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On Time Uniform Wong-Zakai Approximation Theorems

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arXiv 2023年

作者： Del Moral, Pierre Hu, Shulan Jasra, Ajay Ruzayqat, Hamza Wang, Xinyu Institut de Mathematiques de Bordeaux Bordeaux33405 France School of Statistics and Mathematics Zhongnan University of Economics and Law 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 Wenlan School of Business Zhongnan University of Economics and Law China

We consider the long time behavior of Wong-Zakai approximations of stochastic differential equations. These piecewise smooth diffusion approximations are of great importance in many areas, such as those with ordinary differential equations associated to random smooth fluctuations;e.g. robust filtering problems. In many examples, the mean error estimate bounds that have been derived in the literature can grow exponentially with respect to the time horizon. We show in a simple example that indeed mean error estimates do explode exponentially in the time parameter, i.e. in that case a Wong-Zakai approximation is only useful for extremely short time intervals. Under spectral conditions, we present some quantitative time-uniform convergence theorems, i.e. time-uniform mean error bounds, yielding what seems to be the first results of this type for Wong-Zakai diffusion *** Codes 60H35(Primary), 65C30(Secondary) Copyright © 2023, The Authors. All rights reserved.

关键词： Brownian movement

A deep learning system for predicting time to progression of diabetic retinopathy

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NATURE MEDICINE 2024年第2期30卷 358-359页

作者： [Anonymous] Shanghai Belt and Road International Joint Laboratory for Intelligent Prevention and Treatment of Metabolic Disorders Department of Computer Science and Engineering School of Electronic Information and Electrical Engineering Shanghai Jiao Tong University Department of Endocrinology and Metabolism Shanghai Sixth People’s Hospital Affiliated to Shanghai Jiao Tong University School of Medicine Shanghai Diabetes Institute Shanghai Clinical Center for Diabetes Shanghai China MOE Key Laboratory of AI School of Electronic Information and Electrical Engineering Shanghai Jiao Tong University Shanghai China Department of Ophthalmology Huadong Sanatorium Wuxi China Department of Ophthalmology Shanghai Sixth People’s Hospital Affiliated to Shanghai Jiao Tong University School of Medicine Shanghai China Department of Ophthalmology and Visual Sciences The Chinese University of Hong Kong Hong Kong China Singapore Eye Research Institute Singapore National Eye Centre Singapore Singapore Department of Computer Science and Engineering The Hong Kong University of Science and Technology Hong Kong China Department of Chemical and Biological Engineering The Hong Kong University of Science and Technology Hong Kong China State Key Laboratory of Ophthalmology Zhongshan Ophthalmic Center Sun Yat-sen University Guangdong Provincial Key Laboratory of Ophthalmology and Visual Science Guangzhou China Department of Ophthalmology Peking Union Medical College Hospital Peking Union Medical College Chinese Academy of Medical Sciences Beijing China Medical Records and Statistics Office Shanghai Sixth People’s Hospital Affiliated to Shanghai Jiao Tong University School of Medicine Shanghai China Department of Geriatrics Tongji Hospital Tongji Medical College Huazhong University of Science and Technology Wuhan China National Engineering Research Center for Big Data Technology and System Services Computing Technology and System Lab Cluster and Grid Computing Lab School of Computer Science and Tech

We developed and validated a deep learning system (termed DeepDR Plus) in a diverse, multiethnic, multi-country dataset to predict personalized risk and time to progression of diabetic retinopathy. We show that DeepDR Plus can be integrated into the clinical workflow to promote individualized intervention strategies for the management of diabetic retinopathy.

关键词： Diabetes complications Machine learning Predictive markers

Opto-thermoelectric pulling of light-absorbing particles

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Light(Science & Applications) 2020年第1期9卷 1686-1696页

作者： Linhan Lin Pavana Siddhartha Kollipara Abhay Kotnala Taizhi Jiang Yaoran Liu Xiaolei Peng Brian A.Korgel Yuebing Zheng Walker Department of Mechanical Engineering The University of Texas at AustinAustinTX 78712USA Materials Science&Engineering Program and Texas Materials Institute The University of Texas at AustinAustinTX 78712USA State Key Laboratory of Precision Measurement Technology and Instruments Department of Precision InstrumentTsinghua UniversityBeijing 100084People’s Republic of China McKetta Department of Chemical Engineering The University of Texas at AustinAustinTX 78712USA Department of Electrical and Computer Engineering The University of Texas at AustinAustinTX 78712USA

Optomechanics arises from the photon momentum and its exchange with low-dimensional *** is well known that optical radiation exerts pressure on objects,pushing them along the light ***,optical pulling of an object against the light path is still a counter-intuitive ***,we present a general concept of optical pulling-opto-thermoelectric pulling(OTEP)—where the optical heating of a light-absorbing particle using a simple plane wave can pull the particle itself against the light *** irradiation orientation-directed pulling force imparts self-restoring behaviour to the particles,and three-dimensional(3D)trapping of single particles is achieved at an extremely low optical intensity of 10^(−2)mWμm^(−2).Moreover,the OTEP force can overcome the short trapping range of conventional optical tweezers and optically drive the particle flow up to a macroscopic *** concept of selfinduced opto-thermomechanical coupling is paving the way towards freeform optofluidic technology and lab-on-achip devices.

关键词： absorbing light trapping

Towards Robust and Scalable Dispatch Modeling of Long-Duration Energy Storage

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arXiv 2024年

作者： Guerra, Omar J. Dalvi, Sourabh Thatte, Amogh A. Cowiestoll, Brady Jorgenson, Jennie Hodge, Bri-Mathias National Renewable Energy Laboratory 15013 Denver West Parkway GoldenCO80401 United States Colorado School of Mines Advanced Energy Systems Graduate Program 1500 Illinois Street GoldenCO80401 United States Renewable and Sustainable Energy Institute University of Colorado BoulderCO80309 United States Department of Electrical Computer & Energy Engineering University of Colorado BoulderCO80309 United States

Energy storage technologies, including short-duration, long-duration, and seasonal storage, are seen as technologies that can facilitate the integration of larger shares of variable renewable energy, such as wind and solar photovoltaics, in power systems. However, despite recent advances in the techno-economic modeling of energy storage (particularly for short-duration applications), the operation and economics of long-duration energy storage are still incomplete in power systems modeling platforms. For instance, existing modeling approaches for long-duration storage are often based either on an oversimplified representation of power system operations or limited representation of storage technologies, e.g., evaluation of only a single application. This manuscript presents an overview of the challenges of modeling long-duration energy storage technologies, as well as a discussion regarding the capabilities and limitations of existing approaches. We used two test power systems with high shares of both solar photovoltaics- and wind (70% - 90% annual variable renewable energy shares) to assess long-duration energy storage dispatch approaches. Our results estimate that better dispatch modeling of long-duration energy storage could increase the associated operational value by 4% - 14% and increase the standard capacity credit by 14% - 34%. Thus, a better long-duration energy storage dispatch could represent significant cost saving opportunities for electric utilities and system operators. In addition, existing long-duration dispatch modeling approaches were tested in terms of both improved system value (e.g., based on production cost and standard capacity credit) and scalability (e.g., based on central processing unit time and peak memory usage). Both copper plate and nodal representations of the power system were considered. Although the end volume target dispatch approach, i.e., based on mid-term scheduling, showed promising performance in terms of both improved system

关键词： Scalability

On the Particle Approximation of Lagged Feynman-Kac Formulae

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arXiv 2024年

作者： Awadelkarim, Elsiddig Caffarel, Michel Moral, Pierre Del Jasra, Ajay 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 University of Toulouse CNRS-Lab. de Chimie et Physique Quantiques Toulouse31062 France Centre de Recherche Inria Bordeaux Sud-Ouest Talence33405 France School of Data Science The Chinese University Hong Kong Shenzhen China

In this paper we examine the numerical approximation of the limiting invariant measure associated with Feynman-Kac formulae. These are expressed in a discrete time formulation and are associated with a Markov chain and a potential function. The typical application considered here is the computation of eigenvalues associated with non-negative operators as found, for example, in physics or particle simulation of rare-events. We focus on a novel lagged approximation of this invariant measure, based upon the introduction of a ratio of time-averaged Feynman-Kac marginals associated with a positive operator iterated l ∈ N times;a lagged Feynman-Kac formula. This estimator and its approximation using Diffusion Monte Carlo (DMC) have been extensively employed in the physics literature. In short, DMC is an iterative algorithm involving N ∈ N particles or walkers simulated in parallel, that undergo sampling and resampling operations. In this work, it is shown that for the DMC approximation of the lagged Feynman-Kac formula, one has an almost sure characterization of the L1-error as the time parameter (iteration) goes to infinity and this is at most of O(exp{−κl}/N), for_ κ > 0. In addition a non-asymptotic in time, and time uniform L1−bound is proved which is O(l/√N). We also prove a novel central limit theorem to give a characterization of the exact asymptotic in time variance. This analysis demonstrates that the strategy used in physics, namely, to run DMC with N and l small and, for long time enough, is mathematically justified. Our results also suggest how one should choose N and l in practice. We emphasize that these results are not restricted to physical applications;they have broad relevance to the general problem of particle simulation of the Feynman-Kac formula, which is utilized in a great variety of scientific and engineering fields. © 2024, CC BY.

关键词： Eigenvalues and eigenfunctions

Using tracheal breathing sounds and anthropometric information for screening obstructive sleep apnoea during wakefulness

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Journal of Medical engineering and Technology 2019年第2期43卷 111-123页

作者： Elwali, Ahmed Meza-Vargas, Sonia Moussavi, Zahra Biomedical Engineering Program University of Manitoba Winnipeg Canada Respirology Department University of Manitoba Winnipeg Canada Electrical and Computer Engineering Department University of Manitoba Winnipeg Canada

Obstructive sleep apnoea (OSA) is a common yet underdiagnosed disorder. Undiagnosed OSA significantly increases perioperative morbidity and mortality for OSA patients undergoing surgery, requiring full anaesthesia. Tracheal breathing sounds characteristics during wakefulness have shown a high correlation with the apnoea–hypopnea index (AHI), while they are also affected by the anthropometric parameters, e.g., sex, age, etc. This study investigates the effects of the anthropometric parameters on our new quick objective OSA screening tool during wakefulness. Breathing sounds of 122 individuals (71 with AHI 15 as OSA) were recorded during wakefulness in the supine position. The spectra and bi-spectra of 81 (47 non-OSA) individuals’ signals, which were randomly selected, were analysed as a training dataset to extract the most significant features with the lowest sensitivity to the anthropometric parameters. Using a support vector machine (SVM) classifier, these features resulted in 72.1, 64.7 and 77.5% testing classification accuracy, sensitivity and specificity, respectively. We also investigated classifying subjects into subgroups related to each anthropometric parameter and incorporating a voting procedure. This routine resulted in 83.6, 74.5 and 90.1% testing classification accuracy, sensitivity and specificity, respectively. In conclusion, it is possible to positively utilise the anthropometric information to enhance the classification accuracy for a reliable OSA screening procedure during wakefulness. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.

关键词： Classification (of information)

Enhancing Deep Reinforcement Learning: A Tutorial on Generative Diffusion Models in Network Optimization

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arXiv 2023年

作者： Du, Hongyang Zhang, Ruichen Liu, Yinqiu Wang, Jiacheng Lin, Yijing Li, Zonghang Niyato, Dusit Kang, Jiawen Xiong, Zehui Cui, Shuguang Ai, Bo Zhou, Haibo Kim, Dong In The School of Computer Science and Engineering The Energy Research Institute @ NTU Interdisciplinary Graduate Program Nanyang Technological University Singapore The School of Computer Science and Engineering Nanyang Technological University Singapore The State Key Laboratory of Networking and Switching Technology Beijing University of Posts and Telecommunications China The School of Information and Communication Engineering University of Electronic Sciences and Technology of China Chengdu China The School of Automation Guangdong University of Technology China The Pillar of Information Systems Technology and Design Singapore University of Technology and Design Singapore Shenzhen China The State Key Laboratory of Rail Traffic Control and Safety Beijing Jiaotong University Beijing100044 China School of Electronic Science and Engineering Nanjing University Jiangsu Nanjing210093 China The Department of Electrical and Computer Engineering Sungkyunkwan University Suwon16419 Korea Republic of

Generative Diffusion Models (GDMs) have emerged as a transformative force in the realm of Generative Artificial Intelligence (GenAI), demonstrating their versatility and efficacy across various applications. The ability to model complex data distributions and generate high-quality samples has made GDMs particularly effective in tasks such as image generation and reinforcement learning. Furthermore, their iterative nature, which involves a series of noise addition and denoising steps, is a powerful and unique approach to learning and generating data. This paper serves as a comprehensive tutorial on applying GDMs in network optimization tasks. We delve into the strengths of GDMs, emphasizing their wide applicability across various domains, such as vision, text, and audio generation. We detail how GDMs can be effectively harnessed to solve complex optimization problems inherent in networks. The paper first provides a basic background of GDMs and their applications in network optimization. This is followed by a series of case studies, showcasing the integration of GDMs with Deep Reinforcement Learning (DRL), incentive mechanism design, Semantic Communications (SemCom), Internet of Vehicles (IoV) networks, etc. These case studies underscore the practicality and efficacy of GDMs in real-world scenarios, offering insights into network design. We conclude with a discussion on potential future directions for GDM research and applications, providing major insights into how they can continue to shape the future of network optimization. © 2023, CC BY.

关键词： Reinforcement learning

Minimizing Number of Nodes in Decision Trees with Hypotheses

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Procedia computer Science 2021年 192卷 232-240页

作者： Mohammad Azad Igor Chikalov Shahid Hussain Mikhail Moshkov Jouf University College of Computer and Information Sciences Department of Computer Science Sakaka 72441 Saudi Arabia Intel Corporation 5000 W Chandler Blvd Chandler AZ 85226 USA Habib University Dhanani School of Science and Engineering Computer Science Program Karachi 75290 Pakistan King Abdullah University of Science and Technology (KAUST) Computer Electrical and Mathematical Sciences & Engineering Division Thuwal 23955-6900 Saudi Arabia

In this paper, we consider decision trees that use both conventional queries based on one attribute each and queries based on hypotheses about values of all attributes. This approach is similar to one studied in exact learning, where membership and equivalence queries are considered. We propose dynamic programming algorithms for the minimization of the number of nodes in such decision trees and discuss results of computer experiments.

关键词： Decision tree Hypothesis Number of nodes

Multi-index Sequential Monte Carlo ratio estimators for Bayesian Inverse problems

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arXiv 2022年

作者： Law, Kody J.H. Walton, Neil Yang, Shangda Jasra, Ajay School of Mathematics University of Manchester ManchesterM13 9PL United Kingdom 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

We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. This setting is ubiquitous across science and engineering applications, for example in the context of Bayesian inference where a physics-based model governed by an intractable partial differential equation (PDE) appears in the likelihood. A multi-index Sequential Monte Carlo (MISMC) method is used to construct ratio estimators which provably enjoy the complexity improvements of multi-index Monte Carlo (MIMC) as well as the efficiency of Sequential Monte Carlo (SMC) for inference. In particular, the proposed method provably achieves the canonical complexity of MSE−1, while single level methods require MSE−ξ for ξ > 1. This is illustrated on examples of Bayesian inverse problems with an elliptic PDE forward model in 1 and 2 spatial dimensions, where ξ = 5/4 and ξ = 3/2, respectively. It is also illustrated on more challenging log Gaussian process models, where single level complexity is approximately ξ = 9/4 and multilevel Monte Carlo (or MIMC with an inappropriate index set) gives ξ = 5/4 + ω, for any ω > 0, whereas our method is again canonical. We also provide novel theoretical verification of the product-form convergence results which MIMC requires for Gaussian processes built in spaces of mixed regularity defined in the spectral domain, which facilitates acceleration with fast Fourier transform methods via a cumulant embedding strategy, and may be of independent interest in the context of spatial statistics and machine learning. Copyright © 2022, The Authors. All rights reserved.

关键词： Inverse problems