From large deviations to Wasserstein gradient flows in multiple dimensions

We study the large deviation rate functional for the empirical distribution of independent Brownian particles with drift. In one dimension, it has been shown by Adams, Dirr, Peletier and Zimmer that this functional is asymptotically equivalent (in the sense of $\Gamma$-convergence) to the Jordan-Kinderlehrer-Otto functional arising in the Wasserstein gradient flow structure of the Fokker-Planck equation. In higher dimensions, part of this statement (the lower bound) has been recently proved by Duong, Laschos and Renger, but the upper bound remained open, since the proof of Duong et al relies on regularity properties of optimal transport maps that are restricted to one dimension. In this note we present a new proof of the upper bound, thereby generalising the result of Adams et al to arbitrary dimensions

Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

This paper is devoted to a deeper understanding of the heat flow and to the refinement of calculus tools on metric measure spaces (X,d,m). Our main results are: - A general study of the relations between the Hopf-Lax semigroup and Hamilton-Jacobi equation in metric spaces (X,d). - The equivalence of the heat flow in L^2(X,m) generated by a suitable Dirichlet energy and the Wasserstein gradient flow of the relative entropy functional in the space of probability measures P(X). - The proof of density in energy of Lipschitz functions in the Sobolev space W^{1,2}(X,d,m). - A fine and very general analysis of the differentiability properties of a large class of Kantorovich potentials, in connection with the optimal transport problem. Our results apply in particular to spaces satisfying Ricci curvature bounds in the sense of Lott & Villani [30] and Sturm [39,40], and require neither the doubling property nor the validity of the local Poincar\'e inequality.Comment: Minor typos corrected and many small improvements added. Lemma 2.4, Lemma 2.10, Prop. 5.7, Rem. 5.8, Thm. 6.3 added. Rem. 4.7, Prop. 4.8, Prop. 4.15 and Thm 4.16 augmented/reenforced. Proof of Thm. 4.16 and Lemma 9.6 simplified. Thm. 8.6 corrected. A simpler axiomatization of weak gradients, still equivalent to all other ones, has been propose

Ricci curvature of finite Markov chains via convexity of the entropy

We study a new notion of Ricci curvature that applies to Markov chains on discrete spaces. This notion relies on geodesic convexity of the entropy and is analogous to the one introduced by Lott, Sturm, and Villani for geodesic measure spaces. In order to apply to the discrete setting, the role of the Wasserstein metric is taken over by a different metric, having the property that continuous time Markov chains are gradient flows of the entropy. Using this notion of Ricci curvature we prove discrete analogues of fundamental results by Bakry--Emery and Otto--Villani. Furthermore we show that Ricci curvature bounds are preserved under tensorisation. As a special case we obtain the sharp Ricci curvature lower bound for the discrete hypercube.Comment: 39 pages, to appear in Arch. Ration. Mech. Ana

Nipah Virus Infects Specific Subsets of Porcine Peripheral Blood Mononuclear Cells

Nipah virus (NiV), a zoonotic paramyxovirus, is highly contagious in swine, and can cause fatal infections in humans following transmission from the swine host. The main viral targets in both species are the respiratory and central nervous systems, with viremia implicated as a mode of dissemination of NiV throughout the host. The presented work focused on the role of peripheral blood mononuclear cells (PBMC) in the viremic spread of the virus in the swine host. B lymphocytes, CD4−CD8−, as well as CD4+CD8− T lymphocytes were not permissive to NiV, and expansion of the CD4+CD8− cells early post infection was consistent with functional humoral response to NiV infection observed in swine. In contrast, significant drop in the CD4+CD8− T cell frequency was observed in piglets which succumbed to the experimental infection, supporting the hypothesis that antibody development is the critical component of the protective immune response. Productive viral replication was detected in monocytes, CD6+CD8+ T lymphocytes and NK cells by recovery of infectious virus in the cell supernatants. Virus replication was supported by detection of the structural N and the non-structural C proteins or by detection of genomic RNA increase in the infected cells. Infection of T cells carrying CD6 marker, a strong ligand for the activated leukocyte cell adhesion molecule ALCAM (CD166) highly expressed on the microvascular endothelial cell of the blood-air and the blood-brain barrier may explain NiV preferential tropism for small blood vessels of the lung and brain

A Human Lung Xenograft Mouse Model of Nipah Virus Infection

Nipah virus (NiV) is a member of the genus Henipavirus (family Paramyxoviridae) that causes severe and often lethal respiratory illness and encephalitis in humans with high mortality rates (up to 92%). NiV can cause Acute Lung Injury (ALI) in humans, and human-to-human transmission has been observed in recent outbreaks of NiV. While the exact route of transmission to humans is not known, we have previously shown that NiV can efficiently infect human respiratory epithelial cells. The molecu

Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy

Erbar M, Huesmann M, Jalowy J, M\ B. Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy. arXiv:2304.11145. 2023