@unpublished{14703,
  abstract     = {We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when the temporal and spatial stepsize vanish. This convergence result does not require any regularity assumption on the measures, though experiments suggest that the rate is not sharp. Via an analysis of the duality gap we also obtain the convergence rates for the gradient of the optimal potentials and the velocity field under mild regularity assumptions. To obtain such rates we discretize the dual formulation of the dynamic optimal transport problem and use the mature literature related to the error due to discretizing the Hamilton-Jacobi equation.},
  author       = {Ishida, Sadashige and Lavenant, Hugo},
  booktitle    = {arXiv},
  keywords     = {Optimal transport, Hamilton-Jacobi equation, convex optimization},
  title        = {{Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation}},
  doi          = {10.48550/arXiv.2312.12213},
  year         = {2023},
}

@inproceedings{10553,
  abstract     = {The popularity of permissioned blockchain systems demands BFT SMR protocols that are efficient under good network conditions (synchrony) and robust under bad network conditions (asynchrony). The state-of-the-art partially synchronous BFT SMR protocols provide optimal linear communication cost per decision under synchrony and good leaders, but lose liveness under asynchrony. On the other hand, the state-of-the-art asynchronous BFT SMR protocols are live even under asynchrony, but always pay quadratic cost even under synchrony. In this paper, we propose a BFT SMR protocol that achieves the best of both worlds -- optimal linear cost per decision under good networks and leaders, optimal quadratic cost per decision under bad networks, and remains always live.},
  author       = {Gelashvili, Rati and Kokoris Kogias, Eleftherios and Spiegelman, Alexander and Xiang, Zhuolun},
  booktitle    = {Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing},
  isbn         = {9-781-4503-8548-0},
  keywords     = {optimal, state machine replication, fallback, asynchrony, byzantine faults},
  location     = {Virtual, Italy},
  pages        = {187--190},
  publisher    = {Association for Computing Machinery},
  title        = {{Brief announcement: Be prepared when network goes bad: An asynchronous view-change protocol}},
  doi          = {10.1145/3465084.3467941},
  year         = {2021},
}