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作者： Panayiotou, Christos G. Howell, William C. Fu, Michael Department of Electrical and Computer Engineering University of Cyprus Nicosia Cyprus Applied Mathematics Scientific Computation Program Department of Mathematics University of Maryland College Park MD 20742 United States Smith School of Business and Institute for Systems Research University of Maryland College Park MD 20742 United States

ISBN: (纸本)008045108X

in this paper, we consider the problem of dynamically regulating the timing of traffic light controllers in busy cities. We use a Stochastic Fluid Model (SFM) to model the dynamics of the queues formed at an intersection. Based on this model, we derive gradients of the queue lengths with respect to the green/red light lengths within a signal cycle. We report preliminary numerical results comparing the performance of the estimates with finite-difference and smoothed perturbation analysis estimates. Then all estimators are used to optimize the traffic system via Stochastic Approximation. Copyright © 2005 IFAC.

关键词： Stochastic systems

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A Dynamic Pyramidal Relaxation Method of AC OPF 9

A Dynamic Pyramidal Relaxation Method of AC OPF

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9th Asia Conference on Power and electrical engineering, ACPEE 2024

作者： Tang, Yu-Yang Chen, Liang Du, Hongbo Chen, Sheng-Jie Kou, Caixia Ai, Xiaomeng Zhou, Bo Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Beijing University of Posts and Telecommunications College of Sciences Beijing China Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Huazhong University of Science and Technology School of Electrical and Electronic Engineering Wuhan China University of Michigan Department of Industrial and Operations Engineering Ann Arbor United States

ISBN: (纸本)9798350309638

The Alternating Current Optimal Power Flow (AC OPF) is crucial for power system analysis, yet existing algorithms face challenges in meeting the diverse requirements of practical applications. This paper presents a Pyramidal Relaxation (PR) formulation of the Branch Flow Model (BFM) for AC OPF, where surface conical constraints are approximated through a union of tetrahedrons in a Mixed Integer Linear programming (MILP) relaxation. To reduce problem size and to enhance computational efficiency, we proposed a Dynamic Pyramidal Relaxation (DPR) method, where the cuts (inner approximation and outer approximation) are adaptively added. In practice, the DPR method is embedded into a MILP commercial solver based on the branch-and-cut framework. Case studies in different test systems validate the effectiveness in terms of feasibility, accuracy, and efficiency of our proposed method. © 2024 IEEE.

关键词： computational efficiency

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Group synchronization on grids

arXiv

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arXiv 2017年

作者： Abbe, Emmanuel Massoulie, Laurent Montanari, Andrea Sly, Allan Srivastava, Nikhil Program in Applied and Computational Mathematics EE Department Princeton University Inria MSR-Inria Joint Centre Department of Electrical Engineering Department of Sttistics Stanford University Department of Mathematics Princeton University Department of Mathematics University of California Berkeley United States

Group synchronization requires to estimate unknown elements (θv)v∈V of a compact group G associated to the vertices of a graph G = (V, E), using noisy observations of the group differences associated to the edges. This model is relevant to a variety of applications ranging from structure from motion in computer vision to graph localization and positioning, to certain families of community detection problems. We focus on the case in which the graph G is the d-dimensional grid. Since the unknowns θv are only determined up to a global action of the group, we consider the following weak recovery question. Can we determine the group difference θ−u1θv between far apart vertices u, v better than by random guessing? We prove that weak recovery is possible (provided the noise is small enough) for d ≥ 3 and, for certain finite groups, for d ≥ 2. Viceversa, for some continuous groups, we prove that weak recovery is impossible for d = 2. Finally, for strong enough noise, weak recovery is always impossible. Copyright © 2017, The Authors. All rights reserved.

关键词： Recovery

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Erratum to: Some Joys and Trials of Mathematical Neuroscience

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Journal of Nonlinear Science 2014年第2期24卷 243-244页

作者： Holmes, Philip Department of Mechanical and Aerospace Engineering Program in Applied and Computational Mathematics Princeton University Princeton USA Princeton Neuroscience Institute Princeton University Princeton USA

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Collaborative Spectrum Sensing from Sparse Observations Using Matrix Completion for Cognitive Radio Networks

Collaborative Spectrum Sensing from Sparse Observations Usin...

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IEEE International Conference on Acoustics, Speech, and Signal Processing

作者： Jia (Jasmine) Meng Wotao Yin Husheng Li Ekram Houssain Zhu Han Department of Electrical and Computer Engineering University of Houston Department of Computational and Applied Mathematics Rice University Department of Electrical Engineering and Computer Science University of Tennessee at Knoxville Department of Electrical and Computer Engineering University of Manitoba Canada

ISBN: (纸本)9781424442959

In cognitive radio, spectrum sensing is a key component to detect spectrum holes (i.e., channels not used by any primary users). Collaborative spectrum sensing among the cognitive radio nodes is expected to improve the ability of checking complete spectrum usage states. Unfortunately, due to power limitation and channel fading, available channel sensing information is far from being sufficient to tell the unoccupied channels directly. Aiming at breaking this bottleneck, we apply recent matrix completion techniques to greatly reduce the sensing information needed. We formulate the collaborative sensing problem as a matrix completion subproblem and a joint-sparsity reconstruction subproblem. Results of numerical simulations that validated the effectiveness and robustness of the proposed approach are presented. In particular, in noiseless cases, when number of primary user is small, exact detection was obtained with no more than 8percent of the complete sensing information, whilst as number of primary user increases, to achieve a detection rate of 95.55percent, the required information percentage was merely 16.8percent.

关键词： Cognitive radio detection rate (DR) Spectra Completion Radio networks matrices

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Coarse molecular-dynamics determination of the onset of structural transitions: Melting of crystalline solids

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Physical Review B 2006年第13期74卷 132201-132201页

作者： Miguel A. Amat Ioannis G. Kevrekidis Dimitrios Maroudas Department of Chemical Engineering University of Massachusetts Amherst Massachusetts 01003 USA Department of Chemical Engineering and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Using a coarse molecular-dynamics (CMD) approach with an appropriate choice of coarse variable (order parameter), we map the underlying effective free-energy landscape for the melting of a crystalline solid. Implementation of this approach provides a means for constructing effective free-energy landscapes of structural transitions in condensed matter. The predictions of the approach for the thermodynamic melting point of a model silicon system are in excellent agreement with those of “traditional” techniques for melting-point calculations, as well as with literature values.

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Implications of Delayed Reopening in Controlling the COVID-19 Surge in Southern and West-Central USA

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Health Data Science 2021年第1期2021卷 78-87页

作者： Raj Dandekar Emma Wang George Barbastathis Chris Rackauckas Department of Computational Science and Engineering Massachusetts Institute of TechnologyCambridgeUSA MA 02139 Department of Electrical Engineering and Computer Sciences Massachusetts Institute of TechnologyCambridgeMA 02139USA Department of Mechanical Engineering Massachusetts Institute of TechnologyCambridgeMA 02139USA Singapore-MIT Alliance for Research and Technology(SMART)Centre Singapore 138602 Department of Applied Mathematics Massachusetts Institute of TechnologyCambridgeMA 02139USA

In the wake of the rapid surge in the COVID-19-infected cases seen in Southern and West-Central USA in the period of June-July 2020,there is an urgent need to develop robust,data-driven models to quantify the effect which early reopening had on the infected case count *** particular,it is imperative to address the question:How many infected cases could have been prevented,had the worst affected states not reopened early?To address this question,we have developed a novel COVID-19 model by augmenting the classical SIR epidemiological model with a neural network *** model decomposes the contribution of quarantine strength to the infection time series,allowing us to quantify the role of quarantine control and the associated reopening policies in the US states which showed a major surge in *** show that the upsurge in the infected cases seen in these states is strongly corelated with a drop in the quarantine/lockdown strength diagnosed by our ***,our results demonstrate that in the event of a stricter lockdown without early reopening,the number of active infected cases recorded on 14 July could have been reduced by more than 40%in all states considered,with the actual number of infections reduced being more than 100,000 for the states of Florida and *** we continue our fight against COVID-19,our proposed model can be used as a valuable asset to simulate the effect of several reopening strategies on the infected count evolution,for any region under consideration.

关键词： COV neural Central

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Image Recovery from Rotational And Translational Invariants

Image Recovery from Rotational And Translational Invariants

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IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Nicholas F. Marshall Ti-Yen Lan Tamir Bendory Amit Singer Department of Mathematics Princeton University Princeton NJ USA The Program in Applied and Computational Mathematics Princeton University Princeton NJ USA School of Electrical Engineering Tel Aviv University Tel Aviv Israel

ISBN: (数字)9781509066315

ISBN: (纸本)9781509066322

We introduce a framework for recovering an image from its rotationally and translationally invariant features based on autocorrelation analysis. This work is an instance of the multi-target detection statistical model, which is mainly used to study the mathematical and computational properties of single-particle reconstruction using cryo-electron microscopy (cryo-EM) at low signal-to-noise ratios. We demonstrate with synthetic numerical experiments that an image can be reconstructed from rotational and translational invariants and show that the reconstruction is robust to noise. These results constitute an important step towards the goal of structure determination of small biomolecules using cryo-EM.

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Coarse graining the dynamics of heterogeneous oscillators in networks with spectral gaps

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Physical Review E 2011年第3期84卷 036708-036708页

作者： Karthikeyan Rajendran Ioannis G. Kevrekidis Department of Chemical and Biological Engineering Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA

We present a computer-assisted approach to coarse graining the evolutionary dynamics of a system of nonidentical oscillators coupled through a (fixed) network structure. The existence of a spectral gap for the coupling network graph Laplacian suggests that the graph dynamics may quickly become low dimensional. Our first choice of coarse variables consists of the components of the oscillator states—their (complex) phase angles—along the leading eigenvectors of this Laplacian. We then use the equation-free framework, circumventing the derivation of explicit coarse-grained equations, to perform computational tasks such as coarse projective integration, coarse fixed-point, and coarse limit-cycle computations. In a second step, we explore an approach to incorporating oscillator heterogeneity in the coarse-graining process. The approach is based on the observation of fast-developing correlations between oscillator state and oscillator intrinsic properties and establishes a connection with tools developed in the context of uncertainty quantification.

关键词： GRAINING COMPUTER-aided design LAPLACIAN operator EIGENVECTORS HARMONIC oscillators

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An information-geometric distance on the space of tasks

arXiv

引用

arXiv 2020年

作者： Gao, Yansong Chaudhari, Pratik Department of Applied Mathematics and Computational Science University of Pennsylvania United States Department of Electrical and Systems Engineering University of Pennsylvania United States

This paper prescribes a distance between learning tasks modeled as joint distributions on data and labels. Using tools in information geometry, the distance is defined to be the length of the shortest weight trajectory on a Riemannian manifold as a classifier is fitted on an interpolated task. The interpolated task evolves from the source to the target task using an optimal transport formulation. This distance, which we call the "coupled transfer distance" can be compared across different classifier architectures. We develop an algorithm to compute the distance which iteratively transports the marginal on the data of the source task to that of the target task while updating the weights of the classifier to track this evolving data distribution. We develop theory to show that our distance captures the intuitive idea that a good transfer trajectory is the one that keeps the generalization gap small during transfer, in particular at the end on the target task. We perform thorough empirical validation and analysis across diverse image classification datasets to show that the coupled transfer distance correlates strongly with the difficulty of fine-tuning. Copyright © 2020, The Authors. All rights reserved.

关键词： Iterative methods

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