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Source: paper_references, paper_reference_links, observed 2026-07-31T23:27:15.322899Z
Paper Citation Record · LEDGER
As of 24 August 2026, this Paper Citation Record lists 100 of 105 outbound references and 0 inbound Pith citation observations for arXiv:2607.23973.
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100 of 105 outbound references displayed
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Observation 4e09ae7d-2043-4eb0-bcb0-d4270ce2cfa1 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors We placeN p points randomly and isotropically distributed on the sphere, assigning each point anglesϕ i = 2πu i, θi = cos −1(2vi −1) whereu i, vi ∼ U(0,1] are uniformly distributed
Reference 1
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Observation 5d9a5914-e5fe-4c10-8b50-d91fb0120a64 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Isotropy is broken by couplingℓandℓ±1 modes
Reference 2
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Observation 48877804-198f-4aa9-b150-e7446ca83ecc · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Unresolved cited work
Reference 3
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Observation 713024ce-d7f6-4dbf-a389-496d4c9cc751 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors 1 +λ r 3 4π cosθ # = 0,⟨δ 2⟩=⟨δ 2 iso⟩
Reference 4
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Observation 1f4cc7cd-6893-47e9-807a-b88a4f87363e · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Battye and A
Reference 5
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Observation 10959a07-06e3-4729-bf06-509b10134d57 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Points/error bars are the mean and standard error ofN real = 400 realisations
Reference 6
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Observation 0fbda78c-0abc-4a5c-b5f6-24ba6b32e0e9 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Unresolved cited work
Reference 7
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Observation 3bf5e030-f1e8-4c09-8976-09a05c54617f · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors The area enclosed by the four vertices (t 1,t 2,p k,p k+1) is added toW 0 and the length of the great arc segmente 12 between [t 1,t 2] onS 2 is added toW 1
Reference 8
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Observation a203f50a-fc54-4153-aa2f-46834c226a98 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors The area enclosed by the three vertices (t1,t 2,p k) is added toW 0 and the length|e 12|of the segment [t 1,t 2] onS 2 is added toW 1
Reference 9
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Observation e4a20450-05ad-4435-847e-2772bda5d438 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors The Betti numbers are calculated using a graph search on adjacent triangles
Reference 10
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Observation 92d503f1-521b-4f4a-8a77-51b9f0e4a6c6 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Is the Observable Universe Consistent with the Cosmological Principle?
Reference 11
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Observation f3c12685-1f12-4c99-a43c-4e46924c1e05 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors A Test of the Cosmological Principle with Quasars
Reference 12
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Observation 1316cfc0-0542-4189-b4f3-ccd13aa90d7a · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Jones, C.J
Reference 13
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Observation 7efe7146-c897-4cc4-ad8e-13eb3f5c37c1 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Asymmetries in the CMB anisotropy field
Reference 14
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Observation c0c4f6de-3c93-4821-9770-8345b5463aa8 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Power Asymmetry in Cosmic Microwave Background Fluctuations from Full Sky to Sub-degree Scales: Is the Universe Isotropic?
Reference 15
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Observation b7bc889c-77eb-49c5-a155-9cdbf08b4602 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Cosmic radio dipole from NVSS and WENSS
Reference 16
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Observation 1e55d0fe-5871-437e-b598-5773ec0c9043 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors A large disparity in cosmic reference frames determined from the sky distributions of radio sources and the microwave background radiation
Reference 17
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Observation 7be7494c-718b-4eef-8eb3-7248817b84f3 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Measuring Statistical isotropy of the CMB anisotropy
Reference 18
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Observation aae0b693-e707-4932-8164-16a94689e511 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors The Cosmic Microwave Background Bipolar Power Spectrum: Basic Formalism and Applications
Reference 19
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Observation cc67ba6a-55cc-4a9f-b7ef-898723894cc0 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Integrated perturbation theory for cosmological tensor fields. I. Basic formulation
Reference 20
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Observation 913e1019-874b-49b7-8c25-4af114418ca4 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Integrated perturbation theory for cosmological tensor fields. II. Loop corrections
Reference 21
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Observation 44cf54a0-fdfd-4d24-905a-1abb2f84e528 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Integrated perturbation theory for cosmological tensor fields. III. Projection effects
Reference 22
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Observation 6540fd50-c28a-4ec9-b1be-b705f77331c1 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Integrated perturbation theory for cosmological tensor fields. IV. Full-sky formulation
Reference 23
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Observation f5aebe45-b92e-40b6-b664-e3d0e556e37e · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Information content in anisotropic cosmological fields: Impact of different multipole expansion scheme for galaxy density and ellipticity correlations
Reference 24
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Observation 42809fe2-54ac-4935-b1b8-1e5bdceb09b7 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Probing dipolar power asymmetry with galaxy clustering and intrinsic alignments
Reference 25
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Observation b1572a72-9db6-47f9-90c9-4c22c58a027a · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Robust Morphological Measures for Large-Scale Structure in the Universe
Reference 26
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Observation 12840e1a-3cf6-471e-8352-24ddec86b97e · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Schmalzing, M
Reference 27
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Observation 72b86464-90c0-4157-a812-85fed33942d8 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Limits on Primordial Non-Gaussianity from Minkowski Functionals of the WMAP Temperature Anisotropies
Reference 28
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Observation 232434df-095f-468f-8d17-3ea7e71f692e · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Local analyses of Planck maps with Minkowski Functionals
Reference 29
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Observation 24d4c597-d077-4dba-acfd-c6dc7e0eafa4 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors On Minkowski Functionals of CMB polarization
Reference 30
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Observation 76a82b8c-8192-4a76-b79f-3cd3b2e427c1 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Minkowski Functionals of SDSS-III BOSS : Hints of Possible Anisotropy in the Density Field?
Reference 31
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Observation 3fe7643e-d464-4e0b-8727-07ad2670440b · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Gott, III, C
Reference 32
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Observation 91e8df7e-c3a4-429c-956d-2cbc51ebd8bc · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Park and J.R
Reference 33
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Observation a34b79d8-e229-4f37-b5c2-594c46904c42 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Beyond genus statistics: a unifying approach to the morphology of cosmic structure
Reference 34
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Observation 94a8060b-f46e-490f-ad00-137d14ce4521 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Schmalzing and K.M
Reference 35
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Observation 3f9a6a9d-776d-4209-b9e4-1547dd798f50 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Melott, A.P
Reference 36
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Observation 749535e1-5e2e-4a13-82d6-85a05ef27fd6 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Park, J.R
Reference 37
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Observation 0e6b97a3-77b2-40e4-a6e2-63fa0ba1eea9 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Fluctuations in the IRAS 1.2 Jy Catalogue
Reference 38
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Observation 32f12389-5a37-4552-b870-fbe73eb8ba78 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Park, J.R
Reference 39
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Observation db27e96b-c95d-4709-9de5-913fde23d8ed · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Park and Y.-R
Reference 40
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Observation 8ccb6024-f33a-4689-a2f7-cb6f334d13a2 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Zunckel, J.R
Reference 41
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Observation 5118210b-6f8c-4249-a012-39d99df922f2 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Shapefinders: A new shape diagnostic for large scale structure
Reference 42
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Observation 022ca5ec-9e58-4032-a350-810d4de26516 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Evidence for Filamentarity in the Las Campanas Redshift Survey
Reference 43
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Observation dd0ef839-7b95-4455-b07b-85cbb46a0cc0 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Matsubara,Statistics of Smoothed Cosmic Fields in Perturbation Theory
Reference 44
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Observation ef902dad-00ac-4be6-8efb-866f15efcad8 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Probing Dark Energy with Alpha Shapes and Betti Numbers
Reference 45
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Observation b1a25bf0-5559-42a4-8c92-f7f3896a0ef2 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Betti numbers of Gaussian fields
Reference 46
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Observation d5ccbf39-b98c-4237-bcad-42227fcae1a8 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Alpha, Betti and the Megaparsec Universe: on the Topology of the Cosmic Web
Reference 47
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Observation 8bb735d6-4f53-44ab-b21a-c39279a44695 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Residual foreground contamination in the WMAP data and bias in non-Gaussianity estimation
Reference 48
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Observation 5cb3f542-1e47-4763-a2af-adbb0b768a85 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Felix: A Topology based Framework for Visual Exploration of Cosmic Filaments
Reference 49
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Observation 75b76e10-44df-4687-a85e-68788f4f8e90 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors The Topology of the Cosmic Web in Terms of Persistent Betti Numbers
Reference 50
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Observation b151b857-bd44-49cf-b182-0799b96330a7 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background
Reference 51
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Observation aca127f7-a2ee-4ba6-8db0-8c75a133c6fa · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Topology and Geometry of Gaussian random fields I: on Betti Numbers, Euler characteristic and Minkowski functionals
Reference 52
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Observation ca987306-e04c-4cd9-8041-44737df93c97 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Stochastic Homology of Gaussian vs. non-Gaussian Random Fields: Graphs towards Betti Numbers and Persistence Diagrams
Reference 53
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Observation 3c46389b-4f9f-4b64-a689-585ec07df0e0 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Persistent homology of the cosmic web. I: Hierarchical topology in $\Lambda$CDM cosmologies
Reference 54
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Observation f7c1e322-3c8a-4899-a929-04b05a4851f9 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Morphology of Weak Lensing Convergence Maps
Reference 55
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Observation 7ee3180b-d1dc-4726-9b08-a3a1e754efeb · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Probing massive neutrinos with the Minkowski functionals of large-scale structure
Reference 56
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Observation 0b6bc16a-28cf-4c74-83a5-6c45c0e81ce4 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Probing massive neutrinos with the Minkowski functionals of the galaxy distribution
Reference 57
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Observation 817bf919-b84d-46a5-9bc4-32b63567bd87 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Cosmological constraints from the Minkowski functionals of the BOSS CMASS galaxy sample
Reference 58
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Observation 6017e91a-44f7-47ff-b8b1-3b0f267f355f · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Non-Gaussianity of diffuse Galactic synchrotron emission at 408 MHz
Reference 59
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Observation 9055c5a8-1b9c-4281-8eb1-7bfb113adcc7 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors The nature of non-Gaussianity and statistical isotropy of the 408 MHz Haslam synchrotron map
Reference 60
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Observation fea8ed10-2964-47b6-9b9a-3e549c699117 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Afzal, M
Reference 61
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Observation 00b5ac1f-3907-4b7f-9e33-1342038d1145 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Santalo,Integral geometry and geometric probability, Addison-Wesley Pub
Reference 62
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Observation 2e00cf88-8c11-44bc-bff0-f0143da2596e · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors McMullen,Isometry covariant valuations on convex bodies,Rend
Reference 63
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Observation 2c531c8e-dad6-430e-bd35-963ab4fbb000 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Alesker,Description of continuous isometry covariant valuations on convex sets,Geometriae Dedicata74(1999) 241
Reference 64
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Observation 52c70926-3983-4975-a8f2-513600479c1a · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Beisbart, R
Reference 65
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Observation 9eddc702-1dac-4a63-8f99-8ad541ca0c6d · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Unresolved cited work
Reference 66
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Observation e7aadf87-86b8-4a78-9212-4a7f04f56a35 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Schroder-Turk, W
Reference 67
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Observation 3ef546d9-fcbb-4534-927d-8750a9685bc2 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Schroder-Turk, S
Reference 68
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Observation 7b627fab-24a9-49df-81c5-7c8858ae2511 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Beisbart, T
Reference 69
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Observation 869c1de5-5a39-4f45-af39-45087b846688 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Hadwiger,Vorlesungen ¨ uber Inhalt, Oberfl¨ ache und Isoperimetrie, Springer, Grundlehren der mathematischen Wissenschaften (1957)
Reference 70
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Observation 8804bec4-da26-49da-bd4e-3999b09eff37 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Matheron,Random sets and integral geometry, Wiley New York (1974)
Reference 71
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Observation 35aec191-cc92-4603-aadd-c404f3334b7c · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Morphometry on the sphere: Cartesian and irreducible Minkowski tensors explained and implemented
Reference 72
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Observation 926d7afe-9ae8-48fd-a52b-22cfaf9747e6 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Rehse, K
Reference 73
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Observation 4f1d4066-5eee-411e-9852-aee51ba70067 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Becker, G
Reference 74
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Observation f0e18707-2dde-492d-93a6-dd56bc7985e3 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Olszowka, M
Reference 75
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Observation 448c6798-b1fa-4c05-b4f5-2f91105cf60c · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Beisbart, R
Reference 76
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Observation 8e6580a9-9f41-4650-9771-523ba60af341 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Tensor Minkowski Functionals: first application to the CMB
Reference 77
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Observation af4d421d-a7c4-4f2d-a4c7-a9448a90e988 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Tensor Minkowski Functionals for random fields on the sphere
Reference 78
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Observation c95c90a7-377c-425d-ae69-b746efdff632 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors The geometrical meaning of statistical isotropy of smooth random fields in two dimensions
Reference 79
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Observation 7ad910ec-cb4c-4ba0-ad00-3a2a2f016d3f · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Unresolved cited work
Reference 80
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Observation ed17b097-cbc0-4f5a-a9c7-4c1e249dd508 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Unresolved cited work
Reference 81
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Observation 36fb6419-8b5a-478f-a7bb-2c252e4a6073 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Morphology of CMB fields -- effect of weak gravitational lensing
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Observation 42002ca6-dbe2-4643-8003-febc8e08f76d · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Local patch analysis for testing statistical isotropy of the Planck convergence map
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Observation c9e144f1-efc7-408d-9694-827c1883db92 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors A novel probe of bubble size statistics and time scales of the epoch of reionization using the contour Minkowski Tensor
Reference 84
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Observation 66827f65-0a0a-42fa-823d-c1b4a40623e7 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Morphology of 21cm brightness temperature during the Epoch of Reioinization using Contour Minkowski Tensor
Reference 85
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Observation 1c6fe797-c31f-4c36-b216-dd5507d835f9 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Prospects of constraining reionization model parameters using Minkowski tensors and Betti numbers
Reference 86
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Observation 42d273b6-d46f-4aae-b1cb-5c6eb2c77f85 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Appleby, P
Reference 87
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Observation 17e17eb8-892c-44fe-92a0-0fef667e5e26 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Minkowski Tensors in Three Dimensions - Probing the Anisotropy Generated by Redshift Space Distortion
Reference 88
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Observation 77500b88-9448-4f56-bc73-ea6f4d27b294 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Ensemble Average of Three-Dimensional Minkowski Tensors of a Gaussian Random Field in Redshift Space
Reference 89
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Observation bb77257e-f84c-4191-823e-5c79ce1aa4f2 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Appleby, J.P
Reference 90
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Observation a50f83bb-827a-479f-8226-1f0a862a13b6 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Non-Gaussian Expansion of Minkowski Tensors in Redshift Space
Reference 91
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Observation 0fd51d34-d5b2-43fc-8d96-2bb5d174dbcb · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Klatt, M
Reference 92
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Testing Statistical Isotropy on the Sphere with Minkowski Tensors Schaller, J
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Testing Statistical Isotropy on the Sphere with Minkowski Tensors Probing the Anisotropy and Non-Gaussianity in the Redshift Space through the Conditional Moments of the First Derivative
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Testing Statistical Isotropy on the Sphere with Minkowski Tensors Impact of Redshift Space Distortion on Persistent Homology of cosmic matter density field
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Testing Statistical Isotropy on the Sphere with Minkowski Tensors Quantifying Weighted Morphological Content of Large-Scale Structures via Simulation-Based Inference
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Observation 942270a4-2fee-4fea-84f5-f650ed7168c4 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Statistical Isotropy of the CMB E-mode signal
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Observation 75e1836b-686f-4761-ac55-d5aad874bf8a · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Local patch analysis of ACT DR6 convergence map using morphological statistics
Reference 98
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Observation 7b22f12f-ee44-4ced-b7dc-bc055cf10025 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Miralda-Escude,The Correlation Function of Galaxy Ellipticities Produced by Gravitational Lensing, ApJ380(1991) 1
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Observation ca19041c-a4a5-4e01-a8e0-86201b7c9358 · outbound
Testing Statistical Isotropy on the Sphere with Minkowski Tensors Kaiser,Weak gravitational lensing of distant galaxies,Astrophys
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