@article{7905, abstract = {We investigate a sheaf-theoretic interpretation of stratification learning from geometric and topological perspectives. Our main result is the construction of stratification learning algorithms framed in terms of a sheaf on a partially ordered set with the Alexandroff topology. We prove that the resulting decomposition is the unique minimal stratification for which the strata are homogeneous and the given sheaf is constructible. In particular, when we choose to work with the local homology sheaf, our algorithm gives an alternative to the local homology transfer algorithm given in Bendich et al. (Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1355–1370, ACM, New York, 2012), and the cohomology stratification algorithm given in Nanda (Found. Comput. Math. 20(2), 195–222, 2020). Additionally, we give examples of stratifications based on the geometric techniques of Breiding et al. (Rev. Mat. Complut. 31(3), 545–593, 2018), illustrating how the sheaf-theoretic approach can be used to study stratifications from both topological and geometric perspectives. This approach also points toward future applications of sheaf theory in the study of topological data analysis by illustrating the utility of the language of sheaf theory in generalizing existing algorithms.}, author = {Brown, Adam and Wang, Bei}, issn = {1432-0444}, journal = {Discrete and Computational Geometry}, pages = {1166--1198}, publisher = {Springer Nature}, title = {{Sheaf-theoretic stratification learning from geometric and topological perspectives}}, doi = {10.1007/s00454-020-00206-y}, volume = {65}, year = {2021}, } @article{7925, abstract = {In this paper, we introduce a relaxed CQ method with alternated inertial step for solving split feasibility problems. We give convergence of the sequence generated by our method under some suitable assumptions. Some numerical implementations from sparse signal and image deblurring are reported to show the efficiency of our method.}, author = {Shehu, Yekini and Gibali, Aviv}, issn = {1862-4480}, journal = {Optimization Letters}, pages = {2109--2126}, publisher = {Springer Nature}, title = {{New inertial relaxed method for solving split feasibilities}}, doi = {10.1007/s11590-020-01603-1}, volume = {15}, year = {2021}, } @article{7939, abstract = {We design fast deterministic algorithms for distance computation in the Congested Clique model. Our key contributions include: A (2+ϵ)-approximation for all-pairs shortest paths in O(log2n/ϵ) rounds on unweighted undirected graphs. With a small additional additive factor, this also applies for weighted graphs. This is the first sub-polynomial constant-factor approximation for APSP in this model. A (1+ϵ)-approximation for multi-source shortest paths from O(n−−√) sources in O(log2n/ϵ) rounds on weighted undirected graphs. This is the first sub-polynomial algorithm obtaining this approximation for a set of sources of polynomial size. Our main techniques are new distance tools that are obtained via improved algorithms for sparse matrix multiplication, which we leverage to construct efficient hopsets and shortest paths. Furthermore, our techniques extend to additional distance problems for which we improve upon the state-of-the-art, including diameter approximation, and an exact single-source shortest paths algorithm for weighted undirected graphs in O~(n1/6) rounds. }, author = {Censor-Hillel, Keren and Dory, Michal and Korhonen, Janne and Leitersdorf, Dean}, issn = {1432-0452}, journal = {Distributed Computing}, pages = {463--487}, publisher = {Springer Nature}, title = {{Fast approximate shortest paths in the congested clique}}, doi = {10.1007/s00446-020-00380-5}, volume = {34}, year = {2021}, } @inbook{7941, abstract = {Expansion microscopy is a recently developed super-resolution imaging technique, which provides an alternative to optics-based methods such as deterministic approaches (e.g. STED) or stochastic approaches (e.g. PALM/STORM). The idea behind expansion microscopy is to embed the biological sample in a swellable gel, and then to expand it isotropically, thereby increasing the distance between the fluorophores. This approach breaks the diffraction barrier by simply separating the emission point-spread-functions of the fluorophores. The resolution attainable in expansion microscopy is thus directly dependent on the separation that can be achieved, i.e. on the expansion factor. The original implementation of the technique achieved an expansion factor of fourfold, for a resolution of 70–80 nm. The subsequently developed X10 method achieves an expansion factor of 10-fold, for a resolution of 25–30 nm. This technique can be implemented with minimal technical requirements on any standard fluorescence microscope, and is more easily applied for multi-color imaging than either deterministic or stochastic super-resolution approaches. This renders X10 expansion microscopy a highly promising tool for new biological discoveries, as discussed here, and as demonstrated by several recent applications.}, author = {Truckenbrodt, Sven M and Rizzoli, Silvio O.}, booktitle = {Methods in Cell Biology}, isbn = {978012820807-6}, issn = {0091-679X}, pages = {33--56}, publisher = {Elsevier}, title = {{Simple multi-color super-resolution by X10 microscopy}}, doi = {10.1016/bs.mcb.2020.04.016}, volume = {161}, year = {2021}, } @article{8196, abstract = {This paper aims to obtain a strong convergence result for a Douglas–Rachford splitting method with inertial extrapolation step for finding a zero of the sum of two set-valued maximal monotone operators without any further assumption of uniform monotonicity on any of the involved maximal monotone operators. Furthermore, our proposed method is easy to implement and the inertial factor in our proposed method is a natural choice. Our method of proof is of independent interest. Finally, some numerical implementations are given to confirm the theoretical analysis.}, author = {Shehu, Yekini and Dong, Qiao-Li and Liu, Lu-Lu and Yao, Jen-Chih}, issn = {1573-2924}, journal = {Optimization and Engineering}, pages = {2627--2653}, publisher = {Springer Nature}, title = {{New strong convergence method for the sum of two maximal monotone operators}}, doi = {10.1007/s11081-020-09544-5}, volume = {22}, year = {2021}, } @article{14800, abstract = {Research on two-dimensional (2D) materials has been explosively increasing in last seventeen years in varying subjects including condensed matter physics, electronic engineering, materials science, and chemistry since the mechanical exfoliation of graphene in 2004. Starting from graphene, 2D materials now have become a big family with numerous members and diverse categories. The unique structural features and physicochemical properties of 2D materials make them one class of the most appealing candidates for a wide range of potential applications. In particular, we have seen some major breakthroughs made in the field of 2D materials in last five years not only in developing novel synthetic methods and exploring new structures/properties but also in identifying innovative applications and pushing forward commercialisation. In this review, we provide a critical summary on the recent progress made in the field of 2D materials with a particular focus on last five years. After a brief background introduction, we first discuss the major synthetic methods for 2D materials, including the mechanical exfoliation, liquid exfoliation, vapor phase deposition, and wet-chemical synthesis as well as phase engineering of 2D materials belonging to the field of phase engineering of nanomaterials (PEN). We then introduce the superconducting/optical/magnetic properties and chirality of 2D materials along with newly emerging magic angle 2D superlattices. Following that, the promising applications of 2D materials in electronics, optoelectronics, catalysis, energy storage, solar cells, biomedicine, sensors, environments, etc. are described sequentially. Thereafter, we present the theoretic calculations and simulations of 2D materials. Finally, after concluding the current progress, we provide some personal discussions on the existing challenges and future outlooks in this rapidly developing field. }, author = {Chang, Cheng and Chen, Wei and Chen, Ye and Chen, Yonghua and Chen, Yu and Ding, Feng and Fan, Chunhai and Fan, Hong Jin and Fan, Zhanxi and Gong, Cheng and Gong, Yongji and He, Qiyuan and Hong, Xun and Hu, Sheng and Hu, Weida and Huang, Wei and Huang, Yuan and Ji, Wei and Li, Dehui and Li, Lain Jong and Li, Qiang and Lin, Li and Ling, Chongyi and Liu, Minghua and Liu, Nan and Liu, Zhuang and Loh, Kian Ping and Ma, Jianmin and Miao, Feng and Peng, Hailin and Shao, Mingfei and Song, Li and Su, Shao and Sun, Shuo and Tan, Chaoliang and Tang, Zhiyong and Wang, Dingsheng and Wang, Huan and Wang, Jinlan and Wang, Xin and Wang, Xinran and Wee, Andrew T.S. and Wei, Zhongming and Wu, Yuen and Wu, Zhong Shuai and Xiong, Jie and Xiong, Qihua and Xu, Weigao and Yin, Peng and Zeng, Haibo and Zeng, Zhiyuan and Zhai, Tianyou and Zhang, Han and Zhang, Hui and Zhang, Qichun and Zhang, Tierui and Zhang, Xiang and Zhao, Li Dong and Zhao, Meiting and Zhao, Weijie and Zhao, Yunxuan and Zhou, Kai Ge and Zhou, Xing and Zhou, Yu and Zhu, Hongwei and Zhang, Hua and Liu, Zhongfan}, issn = {1001-4861}, journal = {Acta Physico-Chimica Sinica}, number = {12}, publisher = {Peking University}, title = {{Recent progress on two-dimensional materials}}, doi = {10.3866/PKU.WHXB202108017}, volume = {37}, year = {2021}, } @article{14889, abstract = {We consider the Fröhlich Hamiltonian with large coupling constant α. For initial data of Pekar product form with coherent phonon field and with the electron minimizing the corresponding energy, we provide a norm approximation of the evolution, valid up to times of order α2. The approximation is given in terms of a Pekar product state, evolved through the Landau-Pekar equations, corrected by a Bogoliubov dynamics taking quantum fluctuations into account. This allows us to show that the Landau-Pekar equations approximately describe the evolution of the electron- and one-phonon reduced density matrices under the Fröhlich dynamics up to times of order α2.}, author = {Leopold, Nikolai K and Mitrouskas, David Johannes and Rademacher, Simone Anna Elvira and Schlein, Benjamin and Seiringer, Robert}, issn = {2578-5885}, journal = {Pure and Applied Analysis}, number = {4}, pages = {653--676}, publisher = {Mathematical Sciences Publishers}, title = {{Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron}}, doi = {10.2140/paa.2021.3.653}, volume = {3}, year = {2021}, } @article{14890, abstract = {We consider a system of N interacting bosons in the mean-field scaling regime and construct corrections to the Bogoliubov dynamics that approximate the true N-body dynamics in norm to arbitrary precision. The N-independent corrections are given in terms of the solutions of the Bogoliubov and Hartree equations and satisfy a generalized form of Wick's theorem. We determine the n-point correlation functions of the excitations around the condensate, as well as the reduced densities of the N-body system, to arbitrary accuracy, given only the knowledge of the two-point functions of a quasi-free state and the solution of the Hartree equation. In this way, the complex problem of computing all n-point correlation functions for an interacting N-body system is essentially reduced to the problem of solving the Hartree equation and the PDEs for the Bogoliubov two-point functions.}, author = {Bossmann, Lea and Petrat, Sören P and Pickl, Peter and Soffer, Avy}, issn = {2578-5885}, journal = {Pure and Applied Analysis}, number = {4}, pages = {677--726}, publisher = {Mathematical Sciences Publishers}, title = {{Beyond Bogoliubov dynamics}}, doi = {10.2140/paa.2021.3.677}, volume = {3}, year = {2021}, } @inbook{14984, abstract = {Hybrid zones are narrow geographic regions where different populations, races or interbreeding species meet and mate, producing mixed ‘hybrid’ offspring. They are relatively common and can be found in a diverse range of organisms and environments. The study of hybrid zones has played an important role in our understanding of the origin of species, with hybrid zones having been described as ‘natural laboratories’. This is because they allow us to study,in situ, the conditions and evolutionary forces that enable divergent taxa to remain distinct despite some ongoing gene exchange between them.}, author = {Stankowski, Sean and Shipilina, Daria and Westram, Anja M}, booktitle = {Encyclopedia of Life Sciences}, isbn = {9780470016176}, publisher = {Wiley}, title = {{Hybrid Zones}}, doi = {10.1002/9780470015902.a0029355}, volume = {2}, year = {2021}, } @inbook{14987, abstract = {The goal of zero-shot learning is to construct a classifier that can identify object classes for which no training examples are available. When training data for some of the object classes is available but not for others, the name generalized zero-shot learning is commonly used. In a wider sense, the phrase zero-shot is also used to describe other machine learning-based approaches that require no training data from the problem of interest, such as zero-shot action recognition or zero-shot machine translation.}, author = {Lampert, Christoph}, booktitle = {Computer Vision}, editor = {Ikeuchi, Katsushi}, isbn = {9783030634155}, pages = {1395--1397}, publisher = {Springer}, title = {{Zero-Shot Learning}}, doi = {10.1007/978-3-030-63416-2_874}, year = {2021}, } @misc{14988, abstract = {Raw data generated from the publication - The TPLATE complex mediates membrane bending during plant clathrin-mediated endocytosis by Johnson et al., 2021 In PNAS}, author = {Johnson, Alexander J}, publisher = {Zenodo}, title = {{Raw data from Johnson et al, PNAS, 2021}}, doi = {10.5281/ZENODO.5747100}, year = {2021}, } @article{15013, abstract = {We consider random n×n matrices X with independent and centered entries and a general variance profile. We show that the spectral radius of X converges with very high probability to the square root of the spectral radius of the variance matrix of X when n tends to infinity. We also establish the optimal rate of convergence, that is a new result even for general i.i.d. matrices beyond the explicitly solvable Gaussian cases. The main ingredient is the proof of the local inhomogeneous circular law [arXiv:1612.07776] at the spectral edge.}, author = {Alt, Johannes and Erdös, László and Krüger, Torben H}, issn = {2690-1005}, journal = {Probability and Mathematical Physics}, number = {2}, pages = {221--280}, publisher = {Mathematical Sciences Publishers}, title = {{Spectral radius of random matrices with independent entries}}, doi = {10.2140/pmp.2021.2.221}, volume = {2}, year = {2021}, } @article{13455, abstract = {The majority of massive stars live in binary or multiple systems and will interact with a companion during their lifetimes, which helps to explain the observed diversity of core-collapse supernovae. Donor stars in binary systems can lose most of their hydrogen-rich envelopes through mass transfer. As a result, not only are the surface properties affected, but so is the core structure. However, most calculations of the core-collapse properties of massive stars rely on single-star models. We present a systematic study of the difference between the pre-supernova structures of single stars and stars of the same initial mass (11–21 M⊙) that have been stripped due to stable post-main-sequence mass transfer at solar metallicity. We present the pre-supernova core composition with novel diagrams that give an intuitive representation of the isotope distribution. As shown in previous studies, at the edge of the carbon-oxygen core, the binary-stripped star models contain an extended gradient of carbon, oxygen, and neon. This layer remains until core collapse and is more extended in mass for higher initial stellar masses. It originates from the receding of the convective helium core during core helium burning in binary-stripped stars, which does not occur in single-star models. We find that this same evolutionary phase leads to systematic differences in the final density and nuclear energy generation profiles. Binary-stripped star models have systematically higher total masses of carbon at the moment of core collapse compared to single-star models, which likely results in systematically different supernova yields. In about half of our models, the silicon-burning and oxygen-rich layers merge after core silicon burning. We discuss the implications of our findings for the “explodability”, supernova observations, and nucleosynthesis of these stars. Our models are publicly available and can be readily used as input for detailed supernova simulations.}, author = {Laplace, E. and Justham, S. and Renzo, M. and Götberg, Ylva Louise Linsdotter and Farmer, R. and Vartanyan, D. and de Mink, S. E.}, issn = {1432-0746}, journal = {Astronomy & Astrophysics}, keywords = {Space and Planetary Science, Astronomy and Astrophysics}, publisher = {EDP Sciences}, title = {{Different to the core: The pre-supernova structures of massive single and binary-stripped stars}}, doi = {10.1051/0004-6361/202140506}, volume = {656}, year = {2021}, } @unpublished{14278, abstract = {The Birkhoff conjecture says that the boundary of a strictly convex integrable billiard table is necessarily an ellipse. In this article, we consider a stronger notion of integrability, namely, integrability close to the boundary, and prove a local version of this conjecture: a small perturbation of almost every ellipse that preserves integrability near the boundary, is itself an ellipse. We apply this result to study local spectral rigidity of ellipses using the connection between the wave trace of the Laplacian and the dynamics near the boundary and establish rigidity for almost all of them.}, author = {Koval, Illya}, booktitle = {arXiv}, title = {{Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse}}, doi = {10.48550/ARXIV.2111.12171}, year = {2021}, } @article{10000, abstract = {Inhibition or targeted deletion of histone deacetylase 3 (HDAC3) is neuroprotective in a variety neurodegenerative conditions, including retinal ganglion cells (RGCs) after acute optic nerve damage. Consistent with this, induced HDAC3 expression in cultured cells shows selective toxicity to neurons. Despite an established role for HDAC3 in neuronal pathology, little is known regarding the mechanism of this pathology.}, author = {Schmitt, Heather M. and Fehrman, Rachel L. and Maes, Margaret E and Yang, Huan and Guo, Lian Wang and Schlamp, Cassandra L. and Pelzel, Heather R. and Nickells, Robert W.}, issn = {1552-5783}, journal = {Investigative Ophthalmology and Visual Science}, number = {10}, publisher = {Association for Research in Vision and Ophthalmology}, title = {{Increased susceptibility and intrinsic apoptotic signaling in neurons by induced HDAC3 expression}}, doi = {10.1167/IOVS.62.10.14}, volume = {62}, year = {2021}, } @inproceedings{10002, abstract = {We present a faster symbolic algorithm for the following central problem in probabilistic verification: Compute the maximal end-component (MEC) decomposition of Markov decision processes (MDPs). This problem generalizes the SCC decomposition problem of graphs and closed recurrent sets of Markov chains. The model of symbolic algorithms is widely used in formal verification and model-checking, where access to the input model is restricted to only symbolic operations (e.g., basic set operations and computation of one-step neighborhood). For an input MDP with n vertices and m edges, the classical symbolic algorithm from the 1990s for the MEC decomposition requires O(n2) symbolic operations and O(1) symbolic space. The only other symbolic algorithm for the MEC decomposition requires O(nm−−√) symbolic operations and O(m−−√) symbolic space. A main open question is whether the worst-case O(n2) bound for symbolic operations can be beaten. We present a symbolic algorithm that requires O˜(n1.5) symbolic operations and O˜(n−−√) symbolic space. Moreover, the parametrization of our algorithm provides a trade-off between symbolic operations and symbolic space: for all 0<ϵ≤1/2 the symbolic algorithm requires O˜(n2−ϵ) symbolic operations and O˜(nϵ) symbolic space ( O˜ hides poly-logarithmic factors). Using our techniques we present faster algorithms for computing the almost-sure winning regions of ω -regular objectives for MDPs. We consider the canonical parity objectives for ω -regular objectives, and for parity objectives with d -priorities we present an algorithm that computes the almost-sure winning region with O˜(n2−ϵ) symbolic operations and O˜(nϵ) symbolic space, for all 0<ϵ≤1/2 .}, author = {Chatterjee, Krishnendu and Dvorak, Wolfgang and Henzinger, Monika H and Svozil, Alexander}, booktitle = {Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science}, isbn = {978-1-6654-4896-3}, issn = {1043-6871}, keywords = {Computer science, Computational modeling, Markov processes, Probabilistic logic, Formal verification, Game Theory}, location = {Rome, Italy}, pages = {1--13}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Symbolic time and space tradeoffs for probabilistic verification}}, doi = {10.1109/LICS52264.2021.9470739}, year = {2021}, } @inproceedings{10004, abstract = {Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical optimization criterion is the maximal expected total reward where the MDP stops after T steps, which can be computed by a simple dynamic programming algorithm. We consider a natural generalization of the problem where the stopping times can be chosen according to a probability distribution, such that the expected stopping time is T, to optimize the expected total reward. Quite surprisingly we establish inter-reducibility of the expected stopping-time problem for Markov chains with the Positivity problem (which is related to the well-known Skolem problem), for which establishing either decidability or undecidability would be a major breakthrough. Given the hardness of the exact problem, we consider the approximate version of the problem: we show that it can be solved in exponential time for Markov chains and in exponential space for MDPs.}, author = {Chatterjee, Krishnendu and Doyen, Laurent}, booktitle = {Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science}, isbn = {978-1-6654-4896-3}, issn = {1043-6871}, keywords = {Computer science, Heuristic algorithms, Memory management, Automata, Markov processes, Probability distribution, Complexity theory}, location = {Rome, Italy}, pages = {1--13}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Stochastic processes with expected stopping time}}, doi = {10.1109/LICS52264.2021.9470595}, year = {2021}, } @article{10005, abstract = {We study systems of nonlinear partial differential equations of parabolic type, in which the elliptic operator is replaced by the first-order divergence operator acting on a flux function, which is related to the spatial gradient of the unknown through an additional implicit equation. This setting, broad enough in terms of applications, significantly expands the paradigm of nonlinear parabolic problems. Formulating four conditions concerning the form of the implicit equation, we first show that these conditions describe a maximal monotone p-coercive graph. We then establish the global-in-time and large-data existence of a (weak) solution and its uniqueness. To this end, we adopt and significantly generalize Minty’s method of monotone mappings. A unified theory, containing several novel tools, is developed in a way to be tractable from the point of view of numerical approximations.}, author = {Bulíček, Miroslav and Maringová, Erika and Málek, Josef}, issn = {1793-6314}, journal = {Mathematical Models and Methods in Applied Sciences}, keywords = {Nonlinear parabolic systems, implicit constitutive theory, weak solutions, existence, uniqueness}, number = {09}, publisher = {World Scientific}, title = {{On nonlinear problems of parabolic type with implicit constitutive equations involving flux}}, doi = {10.1142/S0218202521500457}, volume = {31}, year = {2021}, } @phdthesis{10007, abstract = {The present thesis is concerned with the derivation of weak-strong uniqueness principles for curvature driven interface evolution problems not satisfying a comparison principle. The specific examples being treated are two-phase Navier-Stokes flow with surface tension, modeling the evolution of two incompressible, viscous and immiscible fluids separated by a sharp interface, and multiphase mean curvature flow, which serves as an idealized model for the motion of grain boundaries in an annealing polycrystalline material. Our main results - obtained in joint works with Julian Fischer, Tim Laux and Theresa M. Simon - state that prior to the formation of geometric singularities due to topology changes, the weak solution concept of Abels (Interfaces Free Bound. 9, 2007) to two-phase Navier-Stokes flow with surface tension and the weak solution concept of Laux and Otto (Calc. Var. Partial Differential Equations 55, 2016) to multiphase mean curvature flow (for networks in R^2 or double bubbles in R^3) represents the unique solution to these interface evolution problems within the class of classical solutions, respectively. To the best of the author's knowledge, for interface evolution problems not admitting a geometric comparison principle the derivation of a weak-strong uniqueness principle represented an open problem, so that the works contained in the present thesis constitute the first positive results in this direction. The key ingredient of our approach consists of the introduction of a novel concept of relative entropies for a class of curvature driven interface evolution problems, for which the associated energy contains an interfacial contribution being proportional to the surface area of the evolving (network of) interface(s). The interfacial part of the relative entropy gives sufficient control on the interface error between a weak and a classical solution, and its time evolution can be computed, at least in principle, for any energy dissipating weak solution concept. A resulting stability estimate for the relative entropy essentially entails the above mentioned weak-strong uniqueness principles. The present thesis contains a detailed introduction to our relative entropy approach, which in particular highlights potential applications to other problems in curvature driven interface evolution not treated in this thesis.}, author = {Hensel, Sebastian}, issn = {2663-337X}, pages = {300}, publisher = {Institute of Science and Technology Austria}, title = {{Curvature driven interface evolution: Uniqueness properties of weak solution concepts}}, doi = {10.15479/at:ista:10007}, year = {2021}, } @unpublished{10011, abstract = {We propose a new weak solution concept for (two-phase) mean curvature flow which enjoys both (unconditional) existence and (weak-strong) uniqueness properties. These solutions are evolving varifolds, just as in Brakke's formulation, but are coupled to the phase volumes by a simple transport equation. First, we show that, in the exact same setup as in Ilmanen's proof [J. Differential Geom. 38, 417-461, (1993)], any limit point of solutions to the Allen-Cahn equation is a varifold solution in our sense. Second, we prove that any calibrated flow in the sense of Fischer et al. [arXiv:2003.05478] - and hence any classical solution to mean curvature flow - is unique in the class of our new varifold solutions. This is in sharp contrast to the case of Brakke flows, which a priori may disappear at any given time and are therefore fatally non-unique. Finally, we propose an extension of the solution concept to the multi-phase case which is at least guaranteed to satisfy a weak-strong uniqueness principle.}, author = {Hensel, Sebastian and Laux, Tim}, booktitle = {arXiv}, keywords = {Mean curvature flow, gradient flows, varifolds, weak solutions, weak-strong uniqueness, calibrated geometry, gradient-flow calibrations}, title = {{A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness}}, doi = {10.48550/arXiv.2109.04233}, year = {2021}, }