Abstract: In this paper, the backward MPSD (Modified Preconditioned
Simultaneous Displacement) iterative matrix is firstly
proposed. The relationship of eigenvalues between the backward
MPSD iterative matrix and backward Jacobi iterative matrix for block
p-cyclic case is obtained, which improves and refines the results in
the corresponding references.
Abstract: In this paper we propose a novel method for human
face segmentation using the elliptical structure of the human head. It
makes use of the information present in the edge map of the image.
In this approach we use the fact that the eigenvalues of covariance
matrix represent the elliptical structure. The large and small
eigenvalues of covariance matrix are associated with major and
minor axial lengths of an ellipse. The other elliptical parameters are
used to identify the centre and orientation of the face. Since an
Elliptical Hough Transform requires 5D Hough Space, the Circular
Hough Transform (CHT) is used to evaluate the elliptical parameters.
Sparse matrix technique is used to perform CHT, as it squeeze zero
elements, and have only a small number of non-zero elements,
thereby having an advantage of less storage space and computational
time. Neighborhood suppression scheme is used to identify the valid
Hough peaks. The accurate position of the circumference pixels for
occluded and distorted ellipses is identified using Bresenham-s
Raster Scan Algorithm which uses the geometrical symmetry
properties. This method does not require the evaluation of tangents
for curvature contours, which are very sensitive to noise. The method
has been evaluated on several images with different face orientations.
Abstract: This study employs the use of the fourth order
Numerov scheme to determine the eigenstates and eigenvalues of
particles, electrons in particular, in single and double delta function
potentials. For the single delta potential, it is found that the
eigenstates could only be attained by using specific potential depths.
The depth of the delta potential well has a value that varies depending
on the delta strength. These depths are used for each well on the
double delta function potential and the eigenvalues are determined.
There are two bound states found in the computation, one with a
symmetric eigenstate and another one which is antisymmetric.
Abstract: In this paper we study the inverse eigenvalue problem for symmetric special matrices and introduce sufficient conditions for obtaining nonnegative matrices. We get the HROU algorithm from [1] and introduce some extension of this algorithm. If we have some eigenvectors and associated eigenvalues of a matrix, then by this extension we can find the symmetric matrix that its eigenvalue and eigenvectors are given. At last we study the special cases and get some remarkable results.
Abstract: An accurate procedure to determine free vibrations of
beams and plates is presented.
The natural frequencies are exact solutions of governing vibration
equations witch load to a nonlinear homogeny system.
The bilinear and linear structures considered simulate a bridge.
The dynamic behavior of this one is analyzed by using the theory of
the orthotropic plate simply supported on two sides and free on the
two others. The plate can be excited by a convoy of constant or
harmonic loads. The determination of the dynamic response of the
structures considered requires knowledge of the free frequencies and
the shape modes of vibrations. Our work is in this context. Indeed,
we are interested to develop a self-consistent calculation of the Eigen
frequencies.
The formulation is based on the determination of the solution of
the differential equations of vibrations. The boundary conditions
corresponding to the shape modes permit to lead to a homogeneous
system. Determination of the noncommonplace solutions of this
system led to a nonlinear problem in Eigen frequencies.
We thus, develop a computer code for the determination of the
eigenvalues. It is based on a method of bisection with interpolation
whose precision reaches 10 -12. Moreover, to determine the
corresponding modes, the calculation algorithm that we develop uses
the method of Gauss with a partial optimization of the "pivots"
combined with an inverse power procedure. The Eigen frequencies
of a plate simply supported along two opposite sides while
considering the two other free sides are thus analyzed. The results
could be generalized with the case of a beam by regarding it as a
plate with low width.
We give, in this paper, some examples of treated cases. The
comparison with results presented in the literature is completely
satisfactory.
Abstract: A multi-rate discrete-time model, whose response
agrees exactly with that of a continuous-time original at all sampling
instants for any sampling periods, is developed for a linear system,
which is assumed to have multiple real eigenvalues. The sampling
rates can be chosen arbitrarily and individually, so that their ratios
can even be irrational. The state space model is obtained as a
combination of a linear diagonal state equation and a nonlinear output
equation. Unlike the usual lifted model, the order of the proposed
model is the same as the number of sampling rates, which is less than
or equal to the order of the original continuous-time system. The
method is based on a nonlinear variable transformation, which can be
considered as a generalization of linear similarity transformation,
which cannot be applied to systems with multiple eigenvalues in
general. An example and its simulation result show that the proposed
multi-rate model gives exact responses at all sampling instants.
Abstract: In this paper, we present an algorithm for computing a
Schur factorization of a real nonsymmetric matrix with ordered diagonal
blocks such that upper left blocks contains the largest magnitude
eigenvalues. Especially in case of multiple eigenvalues, when matrix
is non diagonalizable, we construct an invariant subspaces with few
additional tricks which are heuristic and numerical results shows the
stability and accuracy of the algorithm.
Abstract: In this paper, we represent protein structure by using
graph. A protein structure database will become a graph database.
Each graph is represented by a spectral vector. We use Jacobi
rotation algorithm to calculate the eigenvalues of the normalized
Laplacian representation of adjacency matrix of graph. To measure
the similarity between two graphs, we calculate the Euclidean
distance between two graph spectral vectors. To cluster the graphs,
we use M-tree with the Euclidean distance to cluster spectral vectors.
Besides, M-tree can be used for graph searching in graph database.
Our proposal method was tested with graph database of 100 graphs
representing 100 protein structures downloaded from Protein Data
Bank (PDB) and we compare the result with the SCOP hierarchical
structure.
Abstract: This paper reports work done to improve the modeling of complex processes when only small experimental data sets are available. Neural networks are used to capture the nonlinear underlying phenomena contained in the data set and to partly eliminate the burden of having to specify completely the structure of the model. Two different types of neural networks were used for the application of pulping problem. A three layer feed forward neural networks, using the Preconditioned Conjugate Gradient (PCG) methods were used in this investigation. Preconditioning is a method to improve convergence by lowering the condition number and increasing the eigenvalues clustering. The idea is to solve the modified odified problem M-1 Ax= M-1b where M is a positive-definite preconditioner that is closely related to A. We mainly focused on Preconditioned Conjugate Gradient- based training methods which originated from optimization theory, namely Preconditioned Conjugate Gradient with Fletcher-Reeves Update (PCGF), Preconditioned Conjugate Gradient with Polak-Ribiere Update (PCGP) and Preconditioned Conjugate Gradient with Powell-Beale Restarts (PCGB). The behavior of the PCG methods in the simulations proved to be robust against phenomenon such as oscillations due to large step size.
Abstract: Leptospirosis is recognized as an important zoonosis
in tropical regions well as an important animal disease with
substantial loss in production. In this study, the model for the
transmission of the Leptospirosis disease to human population are
discussed. Model is described the vector population dynamics and
the Leptospirosis transmission to the human population are
discussed. Local analysis of equilibria are given. We confirm the
results by using numerical results.
Abstract: The projection methods, usually viewed as the methods
for computing eigenvalues, can also be used to estimate pseudospectra.
This paper proposes a kind of projection methods for computing
the pseudospectra of large scale matrices, including orthogonalization
projection method and oblique projection method respectively. This
possibility may be of practical importance in applications involving
large scale highly nonnormal matrices. Numerical algorithms are
given and some numerical experiments illustrate the efficiency of
the new algorithms.
Abstract: In this paper we introduce an efficient solution
method for the Eigen-decomposition of bisymmetric and per
symmetric matrices of symmetric structures. Here we decompose
adjacency and Laplacian matrices of symmetric structures to submatrices
with low dimension for fast and easy calculation of
eigenvalues and eigenvectors. Examples are included to show the
efficiency of the method.
Abstract: Restarted GMRES methods augmented with approximate eigenvectors are widely used for solving large sparse linear systems. Recently a new scheme of augmenting with error approximations is proposed. The main aim of this paper is to develop a restarted GMRES method augmented with the combination of harmonic Ritz vectors and error approximations. We demonstrate that the resulted combination method can gain the advantages of two approaches: (i) effectively deflate the small eigenvalues in magnitude that may hamper the convergence of the method and (ii) partially recover the global optimality lost due to restarting. The effectiveness and efficiency of the new method are demonstrated through various numerical examples.
Abstract: The Detour matrix (DD) of a graph has for its ( i , j)
entry the length of the longest path between vertices i and j. The
DD-eigenvalues of a connected graph G are the eigenvalues for its
detour matrix, and they form the DD-spectrum of G. The DD-energy
EDD of the graph G is the sum of the absolute values of its DDeigenvalues.
Two connected graphs are said to be DD- equienergetic
if they have equal DD-energies. In this paper, the DD- spectra of a
variety of graphs and their DD-energies are calculated.
Abstract: In this paper we present a new method for coin
identification. The proposed method adopts a hybrid scheme using
Eigenvalues of covariance matrix, Circular Hough Transform (CHT)
and Bresenham-s circle algorithm. The statistical and geometrical
properties of the small and large Eigenvalues of the covariance
matrix of a set of edge pixels over a connected region of support are
explored for the purpose of circular object detection. Sparse matrix
technique is used to perform CHT. Since sparse matrices squeeze
zero elements and contain only a small number of non-zero elements,
they provide an advantage of matrix storage space and computational
time. Neighborhood suppression scheme is used to find the valid
Hough peaks. The accurate position of the circumference pixels is
identified using Raster scan algorithm which uses geometrical
symmetry property. After finding circular objects, the proposed
method uses the texture on the surface of the coins called texton,
which are unique properties of coins, refers to the fundamental micro
structure in generic natural images. This method has been tested on
several real world images including coin and non-coin images. The
performance is also evaluated based on the noise withstanding
capability.
Abstract: This paper reports work done to improve the modeling of complex processes when only small experimental data sets are available. Neural networks are used to capture the nonlinear underlying phenomena contained in the data set and to partly eliminate the burden of having to specify completely the structure of the model. Two different types of neural networks were used for the application of Pulping of Sugar Maple problem. A three layer feed forward neural networks, using the Preconditioned Conjugate Gradient (PCG) methods were used in this investigation. Preconditioning is a method to improve convergence by lowering the condition number and increasing the eigenvalues clustering. The idea is to solve the modified problem where M is a positive-definite preconditioner that is closely related to A. We mainly focused on Preconditioned Conjugate Gradient- based training methods which originated from optimization theory, namely Preconditioned Conjugate Gradient with Fletcher-Reeves Update (PCGF), Preconditioned Conjugate Gradient with Polak-Ribiere Update (PCGP) and Preconditioned Conjugate Gradient with Powell-Beale Restarts (PCGB). The behavior of the PCG methods in the simulations proved to be robust against phenomenon such as oscillations due to large step size.
Abstract: This paper proposes a novel system for monitoring the
health of underground pipelines. Some of these pipelines transport
dangerous contents and any damage incurred might have catastrophic
consequences. However, most of these damage are unintentional and
usually a result of surrounding construction activities. In order to
prevent these potential damages, monitoring systems are
indispensable. This paper focuses on acoustically recognizing road
cutters since they prelude most construction activities in modern
cities. Acoustic recognition can be easily achieved by installing a
distributed computing sensor network along the pipelines and using
smart sensors to “listen" for potential threat; if there is a real threat,
raise some form of alarm. For efficient pipeline monitoring, a novel
monitoring approach is proposed. Principal Component Analysis
(PCA) was studied and applied. Eigenvalues were regarded as the
special signature that could characterize a sound sample, and were
thus used for the feature vector for sound recognition. The denoising
ability of PCA could make it robust to noise interference. One class
SVM was used for classifier. On-site experiment results show that the
proposed PCA and SVM based acoustic recognition system will be
very effective with a low tendency for raising false alarms.
Abstract: In this work, we present a comparison between two
techniques of image compression. In the first case, the image is
divided in blocks which are collected according to zig-zag scan. In
the second one, we apply the Fast Cosine Transform to the image,
and then the transformed image is divided in blocks which are
collected according to zig-zag scan too. Later, in both cases, the
Karhunen-Loève transform is applied to mentioned blocks. On the
other hand, we present three new metrics based on eigenvalues for a
better comparative evaluation of the techniques. Simulations show
that the combined version is the best, with minor Mean Absolute
Error (MAE) and Mean Squared Error (MSE), higher Peak Signal to
Noise Ratio (PSNR) and better image quality. Finally, new technique
was far superior to JPEG and JPEG2000.
Abstract: This paper addresses the problem of the partial state
feedback stabilization of a class of nonlinear systems. In order to
stabilization this class systems, the especial place of this paper is
to reverse designing the state feedback control law from the method
of judging system stability with the center manifold theory. First of
all, the center manifold theory is applied to discuss the stabilization
sufficient condition and design the stabilizing state control laws for a
class of nonlinear. Secondly, the problem of partial stabilization for a
class of plane nonlinear system is discuss using the lyapunov second
method and the center manifold theory. Thirdly, we investigate specially
the problem of the stabilization for a class of homogenous plane
nonlinear systems, a class of nonlinear with dual-zero eigenvalues and
a class of nonlinear with zero-center using the method of lyapunov
function with homogenous derivative, specifically. At the end of this
paper, some examples and simulation results are given show that the
approach of this paper to this class of nonlinear system is effective
and convenient.
Abstract: This paper proposed a stiffness analysis method for a
3-PRS mechanism for welding thick aluminum plate using FSW
technology. In the molding process, elastic deformation of lead-screws
and links are taken into account. This method is based on the virtual
work principle. Through a survey of the commonly used stiffness
performance indices, the minimum and maximum eigenvalues of the
stiffness matrix are used to evaluate the stiffness of the 3-PRS
mechanism. Furthermore, A FEA model has been constructed to verify
the method. Finally, we redefined the workspace using the stiffness
analysis method.