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Data-driven model reduction and transfer operator approximation

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arXiv 2017年

作者： Klus, Stefan Nüske, Feliks Koltai, Péter Wu, Hao Kevrekidis, Ioannis Schütte, Christof Noé, Frank Department of Mathematics and Computer Science Freie Universität Berlin Germany Department of Chemical and Biological Engineering & Program in Applied and Computational Mathematics Princeton University United States Zuse Institute Berlin Germany

In this review paper, we will present different data-driven dimension reduction techniques for dynamical systems that are based on transfer operator theory as well as methods to approximate transfer operators and their eigenvalues, eigenfunctions, and eigenmodes. The goal is to point out similarities and differences between methods developed independently by the dynamical systems, fluid dynamics, and molecular dynamics communities such as time-lagged independent component analysis (TICA), dynamic mode decomposition (DMD), and their respective generalizations. As a result, extensions and best practices developed for one particular method can be carried over to other related methods. Copyright © 2017, The Authors. All rights reserved.

关键词： Dynamical systems

The Art of Designing a Curriculum Optimized for Learning Transfer

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Change 2019年第6期51卷 52页

作者： Jensen, Christopher X. J. Brooks, Brian Suh, Keena Shmulevsky, Allegra Marino Wynter, Chris Chris Jensen is Associate Professor of Ecology & Evolution in the Department of Mathematics and Science Pratt Institute. He is an educator writer and scientist with interests in pedagogy cooperation human cultural evolution and sustainability. Brian Brooks is Adjunct Associate Professor in the Foundation Art Program and the K-12 Center for Art and Design and Community Engagement Pratt Institute. He is interested in interdisciplinary and cross-cultural education student self-assessment visual thinking and learning and the Scholarship of Teaching and Learning. Keena Suh is Associate Professor in the Interior Design Program at Pratt Institute and an architect with over 20 years of active professional practice in architecture and interior design in New York City ranging from affordable housing to commercial and high-end residential design. Allegra Marino Shmulevsky is Visiting Instructor and Lecturer in the Intensive English Program Pratt Institute. She teaches English language literature writing and research skills to the international student population. Her interests include pedagogy sociolinguistics visual art and how the three intersect. Chris Wynter is Professor in the Foundation Art Program Pratt Institute and a visual artist working in a variety of media. His practice includes studio work for exhibitions as well as private and public-space commissions working with architects interior designers structural engineers and textile designers.

Teachers hope that students will take what they have learned and apply it to other contexts. Teachers also assume that students bring to the classroom, prior learning skills and conceptual understanding that form the foundation of new learning. Educational scholars call this import to and export from different learning experiences "transfer of learning." Perhaps transfer of learning seems like an obvious goal that any faculty member would--and perhaps should--pursue. After all, should students not utilize what they have learned in courses in their subsequent education, careers, and perhaps personal lives? And yet, many faculty members are unaware of what transfer of learning is. Few faculty members are actually trained in best practices for making learning transferable. That students apply what they have learned in one context to new challenges is often assumed but not always documented in research studies. This suggests the need to design curricula to better foster transfer of learning. For the past three years, the authors have explored how they might use a transfer of learning approach to create a better art and design curriculum for their students. Here they share their experience with looking for ways to maximize the potential for learning transfer, focusing on how they expanded their faculty learning community by fostering faculty conversations about transfer.

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Thermal transport properties of single-layer black phosphorous from extensive molecular dynamics simulations

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arXiv 2018年

作者： Xu, Ke Fan, Zheyong Zhang, Jicheng Wei, Ning Ala-Nissila, Tapio College of Water Resources and Architectural Engineering Northwest A&F University Yangling712100 China School of Mathematics and Physics Bohai University Jinzhou China QTF Centre of Excellence Department of Applied Physics Aalto University AaltoFI-00076 Finland Center for Interdisciplinary Mathematical Modeling Department of Mathematical Sciences Loughborough University Loughborough LeicestershireLE11 3TU United Kingdom

We compute the anisotropic in-plane thermal conductivity of suspended single-layer black phosphorous (SLBP) using three molecular dynamics (MD) based methods, including the equilibrium MD method, the nonequilibrium MD (NEMD) method, and the homogeneous nonequilibrium MD (HNEMD) method. Two existing parameterizations of the Stillinger-Weber (SW) potential for SLBP are used. Consistent results are obtained for all the three methods and conflicting results from previous MD simulations are critically assessed. Among the three methods, the HNEMD method is the most and the NEMD method the least efficient. The thermal conductivity values from our MD simulations are about an order of magnitude larger than the most recent predictions obtained using the Boltzmann transport equation approach considering long-range interactions in density functional theory calculations, suggesting that the short-range SW potential might be inadequate for describing the phonon anharmonicity in SLBP. Copyright © 2018, The Authors. All rights reserved.

关键词： Molecular dynamics

Spatiotemporal Dynamics and Reliable Computations in Recurrent Spiking Neural Networks

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Physical Review Letters 2017年第1期118卷 018103-018103页

作者： Ryan Pyle Robert Rosenbaum Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre Dame Indiana 46556 USA Interdisciplinary Center for Network Science and Applications University of Notre Dame Notre Dame Indiana 46556 USA

Randomly connected networks of excitatory and inhibitory spiking neurons provide a parsimonious model of neural variability, but are notoriously unreliable for performing computations. We show that this difficulty is overcome by incorporating the well-documented dependence of connection probability on distance. Spatially extended spiking networks exhibit symmetry-breaking bifurcations and generate spatiotemporal patterns that can be trained to perform dynamical computations under a reservoir computing framework.

关键词： Neuronal network activity Neuronal networks Spiking neurons Cortical networks

Pre-processing and classification of hyperspectral imagery via selective inpainting

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Pre-processing and classification of hyperspectral imagery v...

IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Victoria Chayes Kevin Miller Rasika Bhalerao Jiajie Luo Wei Zhu Andrea L. Bertozzi Wenzhi Liao Stanley Osher California Research Training Program in Computational and Applied Mathematics United States of America University of California Los Angeles Department of Mathematics United States of America Ghent University Department of Telecommunications and Information Processing Belgium

ISBN: (纸本)9781509041183

We propose a semi-supervised algorithm for processing and classification of hyperspectral imagery. For initialization, we keep 20% of the data intact, and use Principal Component Analysis to discard voxels from noisier bands and pixels. Then, we use either an Accelerated Proximal Gradient algorithm (APGL), or a modified APGL algorithm with a penalty term for distance between inpainted pixels and endmembers (APGL Hyp), on the initialized datacube to inpaint the missing data. APGL and APGL Hyp are distinguished by performance on datasets with full pixels removed or extreme noise. This inpainting technique results in band-by-band datacube sharpening and removal of noise from individual spectral signatures. We can also classify the inpainted cube by assigning each pixel to its nearest endmember via Euclidean distance. We demonstrate improved accuracy in classification over data-mining techniques like k-means, unmixing techniques like Hierarchical Non-Negative Matrix Factorization, and graph-based methods like Non-Local Total Variation.

关键词： Hyperspectral imagery (HSI) data preprocessing image inpainting image classification image enhancement Data preprocessing hyperspectral imagery Image classification image enhancement pixel Pretreatment matrix decomposition initialization Euclidean distance

Probing Shocked Ejecta in SN 1987A with XRISM-Resolve: The Effects of the Gate Valve Closed

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Research Notes of the AAS 2024年第6期8卷 156-156页

作者： Vincenzo Sapienza Marco Miceli Aya Bamba Salvatore Orlando Shiu-Hang Lee Shigehiro Nagataki Masaomi Ono Satoru Katsuda Koji Mori Makoto Sawada Yukikatsu Terada Roberta Giuffrida Fabrizio Bocchino Dipartimento di Fisica e Chimica E. Segrè Università degli Studi di Palermo Piazza del Parlamento 1 90134 Palermo Italy INAF—Osservatorio Astronomico di Palermo Piazza del Parlamento 1 90134 Palermo Italy Department of Physics Graduate School of Science The University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo 113-0033 Japan Research Center for the Early Universe School of Science The University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo 113-0033 Japan Trans-Scale Quantum Science Institute The University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo 113-0033 Japan Department of Astronomy Kyoto University Oiwake-cho Kitashirakawa Sakyo-ku Kyoto 606-8502 Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI) The University of Tokyo Kashiwa 277-8583 Japan RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) 2-1 Hirosawa Wako Saitama 351-0198 Japan Astrophysical Big Bang Laboratory (ABBL) RIKEN Cluster for Pioneering Research 2-1 Hirosawa Wako Saitama 351-0198 Japan Astrophysical Big Bang Group (ABBG) Okinawa Institute of Science and Technology Graduate University 1919-1 Tancha Onna-son Kunigami-gun Okinawa 904-0495 Japan Institute of Astronomy and Astrophysics Academia Sinica Taipei 10617 Taiwan Graduate School of Science and Engineering Saitama University 255 Simo-Ohkubo Sakura-ku Saitama city Saitama 338-8570 Japan Faculty of Engineering University of Miyazaki 1-1 Gakuen Kibanadai Nishi Miyazaki Miyazaki 889-2192 Japan Japan Aerospace Exploration Agency Institute of Space and Astronautical Science 3-1-1 Yoshino-dai Chuo-ku Sagamihara Kanagawa 252-5210 Japan Department of Physics Rikkyo University 3-34-1 Nishi Ikebukuro Toshima-ku Tokyo 171-8501 Japan

Supernova (SN) 1987A is widely regarded as an excellent candidate for leveraging the capabilities of the freshly launched XRISM satellite. Recent researches indicate that the X-ray emission from SN 1987A will increasingly originate from its ejecta in the years to come. In a previous study, we thoroughly examined the proficiency of XRISM-Resolve in identifying signatures of shocked ejecta in SN 1987A, synthesizing the XRISM-Resolve spectrum based on a state-of-the-art magneto-hydrodynamic simulation. However, following the satellite's launch, a technical issue arose with the XRISM instrument's gate valve, which failed to open, thereby affecting observations with the Resolve spectrometer. Here, we update our analysis, reevaluating our diagnostic approach under the assumption that the gate valve remains closed. We find that, even with the reduced instrumental capabilities, it will be possible to pinpoint the ejecta contribution through the study of the line profiles in the XRISM-Resolve spectrum of SN 1987A.

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Forecasting: theory and practice

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arXiv 2020年

作者： Petropoulos, Fotios Apiletti, Daniele Assimakopoulos, Vassilios Babai, Mohamed Zied Barrow, Devon K. Taieb, Souhaib Ben Bergmeir, Christoph Bessa, Ricardo J. Bijak, Jakub Boylan, John E. Browell, Jethro Carnevale, Claudio Castle, Jennifer L. Cirillo, Pasquale Clements, Michael P. Cordeiro, Clara Oliveira, Fernando Luiz Cyrino de Baets, Shari Dokumentov, Alexander Ellison, Joanne Fiszeder, Piotr Franses, Philip Hans Frazier, David T. Gilliland, Michael Gönül, M. Sinan Goodwin, Paul Grossi, Luigi Grushka-Cockayne, Yael Guidolin, Mariangela Guidolin, Massimo Gunter, Ulrich Guo, Xiaojia Guseo, Renato Harvey, Nigel Hendry, David F. Hollyman, Ross Januschowski, Tim Jeon, Jooyoung Jose, Victor Richmond R. Kang, Yanfei Koehler, Anne B. Kolassa, Stephan Kourentzes, Nikolaos Leva, Sonia Li, Feng Litsiou, Konstantia Makridakis, Spyros Martin, Gael M. Martinez, Andrew B. Meeran, Sheik Modis, Theodore Nikolopoulos, Konstantinos Önkal, Dilek Paccagnini, Alessia Panagiotelis, Anastasios Panapakidis, Ioannis Pavía, Jose M. Pedio, Manuela Pedregal, Diego J. Pinson, Pierre Ramos, Patrícia Rapach, David E. Reade, J. James Rostami-Tabar, Bahman Rubaszek, Michal Sermpinis, Georgios Shang, Han Lin Spiliotis, Evangelos Syntetos, Aris A. Talagala, Priyanga Dilini Talagala, Thiyanga S. Tashman, Len Thomakos, Dimitrios Thorarinsdottir, Thordis Todini, Ezio Arenas, Juan Ramón Trapero Wang, Xiaoqian Winkler, Robert L. Yusupova, Alisa Ziel, Florian School of Management University of Bath United Kingdom Politecnico di Torino Turin Italy Forecasting and Strategy Unit School of Electrical and Computer Engineering National Technical University of Athens Greece Kedge Business School France Department of Management Birmingham Business School University of Birmingham United Kingdom Belgium Faculty of Information Technology Monash University Melbourne Australia INESC TEC – Institute for Systems and Computer Engineering Technology and Science Porto Portugal Department of Social Statistics and Demography University of Southampton United Kingdom Centre for Marketing Analytics and Forecasting Lancaster University Management School Lancaster University United Kingdom School of Mathematics and Statistics University of Glasgow United Kingdom Department of Mechanical and Industrial Engineering University of Brescia Italy Magdalen College University of Oxford United Kingdom ZHAW School of Management and Law Zurich University of Applied Sciences Switzerland ICMA Centre Henley Business School University of Reading United Kingdom Faculdade de Ciências e Tecnologia Universidade do Algarve Portugal CEAUL Faculdade de Ciências Universidade de Lisboa Portugal Brazil Department of Business Informatics and Operations Management Faculty of Economics and Business Administration Universiteit Gent Belgium Let’s Forecast Australia Faculty of Economic Sciences and Management Nicolaus Copernicus University in Torun Poland Econometric Institute Erasmus School of Economics Rotterdam Netherlands Department of Econometrics and Business Statistics Monash University Melbourne Australia SAS United States Newcastle Business School Northumbria University Newcastle upon Tyne United Kingdom Department of Statistical Sciences University of Padua Italy Darden School of Business University of Virginia United States Finance Department Bocconi University Baffi-CAREFIN Centre Milan Italy Department of Tourism and Service Management MODUL Un

Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases. © 2020, CC BY.

关键词： Forecasting

Optimal jittered sampling for two points in the unit square

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arXiv 2017年

作者： Pausinger, Florian Rachh, Manas Steinerberger, Stefan TU Munich Germany Applied Mathematics Program Yale University New HavenCT06510 United States Department of Mathematics Yale University New HavenCT06510 United States

Jittered Sampling is a refinement of the classical Monte Carlo sampling method. Instead of picking n points randomly from [0, 1]2, one partitions the unit square into n regions of equal measure and then chooses a point randomly from each partition. Currently, no good rules for how to partition the space are available. In this paper, we present a solution for the special case of subdividing the unit square by a decreasing function into two regions so as to minimize the expected squared L2−discrepancy. The optimal partitions are given by a highly nonlinear integral equation for which we determine an approximate solution. In particular, there is a break of symmetry and the optimal partition is not into two sets of equal measure. We hope this stimulates further interest in the construction of good partitions.65C05 (primary) and 93E20 (secondary). Copyright © 2017, The Authors. All rights reserved.

关键词： Monte Carlo methods

Multi-frequency effect towards High Conductivity Overburden Responses using Vertical Coplanar (VCP) coil configuration for Landslide Instrumentation

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Journal of Physics: Conference Series 2018年第1期1120卷

作者： Muhammad Syukri Surbakti Bukhari Nazli Ismail Nasrullah Idris Elin Yusibani Muhammad Isa Saumi Syahreza Department of Physics Faculty of Mathematics and Natural Sciences University of Syiah Kuala Banda Aceh Indonesia 23111 Doctorate Program of Mathematics and Applied Science (DMAS) Postgraduate Program University of Syiah Kuala Banda Aceh Indonesia 23111

A novel instrumentation for landslide application has been made and calibrated using Vertical Coplanar (VCP) coil orientation. The early instrumentation and commonly used right now for landslide slopes was gradually equipped with standard and automatic instrumentation: three the piezometric cells, two deep-seated steel wire extensometers, four inclinometric tubes, a rainfall gauge, a snow gauge and an air thermometer. This novel instrumentation works in electromagnetic methods similar with electromagnetic methods in geophysics; otherwise, the system was mechanics and electronics. VCP coil orientation is a coplanar array where both coils are vertical. In VCP, the depth of sounding is about 1.5 times of the coils separation. The overburden thicknesses in the field exploration are often covering the tropical area and presented as weathering layer. The more of overburden thickness then the more of energy of electromagnetic wave will be absorbed, as the result that the electromagnetic wave becomes smaller. The electromagnetic wave that reaches the target of the subsurface is also become smaller in amplitude. The multi-frequency application would be helpful in the data interpretation of the anomaly position and the conductive overburden caused by the domination trends between out-of-phase (OP) and in-phase (IP) components could be determined. In the higher frequencies (3037.5 Hz and 1012.5 Hz), the curve of IP is raised up, with the result that the positive peak values become higher and the negative peak values become lower in levels. The multi-frequency application gives the results that in the higher frequency examinations, the anomaly response is influenced significantly by the conductive overburden. In the lower frequency measurements, the anomaly response is not influenced significantly by overburden response. In the higher frequency measurements, when the electromagnetic wave is passing through the conductive material, the amplitude attenuation and the phase shiftin

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