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Convex Optimization Boundary-Control Policies for Stability and Invariance of Traffic Flow Dynamics

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arXiv 2025年

作者： Chiri, Maria Teresa Guglielmi, Roberto Notomista, Gennaro Department of Mathematics and Statistics Queen’s University KingstonON Canada Department of Applied Mathematics University of Waterloo ON Canada Department of Electrical and Computer Engineering University of Waterloo WaterlooON Canada

In this letter we propose an optimization-based boundary controller for traffic flow dynamics capable of achieving both stability and invariance conditions. The approach is based on the definition of Boundary Control Barrier Functionals (BCBFal), from which sets of invariance-preserving boundary controllers are derived. In combination with sets of stabilizing controllers, we reformulate the problem as a convex optimization program solved at each point in time to synthesize the boundary control inputs. Sufficient conditions for the existence of optimal controllers are derived in the case of traffic flow models with stability and invariance conditions. Copyright © 2025, The Authors. All rights reserved.

关键词： Convex optimization

Null Space Properties of Neural Networks with Applications to Image Steganography

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arXiv 2023年

作者： Li, Xiang Short, Kevin M. Integrated Applied Mathematics Program Department of Mathematics and Statistics University of New Hampshire DurhamNH03824 United States

This paper explores the null space properties of neural networks. We extend the null space definition from linear to nonlinear maps and discuss the presence of a null space in neural networks. The null space of a given neural network can tell us the part of the input data that makes no contribution to the final prediction so that we can use it to trick the neural network. This reveals an inherent weakness in neural networks that can be exploited. One application described here leads to a method of image steganography. Through experiments on image datasets such as MNIST, we show that we can use null space components to force the neural network to choose a selected hidden image class, even though the overall image can be made to look like a completely different image. We conclude by showing comparisons between what a human viewer would see, and the part of the image that the neural network is actually using to make predictions and, hence, show that what the neural network "sees" is completely different than what we would expect. Copyright © 2023, The Authors. All rights reserved.

关键词： Machine learning

Deep learning:Applications,architectures,models,tools,and frameworks:A comprehensive survey

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CAAI Transactions on Intelligence Technology 2023年第3期8卷 581-606页

作者： Mehdi Gheisari Fereshteh Ebrahimzadeh Mohamadtaghi Rahimi Mahdieh Moazzamigodarzi Yang Liu Pijush Kanti Dutta Pramanik Mohammad Ali Heravi Abolfazl Mehbodniya Mustafa Ghaderzadeh Mohammad Reza Feylizadeh Saeed Kosari School of Computer Science and Technology Harbin Institute of Technology(Shenzhen)ShenzhenChina Department of Cognitive Computing Institute of Computer Science and EngineeringSaveetha School of EngineeringSaveetha Institute of Medical and Technical SciencesChennaiIndia Department of Computer Science Islamic Azad UniversityTehranIran Computer Engineering Department Bu‐Ali Sina UniversityHamedanIran Department of Mathematics and Statistics Iran University of Science and TechnologyTehranIran Department of Mathematics and Statistics University of Northern British ColumbiaBCCanada Peng Cheng Laboratory ShenzhenChina Deprtment of Technology Jodhpur Institute of Engineering&TechnologyJodhpurIndia Department of Computer Engineering Sadjad University of TechnologyMashhadIran Department of Electronics and Communications Engineering Kuwait College of Science and TechnologyDoha DistrictKuwait Department of Artificial Intelligence Smart University of Medical SciencesTehranIran Department of Industrial Engineering Shiraz BranchIslamic Azad UniversityShirazIran Institute of Computing Science and Technology Guangzhou UniversityGuangzhouChina

Deep Learning(DL)is a subfield of machine learning that significantly impacts extracting new *** using DL,the extraction of advanced data representations and knowledge can be made *** effective DL techniques help to find more hidden *** learning has a promising future due to its great performance and *** need to understand the fundamentals and the state‐of‐the‐art of DL to leverage it effectively.A survey on DL ways,advantages,drawbacks,architectures,and methods to have a straightforward and clear understanding of it from different views is explained in the ***,the existing related methods are compared with each other,and the application of DL is described in some applications,such as medical image analysis,handwriting recognition,and so on.

关键词： data mining data privacy deep learning

Structure prediction, electronic, and mechanical properties of alkali metal MB_(12)(=Be, Mg, Ca, Sr) from first principles

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Chinese Physics B 2021年第1期30卷 464-470页

作者： Chun-Ying Pu Rong-Mei Yu Ting Wang Zhen-Yan Xüe Yong-Sheng Zhu Da-Wei Zhou College of Physics and Electronic Engineering Nanyang Normal UniversityNanyang 473061China Department of Mathematics and Statistics Nanyang Normal UniversityNanyang 473061China

Using the particle swarm optimization algorithm on structural search methods, we focus our crystal structures search on boron-rich alkali metal compounds of MB_(12)(M = Be, Mg, Ca, Sr) with simulation cell sizes of 1–2 formula units(f.u.)at 0 GPa. The structure, electronic, and mechanical properties of MB_(12) are obtained from the density functional theory using the plane-wave pseudopotential method within the generalized gradient approximations. The formation enthalpies of MB_(12) regarding to solid metal M and solid alpha-boron suggested the predicted structures can be synthesized except for BeB12. The calculated band structures show MB_(12)(M = Be, Mg, Ca, Sr) are all indirect semiconductors. All the calculated elastic constants of MB_(12) satisfy the the mechanical stable conditions. The mechanical parameters(i.e., bulk modulus,shear modulus, and Young’s modulus) are derived using the Voigt–Reuss–Hill method. The G/B ratios indicated that the MB_(12) should exhibit brittle behavior. In addition, the hardness, Debye temperature, universal anisotropic index, and the percentage of anisotropy in compression and shear are also discussed in detail. We hope our results can inspire further experimental study on these boron-rich alkali-metal compounds.

关键词： first-principles calculations structure searching mechanical properties boron-rich alkali-metal compounds

A Library of Mirrors: Deep Neural Nets in Low Dimensions are Convex Lasso Models with Reflection Features

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arXiv 2024年

作者： Zeger, Emi Wang, Yifei Mishkin, Aaron Ergen, Tolga Candès, Emmanuel Pilanci, Mert Stanford University United States Department of Electrical Engineering Department of Computer Science Departments of Statistics and Mathematics

We prove that training neural networks on 1-D data is equivalent to solving convex Lasso problems with discrete, explicitly defined dictionary matrices. We consider neural networks with piecewise linear activations and depths ranging from 2 to an arbitrary but finite number of layers. We first show that two-layer networks with piecewise linear activations are equivalent to Lasso models using a discrete dictionary of ramp functions, with breakpoints corresponding to the training data points. In certain general architectures with absolute value or ReLU activations, a third layer surprisingly creates features that reflect the training data about themselves. Additional layers progressively generate reflections of these reflections. The Lasso representation provides valuable insights into the analysis of globally optimal networks, elucidating their solution landscapes and enabling closed-form solutions in certain special cases. Numerical results show that reflections also occur when optimizing standard deep networks using standard non-convex optimizers. Additionally, we demonstrate our theory with autoregressive time series models. Copyright © 2024, The Authors. All rights reserved.

关键词： Deep neural networks

Metal Extraction Informatics: A Conceptual Framework for Sustainable Metal Extraction 8th

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Metal Extraction Informatics: A Conceptual Framework for Sus...

8th installment of the REWAS conference series held at the TMS Annual Meeting and Exhibition focuses on circular economy for the energy transition, 2025

作者： Khanra, Avijit Meshram, Arunabh Katariya, Yogesh Gupta, Siddhant Shikhar Sanjay, Kali Shekhar, Rajiv Department of Management Sciences Indian Institute of Technology Kanpur India Department of Materials Science and Engineering Indian Institute of Technology Kanpur India Department of Mathematics and Statistics Indian Institute of Technology Kanpur India Department of Hydro and Electrometallurgy CSIR - Institute of Minerals and Materials Technology Bhubaneswar India

ISBN: (纸本)9783031808913

Shortfall in the supply of metals critical for transition to the low carbon economy necessitates extraction from low-grade ores and wastes. This requires new flowsheet development where the operating parameters of each unit operation must be optimized. This approach is experiment intensive with a large gestation period. To accelerate flowsheet development for sustainable metal extractionMetal extraction, a conceptual framework of Metal ExtractionMetal extractionInformaticsInformatics (MEI) has been proposed. MEI combines some aspects of material informaticsInformatics and multi-objective optimizationOptimization. Three objective functions have been used: process efficiency, operating costs, and environmental impactEnvironmental impact. A case study of the leachingLeaching of copperCopper from waste printed circuit boards has been modelled to illustrate the MEI framework. © The Minerals, Metals & Materials Society 2025.

关键词： Environmental impact

Nonlinear functionals of master equation unravelings

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arXiv 2024年

作者： Keys, Dustin Wehr, Jan Department of Mechanical Engineering University of North Texas United States Department of Mathematics and Program in Applied Mathematics University of Arizona United States

Unravelings provide a probabilistic representation of solutions of master equations and a method of computation of the density operator dynamics. The trajectories generated by unravelings may also be treated as real—as in the stochastic collapse models. While averages of linear functionals of the unraveling trajectories can be calculated from the master equation, the situation is different for nonlinear functionals, thanks to the corrections with nonzero expected values, coming from the Itô formula. Two types of nonlinear functionals are considered here: variance, and entropy. The corrections are calculated explicitly for two types of unravelings, based on Poisson and Wiener processes. In the case of entropy, these corrections are shown to be negative, expressing the localization introduced by the Lindblad operators. © 2024, CC BY.

关键词： Entropy

Variational solution to the lattice Boltzmann method for Couette flow

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Physical Review E 2024年第5期109卷 055305-055305页

作者： Joseph T. Johnson Mahyar Madadi Daniel R. Ladiges Yong Shi Barry D. Hughes John E. Sader School of Mathematics and Statistics Department of Materials Physics Research School of Physics Center for Computational Sciences and Engineering Department of Mechanical Materials and Manufacturing Engineering Graduate Aerospace Laboratories and Department of Applied Physics

Literature studies of the lattice Boltzmann method (LBM) demonstrate hydrodynamics beyond the continuum limit. This includes exact analytical solutions to the LBM, for the bulk velocity and shear stress of Couette flow under diffuse reflection at the walls through the solution of equivalent moment equations. We prove that the bulk velocity and shear stress of Couette flow with Maxwell-type boundary conditions at the walls, as specified by two-dimensional isothermal lattice Boltzmann models, are inherently linear in Mach number. Our finding enables a systematic variational approach to be formulated that exhibits superior computational efficiency than the previously reported moment method. Specifically, the number of partial differential equations (PDEs) in the variational method grows linearly with quadrature order while the number of moment method PDEs grows quadratically. The variational method directly yields a system of linear PDEs that provide exact analytical solutions to the LBM bulk velocity field and shear stress for Couette flow with Maxwell-type boundary conditions. It is anticipated that this variational approach will find utility in calculating analytical solutions for novel lattice Boltzmann quadrature schemes and other flows.

关键词： Rarefied flows Boltzmann theory Lattice-Boltzmann methods

UAMP-Based Delay-Doppler Channel Estimation for OTFS Systems

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China Communications 2023年第10期20卷 70-84页

作者： Zhongjie Li Weijie Yuan Qinghua Guo Nan Wu Ji Zhang Department of Electronic and Electrical Engineering Southern University of Science and TechonologyShenzhen 518055China School of Electrical Computer and Telecommunications EngineeringUniversity of WollongongWollongongNSW 2522Australia School of Integrated Circuits and Electronics Beijing Institute of TechnologyBeijing 100081China School of Mathematics and Statistics Henan University of Science and TechnologyLuoyang 471000China

Orthogonal time frequency space(OTFS)technique,which modulates data symbols in the delay-Doppler(DD)domain,presents a potential solution for supporting reliable information transmission in highmobility vehicular *** this paper,we study the issues of DD channel estimation for OTFS in the presence of fractional *** first propose a channel estimation algorithm with both low complexity and high accuracy based on the unitary approximate message passing(UAMP),which exploits the structured sparsity of the effective DD domain channel using hidden Markov model(HMM).The empirical state evolution(SE)analysis is then leveraged to predict the performance of our proposed *** refine the hyperparameters in the proposed algorithm,we derive the update criterion for the hyperparameters through the expectation-maximization(EM)***,Our simulation results demonstrate that our proposed algorithm can achieve a significant gain over various baseline schemes.

关键词： orthogonal time frequency space(OTFS) channel estimation hidden Markov model(HMM) unitary approximate message passing(UAMP)