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arXiv 2024年

作者： Liu, Ya-Feng Chang, Tsung-Hui Hong, Mingyi Wu, Zheyu So, Anthony Man-Cho Jorswieck, Eduard A. Yu, Wei 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 School of Science and Engineering The Chinese University of Hong Kong Shenzhen Shenzhen China Shenzhen Research Institute of Big Data China The Department of Electrical and Computer Engineering University of Minnesota MinneapolisMN55455 United States The Department of Systems Engineering and Engineering Management The Chinese University of Hong Kong Hong Kong The Institute for Communication Technology Technische Universitat Braunschweig Germany The Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto TorontoONM5S 3G4 Canada

Mathematical optimization is now widely regarded as an indispensable modeling and solution tool for the design of wireless communications systems. While optimization has played a significant role in the revolutionary progress in wireless communication and networking technologies from 1G to 5G and onto the future 6G, the innovations in wireless technologies have also substantially transformed the nature of the underlying mathematical optimization problems upon which the system designs are based and have sparked significant innovations in the development of methodologies to understand, to analyze, and to solve those problems. In this paper, we provide a comprehensive survey of recent advances in mathematical optimization theory and algorithms for wireless communication system design. We begin by illustrating common features of mathematical optimization problems arising in wireless communication system design. We discuss various scenarios and use cases and their associated mathematical structures from an optimization perspective. We then provide an overview of recently developed optimization techniques in areas ranging from nonconvex optimization, global optimization, and integer programming, to distributed optimization and learning-based optimization. The key to successful solution of mathematical optimization problems is in carefully choosing or developing suitable algorithms (or neural network architectures) that can exploit the underlying problem structure. We conclude the paper by identifying several open research challenges and outlining future research directions. Copyright © 2024, The Authors. All rights reserved.

关键词： Beamforming

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Complexity and performance of an Augmented Lagrangian algorithm

arXiv

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arXiv 2019年

作者： Birgin, E.G. Martínez, J.M. Dept. of Computer Science Institute of Mathematics and Statistics University of São Paulo Rua do Matão 1010 Cidade Universitária São Paulo SP05508-090 Brazil Dept. of Applied Mathematics Institute of Mathematics Statistics and Scientific Computing State University of Campinas Campinas SP13083-859 Brazil

Algencan is a well established safeguarded Augmented Lagrangian algorithm introduced in [R. Andreani, E. G. Birgin, J. M. Martínez and M. L. Schuverdt, On Augmented Lagrangian methods with general lower-level constraints, SIAM Journal on Optimization 18, pp. 1286-1309, 2008]. Complexity results that report its worst-case behavior in terms of iterations and evaluations of functions and derivatives that are necessary to obtain suitable stopping criteria are presented in this work. In addition, the computational performance of a new version of the method is presented, which shows that the updated software is a useful tool for solving large-scale constrained optimization problems. Copyright © 2019, The Authors. All rights reserved.

关键词： Nonlinear programming

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Research on patent recommendation method based on graph neural network

Research on patent recommendation method based on graph neur...

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International Conference on computer Supported Cooperative Work in Design

作者： Enchao Zhang Weidong Liu Shi Liu Yan Cao College of Computer Science Inner Mongolia University China Institute of Scientific and Technical Information of China China National & Local Joint Engineering Research Center of Intelligent Information Processing Technology for Mongolian China Inner Mongolia Key Laboratory of Social Computing and Data Processing China Inner Mongolia Engineering Laboratory for Big Data Analysis Technology China

Intellectual property transactions have shown a strong growth momentum in recent years, but the patent transaction market has been plagued by the matching degree of consumers and sellers, resulting in frequent problems such as low patent transformation efficiency and poor transaction quality. This paper proposes a method of recommending patents to consumers by experts to improve the environment of patent transactions. Through the analysis of the past transaction information of the patent, the effective path information of the target is extracted. The graph neural network is used to describe the characteristics and semantics among experts, patents and consumers, and then capture the potential weight among them through the common attention mechanism, and then dynamically integrate them to predict the occurrence of recommendation behavior. The paper makes reasonable use of social information and expert information in the transaction, which significantly improves the rationality and accuracy of expert recommendation.

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Commutativity of integral quasi-arithmetic means on measure spaces

arXiv

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arXiv 2017年

作者： Lazowska, Dorota G. Leonetti, Paolo Matkowski, Janusz Tringali, Salvatore Faculty of Mathematics Computer Science and Econometrics University of Zielona Góra prof. Z. Szafrana 4a Zielona GóraPL-65516 Department of Statistics Università "Luigi Bocconi" via Roentgen 1 MilanoIT-20136 Institute for Mathematics and Scientific Computing University of Graz Heinrichstr. 36 GrazAT-8010

Let (X, L, λ) and (Y, M, µ) be finite measure spaces for which there exist A ∈ L and B ∈ M with 0 +, then the equation f−1(ZX f ( g−1(ZY g ◦ h dµ )) dλ ) = g−1(ZY g ( f−1(ZX f ◦ h dλ )) dµ ) is sat... 详细信息

Let (X, L, λ) and (Y, M, µ) be finite measure spaces for which there exist A ∈ L and B ∈ M with 0 +, then the equation f−1(ZX f ( g−1(ZY g ◦ h dµ )) dλ ) = g−1(ZY g ( f−1(ZX f ◦ h dλ )) dµ ) is satisfied by every L ⊗M -measurable simple function h: X ×Y → I if and only if f = cg for some c ∈ R+ (it is easy to see that the equation is well posed). An analogous, but essentially different, result, with f and g replaced by continuous injections I → R and λ(X) = µ(Y) = 1, was recently obtained in [Indag. Math. 27 (2016), 945-953].MSC Codes 26E60, 39B22, 39B52 (Primary), 28E99, 60B99, 91B99 (Secondary) Copyright © 2017, The Authors. All rights reserved.

关键词： Functional analysis

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A preliminary study on the effect of motion correction on HARDI reconstruction

A preliminary study on the effect of motion correction on HA...

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IEEE International Symposium on Biomedical Imaging

作者： Shireen Elhabian Yaniv Gur Clement Vachet Joseph Piven Martin Styner Ilana Leppert G. Bruce Pike Guido Gerig Scientific Computing and Imaging Institute Salt Lake City UT USA Dept. of Psychiatry University of North Carolina NC USA Dept. of Computer Science University of North Carolina NC USA Dept. of Neurology and Neurosurgery Montral Neurological Institute Montral Quebec Canada Dept. of Radiology University of Calgary Calgary Canada

Post-acquisition motion correction is widely performed in diffusion-weighted imaging (DWI) to guarantee voxel-wise correspondence between DWIs. Whereas this is primarily motivated to save as many scans as possible if corrupted by motion, users do not fully understand the consequences of different types of interpolation schemes on the final analysis. Nonetheless, interpolation might increase the partial volume effect while not preserving the volume of the diffusion profile, whereas excluding poor DWIs may affect the ability to resolve crossing fibers especially with small separation angles. In this paper, we investigate the effect of interpolating diffusion measurements as well as the elimination of bad directions on the reconstructed fiber orientation diffusion functions and on the estimated fiber orientations. We demonstrate such an effect on synthetic and real HARDI datasets. Our experiments demonstrate that the effect of interpolation is more significant with small fibers separation angles where the exclusion of motion-corrupted directions decreases the ability to resolve such crossing fibers.

关键词： Interpolation Biomedical imaging Image reconstruction Tensile stress Diffusion tensor imaging

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A Research Software Engineering Workflow for Computational science and Engineering

arXiv

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arXiv 2022年

作者： Marić, Tomislav Gläser, Dennis Lehr, Jan-Patrick Papagiannidis, Ioannis Lambie, Benjamin Bischof, Christian Bothe, Dieter Mathematical modeling and analysis Mathematics department TU Darmstadt Darmstadt64287 Germany Institute for Modelling Hydraulic and Environmental Systems Department of Hydromechanics and Modelling of Hydrosystems University of Stuttgart Stuttgart70569 Germany Institute for Scientific Computing Department of Computer Science TU Darmstadt Darmstadt64289 Germany Institute for Technical Thermodynamics TU Darmstadt Darmstadt64287 Germany

University research groups in Computational science and Engineering (CSE) generally lack dedicated funding and personnel for Research Software Engineering (RSE), which, combined with the pressure to maximize the number of scientific publications, shifts the focus away from sustainable research software development and reproducible results. The neglect of RSE in CSE at University research groups negatively impacts the scientific output: research data - including research software - related to a CSE publication cannot be found, reproduced, or re-used, different ideas are not combined easily into new ideas, and published methods must very often be re-implemented to be investigated further. This slows down CSE research significantly, resulting in considerable losses in time and, consequentially, public funding. We propose a RSE workflow for Computational science and Engineering (CSE) that addresses these challenges, that improves the quality of research output in CSE. Our workflow applies established software engineering practices adapted for CSE: software testing, result visualization, and periodical cross-linking of software with reports/publications and data, timed by milestones in the scientific publication process. The workflow introduces minimal work overhead, crucial for university research groups, and delivers modular and tested software linked to publications whose results can easily be reproduced. We define research software quality from a perspective of a pragmatic researcher: the ability to quickly find the publication, data, and software related to a published research idea, quickly reproduce results, understand or re-use a CSE method, and finally extend the method with new research ideas. © 2022, CC BY.

关键词： Software testing

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On reference solutions and the sensitivity of the 2D Kelvin–Helmholtz instability problem

arXiv

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arXiv 2018年

作者： Schroeder, Philipp W. John, Volker Lederer, Philip L. Lehrenfeld, Christoph Lube, Gert Schöberl, Joachim Institute for Numerical and Applied Mathematics Georg-August-Universität Göttingen Göttingen37083 Germany Weierstrass Institute for Applied Analysis and Stochastics Berlin10117 Germany Department of Mathematics and Computer Science Freie Universität Berlin Berlin14195 Germany Institute for Analysis and Scientific Computing TU Wien 1040 Wien Austria

Two-dimensional Kelvin–Helmholtz instability problems are popular examples for assessing discretizations for incompressible flows at high Reynolds number. Unfortunately, the results in the literature differ considerably. This paper presents computational studies of a Kelvin–Helmholtz instability problem with high order divergence-free finite element methods. Reference results in several quantities of interest are obtained for three different Reynolds numbers up to the beginning of the final vortex pairing. A mesh-independent prediction of the final pairing is not achieved due to the sensitivity of the considered problem with respect to small perturbations. A theoretical explanation of this sensitivity to small perturbations is provided based on the theory of self-organization of 2D turbulence. Possible sources of perturbations that arise in almost any numerical simulation are discussed. Copyright © 2018, The Authors. All rights reserved.

关键词： Numerical methods

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Exploring Patent Transformation Event: Forecasting Patent Transfer Time

Exploring Patent Transformation Event: Forecasting Patent Tr...

引用

International Conference on computer Supported Cooperative Work in Design

作者： Jinchen Huo Weidong Liu Yang Li Yan Cao College of Computer Science Inner Mongolia University China Institute of Scientific and Technical Information of China China National & Local Joint Engineering Research Center of Intelligent Information Processing Technology for Mongolian China Inner Mongolia Key Laboratory of Social Computing and Data Processing China Inner Mongolia Engineering Laboratory for Big Data Analysis Technology China

As the largest source of technical information around the world, patents are regarded as an essential crystallization and carrier of knowledge and technological innovation. Patent transformation is conducive not only to enhancing economic efficiency, but also to improving productivity and the rational utilization of resources. There is an imbalance between high patent ownership and low transformation rates. We try to predict the occurrence of transformation events from the patent assignment. However, there are some challenges in predicting patent transformation: (1) how to capture transformation features of patents, especially combined with the transfer time factor. (2) how to predict patent transfer time effectively. To address these challenges, a Patent Transfer Time Forecasting Model (PTTFM) is proposed. The model includes: (1) extraction of time-varying features of patents. (2) the patent transfer time is forecast using a Neural Temporal Point Process. By testing the model on patents under different classifications, the experimental results are obtained to show that the proposed model is applicable to predict the timing of patent assignment within a certain time frame, especially one month. Our work may facilitate patent transformation while interpretability is ensured for transformation events.

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Directional change of tracer trajectories in rotating Rayleigh-Bénard convection

引用

Physical Review E 2018年第6期97卷 063105-063105页

作者： Kim M. J. Alards Hadi Rajaei Rudie P. J. Kunnen Federico Toschi Herman J. H. Clercx Fluid Dynamics Laboratory Department of Applied Physics Eindhoven University of Technology P.O. Box 513 5600 MB Eindhoven The Netherlands Centre of Analysis Scientific Computing and Applications W&I Department of Mathematics and Computer Science Eindhoven University of Technology P.O. Box 513 5600 MB Eindhoven The Netherlands Istituto per le Applicazioni del Calcolo Consiglio Nazionale delle Ricerche Via dei Taurini 19 00185 Rome Italy

The angle of directional change of tracer trajectories in rotating Rayleigh-Bénard convection is studied as a function of the time increment τ between two instants of time along the trajectories, both experimentally and with direct numerical simulations. Our aim is to explore the geometrical characterization of flow structures in turbulent convection in a wide range of timescales and how it is affected by background rotation. We find that probability density functions (PDFs) of the angle of directional change θ(t,τ) show similar behavior as found in homogeneous isotropic turbulence, up to the timescale of the large-scale coherent flow structures. The scaling of the averaged (over particles and time) angle of directional change Θ(τ)=〈|θ(t,τ)|〉 with τ shows a transition from the ballistic regime [Θ(τ)∼τc with c=1] for τ≲τη, with τη the Kolmogorov timescale, to a scaling with smaller exponent c for τη≲τ≲TL, with TL the Lagrangian integral timescale. This scaling exponent is approximately constant in the weakly rotating regime (Rossby number Ro≳2.5) and is decreasing for increasing rotation rates when Ro≲2.5. We show that this trend in the scaling exponent is related with the large-scale coherent structures in the flow; the large-scale circulation for Ro≳2.5 and vertically aligned vortices emerging from the boundary layers (BLs) near the top and bottom plates and penetrating into the bulk for Ro≲2.5. In the viscous BLs, the PDFs of θ(t,τ) and scaling properties of Θ(τ) are in general different from those measured in the bulk and depend on the type of boundary layer, in particular whether the BL is of Prandtl-Blasius type (Ro≳2.5) or of Ekman type (Ro≲2.5). When it is of Ekman type, a stronger dynamic coupling exists between the BL and the bulk of the flow, resulting in similar scaling exponents in BL and bulk.

关键词： Rayleigh-Bénard convection Rotating geophysical flows

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Scalability of high-performance PDE solvers

arXiv

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arXiv 2020年

作者： Fischer, Paul Min, Misun Rathnayake, Thilina Dutta, Som Kolev, Tzanio Dobrev, Veselin Camier, Jean-Sylvain Kronbichler, Martin Warburton, Tim Swirydowicz, Kasia Brown, Jed Mathematics and Computer Science Argonne National Laboratory LemontIL60439 Department of Computer Science University of Illinois at Urbana-Champaign UrbanaIL61801 Department of Mechanical Science and Engineering University of Illinois at Urbana-Champaign UrbanaIL61801 Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA94550 Institute for Computational Mechanics Technical University of Munich Garching b. Muenchen85748 Germany Department of Computer Science University of Colorado BoulderCO80309 National Renewable Energy Laboratory LakewoodCO80401 Department of Mathematics Virginia Tech BlacksburgVA24061 Mechanical & Aerospace Engineering Utah State University UT84322

Performance tests and analyses are critical to effective HPC software development and are central components in the design and implementation of computational algorithms for achieving faster simulations on existing and future computing architectures for large-scale application problems. In this paper, we explore performance and space-time trade-offs for important compute-intensive kernels of large-scale numerical solvers for PDEs that govern a wide range of physical applications. We consider a sequence of PDE-motivated bake-off problems designed to establish best practices for efficient high-order simulations across a variety of codes and platforms. We measure peak performance (degrees of freedom per second) on a fixed number of nodes and identify effective code optimization strategies for each architecture. In addition to peak performance, we identify the minimum time to solution at 80% parallel efficiency. The performance analysis is based on spectral and p-type finite elements but is equally applicable to a broad spectrum of numerical PDE discretizations, including finite difference, finite volume, and h-type finite *** Codes 35-04 Copyright © 2020, The Authors. All rights reserved.

关键词： computer architecture

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