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arXiv 2022年

作者： Maier-Hein, Lena Reinke, Annika Godau, Patrick Tizabi, Minu D. Buettner, Florian Christodoulou, Evangelia Glocker, Ben Isensee, Fabian Kleesiek, Jens Kozubek, Michal Reyes, Mauricio Riegler, Michael A. Wiesenfarth, Manuel Emre Kavur, A. Sudre, Carole H. Baumgartner, Michael Eisenmann, Matthias Heckmann-Nötzel, Doreen Rädsch, Tim Acion, Laura Antonelli, Michela Arbel, Tal Bakas, Spyridon Benis, Arriel Blaschko, Matthew B. Jorge Cardoso, M. Cheplygina, Veronika Cimini, Beth A. Collins, Gary S. Farahani, Keyvan Ferrer, Luciana Galdran, Adrian Ginneken, Bram Van Haase, Robert Hashimoto, Daniel A. Hoffman, Michael M. Huisman, Merel Jannin, Pierre Kahn, Charles E. Kainmueller, Dagmar Kainz, Bernhard Karargyris, Alexandros Karthikesalingam, Alan Kenngott, Hannes Kofler, Florian Kopp-Schneider, Annette Kreshuk, Anna Kurc, Tahsin Landman, Bennett A. Litjens, Geert Madani, Amin Maier-Hein, Klaus Martel, Anne L. Mattson, Peter Meijering, Erik Menze, Bjoern Moons, Karel G.M. Müller, Henning Nichyporuk, Brennan Nickel, Felix Petersen, Jens Rajpoot, Nasir Rieke, Nicola Saez-Rodriguez, Julio Sánchez, Clara I. Shetty, Shravya Smeden, Maarten Van Summers, Ronald M. Taha, Abdel A. Tiulpin, Aleksei Tsaftaris, Sotirios A. Calster, Ben Van Varoquaux, Gaël Jäger, Paul F. Heidelberg Division of Intelligent Medical Systems and HI Helmholtz Imaging Germany Faculty of Mathematics and Computer Science and Medical Faculty Heidelberg University Heidelberg Germany NCT Heidelberg a partnership between DKFZ University Medical Center Heidelberg Germany Faculty of Mathematics and Computer Science Heidelberg University Heidelberg Germany Heidelberg Division of Intelligent Medical Systems Germany partner site Frankfurt/Mainz a partnership between DKFZ and UCT Frankfurt-Marburg Germany Heidelberg Goethe University Frankfurt Germany Department of Medicine Goethe University Frankfurt Germany Department of Informatics Frankfurt Cancer Insititute Germany Department of Computing Imperial College London London United Kingdom Heidelberg Division of Medical Image Computing and HI Applied Computer Vision Lab Germany Institute for AI in Medicine University Medicine Essen Essen Germany Centre for Biomedical Image Analysis Faculty of Informatics Masaryk University Brno Czech Republic ARTORG Center for Biomedical Engineering Research University of Bern Bern Switzerland Department of Radiation Oncology University Hospital Bern University of Bern Bern Switzerland Simula Metropolitan Center for Digital Engineering Oslo Norway UiT The Arctic University of Norway Romsø Norway Heidelberg Division of Biostatistics Germany Heidelberg Division of Intelligent Medical Systems Division of Medical Image Computing HI Applied Computer Vision Lab Germany MRC Unit for Lifelong Health and Ageing UCL Centre for Medical Image Computing Department of Computer Science University College London London United Kingdom School of Biomedical Engineering and Imaging Science King’s College London London United Kingdom Heidelberg Division of Medical Image Computing Germany Instituto de Cálculo CONICET – Universidad de Buenos Aires Buenos Aires Argentina Centre for Medical Image Computing University College London London United Kingdom McGill University Montréal

Increasing evidence shows that flaws in machine learning (ML) algorithm validation are an underestimated global problem. Particularly in automatic biomedical image analysis, chosen performance metrics often do not reflect the domain interest, thus failing to adequately measure scientific progress and hindering translation of ML techniques into practice. To overcome this, we created Metrics Reloaded, a comprehensive framework guiding researchers in the problem-aware selection of metrics. It was developed by a large international consortium in a multi-stage Delphi process and is based on the novel concept of a problem fingerprint – a structured representation of the given problem that captures all aspects that are relevant for metric selection, from the domain interest to the properties of the target structure(s), data set and algorithm output. Based on the problem fingerprint, users are guided through the process of choosing and applying appropriate validation metrics while being made aware of potential pitfalls. Metrics Reloaded targets image analysis problems that can be interpreted as a classification task at image, object or pixel level, namely image-level classification, object detection, semantic segmentation, and instance segmentation tasks. To improve the user experience, we implemented the framework in the Metrics Reloaded online tool. Following the convergence of ML methodology across application domains, Metrics Reloaded fosters the convergence of validation methodology. Its applicability is demonstrated for various biomedical use cases. © 2022, CC BY.

关键词： Semantic Segmentation

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One-Bit precoding and constellation range design for massive MIMO with QAM Signaling

arXiv

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arXiv 2018年

作者： Sohrabi, Foad Liu, Ya-Feng Yu, Wei Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto TorontoONM5S3G4 Canada State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing100190 China

The use of low-resolution digital-to-analog converters (DACs) for transmit precoding provides crucial energy efficiency advantage for massive multiple-input multiple-output (MIMO) implementation. This paper formulates a quadrature amplitude modulation (QAM) constellation range and one-bit symbol-level precoding design problem for minimizing the average symbol error rate (SER) in downlink massive MIMO transmission. A tight upper-bound for SER with low-resolution DAC precoding is first derived. The derived expression suggests that the performance degradation of one-bit precoding can be interpreted as a decrease in the effective minimum distance of the QAM constellation. Using the obtained SER expression, we propose a QAM constellation range design for the singleuser case. It is shown that in the massive MIMO limit, a reasonable choice for constellation range with one-bit precoding is that of the infinite-resolution precoding with per-symbol power constraint, but reduced by a factor of p 2/π or about 0:8. The corresponding minimum distance reduction translates to about 2dB gap between the performance of one-bit precoding and infinite-resolution precoding. This paper further proposes a low-complexity heuristic algorithm for one-bit precoder design. Finally, the proposed QAM constellation range and precoder design are generalized to the multi-user downlink. We propose to scale the constellation range for infinite-resolution zero-forcing (ZF) precoding with per-symbol power constraint by the same factor of p 2/π for one-bit precoding. The proposed one-bit precoding scheme is shown to be within 2dB of infinite-resolution ZF. In term of number of antennas, one-bit precoding requires about 50% more antennas to achieve the same performance as infinite-resolution precoding. Copyright © 2018, The Authors. All rights reserved.

关键词： Quadrature amplitude modulation

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Data-driven polynomial chaos expansions: A weighted least-square approximation

arXiv

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arXiv 2018年

作者： Guo, Ling Liu, Yongle Zhou, Tao Department of Mathematics Shanghai Normal University Shanghai China Department of Mathematics Southern University of Science and Technology Shenzhen China LSEC Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

In this work, we combine the idea of data-driven polynomial chaos expansions with the weighted least-square approach to solve uncertainty quantification (UQ) problems. The idea of data-driven polynomial chaos is to use statistical moments of the input random variables to develop an arbitrary polynomial chaos expansion, and then use such data-driven bases to perform UQ computations. Here we adopt the bases construction procedure by following [1], where the bases are computed by using matrix operations on the Hankel matrix of moments. Different from previous works, in the postprocessing part, we propose a weighted least-squares approach to solve UQ problems. This approach includes a sampling strategy and a least-squares solver. The main features of our approach are two folds: On one hand, our sampling strategy is independent of the random input. More precisely, we propose to sampling with the equilibrium measure, and this measure is also independent of the data-driven bases. Thus, this procedure can be done in prior (or in a off- line manner). On the other hand, we propose to solve a Christoffel function weighted least-square problem, and this strategy is quasi-linearly stable - the required number of PDE solvers depends linearly (up to a logarithmic factor) on the number of (data-driven) bases. This new approach is thus promising in dealing with a class of problems with epistemic uncertainties. Several numerical tests are presented to show the effectiveness of our approach. Copyright © 2018, The Authors. All rights reserved.

关键词： Uncertainty analysis

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On the perturbation of an L2-orthogonal projection

arXiv

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arXiv 2018年

作者： Xu, Xuefeng LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

The L2-orthogonal projection is an important mathematical tool in scientific computing and numerical analysis, which has been widely applied in many fields such as linear least squares problems, eigenvalue problems, ill-posed problems, and randomized algorithms. In some numerical applications, the entries of a matrix will seldom be known exactly, so it is necessary to develop some bounds to characterize the effects of the uncertainties caused by matrix perturbation. In this paper, we establish new perturbation bounds for the L2orthogonal projection onto the column space of a matrix, which involve upper (lower) bounds and combined upper (lower) bounds. The new results contain some sharper counterparts of the existing bounds. Numerical examples are also given to illustrate our theoretical results.15A09, 15A18, 47A55, 65F35 Copyright © 2018, The Authors. All rights reserved.

关键词： Singular value decomposition

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On the perturbation of the Moore–Penrose inverse of a matrix

arXiv

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arXiv 2018年

Over the past decades, the Moore–Penrose inverse has been extensively investigated and widely applied in many fields. One reason for this interest is that the Moore–Penrose inverse can succinctly express some important geometric constructions in finite-dimensional spaces, such as the orthogonal projection onto a subspace and the linear least squares problem. However, the entries of a matrix will seldom be known exactly in numerical applications, so it is necessary to develop some bounds to characterize the effects of matrix perturbation. In this paper, we establish new perturbation bounds for the Moore–Penrose inverse of a matrix, which include some sharper counterparts of the existing upper bounds. Numerical examples are also provided to illustrate our theoretical results. Copyright © 2018, The Authors. All rights reserved.

关键词： Inverse problems

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Geometric Wavelet Scattering Networks on Compact Riemannian Manifolds

arXiv

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arXiv 2019年

作者： Perlmutter, Michael Gao, Feng Wolf, Guy Hirn, Matthew Michigan State University Department of Computational Mathematics Science & Engineering East LansingMI United States Yale University Department of Genetics New HavenCT United States Université de Montréal Department of Mathematics and Statistics Mila Quebec Artificial Intelligence Institute MontréalQC Canada Center for Quantum Computing Science & Engineering East LansingMI United States

The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional neural networks to manifold and graph-structured domains, we define a geometric scattering transform on manifolds. Similar to the Euclidean scattering transform, the geometric scattering transform is based on a cascade of wavelet filters and pointwise nonlinearities. It is invariant to local isometries and stable to certain types of diffeomorphisms. Empirical results demonstrate its utility on several geometric learning tasks. Our results generalize the deformation stability and local translation invariance of Euclidean scattering, and demonstrate the importance of linking the used filter structures to the underlying geometry of the data. Copyright © 2019, The Authors. All rights reserved.

关键词： Geometry

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Capacity optimality of AMP in coded systems

arXiv

引用

arXiv 2019年

作者： Liu, Lei Liang, Chulong Ma, Junjie Ping, Li Hong Kong SAR China Nomi 923-1292 Japan Department of Electrical Engineering City University of Hong Kong Hong Kong SAR China Algorithm Department ZTE Corporation Shenzhen 518057 China State Key Laboratory of Mobile Network Mobile Multimedia Technology ZTE Corporation Shenzhen 518057 China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Science Beijing China Department of Electronic Engineering City University of Hong Kong Hong Kong SAR China

This paper studies a large random matrix system (LRMS) model involving an arbitrary signal distribution and forward error control (FEC) coding. We establish an area property based on the approximate message passing (AMP) algorithm. Under the assumption that the state evolution for AMP is correct for the coded system, the achievable rate of AMP is analyzed. We prove that AMP achieves the constrained capacity of the LRMS with an arbitrary signal distribution provided that a matching condition is satisfied. As a byproduct, we provide an alternative derivation for the constraint capacity of an LRMS using a proved property of AMP. We discuss realization techniques for the matching principle of binary signaling using irregular low-density parity-check (LDPC) codes and provide related numerical results. We show that the optimized codes demonstrate significantly better performance over un-matched ones under AMP. For quadrature phase shift keying (QPSK) modulation, bit error rate (BER) performance within 1 dB from the constrained capacity limit is observed. © 2019, CC BY-NC-SA.

关键词： Message passing

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Collective neutrino oscillations in three flavors on qubit and qutrit processors

引用

Physical Review D 2025年第10期111卷 103054-103054页

作者： Luca Spagnoli Noah Goss Alessandro Roggero Ermal Rrapaj Michael J. Cervia Amol V. Patwardhan Ravi K. Naik A. Baha Balantekin Ed Younis David I. Santiago Irfan Siddiqi Sheakha Aldaihan Physics Department University of Trento Via Sommarive 14 I-38123 Trento Italy INFN-TIFPA Trento Institute of Fundamental Physics and Applications Via Sommarive 14 I-38123 Trento Italy Quantum Nanoelectronics Laboratory Department of Physics University of California at Berkeley Berkeley California 94720 USA Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA INFN-TIFPA Trento Institute of Fundamental Physics and Applications Trento Italy National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory Berkeley California 94720 USA Department of Physics University of California Berkeley California 94720 USA RIKEN iTHEMS Wako Saitama 351-0198 Japan Department of Physics University of Washington Seattle Washington 98195 USA School of Physics and Astronomy University of Minnesota Minneapolis Minnesota 55455 USA Department of Physics New York Institute of Technology New York New York 10023 USA Department of Physics University of Wisconsin Madison Wisconsin 53706 USA Department of Physics and Astronomy College of Science King Saud University Riyadh 11451 Saudi Arabia

Collective neutrino flavor oscillations are of primary importance in understanding the dynamic evolution of core-collapse supernovae and subsequent terrestrial detection, but also among the most challenging aspects of numerical simulations. This situation is complicated by the quantum many-body nature of the problem due to neutrino-neutrino interactions, which demands a quantum treatment. An additional complication is the presence of three flavors, which often is approximated by the electron flavor and a heavy lepton flavor. In this work, we provide both qubit and qutrit encodings for all three flavors, and develop optimized quantum circuits for the time evolution and analyze the Trotter error. We conclude our study with a hardware experiment of a system of two neutrinos with superconducting hardware: the IBM Torino device for qubits and Advanced Quantum Testbed device at the Lawrence Berkeley National Laboratory for qutrits. We find that error mitigation greatly helps in obtaining a signal consistent with simulations. While hardware results are comparable at this stage, we expect the qutrit setup to be more convenient for large-scale simulations since it does not suffer from probability leakage into nonphsycial qubit space, unlike the qubit setup.

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Optimized base-station cache allocation for cloud radio access network with multicast backhaul

arXiv

引用

arXiv 2018年

作者： Dai, Binbin Liu, Ya-Feng Yu, Wei Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto TorontoONM5S 3G4 Canada State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

The performance of cloud radio access network (C-RAN) is limited by the finite capacities of the backhaul links connecting the centralized processor (CP) with the base-stations (BSs), especially when the backhaul is implemented in a wireless medium. This paper proposes the use of wireless multicast together with BS caching, where the BSs pre-store contents of popular files, to augment the backhaul of C-RAN. For a downlink C-RAN consisting of a single cluster of BSs and wireless backhaul, this paper studies the optimal cache size allocation strategy among the BSs and the optimal multicast beamforming transmission strategy at the CP such that the user’s requested messages are delivered from the CP to the BSs in the most efficient way. We first state a multicast backhaul rate expression based on a joint cache-channel coding scheme, which implies that larger cache sizes should be allocated to the BSs with weaker channels. We then formulate a two-timescale joint cache size allocation and beamforming design problem, where the cache is optimized offline based on the long-term channel statistical information, while the beamformer is designed during the file delivery phase based on the instantaneous channel state information. By leveraging the sample approximation method and the alternating direction method of multipliers (ADMM), we develop efficient algorithms for optimizing cache size allocation among the BSs, and quantify how much more cache should be allocated to the weaker BSs. We further consider the case with multiple files having different popularities and show that it is in general not optimal to entirely cache the most popular files first. Numerical results show considerable performance improvement of the optimized cache size allocation scheme over the uniform allocation and other heuristic schemes. Copyright © 2018, The Authors. All rights reserved.

关键词： Base stations

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Max-min fairness user scheduling and power allocation in full-duplex OFDMA systems

arXiv

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arXiv 2018年

作者： Zhang, Xiaozhou Chang, Tsung-Hui Liu, Ya-Feng Shen, Chao Zhu, Gang State Key Laboratory of Rail Traffic Control and Safety Beijing Jiaotong University Beijing China School of Science and Engineering Chinese University of Hong Kong Shenzhen China Shenzhen Research Institute of Big Data Shenzhen China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

In a full-duplex (FD) multi-user network, the system performance is not only limited by the self-interference but also by the co-channel interference due to the simultaneous uplink and downlink transmissions. Joint design of the uplink/downlink transmission direction of users and the power allocation is crucial for achieving high system performance in the FD multi-user network. In this paper, we investigate the joint uplink/downlink transmission direction assignment (TDA), user paring (UP) and power allocation problem for maximizing the system max-min fairness (MMF) rate in a FD multi-user orthogonal frequency division multiple access (OFDMA) system. The problem is formulated with a two-time-scale structure where the TDA and the UP variables are for optimizing a long-term MMF rate while the power allocation is for optimizing an instantaneous MMF rate during each channel coherence interval. We show that the studied joint MMF rate maximization problem is NP-hard in general. To obtain high-quality suboptimal solutions, we propose efficient methods based on simple relaxation and greedy rounding techniques. Simulation results are presented to show that the proposed algorithms are effective and achieve higher MMF rates than the existing heuristic methods. Copyright © 2018, The Authors. All rights reserved.

关键词： Optimization

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