9 Towards the “Shape” of Cosmological Observables and the String …
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63. Hofer, C., Kwitt, R., Niethammer, M., Uhl, A.: Deep learning with topological signatures. In:
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004 (2004). https://doi.org/10.1088/1126-6708/2004/12/004
65. Kim, K., Kim, J., Kim, J.S., Chazal, F., Wasserman, L.: Efficient topological layer based on
persistent landscapes. arXiv preprint arXiv:2002.02778 (2020)
66. Kimura, Y., Imai, K.: Quantification of lss using the persistent homology in the sdss fields.
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67. Klaewer, D., Schlechter, L.: Machine Learning Line Bundle Cohomologies of Hypersurfaces
in Toric Varieties (2018)
68. Klypin, A., Shandarin, S.F.: Percolation technique for galaxy clustering. Astrophys. J. 413,
48–58 (1993)
69. Komatsu, E., Spergel, D.N.: Acoustic signatures in the primary microwave background bispectrum. Phys. Rev. D 63, 063002 (2001). https://doi.org/10.1103/PhysRevD.63.063002
70. Krefl, D., Seong, R.K.: Machine Learning of Calabi-Yau Volumes. Phys. Rev. D 96(6), 066014
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71. Liguori, M., Hansen, F.K., Komatsu, E., Matarrese, S., Riotto, A.: Testing primordial nongaussianity in cmb anisotropies. Phys. Rev. D 73, 043505 (2006). https://doi.org/10.1103/
PhysRevD.73.043505
72. Linde, A.D.: A new inflationary universe scenario: a possible solution of the horizon, flatness,
homogeneity, isotropy and primordial monopole problems. Phys. Lett. 108B, 389–393 (1982).
https://doi.org/10.1016/0370-2693(82)91219-9
73. Maldacena, J.M.: Non-Gaussian features of primordial fluctuations in single field inflationary
models. JHEP 05, 013 (2003). https://doi.org/10.1088/1126-6708/2003/05/013
74. Marchesano, F., Shiu, G., Wang, L.T.: Model building and phenomenology of flux-induced
supersymmetry breaking on D3-branes. Nucl. Phys. B 712, 20–58 (2005). https://doi.org/10.
1016/j.nuclphysb.2005.01.046
75. Matsubara, T.: Analytic minkowski functionals of the cosmic microwave background: secondorder non-gaussianity with bispectrum and trispectrum. Phys. Rev. D 81, 083505 (2010).
https://doi.org/10.1103/PhysRevD.81.083505
76. Mecke, K.R., Buchert, T., Wagner, H.: Robust morphological measures for large scale structure
in the universe. Astron. Astrophys. 288, 697–704 (1994)
77. Milnor, J.: Morse theory (AM-51), vol. 51. Princeton University Press (2016)
78. Mütter, A., Parr, E., Vaudrevange, P.K.S.: Deep learning in the heterotic orbifold landscape
(2018)
79. Mukhanov, V.F.: Gravitational instability of the universe filled with a scalar field. JETP Lett.
41(9), 493–496 (1985)
80. Mukhanov, V.F., Chibisov, G.: Quantum fluctuations and a nonsingular universe. JETP Lett.
33(10), 532–535 (1981)
81. Mukhanov, V.F., Chibisov, G.: Vacuum energy and large-scale structure of the universe. Sov.
Phys.-JETP (Engl. Transl.);(United States) 56(2) (1982)
82. Munkres, J.R.: Elements of Algebraic Topology. CRC Press (2018)
83. Perea, J.A.: A Brief History of Persistence. ArXiv e-prints (Sep 2018)
84. Poulenard, A., Skraba, P., Ovsjanikov, M.: Topological function optimization for continuous
shape matching. In: Computer Graphics Forum. vol. 37, pp. 13–25. Wiley Online Library
(2018)
85. Pranav, P., Adler, R.J., Buchert, T., Edelsbrunner, H., Jones, B.J.T., Schwartzman, A., Wagner,
H., van de Weygaert, R.: Unexpected topology of the temperature fluctuations in the cosmic
microwave background. Astron. Astrophys. 627, A163 (2019). https://doi.org/10.1051/00046361/201834916
86. Pranav, P., Edelsbrunner, H., van de Weygaert, R., Vegter, G., Kerber, M., Jones, B.J.T.,
Wintraecken, M.: The topology of the cosmic web in terms of persistent betti numbers. Mon.
Not. Roy. Astron. Soc. 465(4), 4281–4310 (2017). https://doi.org/10.1093/mnras/stw2862
243
63. Hofer, C., Kwitt, R., Niethammer, M., Uhl, A.: Deep learning with topological signatures. In:
Advances in Neural Information Processing Systems. pp. 1634–1644 (2017)
64. Kallosh, R., Linde, A.D.: Landscape, the scale of SUSY breaking, and inflation. JHEP 12,
004 (2004). https://doi.org/10.1088/1126-6708/2004/12/004
65. Kim, K., Kim, J., Kim, J.S., Chazal, F., Wasserman, L.: Efficient topological layer based on
persistent landscapes. arXiv preprint arXiv:2002.02778 (2020)
66. Kimura, Y., Imai, K.: Quantification of lss using the persistent homology in the sdss fields.
Adv. Space Res. 60(3), 722–736 (2017)
67. Klaewer, D., Schlechter, L.: Machine Learning Line Bundle Cohomologies of Hypersurfaces
in Toric Varieties (2018)
68. Klypin, A., Shandarin, S.F.: Percolation technique for galaxy clustering. Astrophys. J. 413,
48–58 (1993)
69. Komatsu, E., Spergel, D.N.: Acoustic signatures in the primary microwave background bispectrum. Phys. Rev. D 63, 063002 (2001). https://doi.org/10.1103/PhysRevD.63.063002
70. Krefl, D., Seong, R.K.: Machine Learning of Calabi-Yau Volumes. Phys. Rev. D 96(6), 066014
(2017). https://doi.org/10.1103/PhysRevD.96.066014
71. Liguori, M., Hansen, F.K., Komatsu, E., Matarrese, S., Riotto, A.: Testing primordial nongaussianity in cmb anisotropies. Phys. Rev. D 73, 043505 (2006). https://doi.org/10.1103/
PhysRevD.73.043505
72. Linde, A.D.: A new inflationary universe scenario: a possible solution of the horizon, flatness,
homogeneity, isotropy and primordial monopole problems. Phys. Lett. 108B, 389–393 (1982).
https://doi.org/10.1016/0370-2693(82)91219-9
73. Maldacena, J.M.: Non-Gaussian features of primordial fluctuations in single field inflationary
models. JHEP 05, 013 (2003). https://doi.org/10.1088/1126-6708/2003/05/013
74. Marchesano, F., Shiu, G., Wang, L.T.: Model building and phenomenology of flux-induced
supersymmetry breaking on D3-branes. Nucl. Phys. B 712, 20–58 (2005). https://doi.org/10.
1016/j.nuclphysb.2005.01.046
75. Matsubara, T.: Analytic minkowski functionals of the cosmic microwave background: secondorder non-gaussianity with bispectrum and trispectrum. Phys. Rev. D 81, 083505 (2010).
https://doi.org/10.1103/PhysRevD.81.083505
76. Mecke, K.R., Buchert, T., Wagner, H.: Robust morphological measures for large scale structure
in the universe. Astron. Astrophys. 288, 697–704 (1994)
77. Milnor, J.: Morse theory (AM-51), vol. 51. Princeton University Press (2016)
78. Mütter, A., Parr, E., Vaudrevange, P.K.S.: Deep learning in the heterotic orbifold landscape
(2018)
79. Mukhanov, V.F.: Gravitational instability of the universe filled with a scalar field. JETP Lett.
41(9), 493–496 (1985)
80. Mukhanov, V.F., Chibisov, G.: Quantum fluctuations and a nonsingular universe. JETP Lett.
33(10), 532–535 (1981)
81. Mukhanov, V.F., Chibisov, G.: Vacuum energy and large-scale structure of the universe. Sov.
Phys.-JETP (Engl. Transl.);(United States) 56(2) (1982)
82. Munkres, J.R.: Elements of Algebraic Topology. CRC Press (2018)
83. Perea, J.A.: A Brief History of Persistence. ArXiv e-prints (Sep 2018)
84. Poulenard, A., Skraba, P., Ovsjanikov, M.: Topological function optimization for continuous
shape matching. In: Computer Graphics Forum. vol. 37, pp. 13–25. Wiley Online Library
(2018)
85. Pranav, P., Adler, R.J., Buchert, T., Edelsbrunner, H., Jones, B.J.T., Schwartzman, A., Wagner,
H., van de Weygaert, R.: Unexpected topology of the temperature fluctuations in the cosmic
microwave background. Astron. Astrophys. 627, A163 (2019). https://doi.org/10.1051/00046361/201834916
86. Pranav, P., Edelsbrunner, H., van de Weygaert, R., Vegter, G., Kerber, M., Jones, B.J.T.,
Wintraecken, M.: The topology of the cosmic web in terms of persistent betti numbers. Mon.
Not. Roy. Astron. Soc. 465(4), 4281–4310 (2017). https://doi.org/10.1093/mnras/stw2862