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IEEE Symposium on Systems and Information engineering Design, SIEDS

作者： Tulio Tablada Cleon Davis Neil Palumbo Applied and Computational Mathematics Program Johns Hopkins University Electrical and Computer Engineering Program Johns Hopkins University

ISBN: (数字)9798350385144

ISBN: (纸本)9798350385151

In the basic vehicle routing problem (VRP), a vehicle must deliver goods from one centralized warehouse to multiple customers efficiently. Several VRP variants and constraints exist, including different product types, specific delivery times, multiple warehouses, vehicle fuel constraints, and pick-up from one location and delivery to another. This work proposes and demonstrates a flexible algorithm for solving the VRP via ant colony optimization (ACO) that can address many of the variants discussed above. ACO algorithms mimic the behavior of ants, learning optimal paths to a food source and back to the nest based on stigmergic behavior. This work compares a proposed, more flexible ACO algorithm to a traditional optimization algorithm that is implemented in the Google VRP solver. Readily available data were used to test and demonstrate results. Several VRP variants were implemented in both the (proposed) flexible ACO algorithm and the Google VRP solver. The flexible ACO algorithm performed better in terms of distance traveled versus the Google VRP solver for two variants and worse for three other cases. However, the Google VRP solver was not able to solve some of the VRP variant combinations considered here and failed when solving some backhaul datasets. Because the flexible ACO algorithm was able to better handle many case variations, it may be an attractive alternative optimization tool.

关键词： Ant colony optimization Vehicle routing Symbols Internet Fuels Optimization Backhaul networks

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An Efficient Three-Factor Authenticated Key Agreement Technique Using FCM Under HC-IoT Architectures

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Computers, Materials & Continua 2022年第7期72卷 1373-1389页

作者： Chandrashekhar Meshram Agbotiname Lucky Imoize Sajjad Shaukat Jamal Parkash Tambare Adel R.Alharbi Iqtadar Hussain Department of Post Graduate Studies and Research in Mathematics Jayawanti Haksar Government Post-Graduation CollegeCollege of Chhindwara UniversityBetul460001M.P.India Department of Electrical and Electronics Engineering Faculty of EngineeringUniversity of LagosAkokaLagos100213Nigeria Department of Electrical Engineering and Information Technology Institute of Digital CommunicationRuhr University44801BochumGermany Department of Mathematics College of ScienceKing Khalid UniversityAbhaSaudi Arabia Water Resources&Applied Mathematics Research Lab Nagpur440027India College of Computing and Information Technology University of TabukTabuk71491Saudi Arabia Mathematics Program Department of MathematicsStatistics and PhysicsCollege of Arts and SciencesQatar University2713DohaQatar

The Human-Centered Internet of Things(HC-IoT)is fast becoming a hotbed of security and privacy *** users can establish a common session key through a trusted server over an open communication channel using a three-party authenticated key *** of the early authenticated key agreement systems relied on pairing,hashing,or modular exponentiation processes that are computationally intensive and *** order to address this problem,this paper offers a new three-party authenticated key agreement technique based on fractional chaotic *** new scheme uses fractional chaotic maps and supports the dynamic sensing of HC-IoT devices in the network architecture without a password *** projected security scheme utilized a hash function,which works well for the resource-limited HC-IoT *** results show that our new technique is resistant to password guessing attacks since it does not use a ***,our approach provides users with comprehensive privacy protection,ensuring that a user forgery attack causes no ***,our new technique offers better security features than the techniques currently available in the literature.

关键词： Three-party authenticated key agreement anonymity fractional chaotic maps Chebyshev polynomial password table human-centered internet of things(HC-IoT)

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A molecular dynamical study of granular fluids I: The unforced granular gas in two dimensions

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Journal of Scientific Computing 1993年第1期8卷 1-40页

作者： Goldhirsch, I. Tan, M.-L. Zanetti, G. Department of Fluid Mechanics and Heat Transfer Faculty of Engineering Tel-Aviv University Ramat Aviv 69978 Tel-Aviv Israel Program in Applied and Computational Mathematics Princeton University Princeton 08544 New Jersey United States

Results of a numerical study of the dynamics of a collection of disks colliding inelastically in a periodic two-dimensional enclosure are presented. The properties of this system, which is perhaps the simplest model for rapidly flowing granular materials, are markedly different from those known for atomic or moleclar gases, in which collisions are of elastic nature. The most prominent feature characterizing granular systems, even in the idealized situation in which no external forcing exists and the initial condition is statistically homogeneous, is their inherent instability to inhomogeneous fluctuations. Granular "gases" are thus generically nonuniform, a fact that suggests extreme caution in pursuing direct analogies with molecular gases. We find that once an inhomogeneous state sets in, the velocity distribution functions differ from the classical Maxwell-Boltzmann distribution. Other characteristics of the system are different from their counterparts in molecular systems as well. For a given value of the coefficient of restitution, e, a granular system forms clusters of typical separation L₀≈l/(1-e²)^1/2, where l is the mean free path in the corresponding homogeneous system. Most of the fluctuating kinetic energy then resides in the relatively dilute regions that surround the clusters. Systems whose linear dimensions are less then L⁰ do not give rise to clusters;still they are inhomogeneous, the scale of the corresponding inhomogeneity being the longest wavelength allowed by the system's size. The present article is devoted to a detailed numerical study of the above-mentioned clustering phenomenon in two dimensions and in the absence of external forcing. A theoretical framework explaining this phenomenon is outlined. Some general implications as well as practical ramifications are discussed. © 1993 Plenum Publishing Corporation.

关键词： Granular flow dynamics molecular dynamics numerical simulation

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Machine-learning-based non-Newtonian fluid model with molecular fidelity

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Physical Review E 2020年第4期102卷 043309-043309页

作者： Huan Lei Lei Wu Weinan E Department of Computational Mathematics Science & Engineering and Department of Statistics & Probability Michigan State University East Lansing Michigan 48824 USA Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

We introduce a machine-learning-based framework for constructing continuum a non-Newtonian fluid dynamics model directly from a microscale description. Dumbbell polymer solutions are used as examples to demonstrate the essential ideas. To faithfully retain molecular fidelity, we establish a micro-macro correspondence via a set of encoders for the microscale polymer configurations and their macroscale counterparts, a set of nonlinear conformation tensors. The dynamics of these conformation tensors can be derived from the microscale model, and the relevant terms can be parametrized using machine learning. The final model, named the deep non-Newtonian model (DeePN2), takes the form of conventional non-Newtonian fluid dynamics models, with a generalized form of the objective tensor derivative that retains the microscale interpretations. Both the formulation of the dynamic equation and the neural network representation rigorously preserve the rotational invariance, which ensures the admissibility of the constructed model. Numerical results demonstrate the accuracy of DeePN2 where models based on empirical closures show limitations.

关键词： Learning Neuronal networks Complex fluids Non-Newtonian fluids Rheology Viscoelasticity Multiscale modeling

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Deep potentials for materials science

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Materials Futures 2022年第2期1卷 89-115页

作者： Tongqi Wen Linfeng Zhang Han Wang Weinan E David J Srolovitz Department of Mechanical Engineering The University of Hong KongHong KongHong Kong Special Administrative Region of China DP Technology BeijingPeople’s Republic of China AI for Science Institute BeijingPeople’s Republic of China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijingPeople’s Republic of China HEDPS CAPTCollege of EngineeringPeking UniversityBeijingPeople’s Republic of China School of Mathematical Sciences Peking UniversityBeijingPeople’s Republic of China Department of Mathematics and Program in Applied and Computational Mathematics Princeton UniversityPrincetonNJUnited States of America International Digital Economy Academy(IDEA) ShenzhenPeople’s Republic of China

To fill the gap between accurate(and expensive)ab initio calculations and efficient atomistic simulations based on empirical interatomic potentials,a new class of descriptions of atomic interactions has emerged and been widely applied;*** learning potentials(MLPs).One recently developed type of MLP is the deep potential(DP)*** this review,we provide an introduction to DP methods in computational materials *** theory underlying the DP method is presented along with a step-by-step introduction to their development and *** also review materials applications of DPs in a wide range of materials *** DP Library provides a platform for the development of DPs and a database of extant *** discuss the accuracy and efficiency of DPs compared with ab initio methods and empirical potentials.

关键词： deep potential atomistic simulation machine learning potential neural network

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Oscillator models and collective motion

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IEEE Control Systems Magazine 2007年第4期27卷 89-105页

作者： Paley, Derek A. Leonard, Naomi Ehrich Sepulchre, Rodolphe Grünbaum, Daniel Parrish, Julia K. Princeton University Department of Mechanical and Aerospace Engineering Princeton NJ 08544 United States Department of Mechanical and Aerospace Engineering Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States Department Electrical Engineering and Computer Science University of Liège Liège Belgium School of Oceanography Department of Biology University of Washington Seattle WA United States Biology Department School of Aquatic and Fishery Sciences University of Washington Seattle WA United States

A description of the so called "particles with coupled oscillator dynamics" (PCOD) is presented which is used to model, analyze and synthesize collective motion. An oscillator model with spatial dynamics is presented to help describe how to design steering control laws while it is being used to study biological collectives. Lastly, both engineering and biological analysis were described.

关键词： Oscillators (mechanical)

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The Nystrom Extension for Signals Defined on a Graph

The Nystrom Extension for Signals Defined on a Graph

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International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Ayelet Heimowitz Yonina C. Eldar The Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Department of Electrical Engineering Technion Haifa Israel

ISBN: (纸本)9781538646595

In this paper we introduce a computationally efficient solution to the problem of graph signal interpolation. Our solution is derived using the Nyström extension and is due to the properties of the Markov matrix which we use as our graph shift operator, inspired by diffusion maps. We focus on graph signals that are smooth over the graph. This assumption cements the relationship between the graph and the graph signal. We experimentally verify our suggested framework on the MNIST data set of handwritten digits.

关键词： Markov processes Signal processing Interpolation Laplace equations Symmetric matrices Image edge detection Eigenvalues and eigenfunctions

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Linear Optimal State Estimation in Systems with Independent Mode Transitions

Linear Optimal State Estimation in Systems with Independent ...

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IEEE Conference on Decision and Control

作者： Daniel Sigalov Tomer Michaeli Yaakov Oshman Interdepartmental Program for Applied Mathematics Department of Electrical Engineering Department of Aerospace Engineering

ISBN: (纸本)9781612848006

A generalized state space representation of a dynamical system with random modes is presented. The dynamics equation includes the effect of the state's linear minimum mean squared error (LMMSE) optimal estimate, representing the behavior of a closed loop control system featuring a state estimator. The measurement equation is allowed to depend on past LMMSE estimate of the state, which can be used to represent the fact that measurements are obtained from a validation window centered at the predicted measurement position and not from the entire surveillance region. The matrices comprising the system's mode constitute an independent stochastic process. It is shown that the proposed formulation generalizes several important problems considered in the past, and allows a unified modeling of new ones. The LMMSE optimal filter is derived for the considered general problem and is shown to reduce, in some special cases, to some well known classical algorithms. The new concept, as well as the derived algorithm, are demonstrated for the problem of target tracking in clutter, and are shown to attain performance that is competitive to that of several popular nonlinear methods.

关键词： State estimation State-space Representation Closed loop control systems Target tracking clutter Mean square error DYNAMICAL SYSTEMS random fashion UNIFIED MODEL

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MULTI-TARGET DETECTION WITH ROTATIONS

arXiv

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arXiv 2021年

作者： Bendory, Tamir Lan, Ti-Yen Marshall, Nicholas F. Rukshin, Iris Singer, Amit School of Electrical Engineering Tel Aviv University Tel Aviv Israel Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Department of Mathematics Oregon State University Corvallis OR USA Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Program in Applied and Computational Mathematics and the Department of Mathematics Princeton University Princeton NJ USA

We consider the multi-target detection problem of estimating a two-dimensional target image from a large noisy measurement image that contains many randomly rotated and translated copies of the target image. Motivated by single-particle cryo-electron microscopy, we focus on the low signal-to-noise regime, where it is difficult to estimate the locations and orientations of the target images in the measurement. Our approach uses autocorrelation analysis to estimate rotationally and translationally invariant features of the target image. We demonstrate that, regardless of the level of noise, our technique can be used to recover the target image when the measurement is sufficiently large. Copyright © 2021, The Authors. All rights reserved.

关键词： Signal to noise ratio

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Improving the robustness of the immersed interface method through regularized velocity reconstruction

arXiv

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arXiv 2025年

作者： Sun, Qi Kolahdouz, Ebrahim M. Griffith, Boyce E. Department of Mathematics University of North Carolina Chapel HillNC United States Department of Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

Robust, broadly applicable fluid-structure interaction (FSI) algorithms remain a challenge for computational mechanics. Efforts in this area are driven by the need to enhance predictive accuracy and efficiency in FSI simulations, align with experimental observations, and unravel complex multiscale and multiphysics phenomena, while addressing challenges in developing more robust and efficient methodologies. In previous work, we introduced an immersed interface method (IIM) for discrete surfaces and an extension based on an immersed Lagrangia-Eulerian (ILE) coupling strategy for modeling FSI involving complex geometries. The ability of the method to sharply resolve stress discontinuities induced by singular immersed boundary forces in the presence of low-regularity geometrical representations makes it a compelling choice for three-dimensional modeling of complex geometries in diverse engineering applications. Although the IIM we previously introduced offers many desirable advantages, it also imposes a restrictive mesh factor ratio, requiring the surface mesh to be coarser than the fluid grid to ensure stability. This is because when the mesh factor ratio constraint is not satisfied, parts of the structure motion are not controlled by the discrete FSI system. This constraint can significantly increase computational costs, particularly in applications involving multiscale geometries with highly localized complexity or fine-scale features. To address this limitation, we devise a stabilization strategy for the velocity restriction operator inspired by Tikhonov regularization. This study demonstrates that using a stabilized velocity restriction operator in IIM enables a broader range of structure-to-fluid grid-size ratios without compromising accuracy or altering the flow dynamics. This advancement significantly broadens the applicability of the method to real-world FSI problems involving complex geometries and dynamic conditions, offering a robust and computationally effi

关键词： Mesh generation

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