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Statistical and Topological Properties of Gaussian Smoothed Sliced Probability Divergences [article]

Alain Rakotomamonjy, Mokhtar Z. Alaya
2021 arXiv   pre-print
We show that smoothing and slicing preserve the metric property and the weak topology. We also provide results on the sample complexity of such divergences.  ...  In this paper, we analyze the theoretical properties of this distance as well as those of generalized versions denoted as Gaussian smoothed sliced divergences.  ...  Theoretical Properties In this section, we will analyze the properties of the Gaussian smoothed sliced divergence, in term of topological and statistical properties and the influence of the Gaussian smoothing  ... 
arXiv:2110.10524v1 fatcat:c2pv6hlydvhllf2jnfigjx255e

Topology of non-linear structure in the 2dF Galaxy Redshift Survey

J. Berian James, Matthew Colless, Geraint F. Lewis, John A. Peacock
2009 Monthly notices of the Royal Astronomical Society  
of the genus statistic for i) the linear regime case of a Gaussian random field; and ii) a first-order perturbative expansion of the weakly non-linear evolved field.  ...  The two flux-limited galaxy samples, located near the southern galactic pole and the galactic equator, are smoothed with Gaussian filters of width ranging from 5 to 8 Mpc/h to produce a continuous galaxy  ...  This builds upon the analysis of statistical properties of the galaxy distribution with this data set, including the power spectrum (Cole et al. 2005) , void probability function (Croton et al. 2004b  ... 
doi:10.1111/j.1365-2966.2008.14358.x fatcat:xeijzdk4effvxd2wdzlebn7e6a

Statistical and Topological Properties of Sliced Probability Divergences [article]

Kimia Nadjahi, Alain Durmus, Lénaïc Chizat, Soheil Kolouri, Shahin Shahrampour, Umut Şimşekli
2022 arXiv   pre-print
In this paper, we aim at bridging this gap and derive various theoretical properties of sliced probability divergences.  ...  First, we show that slicing preserves the metric axioms and the weak continuity of the divergence, implying that the sliced divergence will share similar topological properties.  ...  Acknowledgments This work is partly supported by the French National Research Agency (ANR) as a part of the FBIMATRIX project (ANR-16-CE23-0014) and by the industrial chair Machine Learning for Big Data  ... 
arXiv:2003.05783v3 fatcat:mzxi2doyvfampnlqlvt63a5rmi

Using the topology of large-scale structure in the WiggleZ Dark Energy Survey as a cosmological standard ruler

Chris Blake, J. Berian James, Gregory B. Poole
2013 Monthly notices of the Royal Astronomical Society  
excursion set of a Gaussian random field, with minimal non-Gaussian corrections for the smoothing scales > 10 Mpc/h considered in this analysis.  ...  We introduce a new method for correcting the topological statistics for the sparse-sampling of the density field by the galaxy tracers, and validate our overall methodology using mock catalogues from N-body  ...  The theory of the statistics of excursion sets of such fields has been studied by many authors in contexts of cosmology and geometric statistics (Doroshkevich 1970; Adler 1981; Bardeen, Steinhardt & Turner  ... 
doi:10.1093/mnras/stt2062 fatcat:2t6fmkdtobetpbdje7sz636ple

Measurement of brain structures based on statistical and geometrical 3D segmentation [chapter]

Miguel ángel, González Ballester, Andrew Zisserman, Michael Brady
1998 Lecture Notes in Computer Science  
In this paper we present a novel method for three-dimensional segmentation and measurement of volumetric data based on the combination of statistical and geometrical information.  ...  A Gaussian model for the tissues present in the image is adopted, and a classification procedure which also estimates and corrects for the bias field present in the MRI is used.  ...  Segmentation of the data is guided by the probabilities computed in the statistical classification, a set of forces implemented on the simplex mesh, and a template of the expected shape built by applying  ... 
doi:10.1007/bfb0056235 fatcat:6kzmejn3jbg4vml6gw6jdbcuga

From spatial regularization to anatomical priors in fMRI analysis

Wanmei Ou, Polina Golland
2005 Information processing in medical imaging : proceedings of the ... conference  
Gaussian smoothing, traditionally employed to boost the signal-to-noise ratio, often removes small activation regions.  ...  In this paper, we study Markov Random Fields as spatial smoothing priors in fMRI detection.  ...  Acknowledgement We thank Sandy Wells for suggesting we look at the MRF regularization for fMRI applications, Eric Cosman and Kilian Pohl for help on this paper, and Dr. L.P.  ... 
pmid:17354687 pmcid:PMC4465967 fatcat:vkh7tuoglbem3dx6gcj2ir3mnq

Evidence for Filamentarity in the Las Campanas Redshift Survey

Somnath Bharadwaj, Varun Sahni, B. S. Sathyaprakash, Sergei F. Shandarin, Capp Yess
2000 Astrophysical Journal  
Consequently the fact that the smoothed LCRS catalogue shows properties consistent with those of a Gaussian random field (Colley 1997) whereas the unsmoothed catalogue demonstrates the presence of filamentarity  ...  Out of L and S a single dimensionless Shapefinder Statistic, F can be constructed (0 <=F <=1). F acquires extreme values on a circle (F = 0) and a filament (F = 1).  ...  Shandarin acknowledges the support of NSF-EPSCoR grant, GRF grant at the University of Kansas and from TAC Copenhagen.  ... 
doi:10.1086/308163 fatcat:fircjkqatvdj7h2vnmqgwqo3jm

T-ReX: a graph-based filament detection method

T. Bonnaire, N. Aghanim, A. Decelle, M. Douspis
2020 Astronomy and Astrophysics  
To obtain a smoothed version of this topological prior, we embedded it in a Gaussian mixtures framework.  ...  In the context of recent and upcoming large galaxy surveys, it becomes essential that we identify and classify features of the Cosmic Web in an automatic way in order to study their physical properties  ...  We are grateful to the scikit-learn (Pedregosa et al. 2011 ) team for making easier and sometimes straightforward the implementation and testing of parts of the algorithm. TB thanks Pr. S.  ... 
doi:10.1051/0004-6361/201936859 fatcat:c7rtgh5sjvgqpkxbbdmsmgbtw4

T-ReX: a graph-based filament detection method [article]

T. Bonnaire, N. Aghanim, A. Decelle, M. Douspis
2019 arXiv   pre-print
To obtain a smoothed version of this topological prior, we embed it in a Gaussian mixtures framework.  ...  In the context of recent and upcoming large galaxy surveys, it becomes essential to identify and classify features of the Cosmic Web in an automatic way to study their physical properties and the impact  ...  Acknowledgments The authors are grateful to the scikit-learn (Pedregosa et al. 2011 ) team for making easier and sometimes straightforward the implementation and testing of parts of the algorithm.  ... 
arXiv:1912.00732v1 fatcat:fimkrkinjjcshp72g4ayvwhg6y

From Spatial Regularization to Anatomical Priors in fMRI Analysis [chapter]

Wanmei Ou, Polina Golland
2005 Lecture Notes in Computer Science  
Gaussian smoothing, traditionally employed to boost the signal-to-noise ratio, often removes small activation regions.  ...  In this paper, we study Markov Random Fields as spatial smoothing priors in fMRI detection.  ...  We thank Sandy Wells for suggesting we look at the MRF regularization for fMRI applications, Eric Cosman and Kilian Pohl for help on this paper, and Dr. L.P. Panych for providing fMRI data.  ... 
doi:10.1007/11505730_8 fatcat:oz75pjll4ngbjgbcv7pfwqgmpe

Confining string and its widening inHP1embedding approach

M. N. Chernodub, F. V. Gubarev
2007 Physical Review D  
Characteristic string scales in terms of the topological and action densities are estimated as well.  ...  Structure of confining string in terms of the topological charge density and the action density is studied in SU(2) Yang-Mills theory on the lattice using HP1 sigma-model embedding approach.  ...  Acknowledgments The authors are grateful to the members of ITEP Lattice Group, Institute for Theoretical Physics of Ka-nazawa University, and Research Institute for Information Science and Education of  ... 
doi:10.1103/physrevd.76.016003 fatcat:u7x6l5or3zhbvovwcib627l7yy

Smooth p-Wasserstein Distance: Structure, Empirical Approximation, and Statistical Applications [article]

Sloan Nietert, Ziv Goldfeld, Kengo Kato
2021 arXiv   pre-print
After establishing basic metric and topological properties of 𝖶_p^(σ), we explore the asymptotic statistical behavior of 𝖶_p^(σ)(μ̂_n,μ), where μ̂_n is the empirical distribution of n independent observations  ...  Motivated by the scalability of this framework to high dimensions, we investigate the structural and statistical behavior of the Gaussian-smoothed p-Wasserstein distance 𝖶_p^(σ), for arbitrary p≥ 1.  ...  Similar metric, topological, and statistical properties were established in [48] for sliced versions of generic statistical distances.  ... 
arXiv:2101.04039v3 fatcat:2llbhev6sbbulan35g56kmjrse

COWS: A filament finder for Hessian cosmic web identifiers [article]

Simon Pfeifer, Noam I. Libeskind, Yehuda Hoffman, Wojciech A. Hellwing, Maciej Bilicki, Krishna Naidoo
2022 arXiv   pre-print
The large scale galaxy and matter distribution is often described by means of the cosmic web made up of voids, sheets, filaments and knots.  ...  This results in a set of filaments with well defined end-point and length.  ...  Probability density function (top) and the cumulative probability density function (bottom) of the filament length for different values of the threshold (left) and sizes of the Gaussian smoothing kernel  ... 
arXiv:2201.04624v1 fatcat:a7smih6inzg7vcyus6nxxttihy

Quantifying the topology of large-scale structure

P. Coles, A. G. Davies, R. C. Pearson
1996 Monthly notices of the Royal Astronomical Society  
We propose and investigate a new algorithm for quantifying the topological properties of cosmological density fluctuations.  ...  We first motivate this algorithm by drawing a formal distinction between two definitions of relevant topological characteristics, based on concepts, on the one hand, from differential topology and, on  ...  We are all extremely grateful to the referee, Thomas Buchert, for his thorough reading of a previous version of this paper, and for his many perceptive comments.  ... 
doi:10.1093/mnras/281.4.1375 fatcat:etargomnavg6he45ohazmwjxaa

Investigating Cosmological GAN Emulators Using Latent Space Interpolation [article]

Andrius Tamosiunas, Hans A. Winther, Kazuya Koyama, David J. Bacon, Robert C. Nichol, Ben Mawdsley
2021 arXiv   pre-print
Our results indicate a 1-20% difference between the power spectra of the GAN-produced and the training data samples depending on the dataset used and whether Gaussian smoothing was applied.  ...  However, like any algorithm, the GAN approach comes with a set of limitations, such as an unstable training procedure and the inherent randomness of the produced outputs.  ...  We also thank Adam Amara for the guidance and the useful discussions. Finally, we thank Minas Karamanis for the help with the statistical analysis.  ... 
arXiv:2004.10223v3 fatcat:ga3zbclcgfco7gig3uyvfllr7a
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