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Blind phaseless short-time fourier transform recovery

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arXiv 2018年

作者： Bendory, Tamir Edidin, Dan Eldar, Yonina C. Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Mathematics University of Missouri ColumbiaMO United States Andrew and Erna Viterbi Faculty of Electrical Engineering Technion - Israel Institute of Technology Haifa Israel

The problem of recovering a pair of signals from their blind phaseless short-time Fourier transform measurements arises in several important phase retrieval applications, including ptychography and ultra-short pulse characterization. In this paper, we prove that in order to determine a pair of generic signals uniquely, up to trivial ambiguities, the number of phaseless measurements one needs to collect is, at most, five times the number of parameters required to describe the signals. This result improves significantly upon previous papers, which required the number of measurements to be quadratic in the number of parameters rather than linear. In addition, we consider the simpler problem of recovering a pair of generic signals from their blind short-time Fourier transform, when the phases are known. In this setting, which can be understood as a special case of the blind deconvolution problem, we show that the number of measurements required to determine the two signals, up to trivial ambiguities, equals exactly the number of parameters to be recovered. As a side result, we study the classical phase retrieval problem-that is, recovering a signal from its Fourier magnitudes-when some entries of the signal are known a priori. We derive a bound on the number of required measurements as a function of the size of the set of known entries. Specifically, we show that if most of the signal's entries are known, then only a few Fourier magnitudes are necessary to determine a signal uniquely. Copyright © 2018, The Authors. All rights reserved.

关键词： Convolution

Manifold learning for organizing unstructured sets of process observations

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arXiv 2018年

作者： Dietrich, Felix Kooshkbaghi, Mahdi Bollt, Erik M. Kevrekidis, Ioannis G. Department of Chemical and Biomolecular Engineering Department of Applied Mathematics and Statistics Johns Hopkins University BaltimoreMD21218 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics Department of Electrical and Computer Engineering Clarkson Center for Complex Systems Science Clarkson University PotsdamNY13699-5815 United States

Data mining is routinely used to organize ensembles of short temporal observations so as to reconstruct useful, low-dimensional realizations of an underlying dynamical system. In this paper, we use manifold learning to organize unstructured ensembles of observations ("trials") of a system's response surface. We have no control over where every trial starts;and during each trial operating conditions are varied by turning "agnostic" knobs, which change system parameters in a systematic but unknown way. As one (or more) knobs "turn" we record (possibly partial) observations of the system response. We demonstrate how such partial and disorganized observation ensembles can be integrated into coherent response surfaces whose dimension and parametrization can be systematically recovered in a data-driven fashion. The approach can be justified through the Whitney and Takens embedding theorems, allowing reconstruction of manifolds/attractors through different types of observations. We demonstrate our approach by organizing unstructured observations of response surfaces, including the reconstruction of a cusp bifurcation surface for Hydrogen combustion in a Continuous Stirred Tank Reactor. Finally, we demonstrate how this observation-based reconstruction naturally leads to informative transport maps between input parameter space and output/state variable *** codes 37M20 Copyright © 2018, The Authors. All rights reserved.

关键词： Dynamical systems

A convex program for bilinear inversion of sparse vectors

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arXiv 2018年

作者： Aghasi, Alireza Ahmed, Ali Hand, Paul Joshi, Babhru J. Mack Robinson College of Business GSU Department of Electrical Engineering ITU Lahore Pakistan Department of Mathematics College of Computer and Information Science Northeastern University Department of Computational and Applied Mathematics Rice University

We consider the bilinear inverse problem of recovering two vectors, x ∈ RL and w ∈ RL, from their entrywise product. We consider the case where x and w have known signs and are sparse with respect to known dictionaries of size K and N, respectively. Here, K and N may be larger than, smaller than, or equal to L. We introduce `1-BranchHull, which is a convex program posed in the natural parameter space and does not require an approximate solution or initialization in order to be stated or solved. We study the case where x and w are S1- and S2-sparse with respect to a random dictionary and present a recovery guarantee that only depends on the number of measurements as L ≥ Ω(S1 + S2) log2(K + N). Numerical experiments verify that the scaling constant in the theorem is not too large. One application of this problem is the sweep distortion removal task in dielectric imaging, where one of the signals is a nonnegative reflectivity, and the other signal lives in a known subspace, for example that given by dominant wavelet coefficients. We also introduce a variants of `1-BranchHull for the purposes of tolerating noise and outliers, and for the purpose of recovering piecewise constant signals. We provide an ADMM implementation of these variants and show they can extract piecewise constant behavior from real images. Copyright © 2018, The Authors. All rights reserved.

关键词： Convex optimization

Colossal enhancement of spin transmission through magnon confinement in an antiferromagnet

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arXiv 2025年

作者： Husain, Sajid Ramesh, Maya Li, Xinyan Prokhorenko, Sergei Ojha, Shashank Kumar Ross, Aiden Das, Koushik Zhao, Boyang Park, Hyeon Woo Meisenheimer, Peter Nahas, Yousra Caretta, Lucas Martin, Lane W. Kim, Se Kwon Yao, Zhi Wen, Haidan Salahuddin, Sayeef Chen, Long-Qing Han, Yimo de Sousa, Rogério Bellaiche, Laurent Bibes, Manuel Schlom, Darrell G. Ramesh, Ramamoorthy Department of Materials Science and Engineering University of California BerkeleyCA94720 United States Rice University Materials Science and NanoEngineering HoustonTX United States Department of Materials Science and Engineering Cornell University IthacaNY14853 United States Rice Advanced Materials Institute Rice University HoustonTX77005 United States Smart Ferroic Materials Center Physics Department Institute for Nanoscience and Engineering University of Arkansas FayettevilleAR United States Department of Materials Science and Engineering Materials Research Institute Pennsylvania State University University ParkPA16802 United States Department of Electrical Engineering and Computer Sciences University of California BerkeleyCA94720 United States Department of Chemistry University of California BerkeleyCA94720 United States Materials Science Division Argonne National Laboratory LemontIL60439 United States Department of Physics Korea Advanced Institute of Science and Technology Daejeon Korea Republic of School of Engineering Brown University ProvidenceRI77005 United States Departments of Chemistry and Physics and Astronomy Rice University HoustonTX77005 United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory CA94720 United States Advanced Photon Source Argonne National Laboratory LemontIL60439 United States Materials Science Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Rice Advanced Materials Institute Smalley-Curl Institute Ken Kennedy Institute Rice University HoustonTX77005 United States Department of Physics and Astronomy University of Victoria VictoriaBCV8W 2Y2 Canada Centre for Advanced Materials and Related Technology University of Victoria VictoriaBCV8W 2Y2 Canada Department of Materials Science and Engineering Tel Aviv University Ramat Aviv Tel Aviv6997801 Israel Laboratoire Albert Fert CNRS Thales Université Paris-Saclay Pa

Since Felix Bloch’s introduction of the concept of spin waves in 1930, magnons (the quanta of spin waves) have been extensively studied in a range of materials for spintronics, particularly for non-volatile logic-in-memory devices. Controlling magnons in conventional antiferromagnets and harnessing them in practical applications, however, remains a challenge. In this letter, we demonstrate highly efficient magnon transport in an LaFeO3/BiFeO3/LaFeO3 all-antiferromagnetic system which can be controlled electrically, making it highly desirable for energy-efficient computation. Leveraging spin-orbit-driven spin-charge transduction, we demonstrate that this material architecture permits magnon confinement in ultrathin antiferromagnets, enhancing the output voltage generated by magnon transport by several orders of magnitude, which provides a pathway to enable magnetoelectric memory and logic functionalities. Additionally, its non-volatility enables ultralow-power logic-in-memory processing, where magnonic devices can be efficiently reconfigured via electrically controlled magnon spin currents within magnetoelectric channels. © 2025, CC BY.

关键词： Antiferromagnetism

Metrics Reloaded: Recommendations for image analysis validation

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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

Gaussian process landmarking on manifolds

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arXiv 2018年

作者： Gaoy, Tingran Kovalsky, Shahar Z. Daubechies, Ingrid Computational and Applied Mathematics Initiative Department of Statistics University of Chicago ChicagoIL United States Department of Mathematics Duke University DurhamNC United States Department of Mathematics Department of Electrical and Computer Engineering Duke University DurhamNC United States

As a means of improving analysis of biological shapes, we propose an algorithm for sampling a Riemannian manifold by sequentially selecting points with maximum uncertainty under a Gaussian process model. This greedy strategy is known to be near-optimal in the experimental design liter- ature, and appears to outperform the use of user-placed landmarks in representing the geometry of biological objects in our application. In the noiseless regime, we establish an upper bound for the mean squared prediction error (MSPE) in terms of the number of samples and geometric quantities of the manifold, demonstrating that the MSPE for our proposed sequential design decays at a rate comparable to the oracle rate achievable by any sequential or non-sequential optimal design;to our knowledge this is the first result of this type for sequential experimental design. The key is to link the greedy algorithm to reduced basis methods in the context of model reduction for partial differential equations. We expect this approach will find additional applications in other fields of research.60G15, 62K05, 65D18 Copyright © 2018, The Authors. All rights reserved.

关键词： Statistics

Patterns of somatic structural variation in human cancer genomes (vol 578, pg 112, 2020)

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NATURE 2023年第7948期614卷 E38-E38页

作者： Li, Yilong Roberts, Nicola D. Wala, Jeremiah A. Shapira, Ofer Schumacher, Steven E. Kumar, Kiran Khurana, Ekta Waszak, Sebastian Korbel, Jan O. Haber, James E. Imielinski, Marcin Weischenfeldt, Joachim Beroukhim, Rameen Campbell, Peter J. Cancer Genome Project Wellcome Trust Sanger Institute Hinxton UK Totient Inc Cambridge MA USA Wellcome Sanger Institute Wellcome Genome Campus Hinxton UK Department of Haematology University of Cambridge Cambridge UK Cambridge University Hospitals NHS Foundation Trust Cambridge UK Korea Advanced Institute of Science and Technology Daejeon South Korea Department of Zoology Genetics and Physical Anthropology University of Santiago de Compostela Santiago de Compostela Spain Centre for Research in Molecular Medicine and Chronic Diseases (CIMUS) University of Santiago de Compostela Santiago de Compostela Spain The Biomedical Research Centre (CINBIO) University of Vigo Vigo Spain Centre for Research in Molecular Medicine and Chronic Diseases (CiMUS) Universidade de Santiago de Compostela Santiago de Compostela Spain Department of Zoology Genetics and Physical Anthropology (CiMUS) Universidade de Santiago de Compostela Santiago de Compostela Spain The Biomedical Research Centre (CINBIO) Universidade de Vigo Vigo Spain The Broad Institute of Harvard and MIT Cambridge MA USA Bioinformatics and Integrative Genomics Harvard University Cambridge MA USA Department of Cancer Biology Dana-Farber Cancer Institute Boston MA USA Broad Institute of MIT and Harvard Cambridge MA USA Department of Medical Oncology Dana-Farber Cancer Institute Boston MA USA Harvard Medical School Boston MA USA Massachusetts General Hospital Center for Cancer Research Charlestown MA USA Dana-Farber Cancer Institute Boston MA USA Department of Biostatistics and Computational Biology Dana-Farber Cancer Institute and Harvard Medical School Boston MA USA Weill Cornell Medical College New York NY USA Department of Physiology and Biophysics Weill Cornell Medicine New York NY USA Institute for Computational Biomedicine Weill Cornell Medicine New York NY USA Controlled Department and Institution New York NY USA Englander Institute for Precision Medicine Weill Cornell Medicine Ne

Publisher Correction: Comprehensive molecular characterization of mitochondrial genomes in human cancers

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Nature genetics 2023年第5期55卷 893页

作者： Yuan Yuan Young Seok Ju Youngwook Kim Jun Li Yumeng Wang Christopher J Yoon Yang Yang Inigo Martincorena Chad J Creighton John N Weinstein Yanxun Xu Leng Han Hyung-Lae Kim Hidewaki Nakagawa Keunchil Park Peter J Campbell Han Liang Department of Bioinformatics and Computational Biology The University of Texas MD Anderson Cancer Center Houston TX USA. Cancer Genome Project Wellcome Trust Sanger Institute Hinxton UK. Graduate School of Medical Science and Engineering Korea Advanced Institute of Science and Technology Daejeon Korea. Department of Health Science and Technology Samsung Advanced Institute for Health Science and Technology Sungkyunkwan University School of Medicine Seoul Korea. Quantitative and Computational Biosciences Graduate Program Baylor College of Medicine Houston TX USA. Division of Biostatistics The University of Texas Health Science Center at Houston School of Public Health Houston TX USA. Department of Medicine and Dan L. Duncan Cancer Center Division of Biostatistics Baylor College of Medicine Houston TX USA. Department of Systems Biology The University of Texas MD Anderson Cancer Center Houston TX USA. Department of Applied Mathematics and Statistics Johns Hopkins University Baltimore MD USA. Department of Biochemistry and Molecular Biology The University of Texas Health Science Center at Houston McGovern Medical School Houston TX USA. Department of Biochemistry Ewha Womans University School of Medicine Seoul Korea. Laboratory for Cancer Genomics RIKEN Center for Integrative Medical Sciences Yokohama Japan. Division of Hematology/Oncology Samsung Medical Center Sungkyunkwan University School of Medicine Seoul Korea. kpark@skku.edu. Cancer Genome Project Wellcome Trust Sanger Institute Hinxton UK. pc8@sanger.ac.uk. Cambridge University Hospitals NHS Foundation Trust Cambridge UK. pc8@sanger.ac.uk. Department of Bioinformatics and Computational Biology The University of Texas MD Anderson Cancer Center Houston TX USA. hliang1@***. Quantitative and Computational Biosciences Graduate Program Baylor College of Medicine Houston TX USA. hliang1@***. Department of Systems Biology The University of Texas MD Anderson Cancer Center Houston TX USA. hliang1@mdanderson

Mixed mode oscillations and phase locking in coupled FitzHugh-Nagumo model neurons

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arXiv 2018年

作者： Davison, Elizabeth N. Aminzare, Zahra Leonard, Naomi Ehrich Dey, Biswadip Department of Mechanical and Aerospace Engineering Princeton University PrincetonNJ08540 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

We study the dynamics of a low-dimensional system of coupled model neurons as a step towards understanding the vastly complex network of neurons in the brain. We analyze the bifurcation structure of a system of two model neurons with unidirectional coupling as a function of two physiologically relevant parameters: the external current input only to the first neuron and the strength of the coupling from the first to the second neuron. Leveraging a timescale separation, we prove necessary conditions for multiple timescale phenomena observed in the coupled system, including canard solutions and mixed mode oscillations. For a larger network of model neurons, we present a sufficient condition for phase locking when external inputs are heterogeneous. Finally, we generalize our results to directed trees of model neurons with heterogeneous inputs.34A26, 34C15, 34C60, 34D15, 34E17, 37G05, 37G10, 92B20, 92C20 Copyright © 2018, The Authors. All rights reserved.

关键词： Bifurcation (mathematics)