Sharif Digital Repository

In this paper, we address the stability problem of a noiseless linear time invariant control system over parallel Gaussian channels with feedback. It is shown that the eigenvalues-rate condition which has been proved as a necessary condition, is also sufficient for stability over parallel Gaussian channels. In fact, it is proved that for stabilizing a control system over the parallel Gaussian channels, it suffices that the Shannon channel capacity obtained by the water filling technique is greater than the sum of the logarithm of the unstable eigenvalues magnitude. In order to prove this sufficient condition, we propose a new nonlinear joint source channel coding for parallel Gaussian... 

Fourier-based modal methods are among the most significant tools for accurate numerical analysis of grating structures. However, they mostly lead to time consuming and memory hungry eigenvalue problems, particularly when large dielectric constants or high contrasts are involved. We have found an asymptotic semi-empirical relationship for the propagation constants of a lamellar grating, obtained from Fourier-based modal methods. Hence, given any truncation order, it is possible to estimate propagation constants without having to solve the eigenvalue equation. We observed propagation constants only depend on permittivities, filling factors, and the unit cell size, while the dependence on the... 

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... 

This article addresses the stabilization of noiseless nonlinear dynamic systems over limited capacity communication channels. It is shown that the stability of nonlinear dynamic systems over memory-less communication channels implies an inequality condition between the Shannon channel capacity and the summation of the positive equilibrium Lyapunov exponents of the dynamic system or, equivalently, the logarithms of the magnitude of the unstable eigenvalues of system Jacobian. Furthermore, we propose an encoder, decoder, and a controller to prove that scalar nonlinear dynamic systems are stabilizable under the aforementioned inequality condition over the digital noiseless and the packet... 

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... 

The eigenvalue perturbation theorem is used to propose a convex fragility criterion with application to control system design. The criterion can be considered as a non-normality measure of the controller state-space matrix. Non-normality of a matrix is defined as its distance to the nearest real normal matrix within a convex normal subspace. Based on the criterion, an H∞ method for the order reduction of linear time-invariant (LTI) controllers is developed which leads to non-fragile reduced order controllers. 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission  

We investigate eigenvectors of rank-one deformations of random matrices boldsymbol B = boldsymbol A + theta boldsymbol {uu}{} in which boldsymbol A in mathbb R{N times N} is a Wigner real symmetric random matrix, theta in mathbb R{+} , and boldsymbol u is uniformly distributed on the unit sphere. It is well known that for theta > 1 the eigenvector associated with the largest eigenvalue of boldsymbol B closely estimates boldsymbol u asymptotically, while for theta < 1 the eigenvectors of boldsymbol B are uninformative about boldsymbol u. We examine mathcal O({1}/{N}) correlation of eigenvectors with boldsymbol u before phase transition and show that eigenvectors with larger eigenvalue exhibit... 

This paper describes an improved version of the recently proposed fast converging algorithm. PNLMS, for network echo cancellers. We have introduced a simple analysis of the PNLMS convergence behavior to show why after the fast initial convergence, it slows down. Also, the method has been worked out to overcome this deficiency is presented. Improvement is shown by several simulation results. © 2002 IEEE  

Recently, an approximate formalism [Opt. Express 23, 2764, (2015)] called diffractive interface theory has been reported for the fast analysis of the optical response of metasurfaces, subwavelength two-dimensional periodic arrays. In this method, the electromagnetic boundary conditions are derived using the susceptibility distribution of the metasurface, such that the analysis of metasurface is possible without solving any eigenvalue equation inside the grating layer. In this paper, we modify the boundary conditions to achieve more accurate results. In addition, in this paper, correct Fourier factorization rules are also applied leading to faster convergence rate. The obtained results are... 

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.... 

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)... 

In this paper, a new approach for solving the problem of pole assignment, using static output feedback, has been proposed. The proposed approach is based on genetic algorithm where it can place all the closed-loop poles at desired locations with a high accuracy, provided that there exists a solution to the problem. It is also shown that how some known difficulties of static output feedback like order of system, multiplicity of the desired poles and the need for having closed-loop poles to be distinct or different from the open loop poles have been solved. Numerical examples at the end of the paper illustrate the applicability and the performance of the proposed method. © 2002 IEEE  

In this paper, we investigate the effect of applying an exponential window on the limiting spectral distribution (l.s.d.) of the exponentially windowed sample covariance matrix (SCM) of complex array data. We use recent advances in random matrix theory which describe the distribution of eigenvalues of the doubly correlated Wishart matrices. We derive an explicit expression for the l.s.d. of the noise-only data. Simulations are performed to support our theoretical claims  

Recently graph theory and complex networks have been widely used as a mean to model functionality of the brain. Among different neuroimaging techniques available for constructing the brain functional networks, electroencephalography (EEG) with its high temporal resolution is a useful instrument of the analysis of functional interdependencies between different brain regions. Alzheimer's disease (AD) is a neurodegenerative disease, which leads to substantial cognitive decline, and eventually, dementia in aged people. To achieve a deeper insight into the behavior of functional cerebral networks in AD, here we study their synchronizability in 17 newly diagnosed AD patients compared to 17 healthy... 

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... 

This study attempts to reach a broad understanding of the stability properties of nonlinear time-periodic flapping wing structures. Two bio-system models, Hummingbird (6DOF) and Hawkmoth (3DOF) are developed for this purpose. Initial analysis on the Hummingbird model, which is based on the Floquet theory, kinetic energy integration, and phase portrait technique, indicates lack of stability in hover flight. Kinetic energy integration is carried out on the extended model of the Hawkmoth to find the domain of attraction and increase the level of stability by varying the design parameters. Here, the hinge location of the wing, flapping amplitude, flapping frequency, and mean angle of attack are... 

Abstract In this paper, the solution of multi-group neutron/adjoint equation using Finite Element Method (FEM) for hexagonal and rectangular reactor cores is reported. The spatial discretization of the neutron diffusion equation is performed based on two different Finite Element Methods (FEMs) using unstructured triangular elements generated by Gambit software. Calculations are performed using Galerkin and Generalized Least Squares FEMs; based on which results are compared. Using the power iteration method for the neutron and adjoint calculations, the neutron and adjoint flux distributions with the corresponding eigenvalues are obtained. The results are then validated against the valid... 

Mesh point positions in Finite Difference Method (FDM) of discretization for the neutron diffusion equation can remarkably affect the averaged neutron fluxes as well as the effective multiplication factor. In this study, by aid of improving the mesh point positions, an enhanced finite difference scheme for the neutron diffusion equation is proposed based on the neutron importance function. In order to determine the neutron importance function, the adjoint (backward) neutron diffusion calculations are performed in the same procedure as for the forward calculations. Considering the neutron importance function, the mesh points can be improved through the entire reactor core. Accordingly, in... 

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... 

From the birth of multi-spectral imaging techniques, there has been a tendency to consider and process this new type of data as a set of parallel gray-scale images, instead of an ensemble of an n-D realization. However, it has been proved that using vector-based tools leads to a more appropriate understanding of color images and thus more efficient algorithms for processing them. Such tools are able to take into consideration the high correlation of the color components and thus to successfully carry out energy compaction. In this paper, a novel method is proposed to utilize the principal component analysis in the neighborhoods of an image in order to extract the corresponding eigenimages....