Topological complexity of smooth random functions

[1]  Jonathan E. Taylor,et al.  Random fields and the geometry of Wiener space , 2011, 1105.3839.

[2]  Jose H. Blanchet,et al.  Efficient Monte Carlo for high excursions of Gaussian random fields , 2010, 1005.0812.

[3]  Omer Bobrowski,et al.  EULER INTEGRATION OF GAUSSIAN RANDOM FIELDS AND PERSISTENT HOMOLOGY , 2010, 1003.5175.

[4]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[5]  W. Marsden I and J , 2012 .

[6]  Moo K. Chung,et al.  Topological Data Analysis , 2012 .

[7]  École d'été de probabilités de Saint-Flour,et al.  Topological Complexity of Smooth Random Functions: École d'Été de Probabilités de Saint-Flour XXXIX-2009 , 2011 .

[8]  F. Flandoli Random perturbation of PDEs and fluid dynamic models , 2011 .

[9]  Herbert K. H. Lee,et al.  Gaussian Processes , 2011, International Encyclopedia of Statistical Science.

[10]  Karl J. Friston,et al.  Topological inference for EEG and MEG , 2010, 1011.2901.

[11]  R. Adler,et al.  Persistent homology for random fields and complexes , 2010, 1003.1001.

[12]  Karl J. Friston,et al.  Topological FDR for neuroimaging , 2010, NeuroImage.

[13]  M. Broué Introduction to Complex Reflection Groups and Their Braid Groups , 2010 .

[14]  O. Barndorff-Nielsen,et al.  Lévy Matters I , 2010 .

[15]  D. Schleicher,et al.  Holomorphic Dynamical Systems , 2010 .

[16]  A. Melchiorri,et al.  BOOMERanG constraints on primordial non-Gaussianity from analytical Minkowski functionals , 2009, 0905.4301.

[17]  J. Azaïs,et al.  Level Sets and Extrema of Random Processes and Fields , 2009 .

[18]  Gunnar E. Carlsson,et al.  Topology and data , 2009 .

[19]  Karl J. Friston,et al.  False discovery rate revisited: FDR and topological inference using Gaussian random fields , 2009, NeuroImage.

[20]  Euler Characteristics and Maxima of Oceanic Sea States , 2009 .

[21]  J. M. Urbano The Method of Intrinsic Scaling: A Systematic Approach to Regularity for Degenerate and Singular PDEs , 2008 .

[22]  Changbom Park,et al.  Genus Topology of Structure in the Sloan Digital Sky Survey: Model Testing , 2006, astro-ph/0610762.

[23]  Vincenzo Capasso,et al.  Multiscale problems in the life sciences : from microscopic to macroscopic : lectures given at the Banach Center and C.I.M.E. joint summer school held in Bȩdlewo, Poland, September 4-9, 2006 , 2008 .

[24]  G. Tian,et al.  Symplectic 4-Manifolds and Algebraic Surfaces , 2008 .

[25]  Olivier Wittenberg Intersections de deux quadriques et pinceaux de courbes de genre 1 = Intersections of two quadrics and pencils of curves of genus 1 , 2015, 1502.04462.

[26]  Y. Benjamini,et al.  False Discovery Rates for Spatial Signals , 2007 .

[27]  R. Ghrist Barcodes: The persistent topology of data , 2007 .

[28]  K. Worsley,et al.  Detecting Sparse Signals in Random Fields, With an Application to Brain Mapping , 2007 .

[29]  V. Berinde Iterative Approximation of Fixed Points , 2007 .

[30]  R. Adler,et al.  Random Fields and Geometry , 2007 .

[31]  Afra Zomorodian,et al.  The Theory of Multidimensional Persistence , 2007, SCG '07.

[32]  M. Dennis,et al.  Nodal densities of planar gaussian random waves , 2007 .

[33]  Vin de Silva,et al.  Coverage in sensor networks via persistent homology , 2007 .

[34]  Korea,et al.  Genus topology of the cosmic microwave background from the WMAP 3-year data , 2006, astro-ph/0610764.

[35]  作間 誠,et al.  Punctured torus groups and 2-bridge knot groups (I) , 2007 .

[36]  Peter Bubenik,et al.  A statistical approach to persistent homology , 2006, math/0607634.

[37]  J. Peacock,et al.  Simulations of the formation, evolution and clustering of galaxies and quasars , 2005, Nature.

[38]  D. Applebaum,et al.  From classical probability to quantum stochastic calculus , 2005 .

[39]  Vin de Silva,et al.  HOMOLOGICAL SENSOR NETWORKS , 2005 .

[40]  R. Nagel,et al.  Functional Analytic Methods for Evolution Equations , 2004 .

[41]  I. Verdinelli,et al.  False Discovery Control for Random Fields , 2004 .

[42]  W. Reichel Uniqueness Theorems For Variational Problems By The Method Of Transformation Groups , 2004 .

[43]  M. Qian,et al.  Mathematical Theory of Nonequilibrium Steady States: On the Frontier of Probability and Dynamical Systems , 2004 .

[44]  D. Zaitsev,et al.  Real methods in complex and CR geometry , 2004 .

[45]  Daniel Hug,et al.  Kinematic and Crofton formulae of integral geometry: recent variants and extensions , 2004 .

[46]  Akimichi Takemura,et al.  MATHEMATICAL ENGINEERING TECHNICAL REPORTS Validity of the expected Euler characteristic heuristic , 2003 .

[47]  Robert J. Adler,et al.  Euler characteristics for Gaussian fields on manifolds , 2003 .

[48]  Jonathan E. Taylor A gaussian kinematic formula , 2006, math/0602545.

[49]  L. Bröcker,et al.  Lipschitz-Killing invariants , 2002 .

[50]  Akimichi Takemura,et al.  ON THE EQUIVALENCE OF THE TUBE AND EULER CHARACTERISTIC METHODS FOR THE DISTRIBUTION OF THE MAXIMUM OF GAUSSIAN FIELDS OVER PIECEWISE SMOOTH DOMAINS , 2002 .

[51]  R. Ghrist,et al.  Finding Topology in a Factory: Configuration Spaces , 2000, Am. Math. Mon..

[52]  T. O’Neil Geometric Measure Theory , 2002 .

[53]  K. Worsley Testing for signals with unknown location and scale in a χ2 random field, with an application to fMRI , 2001, Advances in Applied Probability.

[54]  A. W. van der Vaart,et al.  Uniform Central Limit Theorems , 2001 .

[55]  M. Pflaum Analytic and geometric study of stratified spaces , 2001 .

[56]  L. Bröcker,et al.  Integral Geometry of Tame Sets , 2000 .

[57]  Karl J. Friston,et al.  A test for a conjunction , 2000 .

[58]  R. Adler On excursion sets, tube formulas and maxima of random fields , 2000 .

[59]  P. McMullen INTRODUCTION TO GEOMETRIC PROBABILITY , 1999 .

[60]  K. Gorski,et al.  Minkowski functionals used in the morphological analysis of cosmic microwave background anisotropy maps , 1997, astro-ph/9710185.

[61]  Étale Groupoids,et al.  Homology Theory , 2009 .

[62]  Keith J. Worsley,et al.  The Geometry of Random Images , 1996 .

[63]  Vladimir I. Piterbarg,et al.  Asymptotic Methods in the Theory of Gaussian Processes and Fields , 1995 .

[64]  K. Worsley,et al.  Boundary corrections for the expected Euler characteristic of excursion sets of random fields, with an application to astrophysics , 1995, Advances in Applied Probability.

[65]  K. Worsley Estimating the number of peaks in a random field using the Hadwiger characteristic of excursion sets, with applications to medical images , 1995 .

[66]  D. Siegmund,et al.  Testing for a Signal with Unknown Location and Scale in a Stationary Gaussian Random Field , 1995 .

[67]  M. Lifshits Gaussian Random Functions , 1995 .

[68]  K. Worsley,et al.  Local Maxima and the Expected Euler Characteristic of Excursion Sets of χ 2, F and t Fields , 1994, Advances in Applied Probability.

[69]  Changbom Park,et al.  Topological analysis of the CfA redshift survey , 1994 .

[70]  R. Schneider Convex Bodies: The Brunn–Minkowski Theory: Minkowski addition , 1993 .

[71]  Jiayang Sun Tail probabilities of the maxima of Gaussian random fields , 1993 .

[72]  Alan C. Evans,et al.  Anatomical mapping of functional activation in stereotactic coordinate space , 1992, NeuroImage.

[73]  Alan C. Evans,et al.  Language localization with activation positron emission tomography scanning. , 1992, Neurosurgery.

[74]  Steffen L. Lauritzen,et al.  Finite de Finetti theorems in linear models and multivariate analysis , 1992 .

[75]  M. Talagrand,et al.  Probability in Banach Spaces: Isoperimetry and Processes , 1991 .

[76]  G. F. Roach,et al.  Inverse problems and imaging , 1991 .

[77]  Iain M. Johnstone,et al.  Hotelling's Theorem on the Volume of Tubes: Some Illustrations in Simultaneous Inference and Data Analysis , 1990 .

[78]  R. Adler An introduction to continuity, extrema, and related topics for general Gaussian processes , 1990 .

[79]  D. Siegmund,et al.  On Hotelling's Approach to Testing for a Nonlinear Parameter in Regression , 1989 .

[80]  D. Aldous Probability Approximations via the Poisson Clumping Heuristic , 1988 .

[81]  M. Goresky,et al.  Stratified Morse theory , 1988 .

[82]  D. Freedman,et al.  A dozen de Finetti-style results in search of a theory , 1987 .

[83]  J. Gott,et al.  The Sponge-like Topology of Large-Scale Structure in the Universe , 1986 .

[84]  Correction: On the Average Number of Real Roots of a Random Algebraic Equation , 1987 .

[85]  M. Wschebor Surfaces aléatoires : mesure géométrique des ensembles de niveau , 1985 .

[86]  A. Gorin ON THE VOLUME OF TUBES , 1983 .

[87]  R. Adler,et al.  The Geometry of Random Fields , 1982 .

[88]  W. J. Thron,et al.  Encyclopedia of Mathematics and its Applications. , 1982 .

[89]  J. Kuelbs Probability on Banach spaces , 1978 .

[90]  L. Santaló Integral geometry and geometric probability , 1976 .

[91]  Richard M. Dudley,et al.  Sample Functions of the Gaussian Process , 1973 .

[92]  G. Lindgren Local maxima of Gaussian fields , 1972 .

[93]  R. Dudley The Sizes of Compact Subsets of Hilbert Space and Continuity of Gaussian Processes , 1967 .

[94]  Shiing-Shen Chern,et al.  On the Kinematic Formula in Integral Geometry , 1966 .

[95]  D. Slepian,et al.  Large Excursions of Gaussian Processes , 1959 .

[96]  Gerald M. White Zeros of Gaussian Noise , 1958 .

[97]  A. M. Walker Statistical Analysis of a Random, Moving Surface , 1957, Nature.

[98]  H. Hadwiger Vorlesungen über Inhalt, Oberfläche und Isoperimetrie , 1957 .

[99]  S. Rice Mathematical analysis of random noise , 1944 .

[100]  S. Rice The Distribution of the Maxima of a Random Curve , 1939 .

[101]  H. Hotelling Tubes and Spheres in n-Spaces, and a Class of Statistical Problems , 1939 .

[102]  R. Ho Algebraic Topology , 2022 .

[103]  H. Edelsbrunner,et al.  Persistent Homology — a Survey , 2022 .