= 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}, } @inproceedings{7807, abstract = {In a straight-line embedded triangulation of a point set P in the plane, removing an inner edge and—provided the resulting quadrilateral is convex—adding the other diagonal is called an edge flip. The (edge) flip graph has all triangulations as vertices, and a pair of triangulations is adjacent if they can be obtained from each other by an edge flip. The goal of this paper is to contribute to a better understanding of the flip graph, with an emphasis on its connectivity. For sets in general position, it is known that every triangulation allows at least edge flips (a tight bound) which gives the minimum degree of any flip graph for n points. We show that for every point set P in general position, the flip graph is at least -vertex connected. Somewhat more strongly, we show that the vertex connectivity equals the minimum degree occurring in the flip graph, i.e. the minimum number of flippable edges in any triangulation of P, provided P is large enough. Finally, we exhibit some of the geometry of the flip graph by showing that the flip graph can be covered by 1-skeletons of polytopes of dimension (products of associahedra). A corresponding result ((n – 3)-vertex connectedness) can be shown for the bistellar flip graph of partial triangulations, i.e. the set of all triangulations of subsets of P which contain all extreme points of P. This will be treated separately in a second part.}, author = {Wagner, Uli and Welzl, Emo}, booktitle = {Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms}, isbn = {9781611975994}, location = {Salt Lake City, UT, United States}, pages = {2823--2841}, publisher = {SIAM}, title = {{Connectivity of triangulation flip graphs in the plane (Part I: Edge flips)}}, doi = {10.1137/1.9781611975994.172}, volume = {2020-January}, year = {2020}, } @article{7814, abstract = {Scientific research is to date largely restricted to wealthy laboratories in developed nations due to the necessity of complex and expensive equipment. This inequality limits the capacity of science to be used as a diplomatic channel. Maker movements use open-source technologies including additive manufacturing (3D printing) and laser cutting, together with low-cost computers for developing novel products. This movement is setting the groundwork for a revolution, allowing scientific equipment to be sourced at a fraction of the cost and has the potential to increase the availability of equipment for scientists around the world. Science education is increasingly recognized as another channel for science diplomacy. In this perspective, we introduce the idea that the Maker movement and open-source technologies have the potential to revolutionize science, technology, engineering and mathematics (STEM) education worldwide. We present an open-source STEM didactic tool called SCOPES (Sparking Curiosity through Open-source Platforms in Education and Science). SCOPES is self-contained, independent of local resources, and cost-effective. SCOPES can be adapted to communicate complex subjects from genetics to neurobiology, perform real-world biological experiments and explore digitized scientific samples. We envision such platforms will enhance science diplomacy by providing a means for scientists to share their findings with classrooms and for educators to incorporate didactic concepts into STEM lessons. By providing students the opportunity to design, perform, and share scientific experiments, students also experience firsthand the benefits of a multinational scientific community. We provide instructions on how to build and use SCOPES on our webpage: http://scopeseducation.org.}, author = {Beattie, Robert J and Hippenmeyer, Simon and Pauler, Florian}, issn = {2504-284X}, journal = {Frontiers in Education}, publisher = {Frontiers Media}, title = {{SCOPES: Sparking curiosity through Open-Source platforms in education and science}}, doi = {10.3389/feduc.2020.00048}, volume = {5}, year = {2020}, } @article{6563, abstract = {This paper presents two algorithms. The first decides the existence of a pointed homotopy between given simplicial maps 𝑓,𝑔:𝑋→𝑌, and the second computes the group [𝛴𝑋,𝑌]∗ of pointed homotopy classes of maps from a suspension; in both cases, the target Y is assumed simply connected. More generally, these algorithms work relative to 𝐴⊆𝑋.}, author = {Filakovský, Marek and Vokřínek, Lukas}, issn = {16153383}, journal = {Foundations of Computational Mathematics}, pages = {311--330}, publisher = {Springer Nature}, title = {{Are two given maps homotopic? An algorithmic viewpoint}}, doi = {10.1007/s10208-019-09419-x}, volume = {20}, year = {2020}, } @article{6796, abstract = {Nearby grid cells have been observed to express a remarkable degree of long-rangeorder, which is often idealized as extending potentially to infinity. Yet their strict peri-odic firing and ensemble coherence are theoretically possible only in flat environments, much unlike the burrows which rodents usually live in. Are the symmetrical, coherent grid maps inferred in the lab relevant to chart their way in their natural habitat? We consider spheres as simple models of curved environments and waiting for the appropriate experiments to be performed, we use our adaptation model to predict what grid maps would emerge in a network with the same type of recurrent connections, which on the plane produce coherence among the units. We find that on the sphere such connections distort the maps that single grid units would express on their own, and aggregate them into clusters. When remapping to a different spherical environment, units in each cluster maintain only partial coherence, similar to what is observed in disordered materials, such as spin glasses.}, author = {Stella, Federico and Urdapilleta, Eugenio and Luo, Yifan and Treves, Alessandro}, issn = {10981063}, journal = {Hippocampus}, number = {4}, pages = {302--313}, publisher = {Wiley}, title = {{Partial coherence and frustration in self-organizing spherical grids}}, doi = {10.1002/hipo.23144}, volume = {30}, year = {2020}, }