OTARIE

Optimal transport : Theory and Applications
to cosmological Reconstruction and Image processing

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Names of participants of the OTARIE project are underlined.

For most published papers, a permanent link is available via their DOI; in the few remaining cases the MR number is provided.

Preprints of published papers are linked to whenever they are available from major preprint servers (arXiv, HAL, CVGMT); most other preprints may be found on authors' personal web pages.

Some relevant pre-OTARIE publications

• G. Carlier, Remarks on Toland's duality, convexity constraint and optimal transport, Pacific J. Optimization 4:3 (2008) 423–432 (MR2541254).
• G. Carlier, C. Jimenez, F. Santambrogio, Optimal transportation with traffic congestion and Wardrop equilibria, SIAM J. on Control and Optimization 47:3 (2008) 1330–1350 (doi:10.1137/060672832).
• G. Carlier, B. Nazaret, Optimal transportation for the determinant, ESAIM: Control, Optimization and Calculus of Variations 14:4 (2008) 678–698 (doi:10.1051/cocv:2008006).
• U. Frisch, A. Sobolevskii, Application of Optimal Transport Theory to Reconstruction of the Early Universe, J. Math. Sci. 133:4 (2006) 1539--1542 (doi:10.1007/s10958-006-0068-z).

2008

• Y. Brenier, Generalized solutions and hydrostatic approximation of the Euler equations, Physica D 237:14–17 (2008) 1982–1988 (doi:10.1016/j.physd.2008.02.026).
• G. Carlier, J. Salomon, A monotonic algorithm for the optimal control of the Fokker-Planck equation (2008), Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico, 9–11 December 2008 (preprint hal-00267432).
• U. Frisch, S. Kurien, R. Pandit, W. Pauls, S.S. Ray, A. Wirth, J.-Z. Zhu, Hyperviscosity, Galerkin truncation and bottlenecks in turbulence, Phys. Rev. Lett. 101 (2008) 144501 (doi:10.1103/PhysRevLett.101.144501, preprint arXiv:0803.4269).
• G. Lavaux, Lagrangian reconstruction of cosmic velocity fields, Physica D 237:14–17 (2008), 2139–2144 (doi:10.1016/j.physd.2008.02.016, preprint arXiv:0801.4208)
• R. Mohayaee, P. Salati, The Cosmic Ray Signature of Dark Matter Caustics, Mon. Not. R. Astron. Soc. 390:4 (2008) 1297–1310 (doi:10.1111/j.1365-2966.2008.13707.x, preprint arXiv:0801.3271).
• R. Mohayaee, J. Colin, Dark matter accretion wakes of high-redshift black holes, New Astronomy Review 51:10–12 (2008) 898–905 (doi:10.1016/j.newar.2008.03.022, preprint arXiv:0802.2534).
• R. Mohayaee, J. Colin, J. Silk, Gamma-ray emission from dark matter wakes of recoiled black holes, Astrophysical Journal Letters, 674:1 (2008) L21–L24 (doi:10.1086/528984, preprint arXiv:0709.3321).
• R. Mohayaee, A. Sobolevskii, The Monge–Ampère–Kantorovich approach to reconstruction in cosmology, Physica D 237:14–17 (2008) 2145–2150 (doi:10.1016/j.physd.2008.01.007, preprint arXiv:0712.2561).
• J. Rabin, J. Delon, Y. Gousseau, Circular Earth Mover's distance for the comparison of local features, Proceedings of ICPR, IEEE, 2008 (doi:10.1109/ICPR.2008.4761372).

2008 preprints

• J. Salomon, G. Turinici, A monotonic method for solving nonlinear optimal control problems (2008), preprint arXiv:0906.3361/hal-00335297.

2009

• N. Afshordi, R. Mohayaee, E. Bertschinger, Hierarchical phase space structure of dark matter haloes: Tidal debris, caustics, and dark matter annihilation, Phys. Rev. D 79:8 (2009) 083526 (doi:10.1103/PhysRevD.79.083526, preprint arXiv:0811.1582).
• M. Bernot, A. Figalli, F. Santambrogio, Generalized solutions for the Euler equations in one and two dimensions, J. Math. Pures Appl. 91:2 (2009) 137–155 (doi:10.1016/j.matpur.2008.09.011, preprint hal-00284725).
• Y. Brenier, Optimal transport, convection, magnetic relaxation and generalized Boussinesq equations, J. Nonlin. Sci. 19:5 (2009) 547–570 (doi:10.1007/s00332-009-9044-3).
• Y. Brenier, M. Cullen, Rigorous derivation of the x–z semigeostrophic equations, Comm. Math. Sci. 7:3 (2009) 779–784 (MR2569033).
• G. Carlier, F. Benmansour, G. Peyré and F. Santambrogio, Numerical approximation of continuous traffic congestion equilibria, Networks and Heterogeneous Media 4:3 (2009) 605–623 (doi:10.3934/nhm.2009.4.605, preprint hal-00360796).
• J. Dolbeault, B. Nazaret, G. Savaré, A new class of transport distances between measures, Calc. Var. PDE, 34:2 (2009), 193–231 (doi:10.1007/s00526-008-0182-5; preprint hal-00262455).
• M. Maciejewski, S. Colombi, V. Springel, C. Alard and F. R. Bouchet, Phase-space structures—II. Hierarchical Structure Finder, Mon. Not. R. Astron. Soc. 396:3 (2009) 1329–1348 (doi:10.1111/j.1365-2966.2009.14825.x, preprint arXiv:0812.0288; M. Maciejewski's stay at IAP was supported by OTARIE).
• O. Podvigina, Конвективная устойчивость вращающегося слоя проводящей жидкости во внешнем магнитном поле (2009), Изв. РАН МЖГ (Mekhanika Zhidkosti i Gaza), issue 4 (2009) 29–39 (in Russian; English translation in Fluid Dynamics 44:4 (2009) 502–510, doi:10.1134/S0015462809040036).
• J. Rabin, J. Delon, Y. Gousseau, A Statistical Approach to the Matching of Local Features SIAM J. Imaging Sci. 2:3 (2009) 931–958 (doi:10.1137/090751359, preprint hal-00168285).
• F. Santambrogio, Absolute continuity and summability of transport densities: simpler proofs and new estimates, Calculus of Variations and PDEs 36:3 (2009) 343–354 (doi:10.1007/s00526-009-0231-8; preprint of the Research Group in Calculus of Variations and Geometric Measure Theory in Pisa: link).
• M. Vogelsberger, S. D. M. White, R. Mohayaee and V. Springel, Caustics in growing dark matter haloes Mon. Not. R. Astron. Soc. 400:4 (2009) 2174–2184 (doi:10.1111/j.1365-2966.2009.15615.x, preprint arXiv:0906.4341).
• V.A. Zheligovsky, Amplitude equations for weakly nonlinear two-scale perturbations of free hydromagnetic convective regimes in a rotating layer, Geophys. Astrophys. Fluid Dynamics 103:5 (2009) 397–420 (doi:10.1080/03091920903052580).
• V. Zheligovsky, Determination of a flow generating a neutral magnetic mode, Phys. Rev. E 80 (2009) 036310 (doi:10.1103/PhysRevE.80.036310).

2010

• N. Afshordi, R. Mohayaee, E. Bertschinger, Hierarchy in the Phase Space and Dark Matter Astronomy Phys. Rev. D 81:10 (2010) 101301 (doi:10.1103/PhysRevD.81.101301, preprint arXiv:0911.0414).
• P. Ashwin, O. M. Podvigina, Noise-induced switching near a depth two heteroclinic network arising in Boussinesq convection, Chaos, 20 (2010) 023133 (doi: 10.1088/0951-7715/24/3/009).
• C. Bardos, U. Frisch, W. Pauls, S. S. Ray, E. S. Titi, Entire solutions of hydrodynamical equations with exponential dissipation, Comm. Math. Phys. 293:2 (2010) 519–543 (doi:10.1007/s00220-009-0916-z).
• F. Benmansour, G. Carlier, G. Peyré and F. Santambrogio, Derivatives with respect to metrics and applications: Subgradient marching algorithm, Numerische Mathematik 116:3 (2010) 357–381 (doi:10.1007/s00211-010-0305-8, preprint of the Research Group in Calculus of Variations and Geometric Measure Theory in Pisa: link).
• L. Brasco, G. Buttazzo, F. Santambrogio, A Benamou–Brenier approach to branched transport, SIAM J. Math. Anal. 43:2 (2010) 1023–1040 (doi 10.1137/10079286X, preprint arXiv:1004.3358/hal-00474371).
• L. Brasco, G. Carlier and F. Santambrogio, Congested traffic dynamics, weak flows and very degenerate elliptic equations, J. Math. Pures et Appl. 93:6 (2010) 652–671 (doi:10.1016/j.matpur.2010.03.010, preprint hal-00417462).
• G. Carlier, M. Comte, I. Ionescu, G. Peyré, A Projection Approach to the Numerical Analysis of Limit Load Problems, Math. Models and Methods Appl. Sci., forthcoming (doi 10.1142/S0218202511005325, preprint hal-00450000).
• G. Carlier, L. De Pascale, F. Santambrogio, A strategy for non-strictly convex transport costs and the example of ||x-y||^p in  R², Commun. Math. Sci. 8:4 (2010) 931–941 (article on Project Euclid; preprint arXiv:0909/2804).
• G. Carlier, A. Galichon, F. Santambrogio, From Knothe's transport to Brenier's map and a continuation method for optimal transport, SIAM J. Math. Anal. 41:6 (2010) 2554–2576 (doi:10.1137/080740647, preprint arXiv:0810.4153).
• S. B. S. D. Castro, I. S. Labouriau, O. Podvigina, A heteroclinic network in mode interaction with symmetry, Dynamical Systems 25 (2010) 359–396 (doi: 10.1080/14689367.2010.506183).
• S. Chakraborti, U. Frisch, S. S. Ray, Extended self-similarity works for the Burgers equation and why, J. Fluid Mech. 649 (2010) 275–285 (doi:10.1017/S0022112010000595, preprint arXiv:0912.2406).
• R. Chertovskih, S. M. A. Gama, O. Podvigina, V. Zheligovsky, Dependence of magnetic field generation by thermal convection on the rotation rate, Physica D 239:13 (2010) 1188–1209 (doi:10.1016/j.physd.2010.03.008, preprint arXiv:0908.1891).
• J. Delon, A. Desolneux, Stabilization of flicker-like effects in image sequences through local contrast correction, SIAM J. Imaging Sci. 3:4 (2010) 703&ndahs;734 (doi 10.1137/090766371, preprint hal-00407796).
• J. Delon, J. Salomon, A. Sobolevskii, Fast transport optimization for Monge costs on the circle SIAM J. Appl. Math. 70:7 (2010) 2239–2258 (doi:10.1137/090772708, preprint hal-00362834).
• J. Delon, J. Salomon, A. Sobolevski, Indicateurs d'appariement locaux pour le transport optimal en coût concave, ROADEF 2010 : 11ème congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision, Toulouse, 24–26 février 2010.
• J. Delon, J. Salomon, A. Sobolevskii, Local matching indicators for concave transport costs, C. R. Acad. Sci. Paris, Ser. I 348 (2010) 901–905 (doi:10.1016/j.crma.2010.07.010).
• H. A. Feldman, R. Watkins, and M. J. Hudson, Cosmic Flows on 100 Mpc/h Scales: Standardized Minimum Variance Bulk Flow, Shear and Octupole Moments Mon. Not. R. Astron. Soc. 392:2 (2010) 743–756 (doi:10.1111/j.1365-2966.2008.14089.x, preprint arXiv:0911.5516; M. Hudson's stay at IAP was supported by OTARIE).
• S. Ya. Gertsenshtein, V. A. Zheligovsky, V. A. Nechaev, O. M. Podvigina, R. A. Chertovskih, Hydromagnetic dynamo and stability of three-dimensional convective flows in a horizontal layer of a solution, Doklady Akademii Nauk 433:3 (2010) 341–345 (Russian); Doklady Physics 55:7 (2010) 367–371 (English, doi 10.1134/S1028335810070116).
• K. Khanin, S. Nechaev, G. Oshanin, A. Sobolevski, and O. Vasilyev, Ballistic deposition patterns beneath a growing Kardar-Parisi-Zhang interface, Phys. Rev. E 82 (2010) 061107 (doi:10.1103/PhysRevE.82.061107, preprint arXiv:1006.4576).
• K. Khanin, A. Sobolevski, Particle dynamics inside shocks in Hamilton–Jacobi equations, Theme Issue “Turbulent Mixing and Beyond,” Philosophical Transactions of Royal Society London A 368:1916 (2010) 1579-1593 (doi:10.1098/rsta.2009.0283, preprint arXiv:1001.0498).
• A. Lachapelle, J. Salomon, G. Turinici, A monotonic algorithm for a mean field games model in economics, Math. Models and Methods Appl. Sci. 20:4 (2010) 567–588 (doi:10.1142/S0218202510004349, preprint hal-00346214).
• G. Lavaux, R. Brent Tully, R. Mohayaee, S. Colombi, Cosmic flow from 2MASS redshift survey: The origin of CMB dipole and implications for ΛCDM cosmology Astrophys. J. 709 (2010) 483–498 (doi:10.1088/0004-637X/709/1/483, preprint arXiv:0810.3658).
• O.M. Podvigina, Stability of rolls in rotating magnetoconvection in a layer with no-slip electrically insulating horizontal boundaries, Phys. Rev. E. 81:5 (2010) 056322 (doi 10.1103/PhysRevE.81.056322).
• F. Santambrogio, A Modica–Mortola approximation for branched transport, C. R. Acad. Sci. Paris, Sér. I 348:15–16 (2010) 941–945 (doi 10.1016/j.crma.2010.07.016, preprint of CVGMT: link, extended version arXiv:0909.2930/hal-00417461).
• V. Zheligovsky, Mathematical theory of stability of magnetohydrodynamic regimes with respect to large-scale perturbations, Editorial URSS, Moscow, 2010 (in Russian).
• V. Zheligovsky, Generation of a symmetric magnetic field by thermal convection in a plane rotating layer, Magnetohydrodynamics 46:1 (2010) 3–22 (preprint arXiv:0906.5380).
• V. Zheligovsky, O. Podvigina, U. Frisch, The Monge–Ampère equation: various forms and numerical methods, J. Computational Physics 229:13 (2010) 5043–5061 (doi 10.1016/j.jcp.2010.03.025; preprint arXiv:0910.1301).

2010 preprints

• J. Delon, J. Salomon, A. Sobolevskii, Local matching indicators for concave transport costs, submitted (preprint hal-00525994).
• J. Rabin, J. Delon, Y. Gousseau, Artefact-free color and contrast modification (2010), submitted to IEEE Transactions on Image Processing, preprint hal-00505966.
• J. Rabin, J. Delon, Y. Gousseau, Regularization of Transportation Maps for Color and Contrast Modification, to appear in Proceedings of the International Conference on Image Processing (ICIP), 2010.

2011

• Y. Brenier, A modified least action principle allowing mass concentrations for the early Universe reconstruction problem, accepted in Confl. Math. (2011) (preprint hal-00488716).
• J. Colin, R. Mohayaee, S. Sarkar, A. Shafieloo, Probing the anisotropic local universe and beyond with SNe Ia data, Mon. Not. R. Astron. Soc. 414:1 (2011) 264–271 (doi 10.1111/j.1365-2966.2011.18402.x, preprint 1011.6292)
• A. D. Gilbert, Y. Ponty, V. Zheligovsky, Dissipative structures in a nonlinear dynamo, accepted in Geophys. Astrophys. Fluid Dynamics (2011) (preprint arXiv:1005.5259, doi 10.1080/03091929.2010.513332v).
• E. Oudet, F. Santambrogio, A Modica–Mortola approximation for branched transport and applications, Arch. Rat. Mech. Anal., published online 8 February 2011 (doi 10.1007/s00205-011-0402-6).
• O. Podvigina, The onset of convection in a rotating layer with an imposed magnetic field: dependence on the Prandtl numbers Physics of the Earth, no. 5 (2011) 73–77 (in Russian; Eng. transl.: Izvestiya, Physics of the Solid Earth, no. 5 (2011), 440–445; doi 10.1134/S1069351311040094, preprint arXiv:1102.4092).
• J. Rabin, J. Delon, Y. Gousseau, Transportation distances on the circle, J. Math. Imaging and Vision, published online (doi 10.1007/s10851-011-0284-0, preprint hal-00399832).
• S. S. Ray, U. Frisch, S. Nazarenko, and T. Matsumoto, Resonance phenomenon for the Galerkin-truncated Burgers and Euler equations, Phys. Rev. E 84 (2011) 016301 (doi 10.1103/PhysRevE.84.016301, preprint arXiv:1011.1826).
• M. Vogelsberger, R. Mohayaee, S. D. M. White, Nonspherical similarity solutions for dark halo formation, Mon. Not. R. Astron. Soc. (doi 10.1111/j.1365-2966.2011.18605.x, preprint arXiv:1007.4195).
• V. Zheligovsky, A priori bounds for Gevrey–Sobolev norms of space-periodic three-dimensional solutions to equations of hydrodynamic type, Adv. differential equations 16:9-10 (2011) 955–976 (preprint arXiv:1001.4237).
• V. A. Zheligovsky, Large-scale perturbations of magnetohydrodynamic regimes: linear and weakly nonlinear stability theory. Lecture Notes in Physics, vol. 829. Springer-Verlag, Heidelberg, 2011, in print. 330 pp.

2011 preprints

• J. Delon, J. Salomon, A. Sobolevski, Minimum-weight perfect matching for non-intrinsic distances on the line, submitted (preprint hal-00564173).
• C Jiménez, F Santambrogio, Optimal transportation for a quadratic cost with convex constraints and applications, preprint arXiv:1110.3237.
• G. Lavaux, M. Hudson, The 2M++ galaxy redshift catalogue, submitted (preprint arXiv:1105.6107).
• Yu Qingjuan, Lu Youjun, R. Mohayaee, J. Colin, The low frequency of dual AGNs versus the high merger rate of galaxies: A phenomenological model, preprint arXiv:1105.1963.