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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

K, T and D-like fuzzy Kripke models

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K, T and D-like fuzzy Kripke models

Annual Meeting of The North American Fuzzy Information Processing Society

作者： Bedregal, Benjamin Santiago, Regivan H. N. Benevides, Mario Viana, Petrucio Group of Logic Language Information Theory and Applications - LoLITA Department of Informatics and Applied Mathematics Federal University of Rio Grande Do Norte 59072-970 Natal-RN Brazil Program of Engineering of Systems and Computing - PESC Department of Computer Science Federal University of Rio de Janeiro 21941-972 Rio de Janeiro-RJ Brazil Department of Analysis Fluminense Federal University 24020-140 Niterói-RJ Brazil

ISBN: (纸本)9781612849676

The idea of a Kripke semantics endowed with possibility/plausibility information is not new;in fact there are different approaches for that;see: [6], [13], [16], [19]. This paper follows the approach found in [6], but whereas [6] provides a fixed interpretation for connectives into [0,1] here we provide a characterization of a fuzzy semantics for connectives in such a way that the resulting fuzzy frames: K, T and D, are described precisely by the set of statements which also describes, respectively, the usual modal systems K, T and D. © 2011 IEEE.

关键词： Semantics

Modeling of Measurement Error in Financial Returns Data

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arXiv 2024年

作者： Jasra, Ajay Maama, Mohamed Mijatović, Aleksandar School of Data Science The Chinese University of Hong Kong Shenzhen China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Statistics University of Warwick United Kingdom

In this paper we consider the modeling of measurement error for fund returns data. In particular, given access to a time-series of discretely observed log-returns and the associated maximum over the observation period, we develop a stochastic model which models the true log-returns and maximum via a Lévy process and the data as a measurement error there-of. The main technical difficulty of trying to infer this model, for instance Bayesian parameter estimation, is that the joint transition density of the return and maximum is seldom known, nor can it be simulated exactly. Based upon the novel stick breaking representation of [12] we provide an approximation of the model. We develop a Markov chain Monte Carlo (MCMC) algorithm to sample from the Bayesian posterior of the approximated posterior and then extend this to a multilevel MCMC method which can reduce the computational cost to approximate posterior expectations, relative to ordinary MCMC. We implement our methodology on several applications including for real data. Copyright © 2024, The Authors. All rights reserved.

关键词： Markov chains

ON THE STABILITY OF POSITIVE SEMIGROUPS

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arXiv 2021年

作者： Del Moral, Pierre Horton, Emma Jasra, Ajay Centre de Recherche Inria Bordeaux Sud-Ouest Talence 33405 France Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science & Technology Building 1 Thuwal23955-6900 Saudi Arabia

The stability and contraction properties of positive integral semigroups on Polish spaces are investigated. Our novel analysis is based on the extension of V -norm contraction methods, associated to functionally weighted Banach spaces for Markov semigroups, to positive semigroups. This methodology is applied to a general class of positive and possibly time-inhomogeneous bounded integral semigroups and their normalised versions. The spectral theorems that we develop are an extension of Perron-Frobenius and Krein-Rutman theorems for positive operators to a class of time-varying positive semigroups. In the context of time-homogeneous models, the regularity conditions discussed in the present article appear to be necessary and sufficient condition for the existence of leading eigenvalues. We review and illustrate the impact of these results in the context of positive semigroups arising in transport theory, physics, mathematical biology and signal processing. Copyright © 2021, The Authors. All rights reserved.

关键词： Banach spaces

Periodicity Scoring of Time Series Encodes Dynamical Behavior of the Tumor Suppressor p53 ⁎ ⁎

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IFAC-PapersOnLine 2021年第9期54卷 488-495页

作者： Caroline Moosmüller Christopher J. Tralie Mahdi Kooshkbaghi Zehor Belkhatir Maryam Pouryahya José Reyes Joseph O. Deasy Allen R. Tannenbaum Ioannis G. Kevrekidis C. Moosmüller and C. Tralie contributed equally to this work Department of Mathematics University of California San Diego La Jolla CA 92093 USA Department of Medical Physics Memorial Sloan-Kettering Cancer Center NY USA Department of Chemical and Biomolecular Engineering Johns Hopkins University Baltimore MD 21218 USA Department of Mathematics and Computer Science Ursinus College Collegeville PA USA Program in Applied and Computational Mathematics Princeton University NJ USA School of Engineering and Sustainable Development De Montfort University Leicester UK Cancer Biology and Genetics Program and Computational and Systems Biology Program Memorial Sloan-Kettering Cancer Center New York NY 10065 USA and Department of Systems Biology Harvard Medical School Boston MA 02115 USA Departments of Computer Science and Applied Mathematics & Statistics Stony Brook University NY USA

In this paper we analyze the dynamical behavior of the tumor suppressor protein p53, an essential player in the cellular stress response, which prevents a cell from dividing if severe DNA damage is present. When this response system is malfunctioning, e.g. due to mutations in p53, uncontrolled cell proliferation may lead to the development of cancer. Understanding the behavior of p53 is thus crucial to prevent its failing. It has been shown in various experiments that periodicity of the p53 signal is one of the main descriptors of its dynamics, and that its pulsing behavior (regular vs. spontaneous) indicates the level and type of cellular stress. In the present work, we introduce an algorithm to score the local periodicity of a given time series (such as the p53 signal), which we call Detrended Autocorrelation Periodicity Scoring (DAPS). It applies pitch detection (via autocorrelation) on sliding windows of the entire time series to describe the overall periodicity by a distribution of localized pitch scores. We apply DAPS to the p53 time series obtained from single cell experiments and establish a correlation between the periodicity scoring of a cell’s p53 signal and the number of cell division events. In particular, we show that high periodicity scoring of p53 is correlated to a low number of cell divisions and vice versa. We show similar results with a more computationally intensive state-of-the-art periodicity scoring algorithm based on topology known as Sw1PerS. This correlation has two major implications: It demonstrates that periodicity scoring of the p53 signal is a good descriptor for cellular stress, and it connects the high variability of p53 periodicity observed in cell populations to the variability in the number of cell division events.

关键词： Systems biology cellular systems time series modeling bioinformatics computational biology

Measuring 3D Chemistry at 1 nm Resolution with Fused Multi-Modal Electron Tomography

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Microscopy and microanalysis : the official journal of Microscopy Society of America, Microbeam Analysis Society, Microscopical Society of Canada 2023年第1期29卷 1394-1395页

作者： Schwartz, Jonathan Di, Zichao Wendy Jiang, Yi Cho, Min Gee Qian, Yiwen Gu, Junsi Rozeveld, Steve Ercius, Peter Fessler, Jeffrey A. Xu, Ting Scott, Mary Hovden, Robert Department of Materials Science and Engineering University of Michigan Ann Arbor MI United States Mathematics and Computer Science Division Argonne National Laboratory Lemont IL United States Advanced Photon Source Argonne National Laboratory Lemont IL United States Department of Materials Science and Engineering University of California at Berkeley Berkeley CA United States National Center for Electron Microscopy Lawrence Berkeley National Laboratory Berkeley CA United States Dow Chemical Co. Midland MI United States Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor MI United States Materials Science Division Lawrence Berkeley National Laboratory Berkeley CA United States Applied Physics Program University of Michigan Ann Arbor MI United States

Global-Local Active Contour for Segmenting Images with Simultaneous Inhomogeneity and Texture

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SSRN

SSRN 2024年

作者： Shao, Pei-Chiang Department of Applied Mathematics Chung Yuan Christian University Zhongli District Taoyuan City320314 Taiwan Undergraduate Program in College of Electrical Engineering and Computer Science Chung Yuan Christian University Zhongli District Taoyuan City320314 Taiwan

Severe intensity inhomogeneity (InH) and complex real-world textures cause great difficulties and become two important issues in image segmentation and object extraction applications. Plenty of methods are proposed to tackle these issues, however, they usually perform poorly on images possess both InH and texture. In this paper, we propose a region-based active contour model for segmenting images with simultaneous inhomogeneity and texture. A new bias field possesses both global and local smoothness properties is proposed to handle the InH issue, and a pixel inhomogeneity factor (PIF) is employed to jointly deal with InH and textured images. We also employ the total variation (TV) regularization to further smooth and denoise the transformed PIF image, making the segmentation process to have the nice properties of global convergence and independence of contour initialization. A large number of numerical experiments and comparisons are conducted to demonstrate the effective performance of the newly proposed method. © 2024, The Authors. All rights reserved.

关键词： Textures

Roadmap on Nonlocality in Photonic Materials and Metamaterials

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arXiv 2025年

作者： Monticone, Francesco Mortensen, N. Asger Fernández-Domínguez, Antonio I. Luo, Yu Tserkezis, Christos Khurgin, Jacob B. Shahbazyan, Tigran V. Chaves, André J. Peres, Nuno M.R. Wegner, Gino Busch, Kurt Hu, Huatian della Sala, Fabio Zhang, Pu Ciracì, Cristian Aizpurua, Javier Babaze, Antton Borisov, Andrei G. Chen, Xue-Wen Christensen, Thomas Yan, Wei Yang, Yi Hohenester, Ulrich Huber, Lorenz Wubs, Martijn de Liberato, Simone Gonçalves, P.A.D. de Abajo, F. Javier García Hess, Ortwin Tarasenko, Illya Cox, Joel D. Jelver, Line Dias, Eduardo J.C. Sánchez, Miguel Sánchez Margetis, Dionisios Gómez-Santos, Guillermo Stauber, Tobias Tretyakov, Sergei Simovski, Constantin Pakniyat, Samaneh Gómez-Díaz, J. Sebastián Bondarev, Igor V. Biehs, Svend-Age Boltasseva, Alexandra Shalaev, Vladimir M. Krasavin, Alexey V. Zayats, Anatoly V. Alù, Andrea Song, Jung-Hwan Brongersma, Mark L. Levy, Uriel Long, Olivia Y. Guo, Cheng Fan, Shanhui Bozhevolnyi, Sergey I. Overvig, Adam Prudêncio, Filipa R. Silveirinha, Mário G. Gangaraj, S. Ali Hassani Argyropoulos, Christos Huidobro, Paloma A. Galiffi, Emanuele Yang, Fan Pendry, John B. Miller, David A.B. School of Electrical and Computer Engineering Cornell University IthacaNY14853 United States POLIMA Center for Polariton-driven Light–Matter Interactions University of Southern Denmark Campusvej 55 Odense MDK-5230 Denmark D-IAS—Danish Institute for Advanced Study University of Southern Denmark Campusvej 55 Odense MDK-5230 Denmark Departamento de Física Teórica de la Materia Condensada Universidad Autónoma de Madrid MadridE-28049 Spain Universidad Autónoma de Madrid MadridE-28049 Spain School of Electrical and Electronic Engineering Nanyang Technological University Singapore639798 Singapore Key Laboratory of Radar Imaging and Microwave Photonics Ministry of Education College of Electronic and Information Engineering Nanjing University of Aeronautics and Astronautics Nanjing211106 China Department of Electrical and Computer Engineering Johns Hopkins University BaltimoreMD21218 United States Department of Physics Jackson State University JacksonMS39217 United States Department of Physics Aeronautics Institute of Technology SP So Jos dos Campos12228-900 Brazil Departamento de Física Universidade do Minho BragaP-4710-057 Portugal Av Mestre José Veiga Braga4715-330 Portugal Max-Born-Institut Berlin12489 Germany Humboldt-Universität zu Berlin Institut für Physik AG Theoretische Optik and Photonik Berlin12489 Germany Center for Biomolecular Nanotechnologies Istituto Italiano di Tecnologia Via Barsanti 14 Arnesano73010 Italy Via Monteroni Campus Unisalento Lecce73100 Italy School of physics Huazhong University of Science and Technology Luoyu Road 1037 Wuhan430074 China Donostia International Physics Center DIPC Donostia-San Sebastián20018 Spain Ikerbasque Basque Foundation for Science Bilbao48009 Spain Department of Electricity and Electronics University of the Basque Country Leioa48940 Spain Department of Applied Physics University of the Basque Country Donostia20018 Spain Université Paris-Saclay CNRS Institut des Scienc

Photonic technologies continue to drive the quest for new optical materials with unprecedented responses. A major frontier in this field is the exploration of nonlocal (spatially dispersive) materials, going beyond the local, wavevector-independent assumption traditionally made in optical material modeling. On one end, the growing interest in plasmonic, polaritonic and quantum materials has revealed naturally occurring nonlocalities, emphasizing the need for more accurate models to predict and design their optical responses. This has major implications also for topological, nonreciprocal, and time-varying systems based on these material platforms. Beyond natural materials, artificially structured materials—metamaterials and metasurfaces–can provide even stronger and engineered nonlocal effects, emerging from long-range interactions or multipolar effects. This is a rapidly expanding area in the field of photonic metamaterials, with open frontiers yet to be explored. In the case of metasurfaces, in particular, nonlocality engineering has become a powerful tool for designing strongly wavevector-dependent responses, enabling enhanced wavefront control, spatial compression, multifunctional devices, and wave-based computing. Furthermore, nonlocality and related concepts play a critical role in defining the ultimate limits of what is possible in optics, photonics, and wave physics. This Roadmap aims to survey the most exciting developments in nonlocal photonic materials, highlight new opportunities and open challenges, and chart new pathways that will drive this emerging field forward–toward new scientific discoveries and technological advancements. Copyright © 2025, The Authors. All rights reserved.

关键词： Nanocrystals

Neural Methods for Amortized Inference

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Statistics and Its Application 1000年第1期12卷 311-335页

作者： Andrew Zammit-Mangion Matthew Sainsbury-Dale Raphaël Huser 1School of Mathematics and Applied Statistics University of Wollongong Wollongong New South Wales Australia email: azm@uow.edu.au 2Statistics Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology (KAUST) Thuwal Saudi Arabia

Simulation-based methods for statistical inference have evolved dramatically over the past 50 years, keeping pace with technological advancements. The field is undergoing a new revolution as it embraces the representational capacity of neural networks, optimization libraries, and graphics processing units for learning complex mappings between data and inferential targets. The resulting tools are amortized, in the sense that, after an initial setup cost, they allow rapid inference through fast feed-forward operations. In this article we review recent progress in the context of point estimation, approximate Bayesian inference, summary-statistic construction, and likelihood approximation. We also cover software and include a simple illustration to showcase the wide array of tools available for amortized inference and the benefits they offer over Markov chain Monte Carlo methods. The article concludes with an overview of relevant topics and an outlook on future research directions.

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