The Monge-Ampère-Kantorovich approach to reconstruction in cosmology

Physica D: Nonlinear Phenomena

Volumn 237, Issue 14-17, 2008, Pages 2145-2150

  Mohayaee, Roya ^a   Sobolevskiǐ, Andreǐ ^b,c,d  

^a INSTITUT D'ASTROPHYSIQUE DE PARIS   (France)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

^c INSTITUTE OF EARTHQUAKE PREDICTION THEORY AND MATHEMATICAL GEOPHYSICS   (Russian Federation)

^d UMI 2615 CNRS Laboratoire J V Poncelet   (Russian Federation)

Author keywords

Convex optimization; Dark matter; Proper motions of galaxies; Reconstruction

Indexed keywords

CONVEX OPTIMIZATION; GALAXIES; IMAGE RECONSTRUCTION;

DARK MATTER; FLUID ELEMENT; ITS APPLICATIONS; MASS DENSITIES; OBSERVATIONAL DATA; POLAR DECOMPOSITIONS; PROPER MOTION; SELF-GRAVITATING FLUID;

COSMOLOGY;

EID: 47049120249     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2008.01.007     Document Type: Article

References (25)

1. Brenier Y. Décomposition polaire et réarrangement monotone des champs de vecteurs. C. R. Acad. Sci. Paris Sér. I Math. 305 19 (1987) 805-808
2. Brenier Y. Polar factorization and monotone rearrangement of vector-valued functions. Commun. Pure Appl. Math. 44 4 (1991) 375-417
3. Brenier Y. A combinatorial algorithm for the Euler equations of incompressible flows. Comput. Methods Appl. Mech. Engrg. 75 1-3 (1989) 325-332
4. Tully R.B. Nearby Galaxies Catalog (1988), Cambridge University Press, Cambridge and New York
5. Peacock J., Cole S., Norberg P., Baugh C., Bland-Hawthorn J., Bridges T., Cannon R., Colless M., Collins C., Couch W., et al. A measurement of the cosmological mass density from clustering in the 2dF Galaxy Redshift Survey. Nature 410 (2001) 169-173
6. Tegmark M., Strauss M.A., Blanton M.R., Abazajian K., Dodelson S., Sandvik H., Wang X., Weinberg D.H., Zehavi I., Bahcall N.A., Hoyle F., Schlegel D., Scoccimarro R., Vogeley M.S., Berlind A., Budavari T., Connolly A., Eisenstein D.J., Finkbeiner D., Frieman J.A., Gunn J.E., Hui L., Jain B., Johnston D., Kent S., Lin H., Nakajima R., Nichol R.C., Ostriker J.P., Pope A., Scranton R., Seljak U., Sheth R.K., Stebbins A., Szalay A.S., Szapudi I., Xu Y., Annis J., Brinkmann J., Burles S., Castander F.J., Csabai I., Loveday J., Doi M., Fukugita M., Gillespie B., Hennessy G., Hogg D.W., Ivezić Ž., Knapp G.R., Lamb D.Q., Lee B.C., Lupton R.H., McKay T.A., Kunszt P., Munn J.A., O'Connell L., Peoples J., Pier J.R., Richmond M., Rockosi C., Schneider D.P., Stoughton C., Tucker D.L., vanden Berk D.E., Yanny B., and York D.G. Cosmological parameters from SDSS and WMAP. Phys. Rev. D 69 10 (2004) 103501
7. Kaiser N. On the spatial correlations of Abell clusters. Astrophys. J. 284 (1984) L9-L12
8. Bahcall N., Cen R., Davé R., Ostriker J., and Yu Q. The mass-to-light function: antibias and Omega m. Astrophys. J. 541 1 (2000) 1-9
9. Peebles P.J.E. Tracing galaxy orbits back in time. Astrophys. J. 344 (1989) L53-L56
10. Frisch U., Matarrese S., Mohayaee R., and Sobolevski A. A reconstruction of the initial conditions of the Universe by optimal mass transportation. Nature 417 (2002) 260-262
11. Y. Brenier, Generalized solutions and hydrostatic approximation of the Euler equations, these Proceedings
12. Bernardeau F., Colombi S., Gaztañaga E., and Scoccimarro R. Large-scale structure of the universe and cosmological perturbation theory. Phys. Rep. 367 1-3 (2002) 1-248
13. Catelan P., Lucchin F., Matarrese S., and Moscardini L. Eulerian perturbation theory in non-flat universes: second-order approximation. Monthly Notices R. Astronom. Soc. 276 (1995) 39-56
14. Brenier Y., Frisch U., Hénon M., Loeper G., Matarrese S., Mohayaee R., and Sobolevskiǐ A. Reconstruction of the early Universe as a convex optimization problem. Monthly Notices R. Astronom. Soc. 346 (2003) 501-524
15. A. Nusser, Boundary-value problems in cosmological dynamics, these Proceedings
16. Giavalisco M., Mancinelli B., Mancinelli P.J., and Yahil A. A generalized Zel'dovich approximation to gravitational instability. Astrophys. J. 411 (1993) 9-15
17. Zel'dovich Y.B. Gravitational instability: an approximate theory for large density perturbations. Astronom. Astrophys. 5 (1970) 84-89
18. Papadimitriou C.H., and Steiglitz K. Combinatorial Optimization: Algorithms and Complexity (1982), Prentice-Hall Inc., Englewood Cliffs, NJ
19. Bertsekas D.P. Auction algorithms for network flow problems: A tutorial introduction. Comput. Optim. Appl. 1 1 (1992) 7-66
20. G. Lavaux, Lagrangian reconstruction of cosmic velocity fields, these Proceedings
21. D.M. Mount, S. Arya, ANN: A library for approximate nearest neighbor searching (Apr 2005). URL: http://www.cs.umd.edu/~mount/ANN/
22. Benamou J.D., and Brenier Y. A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer. Math. 84 3 (2000) 375-393
23. Mohayaee R., Mathis H., Colombi S., and Silk J. Reconstruction of primordial density fields. Monthly Notices R. Astronom. Soc. 365 3 (2006) 939-959
24. D.N. Spergel, L. Verde, H.V. Peiris, E. Komatsu, M.R. Nolta, C.L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut, M. Limon, S.S. Meyer, L. Page, G.S. Tucker, J.L. Weiland, E. Wollack, E.L. Wright, First year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Determination of cosmological parameters (2003). arXiv:astro-ph/0302209
25. Mohayaee R., and Tully R.B. The cosmological mean density and its local variations probed by peculiar velocities. Astrophys. J. 635 (2005) L113-L116