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arXiv 2025年

作者： Partohaghighi, Mohammad Marcia, Roummel Chen, YangQuan Electrical Engineering and Computer Science graduate program University of California Merced United States Department of Applied Mathematics University of California Merced MercedCA United States Lab Department of Mechanical Engineering School of Engineering University of California MercedCA95343 United States

Fractional-order stochastic gradient descent (FOSGD) leverages a fractional exponent to capture long-memory effects in optimization, yet its practical impact is often constrained by the difficulty of tuning and stabilizing this exponent. In this work, we introduce 2SED Fractional-Order Stochastic Gradient Descent (2SEDFOSGD), a novel method that synergistically combines the Two-Scale Effective Dimension (2SED) algorithm with FOSGD to automatically calibrate the fractional exponent in a data-driven manner. By continuously gauging model sensitivity and effective dimensionality, 2SED dynamically adjusts the exponent to curb erratic oscillations and enhance convergence rates. Theoretically, we demonstrate how this dimension-aware adaptation retains the benefits of fractional memory while averting the sluggish or unstable behaviors frequently observed in naive fractional SGD. Empirical evaluations across multiple benchmarks confirm that our 2SED-driven fractional exponent approach not only converges faster but also achieves more robust final performance, suggesting broad applicability for fractional-order methodologies in large-scale machine learning and related domains. © 2025, CC BY.

关键词： Convex optimization

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Nonbacktracking bounds on the influence in independent cascade models 17

Nonbacktracking bounds on the influence in independent casca...

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Proceedings of the 31st International Conference on Neural Information Processing Systems

作者： Emmanuel Abbe Sanjeev Kulkarni Eun Jee Lee Program in Applied and Computational Mathematics and The Department of Electrical Engineering Princeton University The Department of Electrical Engineering Princeton University Program in Applied and Computational Mathematics

ISBN: (纸本)9781510860964

This paper develops upper and lower bounds on the influence measure in a network, more precisely, the expected number of nodes that a seed set can influence in the independent cascade model. In particular, our bounds exploit nonbacktracking walks, Fortuin-Kasteleyn-Ginibre type inequalities, and are computed by message passing algorithms. Nonbacktracking walks have recently allowed for headways in community detection, and this paper shows that their use can also impact the influence computation. Further, we provide parameterized versions of the bounds that control the trade-off between the efficiency and the accuracy. Finally, the tightness of the bounds is illustrated with simulations on various network models.

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Generalized nonbacktracking bounds on the influence in independent cascade models

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2020年第1期21卷 1112-1147页

作者： Emmanuel Abbe Sanjeev Kulkarni Eun Jee Lee Program in Applied and Computational Mathematics and Department of Electrical Engineering Princeton University Princeton NJ Department of Electrical Engineering Princeton University Princeton NJ Program in Applied and Computational Mathematics Princeton University Princeton NJ

This paper develops deterministic upper and lower bounds on the influence measure in a network, more precisely, the expected number of nodes that a seed set can influence in the independent cascade model. In particular, our bounds exploit r-nonbacktracking walks and Fortuin--Kasteleyn--Ginibre (FKG) type inequalities, and are computed by message passing algorithms. Further, we provide parameterized versions of the bounds that control the trade-off between efficiency and accuracy. Finally, the tightness of the bounds is illustrated on various network models.

关键词： influence estimation nonbacktracking walk message passing social networks independent cascade model

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Anomalous suppression of large-scale density fluctuations in classical and quantum spin liquids

arXiv

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arXiv 2025年

作者： Chen, Duyu Samajdar, Rhine Jiao, Yang Torquato, Salvatore Materials Research Laboratory University of California Santa BarbaraCA93106 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Center for Theoretical Science Princeton University PrincetonNJ08544 United States Materials Science and Engineering Arizona State University TempeAZ85287 United States Department of Physics Arizona State University TempeAZ85287 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Princeton Materials Institute Princeton University PrincetonNJ08540 United States Program in Applied and Computational Mathematics PrincetonNJ08544 United States

Classical spin liquids (CSLs) are intriguing states of matter that do not exhibit long-range magnetic order and are characterized by an extensive ground-state degeneracy. Adding quantum fluctuations, which induce dynamics between these different classical ground states, can give rise to quantum spin liquids (QSLs). QSLs are highly entangled quantum phases of matter characterized by fascinating emergent properties, such as fractionalized excitations and topological order. One such exotic quantum liquid is the Z2 QSL, which can be regarded as a resonating valence bond (RVB) state formed from superpositions of dimer coverings of an underlying lattice. In this work, we unveil a hidden large-scale structural property of archetypal CSLs and QSLs known as hyperuniformity, i.e., normalized infinite-wavelength density fluctuations are completely suppressed in these systems. In particular, we first demonstrate that classical ensembles of close-packed dimers and their corresponding quantum RVB states are perfectly hyperuniform in general. Subsequently, we focus on a ruby-lattice spin liquid that was recently realized in a Rydberg-atom quantum simulator, and show that the QSL remains effectively hyperuniform even in the presence of a finite density of spinon and vison excitations, as long as the dimer constraint is still largely preserved. Moreover, we demonstrate that metrics based on the framework of hyperuniformity can be used to distinguish the QSL from other proximate quantum phases. These metrics can help identify potential QSL candidates, which can then be further analyzed using more advanced, computationally-intensive quantum numerics to confirm their status as true QSLs. © 2025, CC BY-NC-ND.

关键词： Quantum entanglement

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Oil spill sensor using multispectral infrared imaging via 1 minimization

Oil spill sensor using multispectral infrared imaging via 1 ...

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36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011

作者： Li, Yingying Shih, Wei-Chuan Han, Zhu Yin, Wotao Electrical and Computer Engineering Department University of Houston United States Computational and Applied Mathematics Rice University United States

ISBN: (纸本)9781457705397

Early detection of oil spill events is the key to environmental protection and disaster management. Current technology lacks the sensitivity and specificity in detecting the early onset of a small-scale oil spill event. Based on an infrared oil-water contrast model recently developed, we propose a novel non-scanning computational infrared sensor that has the potential to achieve unprecedented detection sensitivity. Such a system can be very low-cost and robust for automated outdoor operations, leading to massive offshore deployment. Taking advantage of the characteristic oil thickness multispectral signatures, we have streamlined an algorithm that incorporates 3D image reconstruction and classification in a single inversion step capitalizing on the benefits of 1 minimization. © 2011 IEEE.

关键词： Oil spills

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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields 1

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丛书名： applied Mathematical Sciences

1983年

作者： John Guckenheimer Philip Holmes

ISBN: (数字)9781461211402

ISBN: (纸本)9780387908199;9781461270201

"This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined two-dimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors." #;#1 "An attempt to make research tools concerning `strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations. Applications mainly drawn from nonlinear oscillations." #;#2

关键词： Analysis

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Why Gabor frames? Two fundamental measures of coherence and their role in model selection

Why Gabor frames? Two fundamental measures of coherence and ...

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作者： Bajwa, Waheed U. Calderbank, Robert Jafarpour, Sina Department of Electrical Engineering Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States Department of Computer Science Princeton University Princeton NJ 08544 United States

The problem of model selection arises in a number of contexts, such as subset selection in linear regression, estimation of structures in graphical models, and signal denoising. This paper studies non-asymptotic model selection for the general case of arbitrary (random or deterministic) design matrices and arbitrary nonzero entries of the signal. In this regard, it generalizes the notion of incoherence in the existing literature on model selection and introduces two fundamental measures of coherence- termed as the worst-case coherence and the average coherence-among the columns of a design matrix. It utilizes these two measures of coherence to provide an in-depth analysis of a simple, model-order agnostic one-step thresholding (OST) algorithm for model selection and proves that OST is feasible for exact as well as partial model selection as long as the design matrix obeys an easily verifiable property, which is termed as the coherence property. One of the key insights offered by the ensuing analysis in this regard is that OST can successfully carry out model selection even when methods based on convex optimization such as the lasso fail due to the rank deficiency of the submatrices of the design matrix. In addition, the paper establishes that if the design matrix has reasonably small worst-case and average coherence then OST performs near-optimally when either (i) the energy of any nonzero entry of the signal is close to the average signal energy per nonzero entry or (ii) the signal-to-noise ratio in the measurement system is not too high. Finally, two other key contributions of the paper are that (i) it provides bounds on the average coherence of Gaussian matrices and Gabor frames, and (ii) it extends the results on model selection using OST to low-complexity, model-order agnostic recovery of sparse signals with arbitrary nonzero entries. In particular, this part of the analysis in the paper implies that an Alltop Gabor frame together with OST can successfully carr

关键词： Recovery

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State estimation in hybrid systems with a bounded number of mode transitions in the presence of spurious measurements

State estimation in hybrid systems with a bounded number of ...

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52nd Israel Annual Conference on Aerospace Sciences 2012

作者： Leiter, Noam Kalish, Noga Sigalov, Daniel Oshman, Yaakov Department of Aerospace Engineering Technion - Israel Institute of Technology Israel Department of Electrical Engineering Israel Interdepartmental Program for Applied Mathematics Israel

ISBN: (纸本)9781618399144

We consider the problem of tracking the state of a hybrid system capable of performing a bounded number of mode transitions in the presence of spurious, or cluttered measurements. The system is assumed to follow, at each time, one of a predefined dynamical models. Two types of uncertainties make the problem challenging. The first is the data uncertainty that follows from the fact that the true measurement of the state is indistinguishable from the clutter measurements that do not carry useful information. The second problem is the intrinsic model uncertainty. Both reasons prevent the computation of the optimal estimator. On the other hand, the mode transitions are not Markov thus ruling out the direct use of standard approaches for state estimation in cluttered environment. We derive an efficient estimation scheme for systems in cluttered environments capable of performing a bounded number of mode transitions. At the heart of this scheme is a transformation of the non-Markov model set to an equivalent Markovian one and a subsequent utilization of standard approaches matched to the new mode set. The algorithm's performance is evaluated via a simulation study, and shown to outperform the standard popular approaches in a typical example.

关键词： Hybrid systems

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Artificial intelligence for modelling infectious disease epidemics

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Nature 2025年第8051期638卷 623-635页

作者： Kraemer, Moritz U. G. Tsui, Joseph L.-H. Chang, Serina Y. Lytras, Spyros Khurana, Mark P. Vanderslott, Samantha Bajaj, Sumali Scheidwasser, Neil Curran-Sebastian, Jacob Liam Semenova, Elizaveta Zhang, Mengyan Unwin, H. Juliette T. Watson, Oliver J. Mills, Cathal Dasgupta, Abhishek Ferretti, Luca Scarpino, Samuel V. Koua, Etien Morgan, Oliver Tegally, Houriiyah Paquet, Ulrich Moutsianas, Loukas Fraser, Christophe Ferguson, Neil M. Topol, Eric J. Duchêne, David A. Stadler, Tanja Kingori, Patricia Parker, Michael J. Dominici, Francesca Shadbolt, Nigel Suchard, Marc A. Ratmann, Oliver Flaxman, Seth Holmes, Edward C. Gomez-Rodriguez, Manuel Schölkopf, Bernhard Donnelly, Christl A. Pybus, Oliver G. Cauchemez, Simon Bhatt, Samir Pandemic Sciences Institute University of Oxford Oxford United Kingdom Department of Biology University of Oxford Oxford United Kingdom Department of Electrical Engineering and Computer Science University of California Berkeley Berkeley CA United States UCSF UC Berkeley Joint Program in Computational Precision Health Berkeley CA United States Division of Systems Virology Department of Microbiology and Immunology The Institute of Medical Science The University of Tokyo Tokyo Japan Section of Epidemiology Department of Public Health University of Copenhagen Copenhagen Denmark Oxford Vaccine Group University of Oxford and NIHR Oxford Biomedical Research Centre Oxford United Kingdom Department of Epidemiology and Biostatistics Imperial College London London United Kingdom Department of Computer Science University of Oxford Oxford United Kingdom School of Mathematics University of Bristol Bristol United Kingdom MRC Centre for Global Infectious Disease Analysis School of Public Health Imperial College London London United Kingdom Department of Statistics University of Oxford Oxford United Kingdom Doctoral Training Centre University of Oxford Oxford United Kingdom Institute for Experiential AI Northeastern University MA Boston Thailand Santa Fe Institute Santa Fe NM United States World Health Organization Regional Office for Africa Brazzaville Congo WHO Hub for Pandemic and Epidemic Intelligence Health Emergencies Programme World Health Organization Berlin Germany Centre for Epidemic Response and Innovation (CERI) School for Data Science and Computational Thinking Stellenbosch University Stellenbosch South Africa African Institute for Mathematical Sciences (AIMS) South Africa Muizenberg Cape Town South Africa Genomics England London United Kingdom Scripps Research La Jolla CA United States Department of Biosystems Science and Engineering ETH Zürich Basel Switzerland Swiss Institute of Bioinformatics Lausanne Switzerland The Ethox Centre Nuffield

Infectious disease threats to individual and public health are numerous, varied and frequently unexpected. Artificial intelligence (AI) and related technologies, which are already supporting human decision making in economics, medicine and social science, have the potential to transform the scope and power of infectious disease epidemiology. Here we consider the application to infectious disease modelling of AI systems that combine machine learning, computational statistics, information retrieval and data science. We first outline how recent advances in AI can accelerate breakthroughs in answering key epidemiological questions and we discuss specific AI methods that can be applied to routinely collected infectious disease surveillance data. Second, we elaborate on the social context of AI for infectious disease epidemiology, including issues such as explainability, safety, accountability and ethics. Finally, we summarize some limitations of AI applications in this field and provide recommendations for how infectious disease epidemiology can harness most effectively current and future developments in AI. © Springer Nature Limited 2025.

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Translation of a sphere towards a rigid plane in an Oldroyd-B fluid

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Physical Review Fluids 2024年第8期9卷 083303页

作者： Tachin Ruangkriengsin Rodolfo Brandão Bimalendu Mahapatra Evgeniy Boyko Howard A. Stone Program in Applied and Computational Mathematics Department of Mechanical and Aerospace Engineering Faculty of Mechanical Engineering

We analyze the low-Reynolds-number translation of a sphere towards or away from a rigid plane in an Oldroyd-B fluid under two scenarios: prescribing the sphere's translational velocity, and prescribing the force on the sphere. Leveraging the lubrication approximation and a perturbation expansion in powers of the Deborah number, we develop a comprehensive theoretical analysis that yields analytical approximations for velocity fields, pressures, and forces acting on the sphere. Our framework aids in understanding temporal microstructural changes as the particle-wall gap evolves over time. In particular, we show that alterations in the polymer conformation tensor in response to geometric changes induce additional forces on the sphere. For cases with prescribed velocity, we present a theoretical approach for calculating resistive forces at any order in the Deborah number and utilize a reciprocal theorem to obtain higher-order corrections based on velocity fields in the previous orders. When the sphere translates with a constant velocity, the fluid viscoelasticity decreases the resistive force at the first order. However, at the second-order correction, the direction of the sphere's movement determines whether viscoelasticity increases or decreases the resistive force. For cases with prescribed force, we show that understanding the influence of viscoelasticity on the sphere's translational velocity necessitates a more intricate analysis even at low Deborah numbers. Specifically, we introduce an ansatz for constant force scenarios, and we derive solution forms for general prescribed forces using the method of multiple scales. We find that when a sphere undergoes sedimentation due to its own weight, the fluid viscoelasticity results in a slower settling process, reducing the leading-order sedimentation rate.

关键词： Complex fluids Low Reynolds number flows Lubrication theory Polymer conformation changes Rheology

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