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On Behaviors, Rational Interpolation, and the Lanczos Algorithm

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IFAC Proceedings Volumes 1996年第1期29卷 3957-3962页

作者： A.C. Antoulas E.J. Grimme D.C. Sorensen Department of Electrical and Computer Engineering Rice University Houston TX 77251-1892 USA Coordinated Science Laboratory University of Illinois at Urbana-Champaign Urbana IL 61801-2307 USA Department of Computational and Applied Mathematics Rice University Houston TX 77251-1892 USA

This paper explores the interconnections between two methods which can be used to obtain rational interpolants. The first method, the behavioral approach, constructs a generating system in the frequency domain which explains a given data set composed of trajectories. The second method, the rational Lanczos algorithm, can be used to construct a rational interpolant for the transfer function of a linear system defined by (potentially very high-order) state-space equations. This paper works to merge the theoretical attributes of the behavioral approach with the theoretical and computational properties of rational Lanczos. As a result, it lays the foundation for the computation of reduced-order, stabilizing controllers through rational interpolation.

关键词： linear systems behaviors rational interpolation Lanczos algorithm Krylov subspaces

Blind deconvolutional phase retrieval via convex programming

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arXiv 2018年

作者： Ahmed, Ali Aghasi, Alireza Hand, Paul Department of Electrical Engineering Information Technology University Lahore Pakistan School of Business Georgia State University AtlantaGA United States Department of Computational and Applied Mathematics Rice University HoustonTX United States

We consider the task of recovering two real or complex m-vectors from phaseless Fourier measurements of their circular convolution. Our method is a novel convex relaxation that is based on a lifted matrix recovery formulation that allows a nontrivial convex relaxation of the bilinear measurements from convolution. We prove that if the two signals belong to known random subspaces of dimensions k and n, then they can be recovered up to the inherent scaling ambiguity with m >> (k + n) log2m phaseless measurements. Our method provides the first theoretical recovery guarantee for this problem by a computationally efficient algorithm and does not require a solution estimate to be computed for initialization. Our proof is based Rademacher complexity estimates. Additionally, we provide an ADMM implementation of the method and provide numerical experiments that verify the theory. Copyright © 2018, The Authors. All rights reserved.

关键词： Relaxation processes

Deep Potential generation scheme and simulation protocol for the Li10GeP2S12-type superionic conductors

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arXiv 2020年

作者： Huang, Jianxing Zhang, Linfeng Wang, Han Zhao, Jinbao Cheng, Jun Weinan, E. State Key Laboratory of Physical Chemistry of Solid Surfaces iChEM College of Chemistry and Chemical Engineering Xiamen University Xiamen361005 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China Department of Mathematics Princeton University PrincetonNJ08544 United States

Solid-state electrolyte materials with superior lithium ionic conductivities are vital to the next-generation Li-ion batteries. Molecular dynamics could provide atomic scale information to understand the diffusion process of Li-ion in these superionic conductor materials. Here we implement the Deep Potential Generator (DP-GEN) to set up an efficient protocol to automatically generate interatomic potentials for Li10GeP2S12-type solid-state electrolyte materials (Li10GeP2S12, Li10SiP2S12 and Li10SnP2S12). The reliability and accuracy of the fast interatomic potentials are validated. With the potentials, we extend the simulation of diffusion process to a wide temperature range (300K-1000K) and systems with large size (~1000 atoms). Important technical aspects like the statistical error and size effect are carefully investigated and benchmark tests including the effect of density functional, thermal expansion and configurational disorder are performed. The computed data that considering these factors agrees well with the experimental results and we find that the 3 structures shows different behaviors with respect to configurational disorder. Our work paves the way for further research on computation screening of solid-state electrolyte materials. Copyright © 2020, The Authors. All rights reserved.

关键词： Solid electrolytes

Parametric Amplification of an Optomechanical Quantum Interconnect

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arXiv 2022年

作者： Chen, Huo Vives, Marti Metcalf, Mekena Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Department of Electrical and Computer Engineering Princeton University PrincetonNJ08544 United States

Connecting superconducting qubits to optical fiber necessitates the conversion of microwave photons to optical photons. Modern experimental demonstrations exhibit strong coupling between a microwave resonator and an optical cavity mediated through phononic modes in a mechanical oscillator. This paradigmatic transduction experiment is bounded by a theoretical efficiency with constant driving amplitudes on the electromagnetic resonators. By adding a parametric drive to the microwave resonator and optical cavity we discover the converted signal through the quantum transducer is amplified, while maintaining a lower level of the added noise. We propose a theoretical framework for time-dependent control of the driving lasers based on the input-output formalism of quantum optics, and solve analytically the transduction efficiency and added noise when the control signals parametrically drive the system. Our results show better transduction efficiency and lower added noise in varying parameter regimes relevant to current transduction experiments. Copyright © 2022, The Authors. All rights reserved.

关键词： Quantum optics

Efficient coarse simulation of a growing avascular tumor

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Physical Review E 2012年第3期85卷 031912-031912页

作者： Michail E. Kavousanakis Ping Liu Andreas G. Boudouvis John Lowengrub Ioannis G. Kevrekidis School of Chemical Engineering National Technical University of Athens 9 Heroon Polytechniou St. Zographos Athens GR-15780 Greece Department of Chemical and Biological Engineering Princeton University Princeton New Jersey 08544 USA Department of Mathematics University of California 103 MSTB Irvine California 92697 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

The subject of this work is the development and implementation of algorithms which accelerate the simulation of early stage tumor growth models. Among the different computational approaches used for the simulation of tumor progression, discrete stochastic models (e.g., cellular automata) have been widely used to describe processes occurring at the cell and subcell scales (e.g., cell-cell interactions and signaling processes). To describe macroscopic characteristics (e.g., morphology) of growing tumors, large numbers of interacting cells must be simulated. However, the high computational demands of stochastic models make the simulation of large-scale systems impractical. Alternatively, continuum models, which can describe behavior at the tumor scale, often rely on phenomenological assumptions in place of rigorous upscaling of microscopic models. This limits their predictive power. In this work, we circumvent the derivation of closed macroscopic equations for the growing cancer cell populations; instead, we construct, based on the so-called “equation-free” framework, a computational superstructure, which wraps around the individual-based cell-level simulator and accelerates the computations required for the study of the long-time behavior of systems involving many interacting cells. The microscopic model, e.g., a cellular automaton, which simulates the evolution of cancer cell populations, is executed for relatively short time intervals, at the end of which coarse-scale information is obtained. These coarse variables evolve on slower time scales than each individual cell in the population, enabling the application of forward projection schemes, which extrapolate their values at later times. This technique is referred to as coarse projective integration. Increasing the ratio of projection times to microscopic simulator execution times enhances the computational savings. Crucial accuracy issues arising for growing tumors with radial symmetry are addressed by applying th

关键词： SIMULATION methods & models TUMORS -- Growth MATHEMATICAL models CANCER invasiveness STOCHASTIC models computational biology BIONICS PHENOMENOLOGY

3D ferroelectric phase field simulations of polycrystalline multiphase hafnia and zirconia based ultra-thin films

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arXiv 2024年

作者： Kumar, Prabhat Hoffmann, Michael Nonaka, Andy Salahuddin, Sayeef Yao, Zhi Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory CA94720 United States Department of Electrical Engineering and Computer Sciences University of California BerkeleyCA94720 United States

HfO2- and ZrO2-based ferroelectric thin films have emerged as promising candidates for the gate oxides of next generation electronic devices. Recent work has experimentally demonstrated that a tetragonal/orthorhombic (t/o-) phase mixture with partially in-plane polarization can lead to negative capacitance (NC) stabilization. However, there is a discrepancy between experiments and the theoretical understanding of domain formation and domain wall motion in these multi-phase, polycrystalline materials. Furthermore, the effect of anisotropic domain wall coupling on NC has not been studied so far. Here we apply 3D phase field simulations of HfO2- and ZrO2-based mixed-phase ultra-thin films on silicon to understand the necessary and beneficial conditions for NC stabilization. We find that smaller ferroelectric grains and a larger angle of the polar axis with respect to the out-of-plane direction enhances the NC effect. Furthermore, we show that theoretically predicted negative domain wall coupling even along only one axis prevents NC stabilization. Therefore, we conclude that topological domain walls play a critical role in experimentally observed NC phenomena in HfO2- and ZrO2-based ferroelectrics. © 2024, CC BY.

关键词： Stabilization

Multi-frequency phase synchronization

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arXiv 2019年

作者： Gao, Tingran Zhao, Zhizhen Committee on Computational and Applied Mathematics Department of Statistics University of Chicago ChicagoIL United States Department of Electrical and Computer Engineering Coordinated Science Laboratory University of Illinois at Urbana-Champaign UrbanaIL United States

We propose a novel formulation for phase synchronization- the statistical problem of jointly estimating alignment angles from noisy pairwise comparisons-as a nonconvex optimization problem that enforces consistency among the pairwise comparisons in multiple frequency channels. Inspired by harmonic retrieval in signal processing, we develop a simple yet efficient two-stage algorithm that leverages the multi-frequency information. We demonstrate in theory and practice that the proposed algorithm significantly outperforms state-of-the-art phase synchronization algorithms, at a mild computational costs incurred by using the extra frequency channels. We also extend our algorithmic framework to general synchronization problems over compact Lie groups. Copyright © 2019, The Authors. All rights reserved.

关键词： Signal processing

Removing data heterogeneity influence enhances network topology dependence of decentralized SGD

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The Journal of Machine Learning Research

The Journal of Machine Learning Research 2023年第1期24卷 13275-13327页

作者： Kun Yuan Sulaiman A. Alghunaim Xinmeng Huang Center for Machine Learning Research Peking University AI for Science Institute Beijing P. R. China Department of Electrical Engineering Kuwait University Safat Kuwait Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia PA

We consider decentralized stochastic optimization problems, where a network of n nodes cooperates to find a minimizer of the globally-averaged cost. A widely studied decentralized algorithm for this problem is the decentralized SGD (D-SGD), in which each node averages only with its neighbors. D-SGD is efficient in single-iteration communication, but it is very sensitive to the network topology. For smooth objective functions, the transient stage (which measures the number of iterations the algorithm has to experience before achieving the linear speedup stage) of D-SGD is on the order of O(n/(1 - β)2) and O(n3/(1 - β)4) for strongly and generally convex cost functions, respectively, where 1 - β ∈ (0, 1) is a topology-dependent quantity that approaches 0 for a large and sparse network. Hence, D-SGD suffers from slow convergence for large and sparse *** this work, we revisit the convergence property of the D2/Exact-Diffusion algorithm. By eliminating the influence of data heterogeneity between nodes, D2/Exact-diffusion is shown to have an enhanced transient stage that is on the order of Õ(n/(1 - β)) and O(n3/(1-β)2) for strongly and generally convex cost functions (where Õ (·) hides all logarithm factors), respectively. Moreover, when D2/Exact-Diffusion is implemented with both gradient accumulation and multi-round gossip communications, its transient stage can be further improved to Õ (1/(1-β)1/2) and Õ(n/(1-β)) for strongly and generally convex cost functions, respectively. To our knowledge, these established results for D2/Exact-Diffusion have the best (i.e., weakest) dependence on network topology compared to existing decentralized algorithms. Numerical simulations are conducted to validate our theories.

关键词： decentralized optimization stochastic optimization transient stage

Pump-probe scheme for optical coherence tomography using indocyanine green mixed with albumin or human plasma

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Pump-probe scheme for optical coherence tomography using ind...

Conference on Lasers and Electro-Optics (CLEO)

作者： Z. Yaqoob J.P. Fingler S. Lintner B.E. Applegate Changhuei Yang Electrical Engineering California Institute of Technology Pasadena CA USA Applied Physics California Institute of Technology Pasadena CA USA Applied & Computational Mathematics California Institute of Technology Pasadena CA USA Department of Biomedical Engineering Duke University Durham NC USA

Use of indocyanine green (ICG) in a pump-probe scheme for OCT is proposed. The study illustrates that ICG in protein solution shows unusual pump-probe imaging potential, indicating its usefulness as a contrast agent f... 详细信息

ISBN: (纸本)1557527954

关键词： Optical pumping Tomography Humans Plasmas Biomedical optical imaging High-resolution imaging Absorption Optical imaging Laser beams Pump lasers