@inproceedings{14188, abstract = {Intelligent agents should be able to learn useful representations by observing changes in their environment. We model such observations as pairs of non-i.i.d. images sharing at least one of the underlying factors of variation. First, we theoretically show that only knowing how many factors have changed, but not which ones, is sufficient to learn disentangled representations. Second, we provide practical algorithms that learn disentangled representations from pairs of images without requiring annotation of groups, individual factors, or the number of factors that have changed. Third, we perform a large-scale empirical study and show that such pairs of observations are sufficient to reliably learn disentangled representations on several benchmark data sets. Finally, we evaluate our learned representations and find that they are simultaneously useful on a diverse suite of tasks, including generalization under covariate shifts, fairness, and abstract reasoning. Overall, our results demonstrate that weak supervision enables learning of useful disentangled representations in realistic scenarios.}, author = {Locatello, Francesco and Poole, Ben and Rätsch, Gunnar and Schölkopf, Bernhard and Bachem, Olivier and Tschannen, Michael}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, location = {Virtual}, pages = {6348–6359}, title = {{Weakly-supervised disentanglement without compromises}}, volume = {119}, year = {2020}, } @article{14195, abstract = {The idea behind the unsupervised learning of disentangled representations is that real-world data is generated by a few explanatory factors of variation which can be recovered by unsupervised learning algorithms. In this paper, we provide a sober look at recent progress in the field and challenge some common assumptions. We first theoretically show that the unsupervised learning of disentangled representations is fundamentally impossible without inductive biases on both the models and the data. Then, we train over 14000 models covering most prominent methods and evaluation metrics in a reproducible large-scale experimental study on eight data sets. We observe that while the different methods successfully enforce properties “encouraged” by the corresponding losses, well-disentangled models seemingly cannot be identified without supervision. Furthermore, different evaluation metrics do not always agree on what should be considered “disentangled” and exhibit systematic differences in the estimation. Finally, increased disentanglement does not seem to necessarily lead to a decreased sample complexity of learning for downstream tasks. Our results suggest that future work on disentanglement learning should be explicit about the role of inductive biases and (implicit) supervision, investigate concrete benefits of enforcing disentanglement of the learned representations, and consider a reproducible experimental setup covering several data sets.}, author = {Locatello, Francesco and Bauer, Stefan and Lucic, Mario and Rätsch, Gunnar and Gelly, Sylvain and Schölkopf, Bernhard and Bachem, Olivier}, journal = {Journal of Machine Learning Research}, publisher = {MIT Press}, title = {{A sober look at the unsupervised learning of disentangled representations and their evaluation}}, volume = {21}, year = {2020}, } @inproceedings{14326, abstract = {Learning object-centric representations of complex scenes is a promising step towards enabling efficient abstract reasoning from low-level perceptual features. Yet, most deep learning approaches learn distributed representations that do not capture the compositional properties of natural scenes. In this paper, we present the Slot Attention module, an architectural component that interfaces with perceptual representations such as the output of a convolutional neural network and produces a set of task-dependent abstract representations which we call slots. These slots are exchangeable and can bind to any object in the input by specializing through a competitive procedure over multiple rounds of attention. We empirically demonstrate that Slot Attention can extract object-centric representations that enable generalization to unseen compositions when trained on unsupervised object discovery and supervised property prediction tasks. }, author = {Locatello, Francesco and Weissenborn, Dirk and Unterthiner, Thomas and Mahendran, Aravindh and Heigold, Georg and Uszkoreit, Jakob and Dosovitskiy, Alexey and Kipf, Thomas}, booktitle = {Advances in Neural Information Processing Systems}, isbn = {9781713829546}, location = {Virtual}, pages = {11525--11538}, publisher = {Curran Associates}, title = {{Object-centric learning with slot attention}}, volume = {33}, year = {2020}, } @misc{14592, abstract = {Cryo-electron microscopy (cryo-EM) of cellular specimens provides insights into biological processes and structures within a native context. However, a major challenge still lies in the efficient and reproducible preparation of adherent cells for subsequent cryo-EM analysis. This is due to the sensitivity of many cellular specimens to the varying seeding and culturing conditions required for EM experiments, the often limited amount of cellular material and also the fragility of EM grids and their substrate. Here, we present low-cost and reusable 3D printed grid holders, designed to improve specimen preparation when culturing challenging cellular samples directly on grids. The described grid holders increase cell culture reproducibility and throughput, and reduce the resources required for cell culturing. We show that grid holders can be integrated into various cryo-EM workflows, including micro-patterning approaches to control cell seeding on grids, and for generating samples for cryo-focused ion beam milling and cryo-electron tomography experiments. Their adaptable design allows for the generation of specialized grid holders customized to a large variety of applications.}, author = {Schur, Florian KM}, publisher = {Institute of Science and Technology Austria}, title = {{STL-files for 3D-printed grid holders described in Fäßler F, Zens B, et al.; 3D printed cell culture grid holders for improved cellular specimen preparation in cryo-electron microscopy}}, doi = {10.15479/AT:ISTA:14592}, year = {2020}, } @article{14694, abstract = {We study the unique solution m of the Dyson equation \( -m(z)^{-1} = z\1 - a + S[m(z)] \) on a von Neumann algebra A with the constraint Imm≥0. Here, z lies in the complex upper half-plane, a is a self-adjoint element of A and S is a positivity-preserving linear operator on A. We show that m is the Stieltjes transform of a compactly supported A-valued measure on R. Under suitable assumptions, we establish that this measure has a uniformly 1/3-Hölder continuous density with respect to the Lebesgue measure, which is supported on finitely many intervals, called bands. In fact, the density is analytic inside the bands with a square-root growth at the edges and internal cubic root cusps whenever the gap between two bands vanishes. The shape of these singularities is universal and no other singularity may occur. We give a precise asymptotic description of m near the singular points. These asymptotics generalize the analysis at the regular edges given in the companion paper on the Tracy-Widom universality for the edge eigenvalue statistics for correlated random matrices [the first author et al., Ann. Probab. 48, No. 2, 963--1001 (2020; Zbl 1434.60017)] and they play a key role in the proof of the Pearcey universality at the cusp for Wigner-type matrices [G. Cipolloni et al., Pure Appl. Anal. 1, No. 4, 615--707 (2019; Zbl 07142203); the second author et al., Commun. Math. Phys. 378, No. 2, 1203--1278 (2020; Zbl 07236118)]. We also extend the finite dimensional band mass formula from [the first author et al., loc. cit.] to the von Neumann algebra setting by showing that the spectral mass of the bands is topologically rigid under deformations and we conclude that these masses are quantized in some important cases.}, author = {Alt, Johannes and Erdös, László and Krüger, Torben H}, issn = {1431-0643}, journal = {Documenta Mathematica}, keywords = {General Mathematics}, pages = {1421--1539}, publisher = {EMS Press}, title = {{The Dyson equation with linear self-energy: Spectral bands, edges and cusps}}, doi = {10.4171/dm/780}, volume = {25}, year = {2020}, } @article{14891, abstract = {We give the first mathematically rigorous justification of the local density approximation in density functional theory. We provide a quantitative estimate on the difference between the grand-canonical Levy–Lieb energy of a given density (the lowest possible energy of all quantum states having this density) and the integral over the uniform electron gas energy of this density. The error involves gradient terms and justifies the use of the local density approximation in the situation where the density is very flat on sufficiently large regions in space.}, author = {Lewin, Mathieu and Lieb, Elliott H. and Seiringer, Robert}, issn = {2578-5885}, journal = {Pure and Applied Analysis}, number = {1}, pages = {35--73}, publisher = {Mathematical Sciences Publishers}, title = {{ The local density approximation in density functional theory}}, doi = {10.2140/paa.2020.2.35}, volume = {2}, year = {2020}, } @article{15036, abstract = {The assembly of a septin filament requires that homologous monomers must distinguish between one another in establishing appropriate interfaces with their neighbors. To understand this phenomenon at the molecular level, we present the first four crystal structures of heterodimeric septin complexes. We describe in detail the two distinct types of G-interface present within the octameric particles, which must polymerize to form filaments. These are formed between SEPT2 and SEPT6 and between SEPT7 and SEPT3, and their description permits an understanding of the structural basis for the selectivity necessary for correct filament assembly. By replacing SEPT6 by SEPT8 or SEPT11, it is possible to rationalize Kinoshita's postulate, which predicts the exchangeability of septins from within a subgroup. Switches I and II, which in classical small GTPases provide a mechanism for nucleotide-dependent conformational change, have been repurposed in septins to play a fundamental role in molecular recognition. Specifically, it is switch I which holds the key to discriminating between the two different G-interfaces. Moreover, residues which are characteristic for a given subgroup play subtle, but pivotal, roles in guaranteeing that the correct interfaces are formed.}, author = {Rosa, Higor Vinícius Dias and Leonardo, Diego Antonio and Brognara, Gabriel and Brandão-Neto, José and D'Muniz Pereira, Humberto and Araújo, Ana Paula Ulian and Garratt, Richard Charles}, issn = {0022-2836}, journal = {Journal of Molecular Biology}, keywords = {Molecular Biology, Structural Biology}, number = {21}, pages = {5784--5801}, publisher = {Elsevier}, title = {{Molecular recognition at septin interfaces: The switches hold the key}}, doi = {10.1016/j.jmb.2020.09.001}, volume = {432}, year = {2020}, } @article{15037, abstract = {Protein abundance and localization at the plasma membrane (PM) shapes plant development and mediates adaptation to changing environmental conditions. It is regulated by ubiquitination, a post-translational modification crucial for the proper sorting of endocytosed PM proteins to the vacuole for subsequent degradation. To understand the significance and the variety of roles played by this reversible modification, the function of ubiquitin receptors, which translate the ubiquitin signature into a cellular response, needs to be elucidated. In this study, we show that TOL (TOM1-like) proteins function in plants as multivalent ubiquitin receptors, governing ubiquitinated cargo delivery to the vacuole via the conserved Endosomal Sorting Complex Required for Transport (ESCRT) pathway. TOL2 and TOL6 interact with components of the ESCRT machinery and bind to K63-linked ubiquitin via two tandemly arranged conserved ubiquitin-binding domains. Mutation of these domains results not only in a loss of ubiquitin binding but also altered localization, abolishing TOL6 ubiquitin receptor activity. Function and localization of TOL6 is itself regulated by ubiquitination, whereby TOL6 ubiquitination potentially modulates degradation of PM-localized cargoes, assisting in the fine-tuning of the delicate interplay between protein recycling and downregulation. Taken together, our findings demonstrate the function and regulation of a ubiquitin receptor that mediates vacuolar degradation of PM proteins in higher plants.}, author = {Moulinier-Anzola, Jeanette and Schwihla, Maximilian and De-Araújo, Lucinda and Artner, Christina and Jörg, Lisa and Konstantinova, Nataliia and Luschnig, Christian and Korbei, Barbara}, issn = {1674-2052}, journal = {Molecular Plant}, keywords = {Plant Science, Molecular Biology}, number = {5}, pages = {717--731}, publisher = {Elsevier}, title = {{TOLs function as ubiquitin receptors in the early steps of the ESCRT pathway in higher plants}}, doi = {10.1016/j.molp.2020.02.012}, volume = {13}, year = {2020}, } @article{15055, abstract = {Markov decision processes (MDPs) are the defacto framework for sequential decision making in the presence of stochastic uncertainty. A classical optimization criterion for MDPs is to maximize the expected discounted-sum payoff, which ignores low probability catastrophic events with highly negative impact on the system. On the other hand, risk-averse policies require the probability of undesirable events to be below a given threshold, but they do not account for optimization of the expected payoff. We consider MDPs with discounted-sum payoff with failure states which represent catastrophic outcomes. The objective of risk-constrained planning is to maximize the expected discounted-sum payoff among risk-averse policies that ensure the probability to encounter a failure state is below a desired threshold. Our main contribution is an efficient risk-constrained planning algorithm that combines UCT-like search with a predictor learned through interaction with the MDP (in the style of AlphaZero) and with a risk-constrained action selection via linear programming. We demonstrate the effectiveness of our approach with experiments on classical MDPs from the literature, including benchmarks with an order of 106 states.}, author = {Brázdil, Tomáš and Chatterjee, Krishnendu and Novotný, Petr and Vahala, Jiří}, issn = {2374-3468}, journal = {Proceedings of the 34th AAAI Conference on Artificial Intelligence}, keywords = {General Medicine}, location = {New York, NY, United States}, number = {06}, pages = {9794--9801}, publisher = {Association for the Advancement of Artificial Intelligence}, title = {{Reinforcement learning of risk-constrained policies in Markov decision processes}}, doi = {10.1609/aaai.v34i06.6531}, volume = {34}, year = {2020}, } @article{15057, abstract = {Vaccinia virus–related kinase (VRK) is an evolutionarily conserved nuclear protein kinase. VRK-1, the single Caenorhabditis elegans VRK ortholog, functions in cell division and germline proliferation. However, the role of VRK-1 in postmitotic cells and adult life span remains unknown. Here, we show that VRK-1 increases organismal longevity by activating the cellular energy sensor, AMP-activated protein kinase (AMPK), via direct phosphorylation. We found that overexpression of vrk-1 in the soma of adult C. elegans increased life span and, conversely, inhibition of vrk-1 decreased life span. In addition, vrk-1 was required for longevity conferred by mutations that inhibit C. elegans mitochondrial respiration, which requires AMPK. VRK-1 directly phosphorylated and up-regulated AMPK in both C. elegans and cultured human cells. Thus, our data show that the somatic nuclear kinase, VRK-1, promotes longevity through AMPK activation, and this function appears to be conserved between C. elegans and humans.}, author = {Park, Sangsoon and Artan, Murat and Han, Seung Hyun and Park, Hae-Eun H. and Jung, Yoonji and Hwang, Ara B. and Shin, Won Sik and Kim, Kyong-Tai and Lee, Seung-Jae V.}, issn = {2375-2548}, journal = {Science Advances}, number = {27}, publisher = {American Association for the Advancement of Science}, title = {{VRK-1 extends life span by activation of AMPK via phosphorylation}}, doi = {10.1126/sciadv.aaw7824}, volume = {6}, year = {2020}, } @inproceedings{15059, abstract = {In this paper we present a room temperature radiometer that can eliminate the need of using cryostats in satellite payload reducing its weight and improving reliability. The proposed radiometer is based on an electro-optic upconverter that boosts up microwave photons energy by upconverting them into an optical domain what makes them immune to thermal noise even if operating at room temperature. The converter uses a high-quality factor whispering gallery mode (WGM) resonator providing naturally narrow bandwidth and therefore might be useful for applications like microwave hyperspectral sensing. The upconversion process is explained by providing essential information about photon conversion efficiency and sensitivity. To prove the concept, we describe an experiment which shows state-of-the-art photon conversion efficiency n=10-5 per mW of pump power at the frequency of 80 GHz.}, author = {Wasiak, Michal and Botello, Gabriel Santamaria and Abdalmalak, Kerlos Atia and Sedlmeir, Florian and Rueda Sanchez, Alfredo R and Segovia-Vargas, Daniel and Schwefel, Harald G. L. and Munoz, Luis Enrique Garcia}, booktitle = {14th European Conference on Antennas and Propagation}, location = {Copenhagen, Denmark}, publisher = {IEEE}, title = {{Compact millimeter and submillimeter-wave photonic radiometer for cubesats}}, doi = {10.23919/eucap48036.2020.9135962}, year = {2020}, } @article{15061, abstract = {The actin cytoskeleton, a dynamic network of actin filaments and associated F-actin–binding proteins, is fundamentally important in eukaryotes. α-Actinins are major F-actin bundlers that are inhibited by Ca2+ in nonmuscle cells. Here we report the mechanism of Ca2+-mediated regulation of Entamoeba histolytica α-actinin-2 (EhActn2) with features expected for the common ancestor of Entamoeba and higher eukaryotic α-actinins. Crystal structures of Ca2+-free and Ca2+-bound EhActn2 reveal a calmodulin-like domain (CaMD) uniquely inserted within the rod domain. Integrative studies reveal an exceptionally high affinity of the EhActn2 CaMD for Ca2+, binding of which can only be regulated in the presence of physiological concentrations of Mg2+. Ca2+ binding triggers an increase in protein multidomain rigidity, reducing conformational flexibility of F-actin–binding domains via interdomain cross-talk and consequently inhibiting F-actin bundling. In vivo studies uncover that EhActn2 plays an important role in phagocytic cup formation and might constitute a new drug target for amoebic dysentery.}, author = {Pinotsis, Nikos and Zielinska, Karolina and Babuta, Mrigya and Arolas, Joan L. and Kostan, Julius and Khan, Muhammad Bashir and Schreiner, Claudia and Testa Salmazo, Anita P and Ciccarelli, Luciano and Puchinger, Martin and Gkougkoulia, Eirini A. and Ribeiro, Euripedes de Almeida and Marlovits, Thomas C. and Bhattacharya, Alok and Djinovic-Carugo, Kristina}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences}, number = {36}, pages = {22101--22112}, publisher = {Proceedings of the National Academy of Sciences}, title = {{Calcium modulates the domain flexibility and function of an α-actinin similar to the ancestral α-actinin}}, doi = {10.1073/pnas.1917269117}, volume = {117}, year = {2020}, } @article{15063, abstract = {We consider the least singular value of a large random matrix with real or complex i.i.d. Gaussian entries shifted by a constant z∈C. We prove an optimal lower tail estimate on this singular value in the critical regime where z is around the spectral edge, thus improving the classical bound of Sankar, Spielman and Teng (SIAM J. Matrix Anal. Appl. 28:2 (2006), 446–476) for the particular shift-perturbation in the edge regime. Lacking Brézin–Hikami formulas in the real case, we rely on the superbosonization formula (Comm. Math. Phys. 283:2 (2008), 343–395).}, author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J}, issn = {2690-1005}, journal = {Probability and Mathematical Physics}, keywords = {General Medicine}, number = {1}, pages = {101--146}, publisher = {Mathematical Sciences Publishers}, title = {{Optimal lower bound on the least singular value of the shifted Ginibre ensemble}}, doi = {10.2140/pmp.2020.1.101}, volume = {1}, year = {2020}, } @article{15064, abstract = {We call a continuous self-map that reveals itself through a discrete set of point-value pairs a sampled dynamical system. Capturing the available information with chain maps on Delaunay complexes, we use persistent homology to quantify the evidence of recurrent behavior. We establish a sampling theorem to recover the eigenspaces of the endomorphism on homology induced by the self-map. Using a combinatorial gradient flow arising from the discrete Morse theory for Čech and Delaunay complexes, we construct a chain map to transform the problem from the natural but expensive Čech complexes to the computationally efficient Delaunay triangulations. The fast chain map algorithm has applications beyond dynamical systems.}, author = {Bauer, U. and Edelsbrunner, Herbert and Jablonski, Grzegorz and Mrozek, M.}, issn = {2367-1734}, journal = {Journal of Applied and Computational Topology}, number = {4}, pages = {455--480}, publisher = {Springer Nature}, title = {{Čech-Delaunay gradient flow and homology inference for self-maps}}, doi = {10.1007/s41468-020-00058-8}, volume = {4}, year = {2020}, } @inproceedings{15074, abstract = {We introduce a new graph problem, the token dropping game, and we show how to solve it efficiently in a distributed setting. We use the token dropping game as a tool to design an efficient distributed algorithm for the stable orientation problem, which is a special case of the more general locally optimal semi-matching problem. The prior work by Czygrinow et al. (DISC 2012) finds a locally optimal semi-matching in O(Δ⁵) rounds in graphs of maximum degree Δ, which directly implies an algorithm with the same runtime for stable orientations. We improve the runtime to O(Δ⁴) for stable orientations and prove a lower bound of Ω(Δ) rounds.}, author = {Brandt, Sebastian and Keller, Barbara and Rybicki, Joel and Suomela, Jukka and Uitto, Jara}, booktitle = {34th International Symposium on Distributed Computing}, location = {Virtual}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Brief announcement: Efficient load-balancing through distributed token dropping}}, doi = {10.4230/LIPIcs.DISC.2020.40}, volume = {179}, year = {2020}, } @inproceedings{15077, abstract = {We consider the following dynamic load-balancing process: given an underlying graph G with n nodes, in each step t≥ 0, one unit of load is created, and placed at a randomly chosen graph node. In the same step, the chosen node picks a random neighbor, and the two nodes balance their loads by averaging them. We are interested in the expected gap between the minimum and maximum loads at nodes as the process progresses, and its dependence on n and on the graph structure. Variants of the above graphical balanced allocation process have been studied previously by Peres, Talwar, and Wieder [Peres et al., 2015], and by Sauerwald and Sun [Sauerwald and Sun, 2015]. These authors left as open the question of characterizing the gap in the case of cycle graphs in the dynamic case, where weights are created during the algorithm’s execution. For this case, the only known upper bound is of 𝒪(n log n), following from a majorization argument due to [Peres et al., 2015], which analyzes a related graphical allocation process. In this paper, we provide an upper bound of 𝒪 (√n log n) on the expected gap of the above process for cycles of length n. We introduce a new potential analysis technique, which enables us to bound the difference in load between k-hop neighbors on the cycle, for any k ≤ n/2. We complement this with a "gap covering" argument, which bounds the maximum value of the gap by bounding its value across all possible subsets of a certain structure, and recursively bounding the gaps within each subset. We provide analytical and experimental evidence that our upper bound on the gap is tight up to a logarithmic factor.}, author = {Alistarh, Dan-Adrian and Nadiradze, Giorgi and Sabour, Amirmojtaba}, booktitle = {47th International Colloquium on Automata, Languages, and Programming}, location = {Saarbrücken, Germany, Virtual}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Dynamic averaging load balancing on cycles}}, doi = {10.4230/LIPIcs.ICALP.2020.7}, volume = {168}, year = {2020}, } @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}, } @article{177, abstract = {We develop a geometric version of the circle method and use it to compute the compactly supported cohomology of the space of rational curves through a point on a smooth affine hypersurface of sufficiently low degree.}, author = {Browning, Timothy D and Sawin, Will}, journal = {Annals of Mathematics}, number = {3}, pages = {893--948}, publisher = {Princeton University}, title = {{A geometric version of the circle method}}, doi = {10.4007/annals.2020.191.3.4}, volume = {191}, year = {2020}, } @article{179, abstract = {An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariski dense subset of the biprojective hypersurface x1y21+⋯+x4y24=0 in ℙ3×ℙ3. This confirms the modified Manin conjecture for this variety, in which the removal of a thin set of rational points is allowed.}, author = {Browning, Timothy D and Heath Brown, Roger}, issn = {0012-7094}, journal = {Duke Mathematical Journal}, number = {16}, pages = {3099--3165}, publisher = {Duke University Press}, title = {{Density of rational points on a quadric bundle in ℙ3×ℙ3}}, doi = {10.1215/00127094-2020-0031}, volume = {169}, 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 = {19410506}, 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}, }