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#### Energy of Graphs

, Ph.D. Dissertation Sharif University of Technology ; 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=...

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 ; 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 ; 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 ; 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 ; 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...

#### 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...

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

, Ph.D. Dissertation Sharif University of Technology ; 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 ; 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 ; 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,...

#### On nodal domains and higher-order Cheeger inequalities of finite reversible Markov processes [electronic resource]

, Article Stochastic Processes and their Applications ; Volume 122, Issue 4, April 2012, Pages 1748–1776 ; Javadi, Ramin ; Miclo, Laurent ; Sharif Univercity of Technology
Abstract

Let LL be a reversible Markovian generator on a finite set View the MathML sourceV. Relations between the spectral decomposition of LL and subpartitions of the state space View the MathML sourceV into a given number of components which are optimal with respect to min–max or max–min Dirichlet connectivity criteria are investigated. Links are made with higher-order Cheeger inequalities and with a generic characterization of subpartitions given by the nodal domains of an eigenfunction. These considerations are applied to generators whose positive rates are supported by the edges of a discrete cycle ZNZN, to obtain a full description of their spectra and of the shapes of their eigenfunctions, as...

#### Robust regulation and tracking system design for multivariable control of the tape transport mechanism

, Article Microsystem Technologies ; Vol. 18, Issue. 5 , 2012 , pp. 557-573 ; ISSN: 09467076 ; Bakhtiari-Nejad, F ; Alasty, A ; Sharif University of Technology
Abstract

Tape mechanisms must be able to transport the tape with a constant velocity for achieving high rate of data transfer. In this paper, a multivariable model of tape transport mechanism including the take-up and supply reel servos for tape tension control and capstan servo for speed control is considered. To achieve desired performance,pole-placement approach based on general canonical control form (GCCF) is used. Instead of using expensive tension sensors, an observer is designed. A regulator system is developed for disturbance rejection; and a modified integral control is designed for perfect tracking of desired setpoints in tape speed and tensions. Since the real dynamic model associates...

#### Performance control of a tape transport mechanism using entire eigenstructure assignment

, Article ASME International Mechanical Engineering Congress and Exposition, Proceedings ; Vol. 10, Issue PART A , 2010 , pp. 133-140 ; ISBN: 9780791843833 ; Hajikolaei, K. H ; Motamedi, M ; Alasty, A ; Sharif University of Technology
Abstract

To achieve high rate of data transfer, tape mechanisms must be able to transport the tape with a constant velocity for scanning. During this process, it is desired to make the rise time minimized without timing and data transfer errors. In this paper, three servo systems including the take-up and supply reel servos for tape tension control and capstan servo for speed control are considered. So, tape transport mechanisms can be described with a nonlinear multi-input multi-output system (MIMO). After state-space representation of the problem, feedback control is designed for tracking objective. It should be mentioned that an increase in the speed of time response of system corresponds to an...

#### Connectedness of users-items networks and recommender systems

, Article Applied Mathematics and Computation ; Vol. 243 , 2014 , Pages 578-584 ; ISSN: 00963003 ; Jalili, M ; Sharif University of Technology
Abstract

Recommender systems have become an important issue in network science. Collaborative filtering and its variants are the most widely used approaches for building recommender systems, which have received great attention in both academia and industry. In this paper, we studied the relationship between recommender systems and connectivity of users-items bipartite network. This results in a novel recommendation algorithm. In our method recommended items are selected based on the eigenvector corresponding to the algebraic connectivity of the graph - the second smallest eigenvalue of the Laplacian matrix. Since recommending an item to a user equals to adding a new link to the users-items bipartite...

#### Optimal ground state energy of two-phase conductors

, Article Electronic Journal of Differential Equations ; Vol. 2014 , 2014 ; ISSN: 10726691 ; Yousefnezhad, M ; Sharif University of Technology
Abstract

We consider the problem of distributing two conducting materials in a ball with xed proportion in order to minimize the rst eigenvalue of a Dirichlet operator. It was conjectured that the optimal distribution consists of putting the material with the highest conductivity in a ball around the center. In this paper, we show that the conjecture is false for all dimensions greater than or equal to two

#### The effects of nonlinearities on the vibration of viscoelastic sandwich plates

, Article International Journal of Non-Linear Mechanics ; Vol. 62 , 2014 , Pages 41-57 ; ISSN: 00207462 ; Haddadpour, H ; Navazi, H. M ; Sharif University of Technology
Abstract

The nonlinear free and forced bending vibration of sandwich plates with incompressible viscoelastic core is investigated under the effects of different source of nonlinearities. For the core constrained between stiffer layers, the transverse shear strains, as well as the rotations are assumed to be moderate. The linear and quadratic displacement fields are also adopted for the in-plane and out-of-plane displacements of the core, respectively. The assumption of moderate transverse strains requires a nonlinear constitutive equation which is obtained from a single-integral nonlinear viscoelastic model using the assumed order of magnitudes for linear strains and rotations. The 5th-order method...

#### The multiplicity of Laplacian eigenvalue two in unicyclic graphs

, Article Linear Algebra and Its Applications ; Vol. 445 , 2014 , pp. 18-28 ; Kiani, D ; Mirzakhah, M ; Sharif University of Technology
Abstract

Let G be a graph and L(G) be the Laplacian matrix of G. In this paper, we explicitly determine the multiplicity of Laplacian eigenvalue 2 for any unicyclic graph containing a perfect matching