The Experts below are selected from a list of 300 Experts worldwide ranked by ideXlab platform
Abdulkadir C Yucel - One of the best experts on this subject based on the ideXlab platform.
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on the compression of Translation Operator tensors in fmm fft accelerated sie simulators via tensor decompositions
IEEE Transactions on Antennas and Propagation, 2021Co-Authors: Cheng Qian, Abdulkadir C YucelAbstract:Tensor decomposition methodologies are proposed to reduce the memory requirement of Translation Operator tensors arising in the fast multipole method-fast Fourier transform (FMM-FFT)-accelerated surface integral equation (SIE) simulators. These methodologies leverage Tucker, hierarchical Tucker (H-Tucker), and tensor train (TT) decompositions to compress the FFT’ed Translation Operator tensors stored in 3-D and 4-D array formats. Extensive numerical tests are performed to demonstrate the memory saving achieved by and computational overhead introduced by these methodologies for different simulation parameters. The numerical results show that the H-Tucker-based methodology for 4-D array format yields the maximum memory saving, while Tucker-based methodology for 3-D array format introduces the minimum computational overhead. For many practical scenarios, all methodologies yield a significant reduction in the memory requirement of Translation Operator tensors while imposing negligible/acceptable computational overhead.
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on the compression of Translation Operator tensors in fmm fft accelerated sie simulators via tensor decompositions
arXiv: Signal Processing, 2020Co-Authors: Cheng Qian, Abdulkadir C YucelAbstract:Tensor decomposition methodologies are proposed to reduce the memory requirement of Translation Operator tensors arising in the fast multipole method-fast Fourier transform (FMM-FFT)-accelerated surface integral equation (SIE) simulators. These methodologies leverage Tucker, hierarchical Tucker (H-Tucker), and tensor train (TT) decompositions to compress the FFT'ed Translation Operator tensors stored in three-dimensional (3D) and four-dimensional (4D) array formats. Extensive numerical tests are performed to demonstrate the memory saving achieved by and computational overhead introduced by these methodologies for different simulation parameters. Numerical results show that the H-Tucker-based methodology for 4D array format yields the maximum memory saving while Tucker-based methodology for 3D array format introduces the minimum computational overhead. For many practical scenarios, all methodologies yield a significant reduction in the memory requirement of Translation Operator tensors while imposing negligible/acceptable computational overhead.
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Tensor Decompositions for Reducing the Memory Requirement of Translation Operator Tensors in FMM-FFT Accelerated IE Solvers
2019Co-Authors: Cheng Qian, Zhuotong Chen, Abdulkadir C YucelAbstract:Tensor decompositions are applied to lessen the memory requirements of Translation Operator tensors in fast multipole method-fast Fourier transform (FMM-FFT) accelerated integral equation (IE) solvers. In particular, methodologies leveraging Tucker and tensor train (TT) decompositions are developed to compress the three-dimensional (3D) arrays and four-dimensional (4D) array storing the FFT'ed Translation Operator values. Preliminary results show the achieved memory reduction as well as imposed computational overhead via the developed methodologies.
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compression of Translation Operator tensors in fmm fft accelerated sie solvers via tucker decomposition
IEEE Antennas and Wireless Propagation Letters, 2017Co-Authors: Abdulkadir C Yucel, Luis J Gomez, Eric MicielssenAbstract:Tucker decompositions (also known as higher order singular value decompositions) are used to lessen the memory requirements of Translation Operator tensors in fast multipole method-fast Fourier transform accelerated surface integral equation solvers. For many practical examples, the proposed drop-in code enhancement results in over 90% reduction in these tensors' storage requirements while imposing negligible computational overhead, thus significantly enhancing the solvers' application range on fixed computational resources.
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tucker decomposition for compressing Translation Operator tensors in fmm fft accelerated sie solvers
USNC-URSI Radio Science Meeting, 2015Co-Authors: Abdulkadir C Yucel, Luis J Gomez, E MichielssenAbstract:Fast multipole method - Fast Fourier transform (FMM-FFT) accelerated surface integral equation (SIE) solvers allow for accurate and efficient analysis of electromagnetic (EM) scattering from and radiation by complex and large scale structures (R. L. Wagner et. al., IEEE Trans. Antennas Propagat., 45(2), 235–245, 1997). These solvers (and their multilevel extensions) provide an increasingly appealing avenue for solving EM scattering problems involving hundreds of millions (and billions) of unknowns (Taboada et. al., IEEE Antennas Propagat. Mag., 51(6), 20–28, 2009; Taboada et. al., Progress in Electromagnetics Research, 105, 15–30, 2010). When used on present high-performance computers to solve practical problems of current interest, these solvers tend to be memory as opposed to CPU-limited. The solvers' memory requirements directly depends on the storage requirements for (i) near-field interaction matrices, (ii) matrices that hold the far-field signatures of basis functions, and (iii) tensors that hold FFT'ed Translation Operator values on a structured grid. In past, the memory requirements of the first two data structures were successfully reduced by singular value decomposition (SVD) (Kapur and Long, IEEE Comp. Sci. Eng., 5(4), 60–67, 1998; Rodriguez et. al., IEEE Trans. Antennas Propagat., 56(8), 2325–2334, 2008). To date, no compression scheme has been reported to reduce the memory requirements of Translation Operator tensors.
Chong-yung Chi - One of the best experts on this subject based on the ideXlab platform.
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stationarity of time series on graph via bivariate Translation invariance
arXiv: Signal Processing, 2020Co-Authors: Amin Jalili, Chong-yung ChiAbstract:Stationarity is a cornerstone in classical signal processing (CSP) for modeling and characterizing various stochastic signals for the ensuing analysis. However, in many complex real world scenarios, where the stochastic process lies over an irregular graph structure, CSP discards the underlying structure in analyzing such structured data. Then it is essential to establish a new framework to analyze the high-dimensional graph structured stochastic signals by taking the underlying structure into account. To this end, looking through the lens of Operator theory, we first propose a new bivariate isometric joint Translation Operator (JTO) consistent with the structural characteristic of Translation Operators in other signal domains. Moreover, we characterize time-vertex filtering based on the proposed JTO. Thereupon, we put forth a new definition of joint wide-sense stationary (JWSS) signals in time-vertex domain using the proposed isometric JTO together with its spectral characterization. Then a new joint power spectral density (JPSD) estimator, called generalized Welch method (GWM), is presented. Simulation results are provided to show the efficacy of this JPSD estimator. Furthermore, to show the usefulness of JWSS modeling, we focus on the classification of time-series on graph. To that end, by modeling the brain Electroencephalography (EEG) signals as JWSS processes, we use JPSD as the feature for the Emotion and Alzheimer's disease (AD) recognition. Experimental results demonstrate that JPSD yields superior Emotion and AD recognition accuracy in comparison with the classical power spectral density (PSD) and graph PSD (GPSD) as the feature set for both applications. Eventually, we provide some concluding remarks.
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Translation Operator in Graph Signal Processing: A Generalized Approach.
arXiv: Signal Processing, 2020Co-Authors: Amin Jalili, Sadid Sahami, Chong-yung ChiAbstract:The notion of Translation (shift) is straightforward in classical signal processing, however, it is challenging on an irregular graph structure. In this work, we present an approach to characterize the Translation Operator in various signal domains. By a natural generalization from classical domains, one can characterize an abstract representation for the graph Translation Operator. Then we propose an isometric Translation Operator in joint time-vertex domain consistent with the abstract form of Translation Operators in other domains. We also demonstrate the connection between this notion and the Schr\"{o}dinger equation on a dynamic system which intriguingly describes the idea behind Translation on graph.
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Translation Operator in joint time vertex domain a generalized approach
arXiv: Signal Processing, 2019Co-Authors: Amin Jalili, Sadid Sahami, Chong-yung ChiAbstract:The notion of Translation (shift) is straightforward in classical signal processing, however, it is challenging on an irregular graph structure. In this work, we present an approach to characterize the Translation Operator in various signal domains. By a natural generalization from classical domains, one can characterize an abstract representation for the graph Translation Operator. Then we propose an isometric Translation Operator in joint time-vertex domain consistent with the abstract form of Translation Operators in other domains. We also demonstrate the connection between this notion and the Schrodinger equation on a dynamic system which intriguingly describes the idea behind Translation on graph.
Xiaoliang Qi - One of the best experts on this subject based on the ideXlab platform.
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momentum polarization an entanglement measure of topological spin and chiral central charge
Physical Review B, 2013Co-Authors: Honghao Tu, Yi Zhang, Xiaoliang QiAbstract:Topologically ordered states are quantum states of matter with topological ground state degeneracy and quasi-particles carrying fractional quantum numbers and fractional statistics. The topological spin $\theta_a=2\pi h_a$ is an important property of a topological quasi-particle, which is the Berry phase obtained in the adiabatic self-rotation of the quasi-particle by $2\pi$. For chiral topological states with robust chiral edge states, another fundamental topological property is the edge state chiral central charge $c$. In this paper we propose a new approach to compute the topological spin and chiral central charge in lattice models by defining a new quantity named as the momentum polarization. Momentum polarization is defined on the cylinder geometry as a universal subleading term in the average value of a "partial Translation Operator". We show that the momentum polarization is a quantum entanglement property which can be computed from the reduced density matrix, and our analytic derivation based on edge conformal field theory shows that the momentum polarization measures the combination $h_a-\frac{c}{24}$ of topological spin and central charge. Numerical results are obtained for two example systems, the non-Abelian phase of the honeycomb lattice Kitaev model, and the $\nu=1/2$ Laughlin state of a fractional Chern insulator described by a variational Monte Carlo wavefunction. The numerical results verifies the analytic formula with high accuracy, and further suggests that this result remains robust even when the edge states cannot be described by a conformal field theory. Our result provides a new efficient approach to characterize and identify topological states of matter from finite size numerics.
Rushan Chen - One of the best experts on this subject based on the ideXlab platform.
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electromagnetic scattering for multiple pec bodies of revolution using equivalence principle algorithm
IEEE Transactions on Antennas and Propagation, 2014Co-Authors: Rushan ChenAbstract:An equivalence principle algorithm (EPA) method is extended to analyze the electromagnetic scattering from multiple bodies of revolution (MBoR) with the axes arbitrarily oriented. Equivalence spheres are used to enclose each BoR and the equivalence currents are expanded by the basis functions of bodies of revolution (BoR). To obtain the scattering Operators and Translation Operators of EPA for Fourier modes independently, the rotational symmetry systems are established in local BoR coordinate systems. The origin of the local BoR coordinate system is located at the center of the equivalence sphere and the z-axis coincides with the axis of the enclosed BoR to obtain the scattering Operator of each equivalence sphere, whereas the origin is located at the observation sphere and z-axis passes through the center of the source sphere to obtain the Translation Operator of each pair of equivalence spheres. The current coefficient transformation algorithm is used to transform the equivalence currents among local BoR coordinate systems. The total equation is iteratively solved in the global coordinate system. The proposed scheme is especially efficient for the analysis of scattering from MBoR randomly distributed in electrically large scale region. Numerical results are given to demonstrate the efficiency.
Sofiane Soussi - One of the best experts on this subject based on the ideXlab platform.
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Riesz bases and Jordan form of the Translation Operator in semi-infinite periodic waveguides
Journal de Mathématiques Pures et Appliquées, 2013Co-Authors: Thorsten Hohage, Sofiane SoussiAbstract:Abstract We study the propagation of time-harmonic acoustic or transverse magnetic (TM) polarized electromagnetic waves in a periodic waveguide lying in the half-strip ( 0 , ∞ ) × ( 0 , L ) . It is shown that there exists a Riesz basis of the space of solutions to the time-harmonic wave equation such that the Translation Operator shifting a function by one periodicity length to the left is represented by an infinite Jordan matrix which contains at most a finite number of Jordan blocks of size >1. Moreover, the Dirichlet-, Neumann- and mixed traces of this Riesz basis on the left boundary also form a Riesz basis. Both the cases of frequencies in a band gap and frequencies in the spectrum and a variety of boundary conditions on the top and bottom are considered.
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riesz bases and jordan form of the Translation Operator in semi infinite periodic waveguides
arXiv: Analysis of PDEs, 2010Co-Authors: Thorsten Hohage, Sofiane SoussiAbstract:We study the propagation of time-harmonic acoustic or transverse magnetic (TM) polarized electromagnetic waves in a periodic waveguide lying in the semi-strip $(0,\infty)\times(0,L)$. It is shown that there exists a Riesz basis of the space of solutions to the time-harmonic wave equation such that the Translation Operator shifting a function by one periodicity length to the left is represented by an infinite Jordan matrix which contains at most a finite number of Jordan blocks of size $> 1$. Moreover, the Dirichlet-, Neumann- and mixed traces of this Riesz basis on the left boundary also form a Riesz basis. Both the cases of frequencies in a band gap and frequencies in the spectrum and a variety of boundary conditions on the top and bottom are considered.
