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Stickiness and recurrence plots: an entropy-based approach

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arXiv 2022年

作者： Sales, Matheus R. Mugnaine, Michele Szezech, José D. Viana, Ricardo L. Caldas, Iberê L. Marwan, Norbert Kurths, Jürgen Graduate Program in Sciences/Physics State University of Ponta Grossa PR Ponta Grossa84030-900 Brazil Potsdam Institute for Climate Impact Research Member of the Leibniz Association P.O. Box 6012 03 PotsdamD-14412 Germany Institute of Mathematics Humboldt University Berlin Berlin12489 Germany Department of Physics Federal University of Paraná PR Curitiba80060-000 Brazil Institute of Physics University of São Paulo SP São Paulo05508-900 Brazil Department of Mathematics and Statistics State University of Ponta Grossa PR Ponta Grossa84030-900 Brazil Institute of Physics Humboldt University Berlin Berlin10099 Germany Division of Dynamics Lodz University of Technology Stefanowskiego 1/15 Lodz90-924 Poland

The stickiness effect is a fundamental feature of quasi-integrable Hamiltonian systems. We propose the use of an entropy-based measure of the recurrence plots (RP), namely, the entropy of the distribution of the recurrence times (estimated from the RP), to characterize the dynamics of a typical quasi-integrable Hamiltonian system with coexisting regular and chaotic regions. We show that the recurrence time entropy (RTE) is positively correlated to the largest Lyapunov exponent, with a high correlation coefficient. We obtain a multi-modal distribution of the finite-time RTE and find that each mode corresponds to the motion around islands of different hierarchical levels. © 2022, CC BY-NC-ND.

关键词： Entropy

Spare principal compenent analysis via variable projection

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SIAM Journal on Applied mathematics 2020年第2期80卷 977-1002页

作者： Erichson, N. Benjamin Zheng, Peng Manohar, Krithika Brunton, Steven L. Kutz, J. Nathan Aravkin, Aleksandr Y. Department of Statistics University of California Berkeley BerkeleyCA94720 United States Department of Applied Mathematics University of Washington SeattleWA98195-3925 United States Department of Mechanical Engineering University of Washington SeattleWA98195-3925 United States

Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating between distinct time scales. We demonstrate a robust and scalable SPCA algorithm by formulating it as a value-function optimization problem. This viewpoint leads to a flexible and computationally efficient algorithm. The approach can further leverage randomized methods from linear algebra to extend SPCA to the large-scale (big data) setting. Our proposed innovation also allows for a robust SPCA formulation which obtains meaningful sparse principal components in spite of grossly corrupted input data. The proposed algorithms are demonstrated using both synthetic and real world data, and show exceptional computational efficiency and diagnostic performance. © 2020 Society for Industrial and Applied mathematics.

关键词： Linear algebra

Networked Integrated Sensing and Communications for 6G Wireless Systems

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arXiv 2024年

作者： Li, Jiapeng Shao, Xiaodan Chen, Feng Wan, Shaohua Liu, Chang Wei, Zhiqiang Ng, Derrick Wing Kwan The College of Artificial Intelligence Southwest University Chongqing400715 China The Brain-Inspired Computing and Intelligent Control Key Laboratory Southwest University Chongqing400715 China The Key Laboratory of Luminescence Analysis and Molecular Sensing Southwest University Chongqing400715 China The Shenzhen Institute for Advanced Study University of Electronic Science and Technology of China Shenzhen518110 China The School of Mathematics and Statistics Xi'an Jiaotong University Xi'An710049 China The Peng Cheng Laboratory Guangdong Shenzhen518055 China Guangdong Guangzhou510555 China The Department of Computer Science and Information Technology La Trobe University MelbourneVIC3150 Australia The School of Electrical Engineering and Telecommunications University of New South Wales SydneyNSW2052 Australia

Integrated sensing and communication (ISAC) is envisioned as a key pillar for enabling the upcoming sixth generation (6G) communication systems, requiring not only reliable communication functionalities but also highly accurate environmental sensing capabilities. In this paper, we design a novel networked ISAC framework to explore the collaboration among multiple users for environmental sensing. Specifically, multiple users can serve as powerful sensors, capturing back scattered signals from a target at various angles to facilitate reliable computational imaging. Centralized sensing approaches are extremely sensitive to the capability of the leader node because it requires the leader node to process the signals sent by all the users. To this end, we propose a two-step distributed cooperative sensing algorithm that allows low-dimensional intermediate estimate exchange among neighboring users, thus eliminating the reliance on the centralized leader node and improving the robustness of sensing. This way, multiple users can cooperatively sense a target by exploiting the block-wise environment sparsity and the interference cancellation technique. Furthermore, we analyze the mean square error of the proposed distributed algorithm as a networked sensing performance metric and propose a beamforming design for the proposed network ISAC scheme to maximize the networked sensing accuracy and communication performance subject to a transmit power constraint. Simulation results validate the effectiveness of the proposed algorithm compared with the state-of-the-art algorithms. Copyright © 2024, The Authors. All rights reserved.

关键词： Beamforming

Comparing the Environmental Impacts of Representative Food Donation and Redistribution Strategies

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SSRN

SSRN 2023年

作者： Guo, Zhijian Mu, Tianhong Bozlak, Christine Feingold, Beth Hosler, Akiko Pettigrew, Stacy Romeiko, Xiaobo Xue Department of Mathematics and Statistics University at Albany State University of New York 1400 Washington Avenue AlbanyNY12222 United States Department of Environmental and Sustainable Engineering University at Albany State University of New York 1400 Washington Avenue AlbanyNY12222 United States Department of Health Policy Management and Behavior University at Albany State University of New York 1 University Place RensselaerNY12144 United States Department of Environmental Health Sciences University at Albany State University of New York 1 University Place RensselaerNY12144 United States Department of Epidemiology and Biostatistics University at Albany State University of New York 1 University Place RensselaerNY12144 United States Radix Ecological Sustainability Center 153 Grand Street AlbanyNY12202 United States

Assessing the environmental impacts of food donation systems is necessary to support food donation policy and management. Few life cycle assessment (LCA) studies investigated the environmental impacts of food donation systems. This comparative LCA study analyzed the environmental impacts of eight different donation scenarios reflecting diverse supply chain configurations and operational management options. The foreground life cycle inventory was built upon actual datasets collected during on-site visits, and the background life cycle inventory was obtained from the Ecoinvent database and literature. The five environmental impact categories considered included global warming potential, cumulative energy demand, acidification, eutrophication, and water resources depletion. Each of the eight scenarios presented net environmental benefits for all five environmental impact categories. The highest magnitudes of environmental benefits were achieved when intermediary organizations collected and gleaned the surplus food from donors and then transported it to food pantries (the eighth scenario). Improving the quality of donated food, augmenting the sorting capacities of emergency organizations, and shortening transportation distances could increase the environmental impacts of food donation systems. The environmental impact intensities of produce production and waste management choices of food waste generated during the redistribution of the surplus food ranked as the top influential factors for the five environmental impacts. Rescuing surplus food from donors who landfilled the wasted food tended to yield larger environmental benefits than from donors who composted it. Overall, improving donation quality and increasing the capacities of emergency food organizations are crucial to maximizing the environmental benefits of the fresh produce donation system. © 2023, The Authors. All rights reserved.

关键词： Environmental impact

Analysis and approximations of dirichlet boundary control of stokes flows in the energy space

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arXiv 2020年

作者： Gong, Wei Mateos, Mariano Singler, John R. Zhang, Yangwen State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics National Center for Mathematics and Interdisciplinary Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Dpto. de Matemáticas Universidad de Oviedo Campus de Gijón Spain Department of Mathematics and Statistics Missouri University of Science and Technology RollaMO United States Department of Mathematical Science University of Delaware NewarkDE United States

We study Dirichlet boundary control of Stokes flows in 2D polygonal domains. We consider cost functionals with two different boundary control regularization terms: the L2 norm and an energy space seminorm. We prove well-posedness and regularity results for both problems, develop finite element discretizations for both problems, and prove finite element error estimates for the latter problem. The motivation to study the energy space problem follows from our analysis: we prove that the choice of the control space L2(Γ) can lead to an optimal control with discontinuities at the corners, even when the domain is convex. We observe this phenomenon in numerical experiments. This behavior does not occur in Dirichlet boundary control problems for the Poisson equation on convex polygonal domains, and may not be desirable in real applications. For the energy space problem, we derive the first order optimality conditions, and show that the solution of the control problem is more regular than the solution of the problem with the L2(Γ) regularization. We also prove a priori error estimates for the control in the energy norm, and present several numerical experiments for both control problems on convex and nonconvex domains. © 2020, CC0.

关键词： Poisson equation

THE SPECTRAL UNDERPINNING OF WORD2VEC

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arXiv 2020年

作者： Jaffe, Ariel Kluger, Yuval Lindenbaum, Ofir Patsenker, Jonathan Peterfreund, Erez Steinerberger, Stefan Program in Applied Mathematics Yale University New Haven United States Department of Pathology Yale School of Medicine New Haven United States School of Computer Science and Engineering Hebrew University Jerusalem Israel Department of Mathematics Yale University New Haven United States

Word2vec due to Mikolov et al. (2013) is a word embedding method that is widely used in natural language processing. Despite its great success and frequent use, theoretical justification is still lacking. The main contribution of our paper is to propose a rigorous analysis of the highly nonlinear functional of word2vec. Our results suggest that word2vec may be primarily driven by an underlying spectral method. This insight may open the door to obtaining provable guarantees for word2vec. We support these findings by numerical simulations. One fascinating open question is whether the nonlinear properties of word2vec that are not captured by the spectral method are beneficial and, if so, by what mechanism. Copyright © 2020, The Authors. All rights reserved.

关键词： Spectroscopy

D-optimal joint best linear unbiased prediction of order statistics

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arXiv 2020年

作者： Balakrishnan, Narayanaswamy Bhattacharya, Ritwik Department of Mathematics and Statistics McMaster University HamiltonONL8S 4K1 Canada Department of Industrial Engineering School of Engineering and Sciences Tecnológico de Monterrey Querétaro76130 Mexico

In life-testing experiments, it is often of interest to predict unobserved future failure times based on observed early failure times. A point best linear unbiased predictor (BLUP) has been developed in this context by Kaminsky and Nelson (1975). In this article, we develop joint BLUPs of two future failure times based on early failure times by minimizing the determinant of the variance-covariance matrix of the predictors. The advantage of applying joint prediction is demonstrated by using a real data set. The non-existence of joint BLUPs in certain setups is also discussed. © 2020, CC BY.

关键词： Lagrange multipliers

An augmented Lagrangian algorithm for recovery of ice thickness in unidirectional flow using the shallow ice approximation

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arXiv 2021年

作者： McGeorge, Elizabeth K. Moyers-Gonzalez, Miguel Wilson, Phillip L. Sellier, Mathieu Te Kura Pāngarau School of Mathematics and Statistics University of Canterbury Jack Erskine Building Level 4 Private Bag 4800 Christchurch8140 New Zealand Te Pūnaha Matatini Centre of Research Excellence University of Auckland Auckland New Zealand Department of Mechanical Engineering University of Canterbury Christchurch New Zealand

A key parameter in ice flow modelling is basal slipping at the ice-bed interface as it can have a large effect on the resultant ice thickness. Unfortunately, its contribution to surface observations can be hard to distinguish from that of bed undulations. Therefore, inferring the ice thickness from surface measurements is an interesting and non-trivial inverse problem. This paper presents a method for recovering dually the ice thickness and the basal slip using only surface elevation and speed measurements. The unidirectional shallow ice approximation is first implemented to model steady state ice flow for given bedrock and basal slip profiles. This surface is then taken as synthetic observed data. An augmented Lagrangian algorithm is then used to find the diffusion coefficient which gives the best fit to observations. Combining this recovered diffusion with observed surface velocity, a simple Newton's method is used to recover both the ice thickness and basal slip. The method was successful in each test case and this implies that it should be possible to recover both of these parameters in two-dimensional cases also. Copyright © 2021, The Authors. All rights reserved.

关键词： Inverse problems

Research on Matching Accuracy of Underwater Terrain Matching Algorithm Based on State Augmented Unscented Kalman Filter 3

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Research on Matching Accuracy of Underwater Terrain Matching...

3rd IEEE International Conference on Robotics and Automation Sciences, ICRAS 2019

作者： Lu, Xiong Jian, Shen Haitao, Liu Department of Radar System Ordnance NCO Academy of Army Engineering University Wuhan China Post-doctoral Program on Control Science and Engineering Naval University of Engineering Wuhan China Department of Basic Mathematics Naval University of Engineering Wuhan China

ISBN: (纸本)9781728108537

Underwater high-precision positioning is the basis of safe sailing and smooth operation for underwater autonomous vehicle (AUV). With the continuous expansion of marine surveys, the requirements for navigation accuracy of AUVs are also increasing. As the unscented Kalman filter (UKF)-based terrain matching method can meet the high-precision positioning demand of underwater navigation, it becomes one of the hot research content in recent years. However, due to the insufficient robustness of UKF algorithm, under the condition of non-additive state noise, the initial distribution of Sigma points is prone to be unreasonable, which will reduce filter accuracy and even cause the recursive result divergence. In order to improve the accuracy and robustness of the underwater terrain matching algorithm, this paper introduces the method of nonlinear filtering state expansion. The system noise and measurement noise information are added into the system state matrix and the variance matrix, and obtains the state expansion UKF-based terrain matching algorithm. Since the noise and the estimation parameters are both participating in the filtering operation, the inaccurate prediction influence of initial noise can be reduced, and finally improves the accuracy and applicability of the underwater terrain matching algorithm. © 2019 IEEE.

关键词： Kalman filters