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Across Scales and Across Dimensions: Temporal Super-Resolution Using Deep Internal Learning 1

16th European Conference on computer Vision, ECCV 2020

作者： Zuckerman, Liad Pollak Naor, Eyal Pisha, George Bagon, Shai Irani, Michal Department of Computer Science and Applied Math The Weizmann Institute of Science Rehovot Israel Rehovot Israel Technion Israel Institute of Technology Haifa Israel

ISBN: (数字)9783030585716

ISBN: (纸本)9783030585709

When a very fast dynamic event is recorded with a low-framerate camera, the resulting video suffers from severe motion blur (due to exposure time) and motion aliasing (due to low sampling rate in time). True Temporal Super-Resolution (TSR) is more than just Temporal-Interpolation (increasing framerate). It can also recover new high temporal frequencies beyond the temporal Nyquist limit of the input video, thus resolving both motion-blur and motion-aliasing – effects that temporal frame interpolation (as sophisticated as it may be) cannot undo. In this paper we propose a "Deep Internal Learning" approach for true TSR. We train a video-specific CNN on examples extracted directly from the low-framerate input video. Our method exploits the strong recurrence of small space-time patches inside a single video sequence, both within and across different spatio-temporal scales of the video. We further observe (for the first time) that small space-time patches recur also across-dimensions of the video sequence – i.e., by swapping the spatial and temporal dimensions. In particular, the higher spatial resolution of video frames provides strong examples as to how to increase the temporal resolution of that video. Such internal video-specific examples give rise to strong self-supervision, requiring no data but the input video itself. This results in Zero-Shot Temporal-SR of complex videos, which removes both motion blur and motion aliasing, outperforming previous supervised methods trained on external video datasets. © 2020, Springer Nature Switzerland AG.

关键词： Interpolation

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Semi-implicit Lagrangian Voronoi Approximation for the incompressible Navier-Stokes equations

arXiv

引用

arXiv 2024年

作者： Kincl, Ondřej Peshkov, Ilya Boscheri, Walter Laboratory of Applied Mathematics DICAM University of Trento via Mesiano 77 Trento38123 Italy Laboratoire de Mathématiques UMR 5127 CNRS Université Savoie Mont Blanc Le Bourget du Lac73376 France Department of Mathematics and Computer Science University of Ferrara Ferrara Italy

We introduce Semi-Implicit Lagrangian Voronoi Approximation (SILVA), a novel numerical method for the solution of the incompressible Euler and Navier-Stokes equations, which combines the efficiency of semi-implicit time marching schemes with the robustness of time-dependent Voronoi tessellations. In SILVA, the numerical solution is stored at particles, which move with the fluid velocity and also play the role of the generators of the computational mesh. The Voronoi mesh is rapidly regenerated at each time step, allowing large deformations with topology changes. As opposed to the reconnection-based Arbitrary-Lagrangian-Eulerian schemes, we need no remapping stage. A semi-implicit scheme is devised in the context of moving Voronoi meshes to project the velocity field onto a divergence-free manifold. We validate SILVA by illustrative benchmarks, including viscous, inviscid, and multi-phase flows. Compared to its closest competitor, the Incompressible Smoothed Particle Hydrodynamics (ISPH) method, SILVA offers a sparser stiffness matrix and facilitates the implementation of no-slip and free-slip boundary conditions. Copyright © 2024, The Authors. All rights reserved.

关键词： Stiffness matrix

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Kemeny consensus complexity

arXiv

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arXiv 2021年

作者： Fitzsimmons, Zack Hemaspaandra, Edith Dept. of Math. and Computer Science College of the Holy Cross WorcesterMA01610 United States Department of Computer Science Rochester Institute of Technology RochesterNY14623 United States

The computational study of election problems generally focuses on questions related to the winner or set of winners of an election. But social preference functions such as Kemeny rule output a full ranking of the candidates (a consensus). We study the complexity of consensus-related questions, with a particular focus on Kemeny and its qualitative version Slater. The simplest of these questions is the problem of determining whether a ranking is a consensus, and we show that this problem is coNP-complete. We also study the natural question of the complexity of manipulative actions that have a specific consensus as a goal. Though determining whether a ranking is a Kemeny consensus is hard, the optimal action for manipulators is to simply vote their desired consensus. We provide evidence that this simplicity is caused by the combination of election system (Kemeny), manipulative action (manipulation), and manipulative goal (consensus). In the process we provide the first completeness results at the second level of the polynomial hierarchy for electoral manipulation and for optimal solution recognition. Copyright © 2021, The Authors. All rights reserved.

关键词： Polynomials

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INVERSE PROBLEMS FOR QUANTUM GRAPH ASSOCIATED WITH SQUARE AND HEXAGONAL LATTICES

arXiv

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arXiv 2024年

作者： Ando, K. Blåsten, E. Exner, P. Isozaki, H. Korotyaev, E. Lassas, M. Lu, J. Morioka, H. Department of Electrical and Electronic Engineering and Computer Science Ehime University Matsuyama790-8577 Japan School of Engineering Science LUT University Lahti Campus Lahti15210 Finland Department of Math. Analysis Saint-Petersburg State University Universitetskaya Nab. 7/9 St. Petersburg199034 Russia National Research University Higher School of Economics St. Petersburg Russia Doppler Institute for Mathematical Physics and Applied Mathematics Czech Technical University in Prague Břehová 7 Prague115 19 Czech Republic Nuclear Physics Institute Czech Academy of Science Rež 250 68 Czech Republic Graduate School of Pure and Applied Sciences University of Tsukuba Tsukuba305-8571 Japan Department of Mathematics and Statistics University of Helsinki HelsinkiFI-00014 Finland

We solve inverse problems from the D-N map for the quantum graph on a finite domain in a square lattice and that on a hexagonal lattice, as well as inverse scattering problems from the S-matrix for a locally perturbed... 详细信息

关键词： Inverse problems

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VIETORIS THICKENINGS AND COMPLEXES HAVE ISOMORPHIC HOMOTOPY GROUPS

arXiv

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arXiv 2022年

作者： Adams, Henry Frick, Florian Virk, Žiga Department of Mathematics Colorado State University Fort CollinsCO80523 United States Dept. Math. Sciences Carnegie Mellon University PittsburghPA15213 United States Inst. Math. Freie Universität Berlin Arnimallee 2 Berlin14195 Germany Faculty of Computer and Information Science Večna pot 113 LjubljanaSI-1000 Slovenia

We study the relationship between metric thickenings and simplicial complexes associated to coverings of metric spaces. Let U be a cover of a separable metric space X by open sets with a uniform diameter bound. The Vietoris complex V(U) contains all simplices with vertex set contained in some U ∈ U, and the Vietoris metric thickening Vm(U) is the space of probability measures with support in some U ∈ U, equipped with an optimal transport metric. We show that Vm(U) and V(U) have isomorphic homotopy groups in all dimensions. In particular, by choosing the cover U appropriately, we get isomorphisms between the homotopy groups of Vietoris-Rips metric thickenings and simplicial complexes πk(VRm(X;r)) ≅ πk(VR(X;r)) for all integers k ≥ 0, where both spaces are defined using the convention "diameter k(Čm(X;r)) ≅ πk(Č(X;r)) for all integers k ≥ 0, where both spaces are defined using open balls (instead of closed balls). Copyright © 2022, The Authors. All rights reserved.

关键词： Set theory

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Qudit Dynamical Decoupling on a Superconducting Quantum Processor

引用

Physical Review Letters 2025年第5期134卷 050601-050601页

作者： Vinay Tripathi Noah Goss Arian Vezvaee Long B. Nguyen Irfan Siddiqi Daniel A. Lidar Department of Physics and Astronomy University of Southern California Los Angeles California 90089 USA Center for Quantum Information Science and Technology University of Southern California Los Angeles California 90089 USA Quantum Nanoelectronics Laboratory Department of Physics University of California at Berkeley Berkeley California 94720 USA Applied Math and Computational Research Division Lawrence Berkeley National Lab Berkeley California 94720 USA Department of Electrical and Computer Engineering University of Southern California Los Angeles California 90089 USA Department of Chemistry University of Southern California Los Angeles California 90089 USA

Multilevel qudit systems are increasingly being explored as alternatives to traditional qubit systems due to their denser information storage and processing potential. However, qudits are more susceptible to decoherence than qubits due to increased loss channels, noise sensitivity, and crosstalk. To address these challenges, we develop protocols for dynamical decoupling (DD) of qudit systems based on the Heisenberg-Weyl group. We implement and experimentally verify these DD protocols on a superconducting transmon processor that supports qudit operation based on qutrits (d=3) and ququarts (d=4). Specifically, we demonstrate single-qudit DD sequences to decouple qutrits and ququarts from system-bath-induced decoherence. We also introduce two-qudit DD sequences designed to suppress the detrimental cross-Kerr couplings between coupled qudits. This allows us to demonstrate a significant improvement in the fidelity of time-evolved qutrit Bell states. Our results highlight the utility of leveraging DD to enable scalable qudit-based quantum computing.

关键词： Qubits

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Good Quantum LDPC Codes with Linear Time Decoders

arXiv

引用

arXiv 2022年

作者： Dinur, Irit Hsieh, Min-Hsiu Lin, Ting-Chun Vidick, Thomas Department of Applied Math and Computer Science The Weizmann Institute of Science Hong Hai Research Institute Taipei Taiwan Department of Physics University of California San DiegoCA United States Department of Computing and Mathematical Sciences California Institute of Technology CA United States

We construct a new explicit family of good quantum low-density parity-check codes which additionally have linear time decoders. Our codes are based on a three-term chain pFm2*mqV ÝÑ δ0 pFm2 qE ÝÑ δ1 FF2 where V (X-checks) are the vertices, E (qubits) are the edges, and F (Z-checks) are the squares of a left-right Cayley complex, and where the maps are defined based on a pair of constant-size random codes CA, CB: Fm2 Ñ F∆2 where ∆ is the regularity of the underlying Cayley graphs. One of the main ingredients in the analysis is a proof of an essentially-optimal robustness property for the tensor product of two random codes. © 2022, CC BY.

关键词： Decoding

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Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence Preface

Proceedings of Machine Learning Research

引用

Proceedings of Machine Learning Research 2021年 161卷 1-11页

作者： de Campos, Cassio Maathuis, Marloes H. Quaeghebeur, Erik Uncertainty in AI Group Dep. of Math. and Computer Science Eindhoven University of Technology Netherlands Seminar for Statistics Department of Mathematics ETH Zurich Switzerland

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Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence: Preface

37th Conference on Uncertainty in Artificial Intelligence, U...

引用

37th Conference on Uncertainty in Artificial Intelligence, UAI 2021 2021年 1-11页

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Graph Fourier MMD for Signals on Graphs

arXiv

引用

arXiv 2023年

作者： Leone, Samuel Venkat, Aarthi Huguet, Guillaume Tong, Alexander Wolf, Guy Krishnaswamy, Smita Applied Math Program New HavenCT United States Computational Biology & Bioinformatics Program Yale University New HavenCT United States Dept. of Math. & Stat Université de Montréal Mila - Quebec AI Institute MontrealQC Canada Dept. of Comp. Sci. & Oper. Res. Université de Montréal Mila - Quebec AI Institute MontrealQC Canada Department of Computer Science Department of Genetics Yale University New HavenCT United States

While numerous methods have been proposed for computing distances between probability distributions in Euclidean space, relatively little attention has been given to computing such distances for distributions on graphs. However, there has been a marked increase in data that either lies on graph (such as protein interaction networks) or can be modeled as a graph (single cell data), particularly in the biomedical sciences. Thus, it becomes important to find ways to compare signals defined on such graphs. Here, we propose Graph Fourier MMD (GFMMD), a novel distance between distributions and signals on graphs. GFMMD is defined via an optimal witness function that is both smooth on the graph and maximizes difference in expectation between the pair of distributions on the graph. We find an analytical solution to this optimization problem as well as an embedding of distributions that results from this method. We also prove several properties of this method including scale invariance and applicability to disconnected graphs. We showcase it on graph benchmark datasets as well on single cell RNA-sequencing data analysis. In the latter, we use the GFMMD-based gene embeddings to find meaningful gene clusters. We also propose a novel type of score for gene selection called gene localization score which helps select genes for cellular state space characterization. Copyright © 2023, The Authors. All rights reserved.

关键词： Genes

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