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Multiscale regression on unknown manifolds

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arXiv 2021年

作者： Liao, Wenjing Maggioni, Mauro Vigogna, Stefano School of Mathematics Georgia Institute of Technology AtlantaGA30313 United States Department of Mathematics Department of Applied Mathematics and Statistics Mathematical Institute of Data Science Johns Hopkins University BaltimoreMD21218 United States MaLGa Center Department of Informatics Bioengineering Robotics and Systems Engineering University of Genova Genova16145 Italy

We consider the regression problem of estimating functions on RD but supported on a d-dimensional manifold M ⊂ RD with d D. Drawing ideas from multi-resolution analysis and nonlinear approximation, we construct low-dimensional coordinates on M at multiple scales, and perform multiscale regression by local polynomial fitting. We propose a data-driven wavelet thresholding scheme that automatically adapts to the unknown regularity of the function, allowing for efficient estimation of functions exhibiting nonuniform regularity at different locations and scales. We analyze the generalization error of our method by proving finite sample bounds in high probability on rich classes of priors. Our estimator attains optimal learning rates (up to logarithmic factors) as if the function was defined on a known Euclidean domain of dimension d, instead of an unknown manifold embedded in RD. The implemented algorithm has quasilinear complexity in the sample size, with constants linear in D and exponential in d. Our work therefore establishes a new framework for regression on low-dimensional sets embedded in high dimensions, with fast implementation and strong theoretical guarantees. Copyright © 2021, The Authors. All rights reserved.

关键词： Regression analysis

Your Face Mirrors Your Deepest Beliefs-Predicting Personality and Morals through Facial Emotion Recognition

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arXiv 2021年

作者： Gloor, Peter A. Colladon, Andrea Fronzetti Altuntas, Erkin Cetinkaya, Cengiz Kaiser, Maximilian F. Ripperger, Lukas Schaefer, Tim MIT Center for Collective Intelligence CambridgeMA02142 United States Department of Engineering University of Perugia Perugia06123 Italy Galaxyadvisors AG Aarau5000 Switzerland Department of Data Science Lucerne University of Applied Sciences and Arts Lucerne6002 Switzerland Department of Information Systems University of Cologne Cologne50923 Germany

Can we really"read the mind in the eyes"? Moreover, can AI assist us in this task? This paper answers these two questions by introducing a machine learning system that predicts personality characteristics of individuals on the basis of their face. It does so by tracking the emotional response of the individual’s face through facial emotion recognition (FER) while watching a series of 15 short videos of different genres. To calibrate the system, we invited 85 people to watch the videos, while their emotional responses were analyzed through their facial expression. At the same time, these individuals also took four well-validated surveys of personality characteristics and moral values: the revised NEO FFI personality inventory, the Haidt moral foundations test, the Schwartz personal value system, and the domain-specific risk-taking scale (DOSPERT). We found that personality characteristics and moral values of an individual can be predicted through their emotional response to the videos as shown in their face, with an accuracy of up to 86% using gradient-boosted trees. We also found that different personality characteristics are better predicted by different videos, in other words, there is no single video that will provide accurate predictions for all personality characteristics, but it is the response to the mix of different videos that allows for accurate prediction. © 2021, CC BY.

关键词： Forecasting

Adaptive test allocation for outbreak detection and tracking in social contact networks

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arXiv 2020年

作者： Batlle, Pau Bruna, Joan Fernandez-Granda, Carlos Preciado, Victor M. Courant Institute of Mathematical Sciences Center for Data Science New York University NY United States Department of Electrical and Systems Engineering Applied Mathematics and Computational Science University of Pennsylvania PA United States

We present a general framework for adaptive allocation of viral tests in social contact networks. We pose and solve several complementary problems. First, we consider the design of a social sensing system whose objective is the early detection of a novel epidemic outbreak. In particular, we propose an algorithm to select a subset of individuals to be tested in order to detect the onset of an epidemic outbreak as fast as possible. We pose this problem as a hitting time probability maximization problem and use submodularity optimization techniques to derive explicit quality guarantees for the proposed solution. Second, once an epidemic outbreak has been detected, we consider the problem of adaptively distributing viral tests over time in order to maximize the information gained about the current state of the epidemic. We formalize this problem in terms of information entropy and mutual information and propose an adaptive allocation strategy with quality guarantees. For these problems, we derive analytical solutions for any stochastic compartmental epidemic model with Markovian dynamics, as well as efficient Monte-Carlo-based algorithms for non-Markovian dynamics. Finally, we illustrate the performance of the proposed framework in numerical experiments involving a model of Covid-19 applied to a real human contact network. Copyright © 2020, The Authors. All rights reserved.

关键词： Epidemiology

Programmable non-Hermitian photonic quantum walks via dichroic metasurfaces

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arXiv 2025年

作者： Savarese, Paola Bansal, Sarvesh Ammendola, Maria Gorizia Amato, Lorenzo Barboza, Raouf Piccirillo, Bruno Di Colandrea, Francesco Marrucci, Lorenzo Cardano, Filippo Dipartimento di Fisica Università degli Studi di Napoli Federico II Complesso Universitario di Monte Sant’Angelo Via Cintia Napoli80126 Italy Scuola Superiore Meridionale Via Mezzocannone 4 Napoli80138 Italy PSI Center for Scientific Computing Theory and Data PSI VilligenCH-5232 Switzerland Laboratory for Solid-State Physics ETH Zurich ZürichCH-8093 Switzerland Dipartimento di Scienze e Ingegneria della Materia dell’Ambiente ed Urbanistica Università Politecnica delle Marche Via Brecce Bianche Ancona60131 Italy CNR-ISASI Institute of Applied Science and Intelligent Systems Via Campi Flegrei 34 NA Pozzuoli80078 Italy

The evolution of a closed quantum system is described by a unitary operator generated by a Hermitian Hamiltonian. However, when certain degrees of freedom are coupled to an environment, the relevant dynamics can be captured by non-unitary evolution operators, arising from non-Hermitian Hamiltonians. Here we introduce a photonic platform that implements non-unitary quantum walks, commonly used to emulate open-system dynamics, in the synthetic space of light transverse momentum. These walks are realized by propagating light through a series of dichroic liquid-crystal metasurfaces, that impart polarization-dependent momentum shifts. The non-unitary behavior stems from dichroic dye molecules with polarization-dependent absorption, whose orientation is coupled to that of the liquid crystals. We demonstrate multiple walks up to five time steps, with adjustable levels of dichroism set by the metasurface voltage, which is controlled remotely. This discrete-time process maps onto two-band tight-binding models with reciprocal yet non-Hermitian nearest-neighbor couplings, corresponding to a less-studied class of non-Hermitian systems. Our platform broadens the range of optical simulators for controlled investigations of non-Hermitian quantum dynamics. Copyright © 2025, The Authors. All rights reserved.

关键词： Hamiltonians

Teaching mechanics with individual exercise assignments and automated correction

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PAMM 2023年第3期23卷

作者： Michael H. Gfrerer Benjamin Marussig Katharina Maitz Mia M. Bangerl Institute of Applied Mechanics Graz Center of Computational Engineering (GCCE) Graz University of Technology Graz Austria Private University College of Teacher Education Augustinum (PPH Augustinum) Graz Austria Institute of Interactive Systems and Data Science Graz University of Technology Graz Austria

Solving exercise problems by yourself is a vital part of developing a mechanical understanding. Yet, most mechanics lectures have more than 200 participants, so the workload for manually creating and correcting assignments limits the number of exercises. The resulting example pool is usually much smaller than the number of participants, making verifying whether students can solve problems themselves considerably harder. At the same time, unreflected copying of tasks already solved does not foster the understanding of the subject and leads to a false self-assessment. We address these issues by providing a scalable approach for creating, distributing, and correcting exercise assignments for problems related to statics, strength of materials, dynamics, and hydrostatics. The overall concept allows us to provide individual exercise assignments for each student. A quantitative survey among students of our recent statics lecture assesses the acceptance of our teaching tool. The feedback indicates a clear added value for the lecture, which fosters self-directed and reflective learning.

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Coupled chemical reactions: Effects of electric field, diffusion, and boundary control

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Physical Review E 2023年第6期108卷 064413-064413页

作者： Shixin Xu Robert Eisenberg Zilong Song Huaxiong Huang Zu Chongzhi Center for Mathematics and Computational Sciences Duke Kunshan University 8 Duke Ave Kunshan Jiangsu 215316 China Department of Applied Mathematics Illinois Institute of Technology Chicago Illinois 60616 USA and Department of Physiology and Biophysics Rush University Chicago Ilinois 60612 USA Math and Statistics Department Utah State University Old Main Hill Logan Utah 84322 USA Research Center for Mathematics Advanced Institute of Natural Sciences Beijing Normal University Zhuhai Guangdong 519088 China Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science BNU-HKBU United International College Zhuhai Guangdong 519088 China Laboratory of Mathematics and Complex Systems MOE Beijing Normal University Beijing 100875 China and Department of Mathematics and Statistics York University Toronto Ontario Canada M3J 1P3

Chemical reactions involve the movement of charges, and this paper presents a mathematical model for describing chemical reactions in electrolytes. The model is developed using an energy variational method that aligns with classical thermodynamics principles. It encompasses both electrostatics and chemical reactions within consistently defined energetic and dissipative functionals. Furthermore, the energy variation method is extended to account for open systems that involve the input and output of charge and mass. Such open systems have the capability to convert one form of input energy into another form of output energy. In particular, a two-domain model is developed to study a reaction system with self-regulation and internal switching, which plays a vital role in the electron transport chain of mitochondria responsible for ATP generation—a crucial process for sustaining life. Simulations are conducted to explore the influence of electric potential on reaction rates and switching dynamics within the two-domain system. It shows that the electric potential inhibits the oxidation reaction while accelerating the reduction reaction.

关键词： Continuum mechanics Dissipative dynamics Electric field effects

Reinforcement Learning-Based Integrated Risk Aware Dynamic Treatment Strategy for Consumer-Centric Next-Gen Healthcare

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IEEE Transactions on Consumer Electronics 2025年

作者： Nimma, Divya Rao, Pinapati Lakshmana Ramesh, Janjhyam Venkata Naga Dahan, Fadl Reddy, Desidi Narsimha Selvakumar, Venkatachalam Ilkhamova, Yodgorkhon Jangir, Pradeep UMMC United States Koneru Lakshmaiah Education Foundation Department of Computer Science and Engineering Guntur Vaddeswaram522302 India Graphic Era Hill University Department of CSE Dehradun248002 India Graphic Era Deemed To Be University Department of CSE Uttarakhand Dehradun248002 India Prince Sattam Bin Abdulaziz University Department of Management Information Systems College of Business Administration Hawtat Bani Tamim Al-Kharj11942 Saudi Arabia Soniks consulting LLC Soniks consulting Data Consultant Telangana E park blvd India Bhavan’s Vivekananda College of Science Humanities and Commerce Department of Maths and Statistics Telangana Hyderabad India Tashkent State University of Economics Department of Digital Economy Tashkent Uzbekistan Saveetha School of Engineering Saveetha Institute of Medical and Technical Sciences Department of Biosciences Chennai602 105 India Al-Ahliyya Amman University Hourani Center for Applied Scientific Research Amman19328 Jordan

Reinforcement learning (RL) has gained prominence in healthcare due to its ability to optimize treatment strategies without relying on predefined mathematical models. However, existing approaches face critical challenges: (1) the optimality of learned strategies is assessed without considering treatment risks, potentially leading to unsafe recommendations;(2) distribution shift issues cause learned strategies to diverge from physician decisions;and (3) past observational data and treatment history are often overlooked, leading to suboptimal state representations. To address these limitations, we propose a Dynamic Treatment Strategy Generation Model that integrates Dead Ends with an Offline Supervised Actor-Critic approach (DOSAC-DTR). Our model incorporates Dead Ends into the Actor-Critic framework to evaluate risks associated with recommended treatments. Additionally, physician oversight is embedded to mitigate distribution shift and align the learned strategy with expert decisions while maximizing expected outcomes. To enhance state representation, we employ an LSTM-based encoder-decoder model to capture essential patient history, ensuring robust decision-making. Experimental results on real-world datasets (MIMIC-III) demonstrate that DOSAC-DTR significantly reduces mortality rates (Sepsis: 3.51%, Ventilation: 13.74%) and improves treatment alignment with physicians (Jaccard similarity: 0.362, 0.126) compared to baseline models. These findings underscore the potential of reinforcement learning in personalized healthcare, improving both treatment efficacy and patient safety. © 1975-2011 IEEE.

关键词： Risk assessment

Anthropogenic emission is the main contributor to the rise of atmospheric methane during 1993-2017

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National science Review 2022年第5期9卷 154-166页

作者：张臻 Benjamin Poulter Sara Knox Ann Stavert Gavin McNicol Etienne Fluet-Chouinard Aryeh Feinberg 赵园红 Philippe Bousquet Josep G.Canadell Anita Ganesan Gustaf Hugelius George Hurtt Robert B.Jackson Prabir K.Patra Marielle Saunois Lena H?glund-Isaksson 黄春林 Abhishek Chatterjee 李新 Department of Geographical Sciences University of Maryland Biospheric Sciences Laboratory NASA Goddard Space Flight Center Department of Geography University of British Columbia Global Carbon Project CSIRO Oceans and Atmosphere Department of Earth and Environmental Sciences University of Illinois Chicago Department of Earth System Science Stanford University Institute for Data Systems and Society Massachusetts Institute of Technology College of Oceanic and Atmospheric Sciences Ocean University of China Laboratoire des Sciences du Climat et de l’Environment LSCE-IPSL (CEA-CNRS-UVSQ)Université Paris-Saclay School of Geographical Sciences University of Bristol Department of Physical Geography and Bolin Centre for Climate Research Stockholm University Woods Institute for the Environment and Precourt Institute for Energy Stanford University Research Institute for Global Change JAMSTEC International Institute for Applied Systems Analysis (IIASA) Northwest Institute of Eco-Environment and Resources Chinese Academy of Sciences Global Modeling and Assimilation Office NASA Goddard Space Flight Center Universities Space Research Association Institute of Tibetan Plateau Research Chinese Academy of Sciences

Atmospheric methane（CH4） concentrations have shown a puzzling resumption in growth since 2007 following a period of stabilization from 2000 to *** hypotheses have been proposed to explain the temporal variations in CH4growth,and attribute the rise of atmospheric CH4either to increases in emissions from fossil fuel activities,agriculture and natural wetlands,or to a decrease in the atmospheric chemical ***,we use a comprehensive ensemble of CH4source estimates and isotopic δ13C-CH4source signature data to show that the resumption of CH4growth is most likely due to increased anthropogenic *** emission scenarios that have the fewest biases with respect to isotopic composition suggest that the agriculture,landfill and waste sectors were responsible for 53±13% of the renewed growth over the period 2007-2017 compared to 2000-2006;industrial fossil fuel sources explained an additional 34 ±24%,and wetland sources contributed the least at 13 ±9%.The hypothesis that a large increase in emissions from natural wetlands drove the decrease in atmospheric δ13C-CH4values cannot be reconciled with current process-based wetland *** finding suggests the need for increased wetland measurements to better understand the contemporary and future role of wetlands in the rise of atmospheric methane and climate *** findings highlight the predominant role of anthropogenic activities in driving the growth of atmospheric CH4concentrations.

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Anthropogenic emission is the main contributor to the rise of atmospheric methane during 1993-2017

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国家科学评论（英文版） 2022年第5期9卷 149-161页

作者： Zhen Zhang Benjamin Poulter Sara Knox Ann Stavert Gavin McNicol Etienne Fluet-Chouinard Aryeh Feinberg Yuanhong Zhao Philippe Bousquet Josep G.Canadell Anita Ganesan Gustaf Hugelius George Hurtt Robert B.Jackson Prabir K.Patra Marielle Saunois Lena H?glund-lsaksson Chunlin Huang Abhishek Chatterjee Xin Li Department of Geographical Sciences University of MarylandCollege ParkMD 20742USA Biospheric Sciences Laboratory NASA Goddard Space Flight CenterGreenbeltMD 20771USA Department of Geography University of British ColumbiaVancouver V6T 1Z2Canada Global Carbon Project CSIRO Oceans and AtmosphereCanberraACT 2601Australia Department of Earth and Environmental Sciences University of Illinois ChicagoChicagoIL 60607USA Department of Earth System Science Stanford UniversityStanfordCA 94305USA Institute for Data Systems and SocietyMassachusetts Institute of TechnologyCambridgeMA 02139USA College of Oceanic and Atmospheric Sciences Ocean University of ChinaQingdao 266000China Laboratoire des Sciences du Climat et de I'Environment LSCE-IPSL(CEA-CNRS-UVSQ)Université Paris-SaclayGif-sur-Yvette 91191France School of Geographical Sciences University of BristolBristol BS8 1RLUK Department of Physical Geography and Bolin Centre for Climate Research Stockholm UniversityStockholm SE-10691Sweden Department of Earth System Science Stanford UniversityStanfordCA 94305USA Woods Institute for the Environment and Precourt Institute for Energy Stanford UniversityStanfordCA 94305USA Research Institute for Global Change JAMSTECYokohama 236-0001Japan International Institute for Applied Systems Analysis(IIASA) Laxenburg A-2361Austria Northwest Institute of Eco-Environment and Resources Chinese Academy of SciencesLanzhou 730000China Global Modeling and Assimilation Office NASA Goddard Space Flight CenterGreenbeltMD 20771USA Universities Space Research Association ColumbiaMD 21046USA Institute of Tibetan Plateau Research Chinese Academy of SciencesBeijing 100101China

Atmospheric methane(CH4)concentrations have shown a puzzling resumption in growth since 2007 following a period of stabilization from 2000 to *** hypotheses have been proposed to explain the temporal variations in CH4 growth,and attribute the rise of atmospheric CH4 either to increases in emissions from fossil fuel activities,agriculture and natural wetlands,or to a decrease in the atmospheric chemical ***,we use a comprehensive ensemble of CH4 source estimates and isotopic δ13C-CH4 source signature data to show that the resumption of CH4 growth is most likely due to increased anthropogenic *** emission scenarios that have the fewest biases with respect to isotopic composition suggest that the agriculture,landfill and waste sectors were responsible for 53±13％of the renewed growth over the period 2007-2017 compared to 2000-2006;industrial fossil fuel sources explained an additional 34±24％,and wetland sources contributed the least at 13±9％.The hypothesis that a large increase in emissions from natural wetlands drove the decrease in atmospheric δ13C-CH4 values cannot be reconciled with current process-based wetland CH4 *** finding suggests the need for increased wetland measurements to better understand the contemporary and future role of wetlands in the rise of atmospheric methane and climate *** findings highlight the predominant role of anthropogenic activities in driving the growth of atmospheric CH4 concentrations.

关键词： greenhouse gas carbon cycle climate mitigation wetland methane isotope