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    Energy of Graphs

    , Ph.D. Dissertation Sharif University of Technology Ghorbani, Ebrahim (Author) ; Akbari, Saeid (Supervisor)
    Abstract
    Let G be a graph with adjacency matrix A and Δ be a diagonal matrix whose diagonal entries are the degree sequence of G. Then the matrices L = Δ− A and Q = Δ+A are called Laplacian matrix and signless Laplacian matrix of G, respectively. The eigenvalues of A, L, and Q are arranged decreasingly and denoted by λ1 ≥ · · · ≥ λn, μ1 ≥ · · · ≥ μn ≥ 0, and q1 ≥ · · · ≥ qn ≥ 0, respectively. The energy of a graph G is defined as E(G) :=
    n
    i=1
    |λi|.
    Furthermore, the incidence energy, the signed incidence energy, and the H¨uckel energy of G are
    defined as
    IE(G) :=
    n
    i=1

    qi, LE(G) :=
    n
    i=1

    μi, HE(G) :=

    2
    r
    i=1 λi, n=... 

    MIMO Radars Waveform Design

    , M.Sc. Thesis Sharif University of Technology Shadi, Kamal (Author) ; Behnia, F (Supervisor)
    Abstract
    MIMO radar is a next generation radar which transmits arbitrary waveforms at each one of its apertures. It has been shown that design of waveforms for MIMO radars in order to synthesize a desired spatial beampattern, is mapped into a waveform correlation matrix (R) design in the narrowband case. Therefore, waveform design in MIMO radar for beamforming could be broken into two steps, namely correlation matrix design and waveform synthesis for achieving given R. As of now, given a desired beampattern or estimated location information of targets, calculating R has been modeled as an optimization problem like SDP. Also, in some special cases like rectangular beampattern, close form solutions for... 

    Blind Steganalysis Based on Multi- resolution Transforms

    , M.Sc. Thesis Sharif University of Technology Zohourian, Mehdi (Author) ; Ghaemmaghami, Shahrokh (Supervisor) ; Gholampour, Iman (Supervisor)
    Abstract
    Blind image steganalysis is a technique used for detecting the existence of the data hidden in an image, where no information about the stenographic algorithm is available or usable. In this way, an important problem is to find sensitive features which make noticeable statistical distinction between cover and stego images. New steganalysis methods based on multi-resolution transform, specifically the wavelet and the contourlet transforms, have been proposed in this thesis in order to enhance the detection accuracy of system especially at low embedding rates. In fact, multi-resolution transforms are powerful space-frequency analysis tools that have been found quite successful in detection of... 

    Control of Chaotic Waves in Hard Disk Drives

    , M.Sc. Thesis Sharif University of Technology Rajabi, Majid (Author) ; Jalali, Mir Abbas (Supervisor)
    Abstract
    Hard disk drives are the main component of computers for permanent data storage. The security of the stored data is related closely to the air gap between the read-write head and the surface of disk. This gap which is created by the aerodynamic force between head and the disk is altered continually by lateral oscillations of disk. In the extreme condition of zero gap and contact between the protective coating layer and subsequently the magnetic material of the disk with the head, the disk will be scratched and damaged. Therefore, the active or passive control of these vibrations has a particular importance in the technology of manufacturing of hard disks. The first step in active control... 

    On Treewidth of Social Networks

    , M.Sc. Thesis Sharif University of Technology Liaee, Mehraneh (Author) ; Safari, Mohammad Ali (Supervisor) ; Habibi, Jafar (Supervisor)
    Abstract
    In this thesis, we study the treewidth of social networks. The importance of studding treewidth is for two reasons. The first is that for the graph with bounded treewidth, many optimization problems that are NP-hard in general, can be solved in polynomial or even linear time. The second is that the high value of treewidth in a graph, reflects some high degree of connectivity and robustness, which is an essential factor in designing many networks. But the problem is that determining the value of treewidth in a graph is NP-complete so, computing the treewidth of real complex networks is not feasible. We first review the related works and mention the weakness of the past works, then introduce a... 

    Damping Critical Electromechanical Oscillations in Power System Through Remedial Actions Using Wide Area Measurement System (WAMS)

    , Ph.D. Dissertation Sharif University of Technology Setareh, Mohammad (Author) ; Parniani, Mostafa (Supervisor) ; Aminifar, Farrokh (Co-Supervisor)
    Abstract
    Nowadays, by proliferation the basis of the phasor-based synchronous wide area measurement system (WAMS), its application for improving electromechanical oscillations damping has been considered by researchers. In interconnected power systems, inter-area modes are usually critical modes. There are two approaches for damping these modes by utilizing WAMS: 1) the traditional approach of using power system stabilizers with wide area signals; and 2) discrete corrective actions by changing the operating conditions. The first approach requires a thorough study at the design stage, installation and testing. Besides, the controller is designed for a specific operating point. Nevertheless, in the... 

    Image Steganalysis of Low Rate Embedding in Spatial Domain

    , Ph.D. Dissertation Sharif University of Technology Farhat, Farshid (Author) ; Ghaemmaghami, Shahrokh (Supervisor) ; Aref, Mohammad Reza (Co-Advisor)
    Abstract
    LSB embedding in spatial domain with very low rate can be easily performed and its detection in spite of many researches is very hard, while BOSS competition has been held to break an adaptive embedding algorithm with low rate. Thus, proposing powerful steganalyzer of very low rate in spatial domain is highly requested. In this thesis it has been tried to present some algorithms to detect secret message with very low rate in spatial domain using eigenvalues analysis and relative auto-correlation of image.First approach is based on the analysis of the eigenvalues of the cover correlation matrix that we used for the first time. Image partitioning, correlation function computation,... 

    Edge Disjoint Spanning Trees and Eigenvalues

    , M.Sc. Thesis Sharif University of Technology Mehdizadeh, Alireza (Author) ; 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 Yazdian, Ehsan (Author) ; 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... 

    Main Eigenvalues of Graphs and Signed Graphs

    , M.Sc. Thesis Sharif University of Technology Kamali, Sara (Author) ; 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 Kianizad, Mosayeb (Author) ; 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,... 

    Improve Performance of Higher Order Statistics in Spatial and Frequency Domains in Blind Image Steganalysis

    , M.Sc. Thesis Sharif University of Technology Shakeri, Ehsan (Author) ; 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... 

    Analysis of Wave Propagation Eigenproblem in Periodic Structures

    , Ph.D. Dissertation Sharif University of Technology Faghihifar, Ehsan (Author) ; 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.... 

    Dynamic response of thin plates on time-varying elastic point supports

    , Article Structural Engineering and Mechanics ; Volume 62, Issue 4 , 2017 , Pages 431-441 ; 12254568 (ISSN) Foyouzat, M. A ; Estekanchia, H. E ; Sharif University of Technology
    Techno Press  2017
    Abstract
    In this article, an analytical-numerical approach is presented in order to determine the dynamic response of thin plates resting on multiple elastic point supports with time-varying stiffness. The proposed method is essentially based on transforming a familiar governing partial differential equation into a new solvable system of linear ordinary differential equations. When dealing with time-invariant stiffness, the solution of this system of equations leads to a symmetric matrix, whose eigenvalues determine the natural frequencies of the point-supported plate. Moreover, this method proves to be applicable for any plate configuration with any type of boundary condition. The results, where... 

    Stability of linear dynamic systems over the packet erasure channel: A co-design approach

    , Article International Journal of Control ; Volume 88, Issue 12 , May , 2015 , Pages 2488-2498 ; 00207179 (ISSN) Farhadi, A ; Sharif University of Technology
    Taylor and Francis Ltd  2015
    Abstract
    This paper is concerned with the stability of linear time-invariant dynamic systems over the packet erasure channel subject to minimum bit rate constraint when an encoder and a decoder are unaware of the control signal. This assumption results in co-designing the encoder, decoder and controller. The encoder, decoder, controller and conditions relating transmission rate to packet erasure probability and eigenvalues of the system matrix A are presented for almost sure asymptotic stability of linear time-invariant dynamic systems over the packet erasure channel with feedback acknowledgment. When the eigenvalues of the system matrix A are real valued, it is shown that the obtained condition for... 

    A note on the algebraic connectivity of a graph and its complement

    , Article Linear and Multilinear Algebra ; 2019 ; 03081087 (ISSN) Afshari, B ; Akbari, S ; Sharif University of Technology
    Taylor and Francis Ltd  2019
    Abstract
    For a graph G, let λ2(G) denote its second smallest Laplacian eigenvalue. It was conjectured that (Formula presented.), where (Formula presented.) is the complement of G. In this paper, it is shown that (Formula presented.). © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group  

    A note on the algebraic connectivity of a graph and its complement

    , Article Linear and Multilinear Algebra ; 2019 ; 03081087 (ISSN) Afshari, B ; Akbari, S
    Taylor and Francis Ltd  2019
    Abstract
    For a graph G, let λ2(G) denote its second smallest Laplacian eigenvalue. It was conjectured that (Formula presented.), where (Formula presented.) is the complement of G. In this paper, it is shown that (Formula presented.). © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group  

    On edge-path eigenvalues of graphs

    , Article Linear and Multilinear Algebra ; 2020 Akbari, S ; Azizi, S ; Ghorbani, M ; Li, X ; Sharif University of Technology
    Taylor and Francis Ltd  2020
    Abstract
    Let G be a graph with vertex set (Formula presented.) and (Formula presented.) be an (Formula presented.) matrix whose (Formula presented.) -entry is the maximum number of internally edge-disjoint paths between (Formula presented.) and (Formula presented.), if (Formula presented.), and zero otherwise. Also, define (Formula presented.), where D is a diagonal matrix whose i-th diagonal element is the number of edge-disjoint cycles containing (Formula presented.), whose (Formula presented.) is a multiple of J−I. Among other results, we determine the spectrum and the energy of the matrix (Formula presented.) for an arbitrary bicyclic graph G. © 2020 Informa UK Limited, trading as Taylor &... 

    Linear spatial stability analysis of particle-laden stratified shear layers

    , Article Journal of the Brazilian Society of Mechanical Sciences and Engineering ; Volume 41, Issue 6 , 2019 ; 16785878 (ISSN) Khavasi, E ; Firoozabadi, B ; Sharif University of Technology
    Springer Verlag  2019
    Abstract
    Hydrodynamic instabilities at the interface of stratified shear layers could occur in various modes. These instabilities have an important role in the mixing process. In this work, the linear stability analysis in spatial framework is used to study the stability characteristics of a particle-laden stratified two-layer flow. The effect of parameters such as velocity-to-density thickness ratio, bed slope, viscosity as well as particle size on the stability is considered. A simple iterative method applying the pseudospectral collocation method that employed Chebyshev polynomials is used to solve two coupled eigenvalue equations. Based on the results, the flow becomes stable for Richardson... 

    Bridged single-walled carbon nanotube-based atomic-scale mass sensors

    , Article Applied Physics A: Materials Science and Processing ; Volume 122, Issue 8 , Volume 122, Issue 8 , 2016 ; 09478396 (ISSN) Ali Akbari, H. R ; Shaat, M ; Abdelkefi, A ; Sharif University of Technology
    Springer Verlag 
    Abstract
    The potentials of carbon nanotubes (CNTs) as mechanical resonators for atomic-scale mass sensing are presented. To this aim, a nonlocal continuum-based model is proposed to study the dynamic behavior of bridged single-walled carbon nanotube-based mass nanosensors. The carbon nanotube (CNT) is considered as an elastic Euler–Bernoulli beam with von Kármán type geometric nonlinearity. Eringen’s nonlocal elastic field theory is utilized to model the interatomic long-range interactions within the structure of the CNT. This developed model accounts for the arbitrary position of the deposited atomic-mass. The natural frequencies and associated mode shapes are determined based on an eigenvalue...