strand of DNA. Stochastic Models 4, 299– 314.
- Vanmarcke, E. (2010). Random Fields: Analysis and Synthesis. World Scientific, Singapore, revised and expanded edition.
- Villa, E. and Rios, P. R. (2010). Transformation kinetics for surface and bulk nucleation. Acta Materialia 58, 2752– 68.
- Vogel, H.-J. (2002). Topological characterization of porous media. In K. R. Mecke and D. Stoyan, eds, Morphology of Condensed Matter. Physics and Geometry of Spatially Complex Systems, Lecture Notes in Physics 600, pp. 75– 92. Springer-Verlag, Berlin.
- Voloshin, V. P., Anikeenko, A. V., Medvedev, N. N., Geiger, A., and Stoyan, D. (2010). Hydration shells in Voronoi tessellations. In M. A. Mostafavi, ed., Seventh International Symposium on Voronoi Diagrams in Science and Engineerng, pp. 254– 9. IEEE Computer Society, Los Alamitos, CA.
- von Economo, C. F. and Koskinas, G. N. (1925). Die Cytoarchitektonik der Hirnrinde des erwachsenen Menschen. Springer-Verlag, Wien.
- Voronoi, G. (1908). Nouvelles applications des parametres continus a la theorie des formes quadratiques. J. Reine angew. Math. 134, 198– 287.
- Voss, F., Gloaguen, C., Fleischer, F., and Schmidt, V. (2011). Densities of shortest path lengths in spatial stochastic networks. Stochastic Models 27, 141– 67.
- Voss, F., Gloaguen, C., and Schmidt, V. (2009). Capacity distributions in spatial stochastic models for telecommunication networks. Image Anal. Stereol. 28, 155– 63.
- Voss, F., Gloaguen, C., and Schmidt, V. (2010). Scaling limits for shortest path lengths along the edges of stationary tessellations. Adv. Appl. Prob. 42, 936– 52.
- Voss, K. (1980). Exakte stereologische Formeln und Näherungslösungen für konvexe Körper. J. Inf. Process. Cybern. 16, 485– 91.
- Voss, K. (1982). Frequencies of n-polygons in planar sections of polyhedra. J. Microsc. 128, 111– 20.
- Voss, K. and Schubert, W. (1975). Zur numerischen Auswertung von Schnittflächenverteilungen. Biometrical J. 17, 189– 95.
- Voss, K. and Stoyan, D. (1985). On the stereological estimation of numerical density of particle systems by an object counting method. Biometrical J. 27, 919– 24.
- Warren, W. G. (1971). The centre satellite concept as a basis for ecological sampling. In G. Patil, E. C. Pielou, and W. E. Waters, eds, Statistical Ecology, Volume 2, pp. 87– 118. Pennsylvania State University Press, University Park.
- Watson, G. S. (1971). Estimation functionals of particle size distributions. Biometrika 58, 483– 90.
- Watts, D. J. and Strogatz, S. H. (1998). Collective dynamics of 'small-world' networks. Nature 393, 440– 2.
- Weaire, D. (1974). Some remarks on the arrangement of grains in a polycrystal. Metallography 7, 157– 60.
- Weber, W. (1977). Zur Methode der Lokalisierung und Charakterisierung tiefer Bruchstrukturen für minerogenetische Untersuchungen. In W. Weber and V. A. Korcemagin, eds, Tiefenbruchstrukturen und postmagmatische Mineralization. Freiberger Forschungshefte C 329, pp. 9– 52. Deutscher Verlag für Grundstoffindustrie, Leipzig.
- Weese, J. (1995). Density estimation and regularization at the example of Wicksell's corpuscle problem. Technical report, Materialforschungszentrum Freiburg.
- Weese, J., Korat, E., Maier, D., and Honerkamp, J. (1997). Unfolding sphere size distributions with a density estimator based on Tikhonov regularization. J. Comput. Phys. 138, 331– 53.
- Weibel, E. R. (1980). Stereological Methods. Volume 2: Theoretical Foundations. Academic Press, London.
- Weil, W. (1982a). An application of the central limit theorem for Banach-space-valued random variables to the theory of random sets. Probab. Theory Related Fields 60, 203– 8.
- Weil, W. (1982b). Inner contact probabilities for convex bodies. Adv. Appl. Prob. 14, 582– 99.
- Weil, W. (1984). Densities of quermassintegrals for stationary random sets. In R. V. Ambartzumian and W. Weil, eds, Stochastic Geometry, Geometric Statistics, Stereology, Teubner-Texte zur Mathematik 65, pp. 233– 47. B. G. Teubner Verlagsgesellschaft, Leipzig.
- Weil, W. (1988). Expectation formulas and isoperimetric properties for non-isotropic Boolean models. J. Microsc. 151, 235– 45.
- Weil, W. (1995). The estimation of mean shape and mean particle number in overlapping particle systems in the plane. Adv. Appl. Prob. 27, 102– 19.
- Weil, W. (1997). The mean normal distribution of stationary random sets and particle processes. In D. Jeulin, ed., Advances in Theory and Applications of Random Sets, pp. 21– 33. World Scientific, Singapore.
- Weil, W. (2007). Random sets (in particular Boolean models). In W. Weil, ed., Stochastic Geometry, Lecture Notes in Mathematics 1892, pp. 185– 245. Springer-Verlag, Berlin.
- Weil, W. and Wieacker, J. A. (1987). A representation theorem for random sets. Prob. Math. Statist. 9, 147– 51.
- Weiss, V. (1995). Second-order quantities for random tessellations of Rd . Stoch. Stoch. Rep. 55, 195– 205.
- Weiss, V. and Cowan, R. (2011). Topological relationships in spatial tessellations. Adv. Appl. Prob. 43, 963– 84.
- Weiss, V. and Nagel, W. (1994). Second-order stereology for planar fibre processes. Adv. Appl. Prob. 26, 906– 18.
- Weiss, V., Ohser, J., and Nagel, W. (2010). Second moment measure and K-function for planar STIT tessellations. Image Anal. Stereol. 29, 121– 31.
- Weiss, V. and Zähle, M. (1988). Geometric measures for random curved mosaics of Rd . Math. Nachr. 138, 313– 26.
- Wicksell, S. D. (1925). The corpuscle problem I. Biometrika 17, 84– 9.
- Wicksell, S. D. (1926). The corpuscle problem II. Biometrika 18, 152– 72.
- Widom, J. S. and Rowlinson, B. (1970). New model for the study of liquid–vapour phase transitions. J. Chem. Phys. 52, 1670– 84.
- Wieacker, J. A. (1985). Intersections of random hypersurfaces and visibility. Prob. Theory Related Fields 71, 405– 33.
- Wieacker, J. A. (1989). Geometric inequalities for random surfaces. Math. Nachr. 142, 73– 106.
- Wiencek, K. and Stoyan, D. (1993). Spatial correlations in metal structures and their analysis, II: The covariance. Mater. Char. 31, 47– 53.
- Wijers, B. J. (1995). Consistent non-parametric estimation for a one-dimensional line segment process observed in an interval. Scand. J. Statist. 22, 335– 60.
- Wilder, R. L. (1963). Topology of Manifolds. American Mathematical Society, New York.
- Willis, J. R. (1978). Variational principles and bounds for the overall properties of composites. In J. W. Provan, ed., Continuum Models of Discrete Systems, pp. 185– 215. University of Waterloo Press, Waterloo.
- Wilson, J. D. (1987). A smoothed EM algorithm for the solution of Wicksell's corpuscle problem. J. Statist. Comput. Simul. 3, 195– 221.
- Winkler, G. (2003). Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: a Mathematical Introduction. Springer-Verlag, New York.
- Wirjadi, O., Schladitz, K., Rack, A., and Breuel, T. (2009). Applications of anisotropic image filters for computing 2D and 3D-fiber orientations. In V. Capasso, G. Aletti, and A. Micheletti, eds, Stereology and Image Analysis: ECS10 –10th European Congress of ISS, The MIRIAM Project Series 4. Societa Editrice Esculapio–Progetto Leonardo, Bologna.
- Worsley, K. J. (1994). Local maxima and the expected Euler characteristic of excursion sets of χ 2, F and t fields. Adv. Appl. Prob. 26, 13– 42.
- Worsley, K. J. (1997). The geometry of random images. Chance 9, 27– 40.
- Wu, H.-I. and Schmidt, P. W. (1973). Intersect distributions and small-angle X-ray scattering theory III. The intersect distribution for an ellipsoid. J. Appl. Cryst. 6, 66– 72.
- Wu, H.-I., Sharpe, P. J. H., Walker, J., and Penridge, L. K. (1985). Ecological field theory: a spatial analysis of resource interference among plants. Ecol. Modelling 29, 215– 43.
- Yadin, M. and Zacks, S. (1985). The visibilty of stationary and moving targets in the plane subject to shadowing elements. J. Appl. Prob. 22, 776– 86.
- Yadin, M. and Zacks, S. (1988). Visibility probabilities on line segments in three-dimensional spaces subject to random Poisson fields of obscuring spheres. Naval Res. Logist. Quart. 35, 558– 69.
- Yeh, J. (2006). Real Analysis. Theory of Measure and Integration. World Scientific, Singapore, 2nd edition.
- Yeong, C. L. Y. and Torquato, S. (1998a). Reconstructing random media. Phys. Rev. E 57, 495– 506.
- Yeong, C. L. Y. and Torquato, S. (1998b). Reconstructing random media. II. Three-dimensional media from two-dimensional cuts. Phys. Rev. E 58, 224– 33.
- Zachary, C. E. and Torquato, S. (2011). Improved reconstructions of random media using dilation and erosion processes. Phys. Rev. E 84, 056102.
- Zacks, S. (1994). Stochastic Visibility in Random Fields. Lecture Notes in Statistics 95. Springer-Verlag, Berlin.
- Zähle, M. (1982). Random processes of Hausdorff-rectifiable closed sets. Math. Nachr. 108, 49– 72.
- Zähle, M. (1983). Random set processes in homogeneous Riemannian spaces. Math. Nachr. 110, 179– 93.
- Zähle, M. (1984a). Curvature measures and random sets I. Math. Nachr. 119, 327– 39.
- Zähle, M. (1984b). Properties of signed curvature measures. In R. V. Ambartzumian and W. Weil, eds, Stochastic Geometry, Geometric Statistics, Stereology, Teubner-Texte zur Mathematik 65, pp. 256– 66. B. G. Teubner Verlagsgesellschaft, Leipzig.
- Zähle, M. (1984c). Thick section stereology for random fibres. Math. Operationsf. Statist., Ser. Statistics 15, 429– 36.
- Zähle, M. (1986). Curvature measures and random sets II. Probab. Theory Related Fields 71, 37– 58.
- Zähle, M. (1987a). Curvatures and currents for unions of sets of positive reach. Geom. Dedicata 23, 155– 71.
- Zähle, M. (1987b). Polyhedron theorems for non-smooth cell complexes. Math. Nachr. 131, 299– 310.
- Zähle, M. (1988). Random cell complexes and generalized sets. Ann. Prob. 16, 1742– 66.
- Zähle, M. (1989). Absolute curvature measures. Math. Nachr. 140, 83– 90.
- Zähle, M. (1990). A kinematic formula and moment measures of random sets. Math. Nachr. 149, 325– 40.
- Zähle, U. (1984d). Local interpretation of Palm distributions of surface measures. Math. Nachr. 119, 341– 56.
- Zaninetti, L. (2006). On the large-scale structure of the universe as given by the Voronoi diagrams. Chin. J. Astron. Astrophys. 6, 387– 95.
- Zessin, H. (1983). The method of moments for random measures. Probab. Theory Related Fields 62, 395– 409.
- Zhang, C., Zhang, Y., and Fang, Y. (2006). Localized coverage boundary detection for wireless sensor networks. In Proceedings of the 3rd International Conference on Quality Service in Heterogeneous Wired/wireless Networks, Waterloo, Ontario, Canada. Session: Algorithms in sensor networks, Article number: 12.
- Zhang, C., Zhang, Y., and Fang, Y. (2009). Localized algorithms for coverage boundary detection in wireless sensor networks. Wireless Networks 15, 3– 20.
- Ziegel, J. and Kiderlen, M. (2010a). Estimation of surface area and surface area measure of three-dimensional sets from digitizations. Image Vision Comput. 28, 64– 77.
- Ziegel, J. and Kiderlen, M. (2010b). Stereolgical estimation of surface area from digital images. Image Anal. Stereol. 29, 99– 110.
- Zuyev, S. (1999). Stopping sets: Gamma-type results and hitting properties. Adv. Appl. Prob. 31, 355– 66.
- Zuyev, S. (2010). Stochastic geometry and telecommunications networks. In W. S. Kendall and I. Molchanov, eds, New Perspectives in Stochastic Geometry, pp. 520– 54. Oxford University Press, Oxford.
- Zuyev, S. and Quintanilla, J. (2003). Estimation of percolation thresholds via percolation in inhomogeneous media. J. Math. Phys. 44, 6040– 6.
- Zuyev, S. A. and Sidorenko, A. F. (1985a). Continuous models of percolation theory. I. Teoret. Mat. Fiz. 62, 76– 86. (English translation: Theor. Math. Phys. 62, 51–8).
- Zuyev, S. A. and Sidorenko, A. F. (1985b). Continuous models of percolation theory. II. Teoret. Mat. Fiz. 62, 253– 262. (English translation: Theor. Math. Phys. 62, 171–7).
Stochastic Geometry Wiley Series In Prob Abiland Mathematical Statistics Pdf
Source: https://onlinelibrary.wiley.com/doi/abs/10.1002/9781118658222.refs
Posted by: moakcamagirse.blogspot.com

0 Response to "Stochastic Geometry Wiley Series In Prob Abiland Mathematical Statistics Pdf"
Post a Comment