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#### Source enumeration in large arrays using moments of eigenvalues and relatively few samples

, Article IET Signal Processing ; Volume 6, Issue 7 , 2012 , Pages 689-696 ; 17519675 (ISSN) ; Gazor, S ; Bastani, H ; Sharif University of Technology
IET
2012

Abstract

This study presents a method based on minimum description length criterion to enumerate the incident waves impinging on a large array using a relatively small number of samples. The proposed scheme exploits the statistical properties of eigenvalues of the sample covariance matrix (SCM) of Gaussian processes. The authors use a number of moments of noise eigenvalues of the SCM in order to separate noise and signal subspaces more accurately. In particular, the authors assume a Marcenko-Pastur probability density function (pdf) for the eigenvalues of SCM associated with the noise subspace. We also use an enhanced noise variance estimator to reduce the bias leakage between the subspaces....

#### Hippocampal shape analysis in the Laplace Beltrami feature space for temporal lobe epilepsy diagnosis and lateralization

, Article Proceedings - International Symposium on Biomedical Imaging ; 2012 , Pages 150-153 ; 19457928 (ISSN) ; 9781457718588 (ISBN) ; Gandomkar, Z ; Soltaman Zadeh, H ; Moghadasi, S. R ; Sharif University of Technology
IEEE
2012

Abstract

Shape analysis plays an important role in many medical imaging studies. One of the recent shape analysis methods uses the Laplace Beltrami operator which is also used in this paper for hippocampal shape comparison. We proposed a feature vector which consists of size measures and shape descriptors based on Laplace Beltrami eigenvalues and eigenfunctions. The aforementioned feature space is utilised for automatic differentiating normal subjects from epileptic patients as well as distinguishing epileptic patients with left temporal lobe epilepsy (LTLE) from patients with right temporal lobe epilepsy (RTLE). Achieved results are diagnostic accuracy of 93% with 95% sensitivity and lateralization...

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

, Article Microsystem Technologies ; Volume 18, Issue 5 , 2012 , Pages 557-573 ; 09467076 (ISSN) ; Bakhtiari Nejad, F ; Alasty, A ; Sharif University of Technology
2012

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...

#### 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...

#### Equations-of-motion method for triplet excitation operators in graphene

, Article Journal of Physics Condensed Matter ; Volume 24, Issue 9 , February , 2012 ; 09538984 (ISSN) ; Baskaran, G ; Sharif University of Technology
2012

Abstract

The particlehole continuum in the Dirac sea of graphene has a unique window underneath, which in principle leaves room for bound state formation in the triplet particlehole channel (Baskaran and Jafari 2002 Phys. Rev. Lett. 89 016402). In this work, we construct appropriate triplet particlehole operators and, using a repulsive Hubbard-type effective interaction, we employ equations of motion to derive approximate eigenvalue equations for such triplet operators. While the secular equation for the spin density fluctuations gives rise to an equation which is second order in the strength of the short range interaction, the explicit construction of the triplet operators obtained here shows that,...

#### Assessment of three preconditioning schemes for solution of the two-dimensional Euler equations at low Mach number flows

, Article International Journal for Numerical Methods in Engineering ; Volume 89, Issue 1 , 2012 , Pages 20-52 ; 00295981 (ISSN) ; Kamali Moghadam, R ; Sharif University of Technology
Abstract

Three preconditioners proposed by Eriksson, Choi and Merkel, and Turkel are implemented in a 2D upwind Euler flow solver on unstructured meshes. The mathematical formulations of these preconditioning schemes for different sets of primitive variables are drawn, and their eigenvalues and eigenvectors are compared with each other. For this purpose, these preconditioning schemes are expressed in a unified formulation. A cell-centered finite volume Roe's method is used for the discretization of the preconditioned Euler equations. The accuracy and performance of these preconditioning schemes are examined by computing steady low Mach number flows over a NACA0012 airfoil and a two-element...

#### A comparative study of two preconditioners for solving 3D inviscid low speed flows

, Article Applied Mechanics and Materials ; Volume 110-116 , 2012 , Pages 423-430 ; 16609336 (ISSN) ; 9783037852620 (ISBN) ; Moghadam, R. K ; Sharif University of Technology
2012

Abstract

In the present study, two preconditioners proposed by Eriksson, and Choi and Merkel are implemented on a 3D upwind Euler flow solver on unstructured meshes. The mathematical formulations of these preconditioning schemes for the set of primitive variables Q→p 1=[ρ u v , w p] T are drawn and their eigenvalues and eigenvectors are compared with each others. A cell-centered finite volume Roe's method is used for discretization of the 3D preconditioned Euler equations. The accuracy and performance of these preconditioning schemes are examined by computing low Mach number flows over the ONERA M6 wing for different conditions

#### Graetz problem extended to mixed electroosmotically and pressure-driven flow

, Article Journal of Thermophysics and Heat Transfer ; Volume 26, Issue 1 , 2012 , Pages 123-133 ; 08878722 (ISSN) ; Veisi, H ; Saidi, M. H ; Chakraborty, S ; Sharif University of Technology
2012

Abstract

Thermally developing mixed electroosmotically and pressure-driven flow in a parallel plate microchannel with a step change in wall temperature is considered in the framework of an extended Graetz problem. Both Joule heating and viscous dissipation effects are taken into consideration. Expressions for the dimensionless temperature and Nusselt number in the form of infinite series are presented. In general, the associated eigenvalue problem is solved numerically. Nevertheless, an analytical solution is also presented for axial locations close to the entrance. Comparisons are made between the present results and those obtained by approximating the electroosmotic velocity with the...

#### Parametric study of the dynamic response of thin rectangular plates traversed by a moving mass

, Article Acta Mechanica ; Volume 223, Issue 1 , September , 2012 , Pages 15-27 ; 00015970 (ISSN) ; Rofooei, F. R ; Sharif University of Technology
2012

Abstract

The governing differential equation of motion of a thin rectangular plate excited by a moving mass is considered. The moving mass is traversing on the plate's surface at arbitrary trajectories. Eigenfunction expansion method is employed to solve the constitutive equation of motion for various boundary conditions. Approximate and exact expressions of the inertial effects are adopted for the problem formulation. In the approximate formulation, only the vertical acceleration component of the moving mass is considered while in the exact formulation all the convective acceleration components are included in the problem formulation as well. Parametric studies are carried out to investigate the...

#### Conformal upper bounds for the eigenvalues of the Laplacian and Steklov problem

, Article Journal of Functional Analysis ; Volume 261, Issue 12 , 2011 , Pages 3419-3436 ; 00221236 (ISSN) ; Sharif University of Technology
2011

Abstract

In this paper, we find upper bounds for the eigenvalues of the Laplacian in the conformal class of a compact Riemannian manifold (M,g). These upper bounds depend only on the dimension and a conformal invariant that we call "min-conformal volume". Asymptotically, these bounds are consistent with the Weyl law and improve previous results by Korevaar and Yang and Yau. The proof relies on the construction of a suitable family of disjoint domains providing supports for a family of test functions. This method is interesting for itself and powerful. As a further application of the method we obtain an upper bound for the eigenvalues of the Steklov problem in a domain with C1 boundary in a complete...

#### Free vibration analysis of FGM beams with different boundary conditions using RKPM meshless method

, Article Proceedings of the ASME Design Engineering Technical Conference, 28 August 2011 through 31 August 2011 ; Volume 1, Issue PARTS A AND B , August , 2011 , Pages 1187-1191 ; 9780791854785 (ISBN) ; Ahmadian, M. T ; Sharif University of Technology
Abstract

This paper presents free vibration analysis of functionally graded material (FGM) beams with different boundary conditions, using RKPM (Reproducing Kernel Particle Method), which is a meshless method. System of equations of motion is derived by using Lagrange's method under the assumption of Euler-Bernoulli beam theory. Boundary conditions of beam are taken into account by using Lagrange multipliers. It is assumed that material properties of the beam vary continuously in the thickness direction according to the power-law form. RKPM is applied to obtain eigenvalue equation of vibration and natural frequencies are obtained. It should be noted that for special cases where the beam is uniform,...

#### Transmit beampattern synthesis using eigenvalue decomposition in MIMO radar

, Article ICICS 2011 - 8th International Conference on Information, Communications and Signal Processing, 13 December 2011 through 16 December 2011 ; December , 2011 , Page(s): 1 - 5 ; 9781457700309 (ISBN) ; Behnia, F ; Sharif University of Technology
2011

Abstract

MIMO radar is the 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. Searching for desired R has been modeled as a convex optimization problem which demands considerable processing power. There are also some close form solutions for special cases like rectangular beampatterns. Here we deal with the problem from a matrix eigenvalue theory perspective and show how close form solutions can be found for more general cases relaxing high computational power demand. Our...

#### 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...

#### Recursive spectral analysis of natural time series based on eigenvector matrix perturbation for online applications

, Article IET Signal Processing ; Volume 5, Issue 6 , 2011 , Pages 515-526 ; 17519675 (ISSN) ; Lucas, C ; Araabi, B. N ; Moshiri, B ; Bidar, M. R ; Sharif University of Technology
2011

Abstract

Singular spectrum analysis (SSA) is a well-studied approach in signal processing. SSA has originally been designed to extract information from short noisy chaotic time series and to enhance the signal-to-noise ratio. SSA is good for offline applications; however, many applications, such as modelling, analysis, and prediction of time-varying and non-stationary time series, demand for online analysis. This study introduces a recursive algorithm called recursive SSA as a modification to regular SSA for dynamic and online applications. The proposed method is based on eigenvector matrix perturbation approach. After recursively calculating the covariance matrix of the trajectory matrix, R-SSA...

#### Hippocampal shape analysis in epilepsy using Laplace-Beltrami spectrum

, Article 2011 19th Iranian Conference on Electrical Engineering, ICEE 2011, 17 May 2011 through 19 May 2011 ; May , 2011 , Page(s): 1 - 5 ; ISSN : 21647054 ; 9789644634284 (ISBN) ; Soltanian Zadeh, H ; Moghadasi, S. R ; Sharif University of Technology
2011

Abstract

Shape analysis plays an important role in many medical imaging studies. One of the recent shape analysis methods uses the Laplace Beltrami eigenvalues which is also used in this paper for global shape comparison of hippocampus of normal subjects and epileptic patients. Popularity of the Laplace Beltrami operator in this field is due to its isometry-invariance which avoids pre-processing steps like mapping, registration, and alignment. In addition, it is capable of revealing fine details in shapes that makes this method a good choice for deformation detecting purposes like epilepsy diagnosis. To examine capability of the proposed method, statistical analysis and two ways of classification,...

#### On edge star sets in trees

, Article Discrete Mathematics ; Volume 311, Issue 13 , July , 2011 , Pages 1172-1178 ; 0012365X (ISSN) ; Ghorbani, E ; Mahmoodi, A ; Sharif University of Technology
2011

Abstract

Let A be a Hermitian matrix whose graph is G (i.e. there is an edge between the vertices i and j in G if and only if the (i,j) entry of A is non-zero). Let λ be an eigenvalue of A with multiplicity mA(λ). An edge e=ij is said to be Parter (resp., neutral, downer) for λ,A if mA(λ)-mA-e(λ) is negative (resp., 0, positive ), where A-e is the matrix resulting from making the (i,j) and (j,i) entries of A zero. For a tree T with adjacency matrix A a subset S of the edge set of G is called an edge star set for an eigenvalue λ of A, if |S|=mA(λ) and A-S has no eigenvalue λ. In this paper the existence of downer edges and edge star sets for non-zero eigenvalues of the adjacency matrix of a tree is...

#### A lower bound for algebraic connectivity based on the connection-graph- stability method

, Article Linear Algebra and Its Applications ; Volume 435, Issue 1 , Sep , 2011 , Pages 186-192 ; 00243795 (ISSN) ; Jalili, M ; Hasler, M ; Sharif University of Technology
2011

Abstract

This paper introduces the connection-graph-stability method and uses it to establish a new lower bound on the algebraic connectivity of graphs (the second smallest eigenvalue of the Laplacian matrix of the graph) that is sharper than the previously published bounds. The connection-graph-stability score for each edge is defined as the sum of the lengths of the shortest paths making use of that edge. We prove that the algebraic connectivity of the graph is bounded below by the size of the graph divided by the maximum connection-graph-stability score assigned to the edges

#### Computing all the Floquet eigenfunctions of oscillators using harmonic balance Jacobian matrices

, Article IET Circuits, Devices and Systems ; Volume 5, Issue 4 , July , 2011 , Pages 257-266 ; 1751858X (ISSN) ; Farzaneh, F ; Sharif University of Technology
2011

Abstract

Floquet eigenfunctions and Floquet exponents are encountered in stability and noise analysis of circuits operating at large signal periodic regime. It is analytically verified that the spectrum vectors of the left-hand and right-hand Floquet eigenfunctions and the Floquet exponents (Floquet eigenpairs) are members of the harmonic balance eigenvalues and eigenvectors (HB eigenpairs). The relationships between other HB eigenpairs with the Floquet eigenpairs are discussed. This discussion leads to a practical algorithm for computing the Floquet eigenpairs through HB eigenpairs. Furthermore, it is analytically verified that the main arguments of the study are consistent with the...

#### On the existence of an analytic solution to the 1-D Ising model with nearest and next-nearest neighbor interactions in the presence of a magnetic field

, Article Phase Transitions ; Volume 84, Issue 1 , Dec , 2011 , Pages 77-84 ; 01411594 (ISSN) ; Daryaei, E ; Abroshan, H ; Akbarzadeh, H ; Parsafar, G ; Fortunelli, A ; Sharif University of Technology
2011

Abstract

To solve the controversy, regarding the existence of an analytic solution to the 1-D Ising model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions in the presence of a magnetic field, we apply the transfer matrix method to solve the 1-D Ising model in the presence of a magnetic field, taking both NN and NNN interactions into account. We show that it is possible to write a transfer matrix only if the number of sites is even. Even in such a case, it is impossible to diagonalize the transfer matrix in an analytic form. Therefore, we employ a numerical method to obtain the eigenvalues of the transfer matrix. Moreover, the heat capacity, magnetization, and magnetic...

#### 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=...