Fetching the paper…
Reading the bibliography…
In this note, we propose an unbalanced version of the quantum mechanical version of optimal mass transport that was based on the Lindblad equation.
L. V. Kantorovich, “On a problem of Monge,” Uspekhi Mat. Nauk
1948
Earlier work this paper cites.
Uhlmann, Armin, “The metric of Bures and the geometric phase,” Groups and related Topics
1992
Earlier work this paper cites.
R. McCann, “A convexity principle for interacting gases,” Adv. Math. 128
1997
Earlier work this paper cites.
R. Jordan, D. Kinderlehrer, and F. Otto, “The variational formulation of the Fokker-Planck equation,” SIAM J. Math. Anal
1998
Earlier work this paper cites.
S. Rachev and L. Rüschendorf, Mass Transportation Problems
1998
Earlier work this paper cites.
J.-D. Benamou and Y. Brenier, “A computational fluid mechanics solution to the Monge–Kantorovich mass transfer problem,” Numerische Mathematik
2000
Earlier work this paper cites.
F. Otto, “The geometry of dissipative evolution equations: the porous medium equation,” Communications in Partial Differential Equations
2001
Earlier work this paper cites.
C. Villani, Topics in Optimal Transportation,
2003
Cited alongside, same era.
U. Alon, An Introduction to Systems Biology: Design Principles of Biological Circuits
2006
Cited alongside, same era.
Y. Olliver, “Ricci curvature of Markov chains on metric spaces,” J. Funct. Anal. 256
2009
Cited alongside, same era.
J.-D. Benamou, “Numerical resolution of an unbalanced mass transport problem,” ESAIM: Mathematical Modelling and Numerical Analysis
2010
Cited alongside, same era.
E. Tannenbaum, T. Georgiou, and A. Tannenbaum, A., “Signals and control aspects of optimal mass transport and the Boltzmann entropy,” in 49th IEEE Conference on Decision and Control (CDC)
2010
Cited alongside, same era.
2015
Later among the works it cites.
L. Ning, T. Georgiou, and A. Tannenbaum, “On matrix–valued Monge-Kantorovich optimal mass transport,” IEEE Transactions on Automatic Control
2015
Later among the works it cites.
R.Sandhu, T. Georgiou, E. Reznik, L. Zhu, I. Kolesov, Y. Senbabaoglu, and A. Tannenbaum1, “Graph curvature for differentiating cancer networks,” Scientific Reports (Nature) , vol. 5, 12323; doi: 10.1038/srep12323 (2015)
2015
Later among the works it cites.
2016
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
S. Gustafson and I. M. Sigal, Mathematical Concepts of Quantum Mechanics
2011
Cited alongside, same era.
M. Mueller, P. Karasev, I. Kolesov, and A. Tannenbaum, “Optical flow estimation for flame detection in videos,” IEEE Trans. Image Processing
2013
Cited alongside, same era.
E. Carlen and J. Maas, “An analog of the 2-Wasserstein metric in non-commutative probability under which the fermionic Fokker-Planck equation is gradient flow for the entropy,” Commun. Math. Phys
Cited in the paper.
F. Hiai, D. Petz, G.Toth, “Curvature in the geometry of canonical correlation,” Studia Sci. Math. Hungar
Cited in the paper.
Y. Chen, T. T. Georgiou, M. Pavon, “On the relation between optimal transport and Schrödinger bridges: A stochastic control viewpoint,” Journal of Optimization Theory and Applications
2016
Closest in time.
2016
Closest in time.
R. Sandhu, T. Georgiou, and A. Tannenbaum, “Ricci curvature: An economic indicator for market fragility and systemic risk,” Science Advances
2016
Closest in time.