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Cramér-rao bound optimization for joint radar-communication design

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arXiv 2021年

作者： Liu, Fan Liu, Ya-Feng Li, Ang Masouros, Christos Eldar, Yonina C. The Department of Electrical and Electronic Engineering Southern University of Science and Technology Shenzhen518055 China The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematicsand Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The School of Information and Communications Engineering Faculty of Electronic and Information Engineering Xi’an Jiaotong University Xi’anShaanxi710049 China The Department of Electronic and Electrical Engineering University College London LondonWC1E 7JE United Kingdom The Faculty of Mathematics and Computer Science Weizmann Institute of Science Rehovot Israel

In this paper, we propose multi-input multi-output (MIMO) beamforming designs towards joint radar sensing and multi-user communications. We employ the Cramér-Rao bound (CRB) as a performance metric of target estimation, under both point and extended target scenarios. We then propose minimizing the CRB of radar sensing while guaranteeing a pre-defined level of signal-to-interference-plus-noise ratio (SINR) for each communication user. For the single-user scenario, we derive a closed form for the optimal solution for both cases of point and extended targets. For the multi-user scenario, we show that both problems can be relaxed into semidefinite programming by using the semidefinite relaxation approach, and prove that the global optimum can always be obtained. Finally, we demonstrate numerically that the globally optimal solutions are reachable via the proposed methods, which provide significant gains in target estimation performance over state-of-the-art benchmarks. Copyright © 2021, The Authors. All rights reserved.

关键词： Signal to noise ratio

A Wall-time Minimizing Parallelization Strategy for Approximate Bayesian Computation

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arXiv 2023年

作者： Alamoudi, Emad Reck, Felipe Bundgaard, Nils Graw, Frederik Brusch, Lutz Hasenauer, Jan Schälte, Yannik University of Bonn Life and Medical Sciences Institute Bonn53113 Germany Heidelberg University BioQuant - Center for Quantitative Biology Heidelberg69120 Germany Heidelberg University Interdisciplinary Center for Scientific Computing Heidelberg69120 Germany Friedrich-Alexander-University Erlangen-Nürnberg Department of Medicine 5 Erlangen91054 Germany Dresden01062 Germany Helmholtz Zentrum München Institute of Computational Biology Neuherberg85764 Germany Technische Universität München Center for Mathematics Garching85748 Germany

Approximate Bayesian Computation (ABC) is a widely applicable and popular approach to estimating unknown parameters of mechanistic models. As ABC analyses are computationally expensive, parallelization on high-performance infrastructure is often necessary. However, the existing parallelization strategies leave resources unused at times and thus do not optimally leverage them yet. We present look-ahead scheduling, a wall-time minimizing parallelization strategy for ABC Sequential Monte Carlo algorithms, which utilizes all available resources at practically all times by proactive sampling for prospective tasks. Our strategy can be integrated in e.g. adaptive distance function and summary statistic selection schemes, which is essential in practice. Evaluation of the strategy on different problems and numbers of parallel cores reveals speed-ups of typically 10-20% and up to 50% compared to the best established approach. Thus, the proposed strategy allows to substantially improve the cost and run-time efficiency of ABC methods on high-performance infrastructure. © 2023, CC BY-NC-ND.

关键词： Bayesian networks

Weighted p-Rényi Entropy Power Inequality: Information Theory to Quantum Shannon Theory

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arXiv 2023年

作者： Lee, Junseo Yeo, Hyeonjun Jeong, Kabgyun School of Electrical and Electronic Engineering Yonsei University Seoul03722 Korea Republic of Quantum Computing R&D Norma Inc. Seoul04799 Korea Republic of Department of Physics and Astronomy Seoul National University Seoul08826 Korea Republic of Research Institute of Mathematics Seoul National University Seoul08826 Korea Republic of School of Computational Sciences Korea Institute for Advanced Study Seoul02455 Korea Republic of

We study the p-Rényi entropy power inequality with a weight factor t on two independent continuous random variables X and Y . The extension essentially relies on a modulation on the sharp Young’s inequality due to Bobkov and Marsiglietti. Our research provides a key result that can be used as a fundamental research finding in quantum Shannon theory, as it offers a Rényi version of the entropy power inequality for quantum systems. Copyright © 2023, The Authors. All rights reserved.

关键词： Information theory

A new discrete energy technique for multi-step backward difference formulas

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arXiv 2021年

作者： Liao, Hong-Lin Tang, Tao Zhou, Tao Department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing211106 China Division of Science and Technology BNU-HKBU United International College ZhuhaiGuangdong China International Center for Mathematics Southern University of Science and Technology ShenzhenGuangdong China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

The backward differentiation formula (BDF) is a useful family of implicit methods for the numerical integration of stiff differential equations. It is well noticed that the stability and convergence of the A-stable BDF1 and BDF2 schemes for parabolic equations can be directly established by using the standard discrete energy analysis. However, such classical analysis technique seems not directly applicable to the BDF-k schemes for 3 ≤ k ≤ 5. To overcome the difficulty, a powerful analysis tool based on the Nevanlinna-Odeh multiplier technique [Numer. Funct. Anal. Optim., 3:377-423, 1981] was developed by Lubich et al. [IMA J. Numer. Anal., 33:1365-1385, 2013]. In this work, by using the so-called discrete orthogonal convolution kernels technique, we will recover the classical energy analysis so that the stability and convergence of the BDF-k schemes for 3 ≤ k ≤ 5 can be established. One of the theoretical advantages of our analysis technique is that less spacial regularity requirement is needed on the initial data. © 2021, CC BY-NC-ND.

关键词： Partial differential equations

On the generalized Calderón formulas for closed- And open-surface elastic scattering problems

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arXiv 2021年

作者： Xu, Liwei Yin, Tao School of Mathematical Sciences University of Electronic Science and Technology of China Sichuan Chengdu611731 China LSEC Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Science University of Chinese Academy of Sciences Beijing100049 China

The Calderón formulas (i.e., the combination of single-layer and hyper-singular boundary integral operators) have been widely utilized in the process of constructing valid boundary integral equation systems which could possess highly favorable spectral properties. This work is devoted to studying the theoretical properties of elastodynamic Calderón formulas which provide us with a solid basis for the design of fast boundary integral equation methods solving elastic wave problems defined on a close-surface or an open-surface in two dimensions. For the closed-surface case, it is proved that the Calderón formula is a Fredholm operator of second-kind except for certain circumstances. Regarding to the open-surface case, we investigate weighted integral operators instead of the original integral operators which are resulted from dealing with edge singularities of potentials corresponding to the elastic scattering problems by open-surfaces, and show that the Calderón formula is a compact perturbation of a bounded and invertible operator. To complete the proof, we need to use the wellposedness result of the elastic scattering problem, the analysis of the zero-frequency integral operators defined on the straight arc, the singularity decompositions of the kernels of integral operators, and a new representation formula of the hyper-singular operator. Moreover, it can be demonstrated that the accumulation point of the spectrum of the invertible operator is the same as that of the eigenvalues of the Calderón formula in the closed-surface case. Copyright © 2021, The Authors. All rights reserved.

关键词： Mathematical operators

Adaptive Surrogate Model for Failure Probability Estimation 21

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Adaptive Surrogate Model for Failure Probability Estimation

5th International Conference on Computer Science and Application engineering, CSAE 2021

作者： Qin, Yi Zhang, Yue Liu, Zexin Zhu, Xueyu Wang, Peng School of Mathematical Sciences Beihang University Haidian District Beijing China School of Integrated Circuit Science and Engineering Beihang University Haidian District Beijing China Department of Mathematics University of Utah Salt Lake CityUtah United States Scientific Computing and Imaging Institute University of Utah Salt Lake CityUtah United States Department of Mathematics University of Iowa Iowa City United States Beijing Advanced Innovation Center for Big Data and Brain Computing Beihang University Haidian District Beijing China

ISBN: (纸本)9781450389853

Estimating failure probability becomes a fundamental task in many complex engineering designs and optimizations. Yet, evaluation of failure probability via direct sampling from a given system can be computationally expensive and sometimes impossible. Although the construction of a response surface/surrogate could reduce such computational cost, reliance on its sampling alone may still yield an erroneous estimate of the failure probability. In this paper, we employ generalized polynomial chaos and develop an adaptive method whose surrogate model evolves with the additional data sampled from the underlying system as the iteration proceeds. It is more flexible by not requiring an accurate surrogate model in priori. Via three distinct numerical examples and one practical problem on a spintronic device, we demonstrate that our novel scheme provides an efficient tool to estimate system failure probability.. © 2021 Association for computing Machinery. All rights reserved.

关键词： Iterative methods

AMG Preconditioners based on Parallel Hybrid Coarsening and Multi-objective Graph Matching

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AMG Preconditioners based on Parallel Hybrid Coarsening and ...

Euromicro Conference on Parallel, Distributed and Network-Based Processing

作者： Pasqua D'Ambra Fabio Durastante S M Ferdous Salvatore Filippone Mahantesh Halappanavar Alex Pothen National Research Council (CNR) Institute for Applied Computing “M. Picone” (IAC) Napoli Italy Department of Mathematics University of Pisa Pisa Italy Pacific Northwest National Laboratory Physical and Computational Sciences Richland WA USA Dept. of Civil and Computer Engineering University of Rome Tor-Vergata Rome Italy Computer Science Department Purdue University West Lafayette IN USA

We describe preliminary results from a multi-objective graph matching algorithm, in the coarsening step of an aggregation-based Algebraic MultiGrid (AMG) preconditioner, for solving large and sparse linear systems of equations on high-end parallel computers. We have two objectives. First, we wish to improve the convergence behavior of the AMG method when applied to highly anisotropic problems. Second, we wish to extend the parallel package PSCToolkit to exploit multi-threaded parallelism at the node level on multi-core processors. Our matching proposal balances the need to simultaneously compute high weights and large cardinalities by a new formulation of the weighted matching problem combining both these objectives using a parameter $\lambda$ . We compute the matching by a parallel $2/3-\varepsilon$ -approximation algorithm for maximum weight matchings. Results with the new matching algorithm show that for a suitable choice of the parameter $\lambda$ we compute effective preconditioners in the presence of anisotropy, i.e., smaller solve times, setup times, iterations counts, and operator complexity.

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Physics-informed neural networks to learn cardiac fiber orientation from multiple electroanatomical maps

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arXiv 2022年

作者： Herrera, Carlos Ruiz Grandits, Thomas Plank, Gernot Perdikaris, Paris Costabal, Francisco Sahli Pezzuto, Simone Department of Mechanical and Metallurgical Engineering School of Engineering Pontificia Universidad Católica de Chile Santiago Chile Institute of Mathematics and Scientific Computing University of Graz Graz Austria Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania Philadelphia United States Institute for Biological and Medical Engineering Schools of Engineering Medicine and Biological Sciences Pontificia Universidad Católica de Chile Santiago Chile Center for Computational Medicine in Cardiology Euler Institute Università della Svizzera italiana via Buffi 13 Lugano6900 Switzerland Gottfried Schatz Research Center Division of Biophysics Medical University of Graz Graz Austria

We propose FiberNet, a method to estimate in-vivo the cardiac fiber architecture of the human atria from multiple catheter recordings of the electrical activation. Cardiac fibers play a central role in the electromechanical function of the heart, yet they are difficult to determine in-vivo, and hence rarely truly patient-specific in existing cardiac models. FiberNet learns the fiber arrangement by solving an inverse problem with physics-informed neural networks. The inverse problem amounts to identifying the conduction velocity tensor of a cardiac propagation model from a set of sparse activation maps. The use of multiple maps enables the simultaneous identification of all the components of the conduction velocity tensor, including the local fiber angle. We extensively test FiberNet on synthetic 2-D and 3-D examples, diffusion tensor fibers, and a patient-specific case. We show that 3 maps are sufficient to accurately capture the fibers, also in the presence of noise. With fewer maps, the role of regularization becomes prominent. Moreover, we show that the fitted model can robustly reproduce unseen activation maps. We envision that FiberNet will help the creation of patient-specific models for personalized medicine. The full code is available at http://***/fsahli/FiberNet. © 2022, CC BY-NC-ND.

关键词： Inverse problems

F*** workflows: when parts of FAIR are missing

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arXiv 2022年

作者： Wilkinson, Sean R. Eisenhauer, Greg Kapadia, Anuj J. Knight, Kathryn Logan, Jeremy Widener, Patrick Wolf, Matthew Oak Ridge Leadership Computing Facility Oak Ridge National Laboratory Oak RidgeTN United States College of Computing Georgia Institute of Technology AtlantaGA United States Computational Sciences and Engineering Oak Ridge National Laboratory Oak RidgeTN United States Computer Science and Mathematics Oak Ridge National Laboratory Oak RidgeTN United States

The FAIR principles for scientific data (Findable, Accessible, Interoperable, Reusable) are also relevant to other digital objects such as research software and scientific workflows that operate on scientific data. The FAIR principles can be applied to the data being handled by a scientific workflow as well as the processes, software, and other infrastructure which are necessary to specify and execute a workflow. The FAIR principles were designed as guidelines, rather than rules, that would allow for differences in standards for different communities and for different degrees of compliance. There are many practical considerations which impact the level of FAIR-ness that can actually be achieved, including policies, traditions, and technologies. Because of these considerations, obstacles are often encountered during the workflow lifecycle that trace directly to shortcomings in the implementation of the FAIR principles. Here, we detail some cases, without naming names, in which data and workflows were Findable but otherwise lacking in areas commonly needed and expected by modern FAIR methods, tools, and users. We describe how some of these problems, all of which were overcome successfully, have motivated us to push on systems and approaches for fully FAIR workflows. © 2022, CC BY.

关键词： Computer software reusability