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Prime-residue-class of uniform charges on the integers

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arXiv 2018年

作者： Spece, Michael Kadane, Joseph B. Department of Statistics & Data Science and Machine Learning Department Carnegie Mellon University PittsburghPA15213 United States Department of Statistics & Data Science Carnegie Mellon University PittsburghPA15213 United States

There is a probability charge on the power set of the integers that gives probability 1/p to every residue class modulo a prime p. There exists such a charge that gives probability w to the set of prime numbers iff w ∈ [0,1/2]. Similarly, there is such a charge that gives probability x to a residue class modulo c, where c is composite, iff x ∈ [0,1/y], where y is the largest prime factor of c. Copyright © 2018, The Authors. All rights reserved.

关键词： C (programming language)

Uplink-downlink duality between multiple-access and broadcast channels with compressing relays

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arXiv 2020年

作者： Liu, Liang Liu, Ya-Feng Patil, Pratik Yu, Wei the Department of Electronic and Information Engineering The Hong Kong Polytechnic University Hong Kong the 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 Edward S. Rogers Sr. Department of Electrical and Computer Engineering the University of Toronto the Department of Statistics and Data Science and the Machine Learning Department Carnegie Mellon University PittsburghPA15213 United States The Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto 10 King’s College Road TorontoONM5S3G4 Canada

—Uplink-downlink duality refers to the fact that under a sum-power constraint, the capacity regions of a Gaussian multiple-access channel and a Gaussian broadcast channel with Hermitian transposed channel matrices are identical. This paper generalizes this result to a cooperative cellular network, in which remote access-points are deployed as relays in serving the users under the coordination of a central processor (CP). In this model, the users and the relays are connected over noisy wireless links, while the relays and the CP are connected over noiseless but rate-limited fronthaul links. Based on a Lagrangian technique, this paper establishes a duality relationship between such a multiple-access relay channel and broadcast relay channel, under the assumption that the relays use compression-based strategies. Specifically, we show that under the same total transmit power constraint and individual fronthaul rate constraints, the achievable rate regions of the Gaussian multiple-access and broadcast relay channels are identical, when either independent compression or Wyner-Ziv and multivariate compression strategies are used. The key observations are that if the beamforming vectors at the relays are fixed, the sum-power minimization problems under the achievable rate and fronthaul constraints in both the uplink and the downlink can be transformed into either a linear programming or a semidefinite programming problem depending on the compression technique, and that the uplink and downlink problems are Lagrangian duals of each other. Moreover, the dual variables corresponding to the downlink rate constraints become the uplink powers;the dual variables corresponding to the downlink fronthaul constraints become the uplink quantization noises. This duality relationship enables an efficient algorithm for optimizing the downlink transmission and relaying strategies based on the uplink. Copyright © 2020, The Authors. All rights reserved.

关键词： Linear programming

Evaluating the Accuracy and Reliability of Real-World Digital Mobility Outcomes in Older Adults After Hip Fracture: Cross-Sectional Observational Study

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JMIR Formative Research 2025年 9卷 e67792页

作者： Berge, Martin A. Paraschiv-Ionescu, Anisoara Kirk, Cameron Küderle, Arne Micó-Amigo, Encarna Becker, Clemens Cereatti, Andrea Del Din, Silvia Engdal, Monika Garcia-Aymerich, Judith Grønvik, Karoline B. Hansen, Clint Hausdorff, Jeffrey M. Helbostad, Jorunn L. Jansen, Carl-Philipp Johnsen, Lars Gunnar Klenk, Jochen Koch, Sarah Maetzler, Walter Megaritis, Dimitrios Müller, Arne Rochester, Lynn Schwickert, Lars Taraldsen, Kristin Vereijken, Beatrix Department of Neuromedicine and Movement Science Norwegian University of Science and Technology Trondheim Norway Laboratory of Movement Analysis and Measurement Ecole Polytechnique Federale de Lausanne Lausanne Switzerland Translational and Clinical Research Institute Faculty of Medical Sciences Newcastle University Newcastle Upon Tyne United Kingdom Machine Learning and Data Analytics Lab Department Artificial Intelligence in Biomedical Engineering Friedrich-Alexander-Universität Erlangen-Nürnberg Erlangen Germany Geriatric Center Medical Faculty Heidelberg Heidelberg University Heidelberg Germany Department of Geriatrics and Rehabilitation Robert Bosch Hospital Stuttgart Germany Department of Electronics and Telecommunications Politecnico di Torino Turin Italy National Institute for Health and Care Research Newcastle Biomedical Research Centre Newcastle University The Newcastle Upon Tyne Hospitals NHS Foundation Trust Newcastle Upon Tyne United Kingdom Barcelona Institute for Global Health Barcelona Spain Department of Medicine and Life Sciences Universitat Pompeu Fabra Catalonia Barcelona Spain CIBER Epidemiología y Salud Pública Madrid Spain Department of Neurology University Hospital Schleswig-Holstein Kiel University Kiel Germany Center for the Study of Movement Cognition and Mobility Neurological Institute Tel Aviv Medical Center Tel Aviv Israel Department of Physical Therapy Faculty of Medical & Health Sciences Tel Aviv University Tel Aviv Israel Sagol School of Neuroscience Tel Aviv University Tel Aviv Israel Rush Alzheimer’s Disease Center Rush University Medical Center Chicago IL United States Department of Orthopedic Surgery Rush Medical College Rush University Chicago IL United States Department of Orthopaedic Surgery St. Olav’s Hospital Trondheim Norway Institute of Epidemiology and Medical Biometry Ulm University Ulm Germany IB University of Health and Social Sciences Study Centre Stuttgart Stuttgart Germany Department of Sport

Background: Algorithms estimating real-world digital mobility outcomes (DMOs) are increasingly validated in healthy adults and various disease cohorts. However, their accuracy and reliability in older adults after hip fracture, who often walk slowly for short durations, is underexplored. Objective: This study examined DMO accuracy and reliability in a hip fracture cohort considering walking bout (WB) duration, physical function, days since surgery, and walking aid use. Methods: In total, 19 community-dwelling participants were real-world monitored for 2.5 hours using a lower back wearable device and a reference system combining inertial modules, distance sensors, and pressure insoles. A total of 6 DMO estimates from 164 WBs from 58% (11/19) of the participants (aged 71-90 years;assessed 32-390 days after surgery;Short Physical Performance Battery [SPPB] scores of 3-12;gait speed range 0.39-1.34 m/s) were assessed against the reference system at the WB and participant level. We stratified by WB duration (all WBs, WBs of >10 seconds, WBs of 10-30 seconds, and WBs of >30 seconds) and lower versus higher SPPB scores and observed whether days since surgery and walking aid use affected DMO accuracy and reliability. Results: Across WBs, walking speed and distance ranged from 0.25 to 1.29 m/s and from 1.7 to 436.5 m, respectively. Estimation of walking speed, cadence, stride duration, number of steps, and distance stratified by WB duration showed intraclass correlation coefficients (ICCs) ranging from 0.50 to 0.99 and mean relative errors (MREs) from –6.9% to 12.8%. Stride length estimation showed poor reliability, with ICCs ranging from 0.30 to 0.49 and MREs from 6.1% to 13.2%. Walking speed and distance ICCs in the higher–SPPB score group ranged from 0.85 to 0.99, and MREs ranged from –10.1% to –1.7%. In the lower–SPPB score group, walking speed and distance ICCs ranged from 0.17 to 0.99, and MREs ranged from 13.5% to 32.6%. There was no discernible effect of time since s

关键词： active aging cadence digital mobility assessment distance free living gait walking speed wearable device

Smart Annotation Tool for Multi-sensor Gait-based Daily Activity data

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Smart Annotation Tool for Multi-sensor Gait-based Daily Acti...

IEEE International Conference on Pervasive Computing and Communications

作者： Christine F. Martindale Nils Roth Julius Hannink Sebastijan Sprager Bjoern M. Eskofier Machine Learning and Data Analytics Lab Computer Science Department Friedrich-Alexander University Erlangen-Nürnberg Germany Faculty of Computer and Information Science University of Ljubljana Slovenia

ISBN: (纸本)9781538632284

The monitoring of patients within a natural, home environment is important in order to close knowledge gaps in the treatment and care of neurodegenerative diseases, such as quantifying the daily fluctuation of Parkinson's patients' symptoms. The combination of machine learning algorithms and wearable sensors for gait analysis is becoming capable of achieving this. However, these algorithms require large, labelled, realistic datasets for training. Most systems used as a ground truth for labelling are restricted to the laboratory environment, as well as being large and expensive. We propose a study design for a realistic activity monitoring dataset, collected with inertial measurement units, pressure insoles and cameras. It is not restricted by a fixed location or capture volume and still enables the labelling of gait phases or, where non-gait movement such as jumping occur: on-the-ground, off-the-ground phases. Additionally, this paper proposes a smart annotation tool which reduces annotation cost by more than 80%. This smart annotation is based on edge detection within the pressure sensor signal. The tool also enables annotators to perform assisted correction of these labels in a post-processing step. This system enables the collection and labelling of large, fairly realistic datasets where 93% of the automatically generated labels are correct and only an additional 10% need to be inserted manually. Our tool and protocol, as a whole, will be useful for efficiently collecting the large datasets needed for training and validation of algorithms capable of cyclic human motion analysis in natural environments.

关键词： Image edge detection Tools Cameras Labeling Pressure sensors Intelligent sensors Edge detection Pressure Sensor Device Component Cameras intelligent sensors ANNOTATIONS laboratory environment dataset Wearable sensors Measurement units Research Design INSOLE Packaging

Gradient descent finds global minima of deep neural networks

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arXiv 2018年

作者： Du, Simon S. Lee, Jason D. Li, Haochuan Wang, Liwei Zhai, Xiyu Machine Learning Department Carnegie Mellon University Data Science and Operations Department University of Southern California School of Physics Peking University Center for Data Science Peking University Beijing Institute of Big Data Research Key Laboratory of Machine Perception Moe School of Eecs Peking University Department of Eecs Massachusetts Institute of Technology

Gradient descent finds a global minimum in training deep neural networks despite the objective function being non-convex. The current paper proves gradient descent achieves zero training loss in polynomial time for a deep over-parameterized neural network with residual connections (ResNet). Our analysis relies on the particular structure of the Gram matrix induced by the neural network architecture. This structure allows us to show the Gram matrix is stable throughout the training process and this stability implies the global optimality of the gradient descent algorithm. We further extend our analysis to deep residual convolutional neural networks and obtain a similar convergence result. Copyright © 2018, The Authors. All rights reserved.

关键词： Gradient methods

Algorithmic regularization in learning deep homogeneous models: layers are automatically balanced 18

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Algorithmic regularization in learning deep homogeneous mode...

Proceedings of the 32nd International Conference on Neural Information Processing Systems

作者： Simon S. Du Wei Hu Jason D. Lee Machine Learning Department School of Computer Science Carnegie Mellon University Computer Science Department Princeton University Department of Data Sciences and Operations Marshall School of Business University of Southern California

We study the implicit regularization imposed by gradient descent for learning multi-layer homogeneous functions including feed-forward fully connected and convolutional deep neural networks with linear, ReLU or Leaky ReLU activation. We rigorously prove that gradient flow (i.e. gradient descent with infinitesimal step size) effectively enforces the differences between squared norms across different layers to remain invariant without any explicit regularization. This result implies that if the weights are initially small, gradient flow automatically balances the magnitudes of all layers. Using a discretization argument, we analyze gradient descent with positive step size for the non-convex low-rank asymmetric matrix factorization problem without any regularization. Inspired by our findings for gradient flow, we prove that gradient descent with step sizes ηt = O(t-(1/2 + δ)) (0 < δ ≤ 1/2) automatically balances two low-rank factors and converges to a bounded global optimum. Furthermore, for rank-1 asymmetric matrix factorization we give a finer analysis showing gradient descent with constant step size converges to the global minimum at a globally linear rate. We believe that the idea of examining the invariance imposed by first order algorithms in learning homogeneous models could serve as a fundamental building block for studying optimization for learning deep models.

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Generating Synthetic Computed Tomography for Radiotherapy: SynthRAD2023 Challenge Report

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arXiv 2024年

作者： Huijben, Evi M.C. Terpstra, Maarten L. Galapon, Arthur Pai, Suraj Thummerer, Adrian Koopmans, Peter Afonso, Manya van Eijnatten, Maureen Gurney-Champion, Oliver Chen, Zeli Zhang, Yiwen Zheng, Kaiyi Li, Chuanpu Pang, Haowen Ye, Chuyang Wang, Runqi Song, Tao Fan, Fuxin Qiu, Jingna Huang, Yixing Ha, Juhyung Park, Jong Sung Alain-Beaudoin, Alexandra Bériault, Silvain Yu, Pengxin Guo, Hongbin Huang, Zhanyao Li, Gengwan Zhang, Xueru Fan, Yubo Liu, Han Xin, Bowen Nicolson, Aaron Zhong, Lujia Deng, Zhiwei Müller-Franzes, Gustav Khader, Firas Li, Xia Zhang, Ye Hémon, Cédric Boussot, Valentin Zhang, Zhihao Wang, Long Bai, Lu Wang, Shaobin Mus, Derk Kooiman, Bram Sargeant, Chelsea A.H. Henderson, Edward G.A. Kondo, Satoshi Kasai, Satoshi Karimzadeh, Reza Ibragimov, Bulat Helfer, Thomas Dafflon, Jessica Chen, Zijie Wang, Enpei Perko, Zoltan Maspero, Matteo Department of Biomedical Engineering Eindhoven University of Technology Eindhoven Netherlands Radiotherapy Department University Medical Center Utrecht Utrecht Netherlands Computational Imaging Group for MR Diagnostics & Therapy University Medical Center Utrecht Utrecht Netherlands Department of Radiation Oncology University Medical Center Groningen University of Groningen Groningen Netherlands GROW School for Oncology Maastricht University Medical Centre Maastricht Netherlands Department of Radiation Oncology LMU University Hospital LMU Munich Munich Germany Department of Radiation Oncology Radboud University Medical Center Nijmegen Netherlands Wageningen University & Research Wageningen Plant Research Wageningen Netherlands Department of Radiology and Nuclear Medicine Amsterdam UMC Location University of Amsterdam Amsterdam Netherlands Cancer Center Amsterdam Imaging and Biomarkers Amsterdam Netherlands School of Biomedical Engineering Southern Medical University Guangzhou China School of Integrated Circuits and Electronics Beijing Institute of Technology Beijing China School of Biomedical Engineering ShanghaiTech University Shanghai China Fudan University Shanghai China Friedrich-Alexander-Universität Erlangen-Nürnberg Erlangen Germany Indiana University Bloomington United States Advanced Development Engineering Elekta Ltd Montreal Canada Infervision Medical Technology Co. Ltd. Beijing China Department of Biomedical Engineering Shantou University China Independent researchers Department of Computer Science Vanderbilt University Nashville United States Australian e-Health Research Centre CSIRO HerstonQLD Australia Los AngelesCA United States University Hospital Aachen Aachen Germany Center for Proton Therapy Paul Scherrer Institut Villigen Switzerland Department of Computer Science ETH Zurich Zurich Switzerland University Rennes 1 CLCC Eugène Marquis INSERM LTSI Rennes France Subtle Medical Shanghai China MedMind Technology Co.

Radiation therapy plays a crucial role in cancer treatment, necessitating precise delivery of radiation to tumors while sparing healthy tissues over multiple days. Computed tomography (CT) is integral for treatment planning, offering electron density data crucial for accurate dose calculations. However, accurately representing patient anatomy is challenging, especially in adaptive radiotherapy, where CT is not acquired daily. Magnetic resonance imaging (MRI) provides superior soft-tissue contrast. Still, it lacks electron density information, while cone beam CT (CBCT) lacks direct electron density calibration and is mainly used for patient positioning. Adopting MRI-only or CBCT-based adaptive radiotherapy eliminates the need for CT planning but presents challenges. Synthetic CT (sCT) generation techniques aim to address these challenges by using image synthesis to bridge the gap between MRI, CBCT, and CT. The SynthRAD2023 challenge was organized to compare synthetic CT generation methods using multi-center ground truth data from 1080 patients, divided into two tasks: 1) MRI-to-CT and 2) CBCT-to-CT. The evaluation included image similarity and dose-based metrics from proton and photon plans. The challenge attracted significant participation, with 617 registrations and 22/17 valid submissions for tasks 1/2. Top-performing teams achieved high structural similarity indices (≥ 0.87/0.90) and gamma pass rates for photon (≥ 98.1%/99.0%) and proton (≥ 97.3%/97.0%) plans. However, no significant correlation was found between image similarity metrics and dose accuracy, emphasizing the need for dose evaluation when assessing the clinical applicability of sCT. SynthRAD2023 facilitated the investigation and benchmarking of sCT generation techniques, providing insights for developing MRI-only and CBCT-based adaptive radiotherapy. It showcased the growing capacity of deep learning to produce high-quality sCT, reducing reliance on conventional CT for treatment planning. © 2024, CC

关键词： Radiotherapy

167-PFlops deep learning for electron microscopy: From learning physics to atomic manipulation

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167-PFlops deep learning for electron microscopy: From learn...

2018 International Conference for High Performance Computing, Networking, Storage, and Analysis, SC 2018

作者： Patton, Robert M. Travis Johnston, J. Young, Steven R. Schuman, Catherine D. March, Don D. Potok, Thomas E. Rose, Derek C. Lim, Seung-Hwan Karnowski, Thomas P. Ziatdinov, Maxim A. Kalinin, Sergei V. Oak Ridge National Laboratory Oak RidgeTN37831-6085 United States Computational Data Analytics Group United States Geographic Information Science and Technology Group United States Imaging Signals and Machine Learning Group United States Institute for Functional Imaging of Materials United States Center for Nanophase Materials Sciences United States

ISBN: (纸本)9781538683842

An artificial intelligence system called MENNDL, which used 25,200 NVIDIA Volta GPUs on Oak Ridge National Laboratory's Summit machine, automatically designed an optimal deep learning network in order to extract structural information from raw atomic-resolution microscopy data. In a few hours, MENNDL creates and evaluates millions of networks using a scalable, parallel, asynchronous genetic algorithm augmented with a support vector machine to automatically find a superior deep learning network topology and hyper-parameter set than a human expert can find in months. For the application of electron microscopy, the system furthers the goal of improving our understanding of the electron-beam-matter interactions and real-time image-based feedback, which enables a huge step beyond human capacity towards nanofabricating materials automatically. MENNDL has been scaled to the 4,200 available nodes of Summit achieving a measured 152.5 PFlops, with an estimated sustained performance of 167 PFlops when the entire machine is available. © 2018 IEEE.

关键词： Genetic algorithms

Constructing Impactful machine learning Research for Astronomy: Best Practices for Researchers and Reviewers

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arXiv 2023年

作者： Huppenkothen, Daniela Ntampaka, Michelle Ho, Matthew Fouesneau, Morgan Nord, Brian Peek, J.E.G. Walmsley, Mike Wu, John F. Avestruz, C. Buck, Tobias Brescia, Massimo Finkbeiner, Douglas P. Goulding, Andy D. Kacprzak, T. Melchior, Peter Pasquato, Mario Ramachandra, Nesar Ting, Yuan-Sen van de Ven, Glenn Villar, Soledad Villar, V.A. Zinger, Elad SRON Netherlands Institute for Space Research Niels Bohrweg 4 Leiden2333CA Netherlands Anton Pannekoek Institute for Astronomy University of Amsterdam Science Park 904 Amsterdam1098 XH Netherlands Space Telescope Science Institute BaltimoreMD21218 United States Department of Physics & Astronomy Johns Hopkins University BaltimoreMD21218 United States UMR 7095 98 bis bd Arago ParisF-75014 France Königstuhl 17 HeidelbergD-69117 Germany Fermi National Accelerator Laboratory P. O. Box 500 BataviaIL60510 United States Kavli Institute for Cosmological Physics University of Chicago ChicagoIL60637 United States Department of Astronomy and Astrophysics University of Chicago ChicagoIL60637 United States Jodrell Bank Centre for Astrophysics Department of Physics & Astronomy University of Manchester ManchesterM13 9PL United Kingdom Dunlap Institute for Astronomy & Astrophysics University of Toronto 50 St. George Street TorontoONM5S 3H4 Canada Leinweber Center for Theoretical Physics University of Michigan Ann ArborMI48109 United States Department of Physics University of Michigan Ann ArborMI48109 United States Universität Heidelberg Interdisziplinäres Zentrum für Wissenschaftliches Rechnen Im Neuenheimer Feld 205 Heidelberg69120 Germany Universität Heidelberg Zentrum für Astronomie Institut für Theoretische Astrophysik Albert-Ueberle-Straße 2 Heidelberg69120 Germany Department of Physics "E. Pancini " University Federico II of Napoli Via Cinthia 21 NapoliI-80126 Italy INAF Astronomical Observatory of Capodimonte Salita Moiariello 16 NapoliI-80131 Italy Department of Physics Harvard University 17 Oxford St. CambridgeMA02138 United States Harvard-Smithsonian Center for Astrophysics 60 Garden St. CambridgeMA02138 United States Department of Astrophysical Sciences Princeton University PrincetonNJ08544 United States Swiss Data Science Center Paul Scherrer Institute Villigen5303 Switzerland Center for Statistics & Machine Learn

machine learning has rapidly become a tool of choice for the astronomical community. It is being applied across a wide range of wavelengths and problems, from the classification of transients to neural network emulators of cosmological simulations, and is shifting paradigms about how we generate and report scientific results. At the same time, this class of method comes with its own set of best practices, challenges, and drawbacks, which, at present, are often reported on incompletely in the astrophysical literature. With this paper, we aim to provide a primer to the astronomical community, including authors, reviewers, and editors, on how to implement machine learning models and report their results in a way that ensures the accuracy of the results, reproducibility of the findings, and usefulness of the method. Copyright © 2023, The Authors. All rights reserved.

关键词： machine learning