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#### Photonic crystal devices analysis based on perturbation theory

, Article Photonic Crystal Materials and Devices IV, San Jose, CA, 23 January 2006 through 26 January 2006 ; Volume 6128 , 2006 ; 0277786X (ISSN); 0819461709 (ISBN); 9780819461704 (ISBN) ; Khorasani, S ; Atabaki, A ; SPIE ; Sharif University of Technology
2006

Abstract

A novel approach for photonic crystals devices analysis, based on perturbation theory is reported. In this method the photonic crystal device is considered as the superposition of a parent lattice and a perturbing one. Then the solution is investigated in terms of the eigensolutions of the parent lattice. This way, one can easily obtain analytic expressions within the first order perturbation, describing the effects of different parameters on the eigensolutions of the structure. The perturbation theory employed in this work is typical of what is conventionally used in quantum mechanics literature. The proposed method is explicit, works fast, and does not involve complicated numerical...

#### A real-time, low-power implementation for high-resolution eigenvalue-based spectrum sensing

, Article Analog Integrated Circuits and Signal Processing ; Volume 77, Issue 3 , December , 2013 , Pages 437-447 ; 09251030 (ISSN) ; Shabany, M ; Sharif University of Technology
2013

Abstract

In this paper, a novel multiple antenna, high-resolution eigenvalue-based spectrum sensing algorithm based on the FFT of the received signal is introduced. The proposed platform overcomes the SNR wall problem in the conventional energy detection (ED) algorithm, enabling the detection of the weak signals at -10 dB SNR. Moreover, the utilization of FFT for the input signal channelization provides a simple, low-power design for a high-resolution spectrum sensing regime. A real-time, low-area, and low-power VLSI architecture is also developed for the algorithm, which is implemented in a 0.18 μm CMOS technology. The implemented design is the first eigenvalue-based detection (EBD) architecture...

#### Noise cancelation of epileptic interictal EEG data based on generalized eigenvalue decomposition

, Article 2012 35th International Conference on Telecommunications and Signal Processing, TSP 2012 - Proceedings ; 2012 , Pages 591-595 ; 9781467311182 (ISBN) ; Shamsollahi, M. B ; Albera, L ; Merlet, I ; Sharif University of Technology
2012

Abstract

Denoising is an important preprocessing stage in some Electroencephalography (EEG) applications such as epileptic source localization. In this paper, we propose a new algorithm for denoising the interictal EEG data. The proposed algorithm is based on Generalized Eigenvalue Decomposition of two covariance matrices of the observations. Since one of these matrices is related to the spike durations, we should estimate the occurrence time of the spike peaks and the exact spike durations. To this end, we propose a spike detection algorithm which is based on the available spike detection methods. The comparison of the results of the proposed algorithm with the results of two well-known ICA...

#### On nodal domains and higher-order Cheeger inequalities of finite reversible Markov processes

, Article Stochastic Processes and their Applications ; Volume 122, Issue 4 , April , 2012 , Pages 1748-1776 ; 03044149 (ISSN) ; Javadi, R ; Miclo, L ; Sharif University of Technology
2012

Abstract

Let L be a reversible Markovian generator on a finite set V. Relations between the spectral decomposition of L and subpartitions of the state space V 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 Z N, to obtain a full description of their spectra and of the shapes of their eigenfunctions, as well as an interpretation of the spectrum...

#### An innovative implementation of Circular Hough Transform using eigenvalues of Covariance Matrix for detecting circles

, Article Proceedings Elmar - International Symposium Electronics in Marine, 14 September 2011 through 16 September 2011, Zadar ; 2011 , Pages 397-400 ; 13342630 (ISSN) ; 9789537044121 (ISBN) ; Mianroodi, J. R ; Norouzi, N ; Khajooeizadeh, A ; Sharif University of Technology
2011

Abstract

In this paper, a fast and accurate algorithm for identifying circular objects in images is proposed. The presented method is a robust, fast and optimized adaption of Circular Hough Transform (CHT), Eigenvalues of Covariance Matrix and K-means clustering techniques. Results are greatly improved by implementing iterative K-means clustering algorithm and establishing an exponential growth instead of updating values in the parameter space of CHT through summation, both in runtime and quality. In fact, using the Eigenvalues of Covariance Matrix as a validating method, a well balanced compromise between the speed and accuracy of results is achieved. This method is tested on several real world...

#### An analytic methodology to determine generators redispatch for proactive damping of critical electromechanical oscillations

, Article International Journal of Electrical Power and Energy Systems ; Volume 123 , 2020 ; Parniani, M ; Aminifar, F ; Sharif University of Technology
Elsevier Ltd
2020

Abstract

This paper presents a model-based method for applying online proactive generators redispatch to improve damping of the critical electromechanical oscillations of power system. The proposed method comprises two stages: 1) monitoring modal characteristics of oscillatory modes in ambient condition, and 2) applying generators redispatch based on sensitivities of the critical mode to the generators active power changes using a new analytic method. An online identification method such as error feedback lattice recursive least square adaptive filter is applied for online estimation of the oscillatory modes. Then, whenever the damping ratio of an identified mode is less than a preset threshold, its...

#### 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...

#### 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...

#### 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...

#### The electro-elastic scattered fields of an SH-wave by an eccentric two-phase circular piezoelectric sensor in an unbounded piezoelectric medium

, Article Mechanics of Materials ; Vol. 75 , 2014 , pp. 1-12 ; ISSN: 01676636 ; Jarfi, H ; Rashidinejad, E ; Sharif University of Technology
Abstract

The dynamic equivalent inclusion method (DEIM) which was first proposed by Fu and Mura (1983), in its original context has some shortcomings, which were pointed out and remedied by Shodja and Delfani (2009) who introduced the new consistency conditions along with the related micromechanically substantiated notion of eigenstress and eigenbody-force fields. However, these theories are bound to elastic media with isotropic phases. The present work extends the idea of the above-mentioned new DEIM to the dynamic electro-mechanical equivalent inclusion method (DEMEIM) for the treatment of the scattering of SH-waves by a two-phase circular piezoelectric obstacle bonded to a third phase...

#### Limiting spectral distribution of the sample covariance matrix of the windowed array data

, Article Eurasip Journal on Advances in Signal Processing ; Volume 2013, Issue 1 , 2013 ; 16876172 (ISSN) ; Gazor, S ; Bastani, M. H ; Sharif University of Technology
2013

Abstract

In this article, we investigate the limiting spectral distribution of the sample covariance matrix (SCM) of weighted/windowed complex data. We use recent advances in random matrix theory and describe the distribution of eigenvalues of the doubly correlated Wishart matrices. We obtain an approximation for the spectral distribution of the SCM obtained from windowed data. We also determine a condition on the coefficients of the window, under which the fragmentation of the support of noise eigenvalues can be avoided, in the noise-only data case. For the commonly used exponential window, we derive an explicit expression for the l.s.d of the noise-only data. In addition, we present a method to...

#### A heterogeneous diffusive logistic model of a single species population dynamics with predation and harvesting terms

, Article Nonlinear Analysis, Theory, Methods and Applications ; Volume 156 , 2017 , Pages 1-16 ; 0362546X (ISSN) ; Torabi Tehrani, H ; Sharif University of Technology
Abstract

We study existence and multiplicity of positive solutions of a heterogeneous diffusive logistic equation with predation and harvesting terms, −Δu=au−b(x)u2−c, where a,c,m and d are positive constants, Ω a bounded smooth domain in RN, and b(x) is a nonnegative function on Ω¯, with Ω0 a region such that Ω¯0⊂Ω and Ω¯0={x∈Ω:b(x)=0}. Under the strong growth rate assumption, that is, when a is greater than the first eigenvalue of −Δ in Ω0 with Dirichlet boundary condition, we show that the equation has at least one positive solution for 0≤d0. In addition, in case c

#### Rewirings based on the eigenvectors of the laplacian matrix for enhancing synchronizability of dynamical networks

, Article 2009 7th IEEE International Conference on Industrial Informatics, INDIN 2009, Cardiff, 23 June 2009 through 26 June 2009 ; 2009 , Pages 588-593 ; 19354576 (ISSN); 9781424437603 (ISBN) ; Ajdari Rad, A ; Sharif University of Technology
2009

Abstract

Synchronizability of dynamical networks can be defined as the ease by which the network synchronizes its activity. We propose a method for enhancing the synchronizability of dynamical networks by efficient rewirings. The method is based on the eigenvectors corresponding to the second smallest and the largest eigenvalue of the Laplacian matrix and a modified version of the simulated annealing approach is used to perform the optimization task. Starting from a simple network, i.e. an undirected and unweighted network, and at each step, an edge is selected for disconnection and two non-adjacent nodes for creating at edge in between. The effectiveness of the algorithm is tested on artificially...

#### Application of the modified reduced-order aerodynamics modelling approach to aeroelastic analysis

, Article Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering ; Volume 223, Issue 3 , 2009 , Pages 257-270 ; 09544100 (ISSN) ; Salehzadeh Nobari, A ; Haddadpour, H ; Behbahani Nejad, M ; Sharif University of Technology
2009

Abstract

This study presents the application of the Proposed Modified Reduced-Order Aerodynamics Modelling approach for aeroelastic analysis based on the boundary element method (BEM) as a novel approach. The used BEM has the capability to capture the thickness effect and geometric complexity of a general three-dimensional model. In this approach the reduced-order aerodynamic model is defined through the eigenvalue problem of unsteady flow based on the unknown wake singularities. Based on the used aerodynamic model an explicit algebraic form of the aeroelastic equations is derived that reduces computational efforts and complexity. This special feature enables us to determine the aeroelastic...

#### Strong structural controllability of signed networks

, Article 58th IEEE Conference on Decision and Control, CDC 2019, 11 December 2019 through 13 December 2019 ; Volume 2019-December , 2019 , Pages 4557-4562 ; 07431546 (ISSN); 9781728113982 (ISBN) ; Haeri, M ; Mesbahi, M ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2019

Abstract

In this paper, we discuss the controllability of a family of linear time-invariant (LTI) networks defined on a signed graph. In this direction, we introduce the notion of positive and negative signed zero forcing sets for the controllability analysis of positive and negative eigenvalues of system matrices with the same sign pattern. A sufficient combinatorial condition that ensures the strong structural controllability of signed networks is then proposed. Moreover, an upper bound on the maximum multiplicity of positive and negative eigenvalues associated with a signed graph is provided. © 2019 IEEE

#### On the minimum energy of regular graphs

, Article Linear Algebra and Its Applications ; Volume 581 , 2019 , Pages 51-71 ; 00243795 (ISSN) ; Akbari, S ; Ghasemian, E ; Ghodrati, A. H ; Hosseinzadeh, M. A ; Koorepazan Moftakhar, F ; Sharif University of Technology
Elsevier Inc
2019

Abstract

The energy of a graph G, E(G), is the sum of absolute values of the eigenvalues of its adjacency matrix. Gutman et al. proved that for every cubic graph of order n, E(G)≥n. Here, we improve this result by showing that if G is a connected subcubic graph of order n≥8, then E(G)≥1.01n. Also, we prove that if G is a traceable subcubic graph of order n≥8, then E(G)>1.1n. Let G be a connected cubic graph of order n≥8, it is shown that E(G)>n+2. It was proved that if G is a connected cubic graph of order n, then E(G)≤1.65n. Also, in this paper we would like to present the best lower bound for the energy of a connected cubic graph. We introduce an infinite family of connected cubic graphs whose for...

#### Choice number and energy of graphs

, Article Linear Algebra and Its Applications ; Volume 429, Issue 11-12 , 2008 , Pages 2687-2690 ; 00243795 (ISSN) ; Ghorbani, E ; Sharif University of Technology
2008

Abstract

The energy of a graph G, denoted by E (G), is defined as the sum of the absolute values of all eigenvalues of the adjacency matrix of G. It is proved that E (G) ≥ 2 (n - χ (over(G, -))) ≥ 2 (ch (G) - 1) for every graph G of order n, and that E (G) ≥ 2 ch (G) for all graphs G except for those in a few specified families, where over(G, -), χ (G), and ch (G) are the complement, the chromatic number, and the choice number of G, respectively. © 2007 Elsevier Inc. All rights reserved

#### On eigensharp and almost eigensharp graphs

, Article Linear Algebra and Its Applications ; Volume 429, Issue 11-12 , 2008 , Pages 2746-2753 ; 00243795 (ISSN) ; Maimani, H. R ; Sharif University of Technology
2008

Abstract

The minimum number of complete bipartite subgraphs needed to partition the edges of a graph G is denoted by b (G). A known lower bound on b (G) states that b (G) ≥max {p (G), q (G)}, where p (G) and q (G) are the numbers of positive and negative eigenvalues of the adjacency matrix of G, respectively. When equality is attained, G is said to be eigensharp and when b (G) = max {p (G), q (G)} + 1, G is called an almost eigensharp graph. In this paper, we investigate the eigensharpness of graphs with at most one cycle and products of some families of graphs. Among the other results, we show that Pm ∨ Pn, Cm ∨ Pn for m ≡ 2, 3 (mod 4) and Qn when n is odd are eigensharp. We obtain some results on...