= 1. Along the argument, we prove Mosco- and I-convergence results for discrete energy functionals, which are of independent interest for convergence of equivalent gradient flow structures in Hilbert spaces. The second part investigates L2-Wasserstein flows on metric graph. The starting point is a Benamou-Brenier formula for the L2-Wasserstein distance, which is proved via a regularisation scheme for solutions of the continuity equation, adapted to the peculiar geometric structure of metric graphs. Based on those results, we show that the L2-Wasserstein space over a metric graph admits a gradient flow which may be identified as a solution of a Fokker-Planck equation. In the third part, we focus again on the discrete gradient flows, already encountered in the first part. We propose a variational structure which extends the gradient flow structure to Markov chains violating the detailed-balance conditions. Using this structure, we characterise contraction estimates for the discrete heat flow in terms of convexity of corresponding path-dependent energy functionals. In addition, we use this approach to derive several functional inequalities for said functionals.}, author = {Forkert, Dominik L}, issn = {2663-337X}, pages = {154}, publisher = {IST Austria}, title = {{Gradient flows in spaces of probability measures for finite-volume schemes, metric graphs and non-reversible Markov chains}}, doi = {10.15479/AT:ISTA:7629}, year = {2020}, } @article{7686, abstract = {The agricultural green revolution spectacularly enhanced crop yield and lodging resistance with modified DELLA-mediated gibberellin signaling. However, this was achieved at the expense of reduced nitrogen-use efficiency (NUE). Recently, Wu et al. revealed novel gibberellin signaling that provides a blueprint for improving tillering and NUE in Green Revolution varieties (GRVs). }, author = {Xue, Huidan and Zhang, Yuzhou and Xiao, Guanghui}, issn = {13601385}, journal = {Trends in Plant Science}, publisher = {Elsevier}, title = {{Neo-gibberellin signaling: Guiding the next generation of the green revolution}}, doi = {10.1016/j.tplants.2020.04.001}, year = {2020}, } @inproceedings{7802, abstract = {The Massively Parallel Computation (MPC) model is an emerging model which distills core aspects of distributed and parallel computation. It has been developed as a tool to solve (typically graph) problems in systems where the input is distributed over many machines with limited space. Recent work has focused on the regime in which machines have sublinear (in $n$, the number of nodes in the input graph) space, with randomized algorithms presented for fundamental graph problems of Maximal Matching and Maximal Independent Set. However, there have been no prior corresponding deterministic algorithms. A major challenge underlying the sublinear space setting is that the local space of each machine might be too small to store all the edges incident to a single node. This poses a considerable obstacle compared to the classical models in which each node is assumed to know and have easy access to its incident edges. To overcome this barrier we introduce a new graph sparsification technique that deterministically computes a low-degree subgraph with additional desired properties. The degree of the nodes in this subgraph is small in the sense that the edges of each node can be now stored on a single machine. This low-degree subgraph also has the property that solving the problem on this subgraph provides \emph{significant} global progress, i.e., progress towards solving the problem for the original input graph. Using this framework to derandomize the well-known randomized algorithm of Luby [SICOMP'86], we obtain $O(\log \Delta+\log\log n)$-round deterministic MPC algorithms for solving the fundamental problems of Maximal Matching and Maximal Independent Set with $O(n^{\epsilon})$ space on each machine for any constant $\epsilon > 0$. Based on the recent work of Ghaffari et al. [FOCS'18], this additive $O(\log\log n)$ factor is conditionally essential. These algorithms can also be shown to run in $O(\log \Delta)$ rounds in the closely related model of CONGESTED CLIQUE, improving upon the state-of-the-art bound of $O(\log^2 \Delta)$ rounds by Censor-Hillel et al. [DISC'17].}, author = {Czumaj, Artur and Davies, Peter and Parter, Merav}, booktitle = {Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2020)}, location = {Philadelphia, PA, United States}, publisher = {Association for Computing Machinery}, title = {{Graph sparsification for derandomizing massively parallel computation with low space}}, year = {2020}, }