Choice Of Eigenvalues Research Articles

Toward Optimal Synthesis of Discrete-Time Hopfield Neural Network.

In this research brief, the relationship between eigenvectors (with {+1, -1} components) of a synaptic weight matrix W and the stable/anti-stable states of discrete-time Hopfield associative memory (HAM) is established. Also, the synthesis of W with desired stable/anti-stable states using spectral representation of W in even/odd dimension is discussed when the threshold vector is a non-zero vector. Freedom in choice of eigenvalues is capitalized to improve the noise immunity of the Hopfield neural network (HNN). Also, the problem of optimal synthesis of Hopfield Associative memory is formulated.

Diffusion and reaction in a two-dimensional multilayer body: Analytical solution and imaginary eigenvalue analysis

Heat and mass transfer in multilayer bodies occur commonly in a number of engineering problems, such as thermal management, manufacturing and reacting systems. Much of the past literature on theoretical analysis of multilayer diffusion-reaction problems is based on the assumption of one-dimensional transport. Given the geometrical complexity of practical engineering systems, two- or three-dimensional analysis may be needed for improved accuracy. This work presents theoretical analysis of coupled diffusion and reaction occurring in a general, two-dimensional multilayer body. The transient temperature distribution is written in the form of an infinite series, and the eigenequation for this problem is derived. Adiabatic or isothermal conditions along the side walls are accounted for by appropriate choice of eigenvalues in that direction. Results are shown to be in good agreement with numerical simulations. It is shown that the temperature distribution may converge or diverge, depending on the specific values of various problem parameters, such as reaction coefficients and diffusivities in each layer, as well as the nature of the boundary conditions in both directions. An analysis for the existence of imaginary eigenvalues, which are related to divergence at large times is presented. The theoretical model is used to predict the limits of design parameters to prevent thermal runaway in a two-layer Li-ion cell. This work improves upon the limited past work on multi-dimensional multilayer transport by accounting for the reaction term, and by identifying the possibility of imaginary eigenvalues in such problems. Due to the close relationship between imaginary eigenvalues and thermal runaway, these results may contribute towards improved safety and reliability of practical engineering systems.

Eigenstructure assignment in linear geometric control

The focus of this paper is the connection between two foundational areas of linear time-invariant (LTI) systems theory: geometric control and eigenstructure assignment. In particular, we study the properties of the null-spaces of the reachability matrix pencil and of the Rosenbrock system matrix, which have been extensively used as two computational building blocks for the calculation of pole placing state feedback matrices and pole placing friends of output-nulling subspaces. Our objective is to show that the subspaces in the chains of kernels obtained in the construction of these feedback matrices interact with each other in ways that are entirely independent from the choice of eigenvalues. So far, these chains of subspaces have only been studied in the case of stationarity. In this case, it is known that these chains converge to the classic Kalman reachable subspace ℛ for the reachability matrix pencil and to the largest reachability subspace ℛ⋆ in the case of the Rosenbrock matrix, respectively. Here we are interested in showing that even before stationarity has been reached, the partial chains are linked to structural properties of the system, and are therefore independent of the closed-loop eigenvalues that we wish to assign. We further characterize these subspaces by investigating the notion of largest subspace on which it is possible to assign the closed-loop spectrum (possibly maintaining the output at zero) without resorting to non-trivial Jordan forms.

Adaptive Lossy Image Compression Based on Singular Value Decomposition

Image compression techniques aim to reduce redundant information in order to allow data storage and transmission in an efficient way. In this work, we propose and analyze a lossy image compression method based on the singular value decomposition using an optimal choice of eigenvalues and an adaptive mechanism for block partitioning. Experiments are conducted on several images to demonstrate the effectiveness of the proposed compression method in comparison with the direct application of the singular value decomposition.

Leak detection of complex pipelines based on the filter diagonalization method: robust technique for eigenvalue assessment

The FDM (filter diagonalization method), an interesting technique used in nuclear magnetic resonance data processing for tackling FFT (fast Fourier transform) limitations, can be used by considering pipelines, especially complex configurations, as a vascular apparatus with arteries, veins, capillaries, etc. Thrombosis, which might occur in humans, can be considered as a leakage for the complex pipeline, the human vascular apparatus. The choice of eigenvalues in FDM or in spectra-based techniques is a key issue in recovering the solution of the main equation (for FDM) or frequency domain transformation (for FFT) in order to determine the accuracy in detecting leaks in pipelines. This paper deals with the possibility of improving the leak detection accuracy of the FDM technique thanks to a robust algorithm by assessing the problem of eigenvalues, making it less experimental and more analytical using Tikhonov-based regularization techniques. The paper starts from the results of previous experimental procedures carried out by the authors.

Impact of eigenvalues on the pseudopotential calculation of superconducting parameters of metals Ga, Cd and In

In the present paper some superconducting (SC) state parameters of metals Ga, Cd and In have been studied through Harrison’s First Principle [HFP] pseudopotential technique using McMillan’s formalism. The impact of choosing two different sets of core energy eigenvalues viz. Herman-Skillman and Clementi (or Experimental) has been studied. It has been observed that the choice of eigenvalues has appreciable impact on the form factor and consequently on the SC state transition parameter viz. electron-phonon coupling strength (λ) and superconducting transition temperature T c . Hence the choice of suitable eigenvalues is essential for these computations. Reasonable agreement with experimental and theoretical data have been obtained.

Determination of eigenvalues in Marshall's model reduction

This paper is concerned with the problem of determining eigenvalues, retained in Marshall's reduced order model, which have the largest effect on the retaining state vector or give the best approximate reduced system in the sense of ISE criterion. The main objective is to show that the usual choice of eigenvalues in Marshall's model reduction technique (decomposition of eigenvalues into fast modes and slow modes) does not necessarily give a well approximated reduced order model. Here the measure of approximation is defined and calculated by means of ISE criterion. The effectiveness of this method is explained by two illustrative examples.