Loading...
Search for:
eigenvalues
0.007 seconds
Total 243 records
Eigenvectors of deformed Wigner random matrices
, Article IEEE Transactions on Information Theory ; 18 November , 2020 ; Amini, A ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2020
Abstract
We investigate eigenvectors of rank-one deformations of random matrices B = A + θuu* in which A ∈ RN×N is a Wigner real symmetric random matrix, θ ∈ R+, and u is uniformly distributed on the unit sphere. It is well known that for θ > 1 the eigenvector associated with the largest eigenvalue of B closely estimates u asymptotically, while for θ < 1 the eigenvectors of B are uninformative about u. We examine O(1/N) correlation of eigenvectors with u before phase transition and show that eigenvectors with larger eigenvalue exhibit stronger alignment with deforming vector through an explicit inverse law 1/θ*-x with θ* := θ + 1/θ. This distribution function will be shown to be the ordinary...
Joint, partially-joint, and individual independent component analysis in multi-subject fMRI data
, Article IEEE Transactions on Biomedical Engineering ; Volume 67, Issue 7 , 2020 , Pages 1969-1981 ; Shamsollahi, M. B ; Sharif University of Technology
IEEE Computer Society
2020
Abstract
Objective: Joint analysis of multi-subject brain imaging datasets has wide applications in biomedical engineering. In these datasets, some sources belong to all subjects (joint), a subset of subjects (partially-joint), or a single subject (individual). In this paper, this source model is referred to as joint/partially-joint/individual multiple datasets unidimensional (JpJI-MDU), and accordingly, a source extraction method is developed. Method: We present a deflation-based algorithm utilizing higher order cumulants to analyze the JpJI-MDU source model. The algorithm maximizes a cost function which leads to an eigenvalue problem solved with thin-SVD (singular value decomposition)...
Multichannel electrocardiogram decomposition using periodic component analysis
, Article IEEE Transactions on Biomedical Engineering ; Volume 55, Issue 8 , August , 2008 , Pages 1935-1940 ; 00189294 (ISSN) ; Jutten, C ; Shamsollahi, M. B ; Sharif University of Technology
2008
Abstract
In this letter, we propose the application of the generalized eigenvalue decomposition for the decomposition of multichannel electrocardiogram (ECG) recordings. The proposed method uses a modified version of a previously presented measure of periodicity and a phase-wrapping of the RR-interval, for extracting the "most periodic" linear mixtures of a recorded dataset. It is shown that the method is an improved extension of conventional source separation techniques, specifically customized for ECG signals. The method is therefore of special interest for the decomposition and compression of multichannel ECG, and for the removal of maternal ECG artifacts from fetal ECG recordings. © 2006 IEEE
Convex Optimization and MIMO RADAR waveform design in the presence of clutter
, Article 2008 2nd International Conference on Signals, Circuits and Systems, SCS 2008, Nabeul, 7 November 2008 through 9 November 2008 ; January , 2008 ; 9781424426287 (ISBN) ; Behnia, F ; Sharif University of Technology
2008
Abstract
Waveform design for Target identification and classification in MIMO radar systems has been studied in several recent works. While the previous works considered signal independent noise and found optimal signals for an e stimation algorithm, here we extend the results to the case where clutter is also present and then we will find the optimum waveform for several estimators differing in the assumptions on the given statistics. Several different approaches to the optimal waveform design are proposed, including minimizing the error of MMSE estimator, minimizing the maximum error of the covariance shaping least square (CSLS) estimator and minimizing the MSE error of scaled least square (SLS)...
A 3D BEM model for liquid sloshing in baffled tanks
, Article International Journal for Numerical Methods in Engineering ; Volume 76, Issue 9 , June , 2008 , Pages 1419-1433 ; 00295981 (ISSN) ; Haddadpour, H ; Noorain, M. A ; Ghasemi, M ; Sharif University of Technology
2008
Abstract
The present work aims at developing a boundary element method to determine the natural frequencies and mode shapes of liquid sloshing in 3D baffled tanks with arbitrary geometries. Green's theorem is used with the governing equation of potential flow and the walls and free surface boundary conditions are applied. A zoning method is introduced to model arbitrary arrangements of baffles. By discretizing the flow boundaries to quadrilateral elements, the boundary integral equation is formulated into a general matrix eigenvalue problem. The governing equations are then reduced to a more efficient form that is merely represented in terms of the potential values of the free surface nodes, which...
Efficient, Fair, and QoS-Aware policies for wirelessly powered communication networks
, Article IEEE Transactions on Communications ; Volume 68, Issue 9 , 2020 , Pages 5892-5907 ; Omidvar, N ; Movahednasab, M ; Pakravan, M. R ; Sun, S ; Guan, Y. L ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2020
Abstract
In this paper, we propose efficient wireless power transfer (WPT) policies for various practical scenarios in wirelessly powered communication networks (WPCNs). First, we consider WPT from an energy access point (E-AP) to multiple energy receivers (E-Rs). We formulate the problem of maximizing the total average received power of the E-Rs subject to power constraints of the E-AP, which is a non-convex stochastic optimization problem. Using eigenvalue decomposition techniques, we derive a closed-form expression for the optimal policy, which requires the distribution of the channel state information (CSI) in the network. We then propose a near-optimal policy that does not require this knowledge...
Planar diffraction analysis of homogeneous and longitudinally inhomogeneous gratings based on legendre expansion of electromagnetic fields
, Article IEEE Transactions on Antennas and Propagation ; Volume 54, Issue 12 , 2006 , Pages 3686-3694 ; 0018926X (ISSN) ; Mehrany, K ; Rashidian, B ; Sharif University of Technology
2006
Abstract
Planar grating diffraction analysis based on Legendre expansion of electromagnetic fields is reported. In contrast to conventional RCWA in which the solution is obtained using state variables representation of the coupled wave amplitudes; here, the solution is expanded in terms of Legendre polynomials. This approach, without facing the problem of numerical instability and inevitable round off errors, yields well-behaved algebraic equations for deriving diffraction efficiencies, and can be employed for analysis of different types of gratings. Thanks to the recursive properties of Legendre polynomials, for longitudinally inhomogeneous gratings, wherein differential equations with non-constant...
Non-Minimality of the realizations and possessing state matrices with integer elements in linear discrete-time controllers
, Article IEEE Transactions on Automatic Control ; 2022 , Pages 1-6 ; 00189286 (ISSN) ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2022
Abstract
It is known that discrete-time controllers, whose state matrices have no non-integer element, are beneficial in homomorphic based encrypted control systems. Nevertheless, it has been recently shown that possessing state matrices with integer elements usually yields unstable discrete-time controllers. In this note, we investigate the problem from a non-minimality perspective. It is shown that non-minimal realizations, in comparison to minimal ones, can theoretically provide a wider framework to obtain controllers having state matrices with integer elements. However, in the case of dealing with BIBO stable controllers, this framework cannot preserve internal stability. But, benefiting from the...
Aeroelastic analysis of helicopter rotor blade in hover using an efficient reduced-order aerodynamic model
, Article Journal of Fluids and Structures ; Volume 25, Issue 8 , 2009 , Pages 1243-1257 ; 08899746 (ISSN) ; Salehzadeh Noubari, A ; Behbahani Nejad, M ; Haddadpour, H ; Sharif University of Technology
2009
Abstract
This paper presents a coupled flap-lag-torsion aeroelastic stability analysis and response of a hingeless helicopter blade in the hovering flight condition. The boundary element method based on the wake eigenvalues is used for the prediction of unsteady airloads of the rotor blade. The aeroelastic equations of motion of the rotor blade are derived by Galerkin's method. To obtain the aeroelastic stability and response, the governing nonlinear equations of motion are linearized about the nonlinear steady equilibrium positions using small perturbation theory. The equilibrium deflections are calculated through the iterative Newton-Raphson method. Numerical results comprising steady equilibrium...
Improve Performance of Higher Order Statistics in Spatial and Frequency Domains in Blind Image Steganalysis
, M.Sc. Thesis Sharif University of Technology ; Ghaemmaghami, Shahrokh (Supervisor)
Abstract
Blind image steganalysis is a technique used to, which require no prior information about the steganographic method applied to the stego im- age, determine whether the image contains an embedded message or not. The basic idea of blind steganalysis is to extract some features sensitive to information hiding, and then exploit classifiers for judging whether a given test image contains a secret message.The main focus of this research is to design an choose features sen-sitive to the embedding changes. In fact, we use high order moments in different domains, such as spatial, DCT and multi-resolution do-main, in order to improve the performance of existing steganalyzers.Accordingly, First, we...
Edge Disjoint Spanning Trees and Eigenvalues
, M.Sc. Thesis Sharif University of Technology ; Akbari, Saeed (Supervisor)
Abstract
The spectrum of a graph is related to many important combinatorial parameters. Let (G), ′(G) be the maximum number of edge-disjoint spanning trees and edge-connectivity of a graph G,respectively. Motivated by a question of Seymour on the relationship between eigenvalues of a graph G and bounds of (G), we use eigenvalue interlacing for quotient matrix associated to graph to get the relationship between eigenvalues of a graph and bounds of (G) and ′(G). We also study the relationship between eigenvalues and bounds of (G) and ′(G) in a multigraph G. In the first chapter we prove eigenvalue interlacing and give several applications of it for obtaining bounds for characteristic numbers of...
Source Enumeration and Identification in Array Processing Systems
, Ph.D. Dissertation Sharif University of Technology ; Bastani, Mohammad Hasan (Supervisor)
Abstract
Employing array of antennas in amny signal processing application has received considerable attention in recent years due to major advances in design and implementation of large dimentional antennas. In many applications we deal with such large dimentional antennas which challenge the traditional signal processing algorithms. Since most of traditional signal processing algorithms assume that the number of samples is much more than the number of array elements while it is not possible to collect so many samples due to hardware and time constraints.
In this thesis we exploit new results in random matrix theory to charachterize and describe the properties of Sample Covariance Matrices...
In this thesis we exploit new results in random matrix theory to charachterize and describe the properties of Sample Covariance Matrices...
Analysis of Wave Propagation Eigenproblem in Periodic Structures
, Ph.D. Dissertation Sharif University of Technology ; Akbari, Mahmood (Supervisor)
Abstract
The Fourier modal method is one of the most important methods in the analysis of flat periodic structures (gratings). Using this method, the problem of wave propagation in the periodic medium leads to an eigenproblem, in which eigenvalues represent the propagation constants and eigenvector or eigenfunctions determine the filed distribution of the modes. On the other side, considering all the generalizations and modifications reported so far, the Fourier modal method still faces two fundamental problems. First, for problems involving large dielectric constants or high contrasts, the matrix form of the eigenproblem (the modal matrix) can be large, dense, and require a high computational cost....
Main Eigenvalues of Graphs and Signed Graphs
, M.Sc. Thesis Sharif University of Technology ; Akbari, Saeed (Supervisor) ; Ghorbani, Ebrahim (Co-Supervisor)
Abstract
Let G be a simple graph. An eigenvalue of G, is a main eigenvalue if the corresponding eigenspace has a non-orthogonal eigenvector to the all-one vector j. A signed graph is a graph with a sign to each edge. If in the adjacency matrix of background graph change elements that corresponded by -1, set -1 and in the other elements don’t make any change, then we reach the sign matrix of a signed graph. By an eigenvalue of a signed graph, we mean an eigenvalue of its sign matrix. In this research, we study main eigenvalues of graphs and signed graphs. At first, we present the necessary and sufficient conditions for any graph which has exactly m main eigenvalues. Then, by introducing and creating...
Signless Laplacian Spectra of Graphs
, M.Sc. Thesis Sharif University of Technology ; Akbari, Saeed (Supervisor)
Abstract
Let G be a graph of order n. The signless Laplacian matrix or Q-matrix of G is Q(G)=D(G)+A(G), where A(G) is the adjacency matrix of G and D(G) is diagonal degree matrix of G. The signless Laplacian characteristic polynomial or Q-polinomial of G is QG(x)=det(xI-Q(G)) and its roots are called signless Laplacian eigenvalues or Q-eigenvalues of G. If R is vertex-degree incidence matrix of G, then Q(G)=RRt. So Q(G) is a positive semi-definite matrix, i.e. its eigenvalues are none-negative. Let q1(G)≥q2(G)≥…≥qn(G) denote the signless Laplacian eigenvalues of G. A theory in which graphs are studied by means of eigenvalues of Q(G) is called signless Laplaciian theory or Q-theory.In this research,...
Improving the Performance of Graph Filters and Learnable Graph Filters in Graph Neural Networks
, M.Sc. Thesis Sharif University of Technology ; Babaiezadeh, Masoud (Supervisor)
Abstract
Graph signals are sets of values residing on sets of nodes that are connected via edges. Graph Neural Networks (GNNs) are a type of machine learning model for working with graph-structured data, such as graph signals. GNNs have applications in graph classification, node classification, and link prediction. They can be thought of as learnable filters. In this thesis, our focus is on graph filters and enhancing the performance of GNNs. In the first part, we aim to reduce computational costs in graph signal processing, particularly in graph filters. We explore methods to transform signals to the frequency domain with lower computational cost. In the latter part, we examine regulations in...
Collective dynamics of interacting particles in unsteady flows
, Article SIAM Journal on Applied Dynamical Systems ; Vol. 13, Issue. 1 , 2014 , pp. 194-209 ; ISSN: 15360040 ; Jalali, M. A ; Sharif University of Technology
Abstract
We use the Fokker-Planck equation and its moment equations to study the collective behavior of interacting particles in unsteady one-dimensional flows. Particles interact according to a longrange attractive and a short-range repulsive potential field known as Morse potential. We assume Stokesian drag force between particles and their carrier fluid and find analytic single-peaked traveling solutions for the spatial density of particles in the catastrophic phase. In steady flow conditions the streaming velocity of particles is identical to their carrier fluid, but we show that particle streaming is asynchronous with an unsteady carrier fluid. Using linear perturbation analysis, the stability...
Thickness optimization of polyurethane floor insulation based on analysis of the heat transfer in a multi-layer
, Article ASME 2014 12th Biennial Conference on Engineering Systems Design and Analysis, ESDA 2014 ; Vol. 3, issue , 2014 ; Saidi, M. H ; Reshadi, M ; Sharif University of Technology
Abstract
During the year, due to weather conditions, the temperature fluctuations at surface level cause problems in underground pipes as a result of freezing water. One of the best prevention strategies is the use of polyurethane floor insulation for keeping the temperature of clay above zero degrees Celsius. In this study to calculate the minimum thickness of polyurethane insulation layer, the differential equation of energy is solved based on principle of separation of variables using imaginary eigenvalues for consistency with the temperature distribution in multi-layer consist of asphalt, gravel and polyurethane with finite thickness and clay as a semiinfinite medium with periodic thermal...
A new orthonormal polynomial series expansion method in vibration analysis of thin beams with non-uniform thickness
, Article Applied Mathematical Modelling ; Volume 37, Issue 18-19 , 2013 , Pages 8543-8556 ; 0307904X (ISSN) ; Nikkhoo, A ; Vaseghi Amiri, J ; Mehri, B ; Sharif University of Technology
2013
Abstract
In this article, OPSEM (Orthonormal Polynomial Series Expansion Method) is developed as a new computational approach for the evaluation of thin beams of variable thickness transverse vibration. Capability of the OPSEM in assessing the free vibration frequencies and mode shapes of an Euler-Bernoulli beam with varying thickness is discussed. Multispan continuous beams with various classical boundary conditions are included. Contribution of BOPs (Basic Orthonormal Polynomials) in capturing the beam vibrations is also illustrated in numerical examples to give a quantitative measure of convergence rate. Furthermore, OPSEM is adopted for the forced vibration of a thin beam caused by a moving mass....
A novel graphical approach to automatic abstraction in reinforcement learning
, Article Robotics and Autonomous Systems ; Volume 61, Issue 8 , 2013 , Pages 821-835 ; 09218890 (ISSN) ; Beigy, H ; Sharif University of Technology
2013
Abstract
Recent researches on automatic skill acquisition in reinforcement learning have focused on subgoal discovery methods. Among them, algorithms based on graph partitioning have achieved higher performance. In this paper, we propose a new automatic skill acquisition framework based on graph partitioning approach. The main steps of this framework are identifying subgoals and discovering useful skills. We propose two subgoal discovery algorithms, which use spectral analysis on the transition graph of the learning agent. The first proposed algorithm, incorporates k′-means algorithm with spectral clustering. In the second algorithm, eigenvector centrality measure is utilized and options are...