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12th International Conference on Learning Representations, ICLR 2024

作者： Arous, Gérard Ben Gheissari, Reza Huang, Jiaoyang Jagannath, Aukosh Courant Institute New York University New YorkNY United States Department of Mathematics Northwestern University EvanstonIL United States Department of Statistics and Data Science University of Pennsylvania PhiladelphiaPA United States Department of Statistics and Actuarial Science Department of Applied Mathematics Cheriton School of Computer Science University of Waterloo WaterlooON Canada

We rigorously study the joint evolution of training dynamics via stochastic gradient descent (SGD) and the spectra of empirical Hessian and gradient matrices. We prove that in two canonical classification tasks for multi-class high-dimensional mixtures and either 1 or 2-layer neural networks, the SGD trajectory rapidly aligns with emerging low-rank outlier eigenspaces of the Hessian and gradient matrices. Moreover, in multi-layer settings this alignment occurs per layer, with the final layer's outlier eigenspace evolving over the course of training, and exhibiting rank deficiency when the SGD converges to sub-optimal classifiers. This establishes some of the rich predictions that have arisen from extensive numerical studies in the last decade about the spectra of Hessian and information matrices over the course of training in overparametrized networks. © 2024 12th International Conference on Learning Representations, ICLR 2024. All rights reserved.

关键词： Statistics

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Electron stopping power of protons in aluminum at finite electron temperature

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Physical Review B 2025年第14期111卷 144303-144303页

作者： Ya-Ting Sun Feng Wang Fei Mao Cong-Zhang Gao School of Physics Beijing Institute of Technology Beijing 100081 China School of Nuclear Science and Technology University of South China Hengyang 421001 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China

We conducted a study on the electron stopping power of protons in aluminum at finite electron temperatures, utilizing time-dependent density functional theory nonadiabatically coupled with molecular dynamics. Our investigation focused on protons with initial velocities ranging from 0.1 to 1.0 a.u., providing a wealth of detailed information on the electronic states involved in the stopping process, with exceptional spatial and temporal resolution. Our results show that the electron temperature can significantly effect the electron stopping power. A quantum-blocking mechanism based on a physical picture of electronic transitions in energy levels has been proposed for explaining the phenomenon of electron stopping power decreasing with the increase of target electron temperature.

关键词： Electronic states

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Analysis of Import Substitution Processes Taking into Account Industry Specifics in the Regional Economy 14th

Analysis of Import Substitution Processes Taking into Acco...

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14th International Conference on Optimization and Applications, OPTIMA 2023

作者： Rassokha, Anastasiia Obrosova, Natalia Moscow Institute of Physics and Technology Dolgoprudny Russia Federal Research Center "Computer Science and Control" of RAS Moscow Russia Center of Fundamental and Applied Mathematics Lomonosov MSU Moscow Russia

ISBN: (纸本)9783031478581

Analysis of import substitution processes is one of the urgent problems for many countries in the context of deglobalization of the world economy. Mathematical methods of convex analysis make it possible to construct a model of input-output balance with non-linear production functions. It can be identified from the official statistics of input-output tables. This model allows us to describe the substitution of production factors. The elasticity of substitution can be estimated using the solution of the Yang dual problem. With the help of the developed model for industries with a significant share of imports, the possibility of replacing imported production factors with domestic ones is studied on the example of the Russian economy. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Regional planning

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Optimized Vaccine Selection Using Machine Learning and Genetic Algorithms: A Study on Side Effects of COVID-19 Vaccines 12th

Optimized Vaccine Selection Using Machine Learning and Genet...

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12th International Conference on Soft Computing for Problem Solving, SocProS 2023

作者： Soni, Vishal Joshi, Shubham Deep, Kusum Pant, Millie Department of Mechatronics Indian Institute of Information Technology Bihar Bhagalpur813210 India Department of Applied Mathematics and Scientific Computing Indian Institute of Technology Uttarakhand Roorkee247667 India Department of Mathematics Indian Institute of Technology Uttarakhand Roorkee247667 India Mehta Family School for Data Science and Artificial Intelligence Indian Institute of Technology Uttarakhand Roorkee247667 India

ISBN: (纸本)9789819732913

The COVID-19 pandemic has necessitated large-scale vaccination campaigns to control the virus's spread. Given the scale of these efforts, it's crucial to scrutinize potential adverse effects, especially in vulnerable population groups. This study combines machine learning and Genetic Algorithms (GA) to analyze the patterns of patient recovery post-vaccination. We use a range of classifiers, including the Gradient Boosting Decision Tree (GBDT), to identify key features and symptom categories that influence patient recovery. We also use Principal Component Analysis (PCA) to reduce dimensionality and uncover patterns within high-dimensional data. The data used in this study have taken from the Vaccine Adverse Event Reporting System (VAERS). With the help of GA, we aim to guide optimal vaccine selection for susceptible demographics, minimizing the risk and severity of side effects. Our research paves the way for more personalized vaccination strategies, promoting healthier outcomes and reducing risks associated with mass vaccination. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.

关键词： COVID-19

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DCE MRI Modality Investigation for Cancerous Prostate Region Detection: Case Analysis 30

DCE MRI Modality Investigation for Cancerous Prostate Region...

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30th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, WSCG 2022

作者： Vaitulevicius, Aleksas Treigys, Povilas Bernataviciene, Jolita Surkant, Roman Markeviciute, Jurgita Naruseviciute, Ieva Trakymas, Mantas Vilnius University Institute of Data Science and Digital Technologies Vilnius Lithuania Vilnius University Institute of Applied Mathematics Vilnius Lithuania National Cancer Institute Vilnius Lithuania

ISBN: (纸本)9788086943336

Typically, prostate evaluation is done by using different imaging sequences of magnetic resonance imaging. Dynamic contrast enhancement, one of such scanning modalities, allow to spot higher vascular permeability and density caused by the malignant tissue. Authors of this paper investigate the ability to identify malignant prostate regions by the functional data analysis and standard machine learning techniques. The dynamic contrast enhanced images of the prostate are divided into the regions and based on those time-signal intensity curves are calculated. Two classification approaches: functional k-Nearest Neighbors and machine learning Support Vector Machine are used to model signal curve behavior on temporal variation matrix and timestamp based prostate region division of image data. Preliminary research shows that both functional data analysis and machine learning classification methods are able to identify highest saturation timestamp that gives best tissue classification results on timestamp based dynamic contrast enhanced region map obtained by Simple Linear Iterative Clustering algorithm. Cancer region classification results are better when the dynamic contrast enhanced images are subdivided into regions at each timestamp than when using a temporal variation matrix. © 2022 University of West Bohemia. All rights reserved.

关键词： Dynamic contrast enhanced MRI

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Entropies of the Y-Junction Type Nanostructures

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Computer Modeling in Engineering & sciences 2023年第6期135卷 2665-2679页

作者： Ricai Luo Aisha Javed Muhammad Azeem Muhammad Kamran Jamil Hassan Raza Muhammad Yasir Ilyas School of Mathematics and Physics Hechi UniversityYizhou456300China Abdus Salam School of Mathematical Sciences Government College UniversityLahore54000Pakistan Department of Mathematics Riphah Institute of Computing and Applied SciencesRiphah International UniversityLahore54000Pakistan School of Mathematical Sciences College of Science and TechnologyWenzhou-Kean UniversityWenzhou325060China Department of Physics COMSATS University IslamabadLahore54000Pakistan

Recent research on nanostructures has demonstrated their importance and application in a variety of *** are used directly or indirectly in drug delivery systems,medicine and pharmaceuticals,biological sensors,photodetectors,transistors,optical and electronic devices,and so *** discovery of carbon nanotubes with Y-shaped junctions is motivated by the development of future advanced electronic *** of their interactionwithY-junctions,electronic switches,amplifiers,and three-terminal transistors are of particular *** is a concept that determines the uncertainty of a system or *** concepts are also used in biology,chemistry,and applied *** on the requirements,entropy in the form of a graph can be classified into several *** 1955,graph-based entropy was *** of the types of entropy is edgeweighted *** examined the abstract form of Y-shaped junctions in this *** edge-weight-based entropy formulas for the generic view of Y-shaped junctions were created,and some edge-weighted and topological index-based concepts for Y-shaped junctions were discussed in the present paper.

关键词： Y-shaped junctions three-terminal junctions nanostuctures entropy carbon nanotube

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The Challenges of the Nonlinear Regime for physics-Informed Neural Networks 38

The Challenges of the Nonlinear Regime for Physics-Informed ...

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38th Conference on Neural Information Processing Systems, NeurIPS 2024

作者： Bonfanti, Andrea Bruno, Giuseppe Cipriani, Cristina BMW AG Basque Center for Applied Mathematics University of the Basque Country Digital Campus Munich Spain BMW AG Digital Campus Munich Germany Technical University of Munich Munich Center for Machine Learning Munich Data Science Institute Germany

The Neural Tangent Kernel (NTK) viewpoint is widely employed to analyze the training dynamics of overparameterized physics-Informed Neural Networks (PINNs). However, unlike the case of linear Partial Differential Equations (PDEs), we show how the NTK perspective falls short in the nonlinear scenario. Specifically, we establish that the NTK yields a random matrix at initialization that is not constant during training, contrary to conventional belief. Another significant difference from the linear regime is that, even in the idealistic infinite-width limit, the Hessian does not vanish and hence it cannot be disregarded during training. This motivates the adoption of second-order optimization methods. We explore the convergence guarantees of such methods in both linear and nonlinear cases, addressing challenges such as spectral bias and slow convergence. Every theoretical result is supported by numerical examples with both linear and nonlinear PDEs, and we highlight the benefits of second-order methods in benchmark test cases. © 2024 Neural information processing systems foundation. All rights reserved.

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Alternating minimization for square root principal component pursuit

arXiv

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arXiv 2024年

作者： Deng, Shengxiang Li, Xudong Zhang, Yangjing School of Data Science Fudan University Shanghai China Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

Recently, the square root principal component pursuit (SRPCP) model has garnered significant research interest. It is shown in the literature that the SRPCP model guarantees robust matrix recovery with a universal, constant penalty parameter. While its statistical advantages are well-documented, the computational aspects from an optimization perspective remain largely unexplored. In this paper, we focus on developing efficient optimization algorithms for solving the SRPCP problem. Specifically, we propose a tuning-free alternating minimization (AltMin) algorithm, where each iteration involves subproblems enjoying closed-form optimal solutions. Additionally, we introduce techniques based on the variational formulation of the nuclear norm and Burer-Monteiro decomposition to further accelerate the AltMin method. Extensive numerical experiments confirm the efficiency and robustness of our *** Codes 90C06, 90C25, 90C26, 90C30 © 2024, CC BY.

关键词： Iterative methods

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Unraveling the early universe’s equation of state and primordial black hole production with PTA,BBN,and CMB observations

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Chinese physics C 2024年第12期48卷 212-220页

作者： Qing-Hua Zhu Zhi-Chao Zhao Sai Wang Xin Zhang Department of Physics and Chongqing Key Laboratory for Strongly Coupled Physics Chongqing UniversityChongqing 401331China Department of Applied Physics College of ScienceChina Agricultural UniversityQinghua East RoadBeijing 100083China Theoretical Physics Division Institute of High Energy PhysicsChinese Academy of SciencesBeijing 100049China Key Laboratory of Cosmology and Astrophysics(Liaoning)&College of Sciences Northeastern UniversityShenyang 110819China National Frontiers Science Center for Industrial Intelligence and Systems Optimization Northeastern UniversityShenyang 110819China Key Laboratory of Data Analytics and Optimization for Smart Industry(Ministry of Education) Northeastern UniversityShenyang 110819China

Pulsar timing array(PTA)data releases show strong evidence for a stochastic gravitational-wave background in the nanohertz *** the signal is interpreted by a scenario of scalar-induced gravitational waves(SIGWs),we encounter overproduction of primordial black holes(PBHs).We wonder if varying the equation of state(EoS)of the early Universe can resolve this issue and thereby lead to a consistent interpretation of the PTA *** a data combination of PTA,big-bang nucleosynthesis,and cosmic microwave background,we find that an epoch with EoS w~O(10^(-2))between the end of inflation and the onset of radiation domination can significantly suppress the production of PBHs,leading to alleviation of the PBH-overproduction *** the inferred interval w=0.44_(-0.40)^(+0.52)at 95%confidence level,our scenario can interpret the PTA data just as well as the conventional scenario of SIGWs produced during the radiation domination.

关键词： physics of the early universe gravitational waves primordial black hole pulsar timing arrays

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Semi-Markov Telecommunication Networks Model

Semi-Markov Telecommunication Networks Model

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2024 International Conference on Actual Problems of Electron Devices Engineering, APEDE 2024

作者： Svetlov, Mikhail S. L’vov, Alexey A. Martirosyan, Arman M. Martirosyan, David M. Bagaev, Igor S. Khasanov, Semen T. Laboratory of Control and Automation Problems in Mechanical Engineering Institute of Precision Mechanics and Control of RAS Saratov Russia Institute of Institute of Electronic Engineering and Instrumentation Yuri Gagarin State Technical University of Saratov Saratov Russia Institute of Applied Information Technologies and Communications Yuri Gagarin State Technical University of Saratov Saratov Russia Phystech-School of Applied Mathematics and Computer Science Moscow Institute of Physics and Technology Moscow Russia

ISBN: (纸本)9798350393316

This paper proposes a semi-Markov model of telecommunication network (TCN). The variant of dynamic traffic adaptive control of queuing system as a special case of TCN is considered. The main purpose of control is to minimize the average cost per unit of time to service the incoming flow of information (packets). This takes into account the different bandwidth of the channels, the processing speed of information in the channel and the information capacity of the buffers. The approach to the organization of dynamic control taking into account noise immunity (information reliability) and information security is discussed. © 2024 IEEE.

关键词： Bandwidth

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