@inproceedings{15082, abstract = {Two plane drawings of geometric graphs on the same set of points are called disjoint compatible if their union is plane and they do not have an edge in common. For a given set S of 2n points two plane drawings of perfect matchings M1 and M2 (which do not need to be disjoint nor compatible) are disjoint tree-compatible if there exists a plane drawing of a spanning tree T on S which is disjoint compatible to both M1 and M2. We show that the graph of all disjoint tree-compatible perfect geometric matchings on 2n points in convex position is connected if and only if 2n ≥ 10. Moreover, in that case the diameter of this graph is either 4 or 5, independent of n.}, author = {Aichholzer, Oswin and Obmann, Julia and Patak, Pavel and Perz, Daniel and Tkadlec, Josef}, booktitle = {36th European Workshop on Computational Geometry}, location = {Würzburg, Germany, Virtual}, title = {{Disjoint tree-compatible plane perfect matchings}}, year = {2020}, } @inproceedings{15086, abstract = {Many communication-efficient variants of SGD use gradient quantization schemes. These schemes are often heuristic and fixed over the course of training. We empirically observe that the statistics of gradients of deep models change during the training. Motivated by this observation, we introduce two adaptive quantization schemes, ALQ and AMQ. In both schemes, processors update their compression schemes in parallel by efficiently computing sufficient statistics of a parametric distribution. We improve the validation accuracy by almost 2% on CIFAR-10 and 1% on ImageNet in challenging low-cost communication setups. Our adaptive methods are also significantly more robust to the choice of hyperparameters. }, author = {Faghri, Fartash and Tabrizian, Iman and Markov, Ilia and Alistarh, Dan-Adrian and Roy, Daniel and Ramezani-Kebrya, Ali }, booktitle = {Advances in Neural Information Processing Systems}, isbn = {9781713829546}, location = {Vancouver, Canada}, publisher = {Neural Information Processing Systems Foundation}, title = {{Adaptive gradient quantization for data-parallel SGD}}, volume = {33}, year = {2020}, } @article{15286, author = {Fäßler, Florian and Dimchev, Georgi A and Hodirnau, Victor-Valentin and Zens, Bettina and Möhl, Christoph and Bradke, Frank and Schur, Florian KM}, issn = {1435-8115}, journal = {Microscopy and Microanalysis}, keywords = {Instrumentation}, number = {S2}, pages = {2518--2519}, publisher = {Oxford University Press}, title = {{Cryo-electron tomography workflows for quantitative analysis of actin networks involved in cell migration}}, doi = {10.1017/s1431927620021881}, volume = {26}, year = {2020}, } @article{19306, author = {Kazatskaya, Anna and Yuan, Lisa and Amin-Wetzel, Niko Paresh and Philbrook, Alison and de Bono, Mario and Sengupta, Piali}, issn = {2578-9430}, journal = {microPublication Biology}, number = {9}, publisher = {Caltech Library}, title = {{The URX oxygen-sensing neurons in C. elegans are ciliated}}, doi = {10.17912/MICROPUB.BIOLOGY.000303}, volume = {2020}, year = {2020}, } @article{5681, abstract = {We introduce dynamically warping grids for adaptive liquid simulation. Our primary contributions are a strategy for dynamically deforming regular grids over the course of a simulation and a method for efficiently utilizing these deforming grids for liquid simulation. Prior work has shown that unstructured grids are very effective for adaptive fluid simulations. However, unstructured grids often lead to complicated implementations and a poor cache hit rate due to inconsistent memory access. Regular grids, on the other hand, provide a fast, fixed memory access pattern and straightforward implementation. Our method combines the advantages of both: we leverage the simplicity of regular grids while still achieving practical and controllable spatial adaptivity. We demonstrate that our method enables adaptive simulations that are fast, flexible, and robust to null-space issues. At the same time, our method is simple to implement and takes advantage of existing highly-tuned algorithms.}, author = {Hikaru, Ibayashi and Wojtan, Christopher J and Thuerey, Nils and Igarashi, Takeo and Ando, Ryoichi}, issn = {1941-0506}, journal = {IEEE Transactions on Visualization and Computer Graphics}, number = {6}, pages = {2288--2302}, publisher = {IEEE}, title = {{Simulating liquids on dynamically warping grids}}, doi = {10.1109/TVCG.2018.2883628}, volume = {26}, year = {2020}, } @article{6184, abstract = {We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal edges of the self-consistent density of states. In particular, we establish a strong form of band rigidity which excludes mismatches between location and label of eigenvalues close to internal edges in these general models.}, author = {Alt, Johannes and Erdös, László and Krüger, Torben H and Schröder, Dominik J}, issn = {0091-1798}, journal = {Annals of Probability}, number = {2}, pages = {963--1001}, publisher = {Institute of Mathematical Statistics}, title = {{Correlated random matrices: Band rigidity and edge universality}}, doi = {10.1214/19-AOP1379}, volume = {48}, year = {2020}, } @article{6185, abstract = {For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are universal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner–Dyson–Mehta universality conjecture for the last remaining universality type in the complex Hermitian class. Our analysis holds not only for exact cusps, but approximate cusps as well, where an extended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp for both symmetry classes. This result is also the key input in the companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where the cusp universality for real symmetric Wigner-type matrices is proven. The novel cusp fluctuation mechanism is also essential for the recent results on the spectral radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian edge universality (Cipolloni et al. in Edge universality for non-Hermitian random matrices, 2019. arXiv:1908.00969).}, author = {Erdös, László and Krüger, Torben H and Schröder, Dominik J}, issn = {1432-0916}, journal = {Communications in Mathematical Physics}, pages = {1203--1278}, publisher = {Springer Nature}, title = {{Cusp universality for random matrices I: Local law and the complex Hermitian case}}, doi = {10.1007/s00220-019-03657-4}, volume = {378}, year = {2020}, } @article{6358, abstract = {We study dynamical optimal transport metrics between density matricesassociated to symmetric Dirichlet forms on finite-dimensional C∗-algebras. Our settingcovers arbitrary skew-derivations and it provides a unified framework that simultaneously generalizes recently constructed transport metrics for Markov chains, Lindblad equations, and the Fermi Ornstein–Uhlenbeck semigroup. We develop a non-nommutative differential calculus that allows us to obtain non-commutative Ricci curvature bounds, logarithmic Sobolev inequalities, transport-entropy inequalities, andspectral gap estimates.}, author = {Carlen, Eric A. and Maas, Jan}, issn = {1572-9613}, journal = {Journal of Statistical Physics}, number = {2}, pages = {319--378}, publisher = {Springer Nature}, title = {{Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems}}, doi = {10.1007/s10955-019-02434-w}, volume = {178}, year = {2020}, } @article{6359, abstract = {The strong rate of convergence of the Euler-Maruyama scheme for nondegenerate SDEs with irregular drift coefficients is considered. In the case of α-Hölder drift in the recent literature the rate α/2 was proved in many related situations. By exploiting the regularising effect of the noise more efficiently, we show that the rate is in fact arbitrarily close to 1/2 for all α>0. The result extends to Dini continuous coefficients, while in d=1 also to all bounded measurable coefficients.}, author = {Dareiotis, Konstantinos and Gerencser, Mate}, issn = {1083-6489}, journal = {Electronic Journal of Probability}, publisher = {Institute of Mathematical Statistics}, title = {{On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift}}, doi = {10.1214/20-EJP479}, volume = {25}, year = {2020}, } @inbook{19986, abstract = {For non-probabilistic programs, a key question in static analysis is termination, which asks whether a given program terminates under a given initial condition. In the presence of probabilistic behaviour, there are two fundamental extensions of the termination question: (a) the almost-sure termination question, which asks whether the termination probability is 1; and (b) the bounded-time termination question, which asks whether the expected termination time is bounded. There are many active research directions to address these two questions; one important such direction is the use of martingale theory for termination analysis. In this chapter, we survey the main techniques of the martingale-based approach to the termination analysis of probabilistic programs.}, author = {Chatterjee, Krishnendu and Fu, Hongfei and Novotný, Petr}, booktitle = {Foundations of Probabilistic Programming}, isbn = {9781108488518}, pages = {221--258}, publisher = {Cambridge University Press}, title = {{Termination Analysis of Probabilistic Programs with Martingales}}, doi = {10.1017/9781108770750.008}, year = {2020}, } @unpublished{10012, abstract = {We prove that in the absence of topological changes, the notion of BV solutions to planar multiphase mean curvature flow does not allow for a mechanism for (unphysical) non-uniqueness. Our approach is based on the local structure of the energy landscape near a classical evolution by mean curvature. Mean curvature flow being the gradient flow of the surface energy functional, we develop a gradient-flow analogue of the notion of calibrations. Just like the existence of a calibration guarantees that one has reached a global minimum in the energy landscape, the existence of a "gradient flow calibration" ensures that the route of steepest descent in the energy landscape is unique and stable.}, author = {Fischer, Julian L and Hensel, Sebastian and Laux, Tim and Simon, Thilo}, booktitle = {arXiv}, title = {{The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions}}, doi = {10.48550/arXiv.2003.05478}, year = {2020}, } @unpublished{10022, abstract = {We consider finite-volume approximations of Fokker-Planck equations on bounded convex domains in R^d and study the corresponding gradient flow structures. We reprove the convergence of the discrete to continuous Fokker-Planck equation via the method of Evolutionary Γ-convergence, i.e., we pass to the limit at the level of the gradient flow structures, generalising the one-dimensional result obtained by Disser and Liero. The proof is of variational nature and relies on a Mosco convergence result for functionals in the discrete-to-continuum limit that is of independent interest. Our results apply to arbitrary regular meshes, even though the associated discrete transport distances may fail to converge to the Wasserstein distance in this generality.}, author = {Forkert, Dominik L and Maas, Jan and Portinale, Lorenzo}, booktitle = {arXiv}, title = {{Evolutionary Γ-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions}}, doi = {10.48550/arXiv.2008.10962}, year = {2020}, } @inproceedings{10328, abstract = {We discus noise channels in coherent electro-optic up-conversion between microwave and optical fields, in particular due to optical heating. We also report on a novel configuration, which promises to be flexible and highly efficient.}, author = {Lambert, Nicholas J. and Mobassem, Sonia and Rueda Sanchez, Alfredo R and Schwefel, Harald G.L.}, booktitle = {OSA Quantum 2.0 Conference}, isbn = {9-781-5575-2820-9}, location = {Washington, DC, United States}, publisher = {Optica Publishing Group}, title = {{New designs and noise channels in electro-optic microwave to optical up-conversion}}, doi = {10.1364/QUANTUM.2020.QTu8A.1}, year = {2020}, } @inproceedings{10556, abstract = {In this paper, we present the first Asynchronous Distributed Key Generation (ADKG) algorithm which is also the first distributed key generation algorithm that can generate cryptographic keys with a dual (f,2f+1)-threshold (where f is the number of faulty parties). As a result, using our ADKG we remove the trusted setup assumption that the most scalable consensus algorithms make. In order to create a DKG with a dual (f,2f+1)- threshold we first answer in the affirmative the open question posed by Cachin et al. [7] on how to create an Asynchronous Verifiable Secret Sharing (AVSS) protocol with a reconstruction threshold of f+1