WorldWideScience

Sample records for eigenvectors

  1. Matrix with Prescribed Eigenvectors

    Science.gov (United States)

    Ahmad, Faiz

    2011-01-01

    It is a routine matter for undergraduates to find eigenvalues and eigenvectors of a given matrix. But the converse problem of finding a matrix with prescribed eigenvalues and eigenvectors is rarely discussed in elementary texts on linear algebra. This problem is related to the "spectral" decomposition of a matrix and has important technical…

  2. Covariance expressions for eigenvalue and eigenvector problems

    Science.gov (United States)

    Liounis, Andrew J.

    There are a number of important scientific and engineering problems whose solutions take the form of an eigenvalue--eigenvector problem. Some notable examples include solutions to linear systems of ordinary differential equations, controllability of linear systems, finite element analysis, chemical kinetics, fitting ellipses to noisy data, and optimal estimation of attitude from unit vectors. In many of these problems, having knowledge of the eigenvalue and eigenvector Jacobians is either necessary or is nearly as important as having the solution itself. For instance, Jacobians are necessary to find the uncertainty in a computed eigenvalue or eigenvector estimate. This uncertainty, which is usually represented as a covariance matrix, has been well studied for problems similar to the eigenvalue and eigenvector problem, such as singular value decomposition. There has been substantially less research on the covariance of an optimal estimate originating from an eigenvalue-eigenvector problem. In this thesis we develop two general expressions for the Jacobians of eigenvalues and eigenvectors with respect to the elements of their parent matrix. The expressions developed make use of only the parent matrix and the eigenvalue and eigenvector pair under consideration. In addition, they are applicable to any general matrix (including complex valued matrices, eigenvalues, and eigenvectors) as long as the eigenvalues are simple. Alongside this, we develop expressions that determine the uncertainty in a vector estimate obtained from an eigenvalue-eigenvector problem given the uncertainty of the terms of the matrix. The Jacobian expressions developed are numerically validated with forward finite, differencing and the covariance expressions are validated using Monte Carlo analysis. Finally, the results from this work are used to determine covariance expressions for a variety of estimation problem examples and are also applied to the design of a dynamical system.

  3. Eigenvector space model to capture features of documents

    Directory of Open Access Journals (Sweden)

    Choi DONGJIN

    2011-09-01

    Full Text Available Eigenvectors are a special set of vectors associated with a linear system of equations. Because of the special property of eigenvector, it has been used a lot for computer vision area. When the eigenvector is applied to information retrieval field, it is possible to obtain properties of documents data corpus. To capture properties of given documents, this paper conducted simple experiments to prove the eigenvector is also possible to use in document analysis. For the experiment, we use short abstract document of Wikipedia provided by DBpedia as a document corpus. To build an original square matrix, the most popular method named tf-idf measurement will be used. After calculating the eigenvectors of original matrix, each vector will be plotted into 3D graph to find what the eigenvector means in document processing.

  4. Image denoising via adaptive eigenvectors of graph Laplacian

    Science.gov (United States)

    Chen, Ying; Tang, Yibin; Xu, Ning; Zhou, Lin; Zhao, Li

    2016-07-01

    An image denoising method via adaptive eigenvectors of graph Laplacian (EGL) is proposed. Unlike the trivial parameter setting of the used eigenvectors in the traditional EGL method, in our method, the eigenvectors are adaptively selected in the whole denoising procedure. In detail, a rough image is first built with the eigenvectors from the noisy image, where the eigenvectors are selected by using the deviation estimation of the clean image. Subsequently, a guided image is effectively restored with a weighted average of the noisy and rough images. In this operation, the average coefficient is adaptively obtained to set the deviation of the guided image to approximately that of the clean image. Finally, the denoised image is achieved by a group-sparse model with the pattern from the guided image, where the eigenvectors are chosen in the error control of the noise deviation. Moreover, a modified group orthogonal matching pursuit algorithm is developed to efficiently solve the above group sparse model. The experiments show that our method not only improves the practicality of the EGL methods with the dependence reduction of the parameter setting, but also can outperform some well-developed denoising methods, especially for noise with large deviations.

  5. Localized eigenvectors of the non-backtracking matrix

    International Nuclear Information System (INIS)

    Kawamoto, Tatsuro

    2016-01-01

    In the case of graph partitioning, the emergence of localized eigenvectors can cause the standard spectral method to fail. To overcome this problem, the spectral method using a non-backtracking matrix was proposed. Based on numerical experiments on several examples of real networks, it is clear that the non-backtracking matrix does not exhibit localization of eigenvectors. However, we show that localized eigenvectors of the non-backtracking matrix can exist outside the spectral band, which may lead to deterioration in the performance of graph partitioning. (paper: interdisciplinary statistical mechanics)

  6. An adaptive left–right eigenvector evolution algorithm for vibration isolation control

    International Nuclear Information System (INIS)

    Wu, T Y

    2009-01-01

    The purpose of this research is to investigate the feasibility of utilizing an adaptive left and right eigenvector evolution (ALREE) algorithm for active vibration isolation. As depicted in the previous paper presented by Wu and Wang (2008 Smart Mater. Struct. 17 015048), the structural vibration behavior depends on both the disturbance rejection capability and mode shape distributions, which correspond to the left and right eigenvector distributions of the system, respectively. In this paper, a novel adaptive evolution algorithm is developed for finding the optimal combination of left–right eigenvectors of the vibration isolator, which is an improvement over the simultaneous left–right eigenvector assignment (SLREA) method proposed by Wu and Wang (2008 Smart Mater. Struct. 17 015048). The isolation performance index used in the proposed algorithm is defined by combining the orthogonality index of left eigenvectors and the modal energy ratio index of right eigenvectors. Through the proposed ALREE algorithm, both the left and right eigenvectors evolve such that the isolation performance index decreases, and therefore one can find the optimal combination of left–right eigenvectors of the closed-loop system for vibration isolation purposes. The optimal combination of left–right eigenvectors is then synthesized to determine the feedback gain matrix of the closed-loop system. The result of the active isolation control shows that the proposed method can be utilized to improve the vibration isolation performance compared with the previous approaches

  7. Semi-supervised eigenvectors for large-scale locally-biased learning

    DEFF Research Database (Denmark)

    Hansen, Toke Jansen; Mahoney, Michael W.

    2014-01-01

    improved scaling properties. We provide several empirical examples demonstrating how these semi-supervised eigenvectors can be used to perform locally-biased learning; and we discuss the relationship between our results and recent machine learning algorithms that use global eigenvectors of the graph......In many applications, one has side information, e.g., labels that are provided in a semi-supervised manner, about a specific target region of a large data set, and one wants to perform machine learning and data analysis tasks nearby that prespecified target region. For example, one might......-based machine learning and data analysis tools. At root, the reason is that eigenvectors are inherently global quantities, thus limiting the applicability of eigenvector-based methods in situations where one is interested in very local properties of the data. In this paper, we address this issue by providing...

  8. EIGENVECTOR-BASED CENTRALITY MEASURES FOR TEMPORAL NETWORKS*

    Science.gov (United States)

    TAYLOR, DANE; MYERS, SEAN A.; CLAUSET, AARON; PORTER, MASON A.; MUCHA, PETER J.

    2017-01-01

    Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network data that changes in time, it is important to extend such eigenvector-based centrality measures to time-dependent networks. In this paper, we introduce a principled generalization of network centrality measures that is valid for any eigenvector-based centrality. We consider a temporal network with N nodes as a sequence of T layers that describe the network during different time windows, and we couple centrality matrices for the layers into a supra-centrality matrix of size NT × NT whose dominant eigenvector gives the centrality of each node i at each time t. We refer to this eigenvector and its components as a joint centrality, as it reflects the importances of both the node i and the time layer t. We also introduce the concepts of marginal and conditional centralities, which facilitate the study of centrality trajectories over time. We find that the strength of coupling between layers is important for determining multiscale properties of centrality, such as localization phenomena and the time scale of centrality changes. In the strong-coupling regime, we derive expressions for time-averaged centralities, which are given by the zeroth-order terms of a singular perturbation expansion. We also study first-order terms to obtain first-order-mover scores, which concisely describe the magnitude of nodes’ centrality changes over time. As examples, we apply our method to three empirical temporal networks: the United States Ph.D. exchange in mathematics, costarring relationships among top-billed actors during the Golden Age of Hollywood, and citations of decisions from the United States Supreme Court. PMID:29046619

  9. Eigenvectors of Open Bazhanov-Stroganov Quantum Chain

    Directory of Open Access Journals (Sweden)

    Nikolai Iorgov

    2006-02-01

    Full Text Available In this contribution we give an explicit formula for the eigenvectors of Hamiltonians of open Bazhanov-Stroganov quantum chain. The Hamiltonians of this quantum chain is defined by the generation polynomial $A_n(lambda$ which is upper-left matrix element of monodromy matrix built from the Bazhanov-Stroganov $L$-operators. The formulas for the eigenvectors are derived using iterative procedure by Kharchev and Lebedev and given in terms of $w_p(s$-function which is a root of unity analogue of $Gamma_q$-function.

  10. Laplacian eigenvectors of graphs Perron-Frobenius and Faber-Krahn type theorems

    CERN Document Server

    Biyikoğu, Türker; Stadler, Peter F

    2007-01-01

    Eigenvectors of graph Laplacians have not, to date, been the subject of expository articles and thus they may seem a surprising topic for a book. The authors propose two motivations for this new LNM volume: (1) There are fascinating subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs. (2) "Geometric" properties of (cost) functions defined on the vertex sets of graphs are of practical interest for heuristic optimization algorithms. The observation that the cost functions of quite a few of the well-studied combinatorial optimization problems are eigenvectors of associated graph Laplacians has prompted the investigation of such eigenvectors. The volume investigates the structure of eigenvectors and looks at the number of their sign graphs ("nodal domains"), Perron components, graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology.

  11. Use of eigenvectors in understanding and correcting storage ring orbits

    International Nuclear Information System (INIS)

    Friedman, A.; Bozoki, E.

    1994-01-01

    The response matrix A is defined by the equation X=AΘ, where Θ is the kick vector and X is the resulting orbit vector. Since A is not necessarily a symmetric or even a square matrix we symmetrize it by using A T A. Then we find the eigenvalues and eigenvectors of this A T A matrix. The physical interpretation of the eigenvectors for circular machines is discussed. The task of the orbit correction is to find the kick vector Θ for a given measured orbit vector X. We are presenting a method, in which the kick vector is expressed as linear combination of the eigenvectors. An additional advantage of this method is that it yields the smallest possible kick vector to correct the orbit. We will illustrate the application of the method to the NSLS X-ray and UV storage rings and the resulting measurements. It will be evident, that the accuracy of this method allows the combination of the global orbit correction and local optimization of the orbit for beam lines and insertion devices. The eigenvector decomposition can also be used for optimizing kick vectors, taking advantage of the fact that eigenvectors with corresponding small eigenvalue generate negligible orbit changes. Thus, one can reduce a kick vector calculated by any other correction method and still stay within the tolerance for orbit correction. The use of eigenvectors in accurately measuring the response matrix and the use of the eigenvalue decomposition orbit correction algorithm in digital feedback is discussed. (orig.)

  12. Eigenvectors phase correction in inverse modal problem

    Science.gov (United States)

    Qiao, Guandong; Rahmatalla, Salam

    2017-12-01

    The solution of the inverse modal problem for the spatial parameters of mechanical and structural systems is heavily dependent on the quality of the modal parameters obtained from the experiments. While experimental and environmental noises will always exist during modal testing, the resulting modal parameters are expected to be corrupted with different levels of noise. A novel methodology is presented in this work to mitigate the errors in the eigenvectors when solving the inverse modal problem for the spatial parameters. The phases of the eigenvector component were utilized as design variables within an optimization problem that minimizes the difference between the calculated and experimental transfer functions. The equation of motion in terms of the modal and spatial parameters was used as a constraint in the optimization problem. Constraints that reserve the positive and semi-positive definiteness and the inter-connectivity of the spatial matrices were implemented using semi-definite programming. Numerical examples utilizing noisy eigenvectors with augmented Gaussian white noise of 1%, 5%, and 10% were used to demonstrate the efficacy of the proposed method. The results showed that the proposed method is superior when compared with a known method in the literature.

  13. Eigenvector of gravity gradient tensor for estimating fault dips considering fault type

    Science.gov (United States)

    Kusumoto, Shigekazu

    2017-12-01

    The dips of boundaries in faults and caldera walls play an important role in understanding their formation mechanisms. The fault dip is a particularly important parameter in numerical simulations for hazard map creation as the fault dip affects estimations of the area of disaster occurrence. In this study, I introduce a technique for estimating the fault dip using the eigenvector of the observed or calculated gravity gradient tensor on a profile and investigating its properties through numerical simulations. From numerical simulations, it was found that the maximum eigenvector of the tensor points to the high-density causative body, and the dip of the maximum eigenvector closely follows the dip of the normal fault. It was also found that the minimum eigenvector of the tensor points to the low-density causative body and that the dip of the minimum eigenvector closely follows the dip of the reverse fault. It was shown that the eigenvector of the gravity gradient tensor for estimating fault dips is determined by fault type. As an application of this technique, I estimated the dip of the Kurehayama Fault located in Toyama, Japan, and obtained a result that corresponded to conventional fault dip estimations by geology and geomorphology. Because the gravity gradient tensor is required for this analysis, I present a technique that estimates the gravity gradient tensor from the gravity anomaly on a profile.

  14. The best of both worlds: Phylogenetic eigenvector regression and mapping

    Directory of Open Access Journals (Sweden)

    José Alexandre Felizola Diniz Filho

    2015-09-01

    Full Text Available Eigenfunction analyses have been widely used to model patterns of autocorrelation in time, space and phylogeny. In a phylogenetic context, Diniz-Filho et al. (1998 proposed what they called Phylogenetic Eigenvector Regression (PVR, in which pairwise phylogenetic distances among species are submitted to a Principal Coordinate Analysis, and eigenvectors are then used as explanatory variables in regression, correlation or ANOVAs. More recently, a new approach called Phylogenetic Eigenvector Mapping (PEM was proposed, with the main advantage of explicitly incorporating a model-based warping in phylogenetic distance in which an Ornstein-Uhlenbeck (O-U process is fitted to data before eigenvector extraction. Here we compared PVR and PEM in respect to estimated phylogenetic signal, correlated evolution under alternative evolutionary models and phylogenetic imputation, using simulated data. Despite similarity between the two approaches, PEM has a slightly higher prediction ability and is more general than the original PVR. Even so, in a conceptual sense, PEM may provide a technique in the best of both worlds, combining the flexibility of data-driven and empirical eigenfunction analyses and the sounding insights provided by evolutionary models well known in comparative analyses.

  15. A subspace preconditioning algorithm for eigenvector/eigenvalue computation

    Energy Technology Data Exchange (ETDEWEB)

    Bramble, J.H.; Knyazev, A.V.; Pasciak, J.E.

    1996-12-31

    We consider the problem of computing a modest number of the smallest eigenvalues along with orthogonal bases for the corresponding eigen-spaces of a symmetric positive definite matrix. In our applications, the dimension of a matrix is large and the cost of its inverting is prohibitive. In this paper, we shall develop an effective parallelizable technique for computing these eigenvalues and eigenvectors utilizing subspace iteration and preconditioning. Estimates will be provided which show that the preconditioned method converges linearly and uniformly in the matrix dimension when used with a uniform preconditioner under the assumption that the approximating subspace is close enough to the span of desired eigenvectors.

  16. Eigenvectors determination of the ribosome dynamics model during mRNA translation using the Kleene Star algorithm

    Science.gov (United States)

    Ernawati; Carnia, E.; Supriatna, A. K.

    2018-03-01

    Eigenvalues and eigenvectors in max-plus algebra have the same important role as eigenvalues and eigenvectors in conventional algebra. In max-plus algebra, eigenvalues and eigenvectors are useful for knowing dynamics of the system such as in train system scheduling, scheduling production systems and scheduling learning activities in moving classes. In the translation of proteins in which the ribosome move uni-directionally along the mRNA strand to recruit the amino acids that make up the protein, eigenvalues and eigenvectors are used to calculate protein production rates and density of ribosomes on the mRNA. Based on this, it is important to examine the eigenvalues and eigenvectors in the process of protein translation. In this paper an eigenvector formula is given for a ribosome dynamics during mRNA translation by using the Kleene star algorithm in which the resulting eigenvector formula is simpler and easier to apply to the system than that introduced elsewhere. This paper also discusses the properties of the matrix {B}λ \\otimes n of model. Among the important properties, it always has the same elements in the first column for n = 1, 2,… if the eigenvalue is the time of initiation, λ = τin , and the column is the eigenvector of the model corresponding to λ.

  17. A spatial-spectral approach for deriving high signal quality eigenvectors for remote sensing image transformations

    DEFF Research Database (Denmark)

    Rogge, Derek; Bachmann, Martin; Rivard, Benoit

    2014-01-01

    Spectral decorrelation (transformations) methods have long been used in remote sensing. Transformation of the image data onto eigenvectors that comprise physically meaningful spectral properties (signal) can be used to reduce the dimensionality of hyperspectral images as the number of spectrally...... distinct signal sources composing a given hyperspectral scene is generally much less than the number of spectral bands. Determining eigenvectors dominated by signal variance as opposed to noise is a difficult task. Problems also arise in using these transformations on large images, multiple flight...... and spectral subsampling to the data, which is accomplished by deriving a limited set of eigenvectors for spatially contiguous subsets. These subset eigenvectors are compiled together to form a new noise reduced data set, which is subsequently used to derive a set of global orthogonal eigenvectors. Data from...

  18. A Markov chain representation of the normalized Perron–Frobenius eigenvector

    OpenAIRE

    Cerf, Raphaël; Dalmau, Joseba

    2017-01-01

    We consider the problem of finding the Perron–Frobenius eigenvector of a primitive matrix. Dividing each of the rows of the matrix by the sum of the elements in the row, the resulting new matrix is stochastic. We give a formula for the normalized Perron–Frobenius eigenvector of the original matrix, in terms of a realization of the Markov chain defined by the associated stochastic matrix. This formula is a generalization of the classical formula for the invariant probability measure of a Marko...

  19. RELATIVISTIC MAGNETOHYDRODYNAMICS: RENORMALIZED EIGENVECTORS AND FULL WAVE DECOMPOSITION RIEMANN SOLVER

    International Nuclear Information System (INIS)

    Anton, Luis; MartI, Jose M; Ibanez, Jose M; Aloy, Miguel A.; Mimica, Petar; Miralles, Juan A.

    2010-01-01

    We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.

  20. Chirality correlation within Dirac eigenvectors from domain wall fermions

    International Nuclear Information System (INIS)

    Blum, T.; Christ, N.; Cristian, C.; Liao, X.; Liu, G.; Mawhinney, R.; Wu, L.; Zhestkov, Y.; Dawson, C.

    2002-01-01

    In the dilute instanton gas model of the QCD vacuum, one expects a strong spatial correlation between chirality and the maxima of the Dirac eigenvectors with small eigenvalues. Following Horvath et al. we examine this question using lattice gauge theory within the quenched approximation. We extend the work of those authors by using weaker coupling, β=6.0, larger lattices, 16 4 , and an improved fermion formulation, domain wall fermions. In contrast with this earlier work, we find a striking correlation between the magnitudes of the chirality density, |ψ † (x)γ 5 ψ(x)|, and the normal density, ψ † (x)ψ(x), for the low-lying Dirac eigenvectors

  1. Distinct types of eigenvector localization in networks

    Science.gov (United States)

    Pastor-Satorras, Romualdo; Castellano, Claudio

    2016-01-01

    The spectral properties of the adjacency matrix provide a trove of information about the structure and function of complex networks. In particular, the largest eigenvalue and its associated principal eigenvector are crucial in the understanding of nodes’ centrality and the unfolding of dynamical processes. Here we show that two distinct types of localization of the principal eigenvector may occur in heterogeneous networks. For synthetic networks with degree distribution P(q) ~ q-γ, localization occurs on the largest hub if γ > 5/2 for γ < 5/2 a new type of localization arises on a mesoscopic subgraph associated with the shell with the largest index in the K-core decomposition. Similar evidence for the existence of distinct localization modes is found in the analysis of real-world networks. Our results open a new perspective on dynamical processes on networks and on a recently proposed alternative measure of node centrality based on the non-backtracking matrix.

  2. A teaching proposal for the study of Eigenvectors and Eigenvalues

    Directory of Open Access Journals (Sweden)

    María José Beltrán Meneu

    2017-03-01

    Full Text Available In this work, we present a teaching proposal which emphasizes on visualization and physical applications in the study of eigenvectors and eigenvalues. These concepts are introduced using the notion of the moment of inertia of a rigid body and the GeoGebra software. The proposal was motivated after observing students’ difficulties when treating eigenvectors and eigenvalues from a geometric point of view. It was designed following a particular sequence of activities with the schema: exploration, introduction of concepts, structuring of knowledge and application, and considering the three worlds of mathematical thinking provided by Tall: embodied, symbolic and formal.

  3. Eigenvector centrality mapping for analyzing connectivity patterns in fMRI data of the human brain.

    Directory of Open Access Journals (Sweden)

    Gabriele Lohmann

    Full Text Available Functional magnetic resonance data acquired in a task-absent condition ("resting state" require new data analysis techniques that do not depend on an activation model. In this work, we introduce an alternative assumption- and parameter-free method based on a particular form of node centrality called eigenvector centrality. Eigenvector centrality attributes a value to each voxel in the brain such that a voxel receives a large value if it is strongly correlated with many other nodes that are themselves central within the network. Google's PageRank algorithm is a variant of eigenvector centrality. Thus far, other centrality measures - in particular "betweenness centrality" - have been applied to fMRI data using a pre-selected set of nodes consisting of several hundred elements. Eigenvector centrality is computationally much more efficient than betweenness centrality and does not require thresholding of similarity values so that it can be applied to thousands of voxels in a region of interest covering the entire cerebrum which would have been infeasible using betweenness centrality. Eigenvector centrality can be used on a variety of different similarity metrics. Here, we present applications based on linear correlations and on spectral coherences between fMRI times series. This latter approach allows us to draw conclusions of connectivity patterns in different spectral bands. We apply this method to fMRI data in task-absent conditions where subjects were in states of hunger or satiety. We show that eigenvector centrality is modulated by the state that the subjects were in. Our analyses demonstrate that eigenvector centrality is a computationally efficient tool for capturing intrinsic neural architecture on a voxel-wise level.

  4. Motivating the Concept of Eigenvectors via Cryptography

    Science.gov (United States)

    Siap, Irfan

    2008-01-01

    New methods of teaching linear algebra in the undergraduate curriculum have attracted much interest lately. Most of this work is focused on evaluating and discussing the integration of special computer software into the Linear Algebra curriculum. In this article, I discuss my approach on introducing the concept of eigenvectors and eigenvalues,…

  5. Correlation of errors in the Monte Carlo fission source and the fission matrix fundamental-mode eigenvector

    International Nuclear Information System (INIS)

    Dufek, Jan; Holst, Gustaf

    2016-01-01

    Highlights: • Errors in the fission matrix eigenvector and fission source are correlated. • The error correlations depend on coarseness of the spatial mesh. • The error correlations are negligible when the mesh is very fine. - Abstract: Previous studies raised a question about the level of a possible correlation of errors in the cumulative Monte Carlo fission source and the fundamental-mode eigenvector of the fission matrix. A number of new methods tally the fission matrix during the actual Monte Carlo criticality calculation, and use its fundamental-mode eigenvector for various tasks. The methods assume the fission matrix eigenvector is a better representation of the fission source distribution than the actual Monte Carlo fission source, although the fission matrix and its eigenvectors do contain statistical and other errors. A recent study showed that the eigenvector could be used for an unbiased estimation of errors in the cumulative fission source if the errors in the eigenvector and the cumulative fission source were not correlated. Here we present new numerical study results that answer the question about the level of the possible error correlation. The results may be of importance to all methods that use the fission matrix. New numerical tests show that the error correlation is present at a level which strongly depends on properties of the spatial mesh used for tallying the fission matrix. The error correlation is relatively strong when the mesh is coarse, while the correlation weakens as the mesh gets finer. We suggest that the coarseness of the mesh is measured in terms of the value of the largest element in the tallied fission matrix as that way accounts for the mesh as well as system properties. In our test simulations, we observe only negligible error correlations when the value of the largest element in the fission matrix is about 0.1. Relatively strong error correlations appear when the value of the largest element in the fission matrix raises

  6. Methods for computing SN eigenvalues and eigenvectors of slab geometry transport problems

    International Nuclear Information System (INIS)

    Yavuz, Musa

    1998-01-01

    We discuss computational methods for computing the eigenvalues and eigenvectors of single energy-group neutral particle transport (S N ) problems in homogeneous slab geometry, with an arbitrary scattering anisotropy of order L. These eigensolutions are important when exact (or very accurate) solutions are desired for coarse spatial cell problems demanding rapid execution times. Three methods, one of which is 'new', are presented for determining the eigenvalues and eigenvectors of such S N problems. In the first method, separation of variables is directly applied to the S N equations. In the second method, common characteristics of the S N and P N-1 equations are used. In the new method, the eigenvalues and eigenvectors can be computed provided that the cell-interface Green's functions (transmission and reflection factors) are known. Numerical results for S 4 test problems are given to compare the new method with the existing methods

  7. Methods for computing SN eigenvalues and eigenvectors of slab geometry transport problems

    International Nuclear Information System (INIS)

    Yavuz, M.

    1997-01-01

    We discuss computational methods for computing the eigenvalues and eigenvectors of single energy-group neutral particle transport (S N ) problems in homogeneous slab geometry, with an arbitrary scattering anisotropy of order L. These eigensolutions are important when exact (or very accurate) solutions are desired for coarse spatial cell problems demanding rapid execution times. Three methods, one of which is 'new', are presented for determining the eigenvalues and eigenvectors of such S N problems. In the first method, separation of variables is directly applied to the S N equations. In the second method, common characteristics of the S N and P N-1 equations are used. In the new method, the eigenvalues and eigenvectors can be computed provided that the cell-interface Green's functions (transmission and reflection factors) are known. Numerical results for S 4 test problems are given to compare the new method with the existing methods. (author)

  8. Simple eigenvectors of unbounded operators of the type “normal plus compact”

    Directory of Open Access Journals (Sweden)

    Michael Gil'

    2015-01-01

    Full Text Available The paper deals with operators of the form \\(A=S+B\\, where \\(B\\ is a compact operator in a Hilbert space \\(H\\ and \\(S\\ is an unbounded normal one in \\(H\\, having a compact resolvent. We consider approximations of the eigenvectors of \\(A\\, corresponding to simple eigenvalues by the eigenvectors of the operators \\(A_n=S+B_n\\ (\\(n=1,2, \\ldots\\, where \\(B_n\\ is an \\(n\\-dimensional operator. In addition, we obtain the error estimate of the approximation.

  9. Acceleration of criticality analysis solution convergence by matrix eigenvector for a system with weak neutron interaction

    Energy Technology Data Exchange (ETDEWEB)

    Nomura, Yasushi; Takada, Tomoyuki; Kuroishi, Takeshi [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment; Kadotani, Hiroyuki [Shizuoka Sangyo Univ., Iwata, Shizuoka (Japan)

    2003-03-01

    In the case of Monte Carlo calculation to obtain a neutron multiplication factor for a system of weak neutron interaction, there might be some problems concerning convergence of the solution. Concerning this difficulty in the computer code calculations, theoretical derivation was made from the general neutron transport equation and consideration was given for acceleration of solution convergence by using the matrix eigenvector in this report. Accordingly, matrix eigenvector calculation scheme was incorporated together with procedure to make acceleration of convergence into the continuous energy Monte Carlo code MCNP. Furthermore, effectiveness of acceleration of solution convergence by matrix eigenvector was ascertained with the results obtained by applying to the two OECD/NEA criticality analysis benchmark problems. (author)

  10. Computing the eigenvalues and eigenvectors of a fuzzy matrix

    Directory of Open Access Journals (Sweden)

    A. Kumar

    2012-08-01

    Full Text Available Computation of fuzzy eigenvalues and fuzzy eigenvectors of a fuzzy matrix is a challenging problem. Determining the maximal and minimal symmetric solution can help to find the eigenvalues. So, we try to compute these eigenvalues by determining the maximal and minimal symmetric solution of the fully fuzzy linear system $widetilde{A}widetilde{X}= widetilde{lambda} widetilde{X}.$

  11. Those Do What? Connecting Eigenvectors and Eigenvalues to the Rest of Linear Algebra: Using Visual Enhancements to Help Students Connect Eigenvectors to the Rest of Linear Algebra

    Science.gov (United States)

    Nyman, Melvin A.; Lapp, Douglas A.; St. John, Dennis; Berry, John S.

    2010-01-01

    This paper discusses student difficulties in grasping concepts from Linear Algebra--in particular, the connection of eigenvalues and eigenvectors to other important topics in linear algebra. Based on our prior observations from student interviews, we propose technology-enhanced instructional approaches that might positively impact student…

  12. Unveiling the significance of eigenvectors in diffusing non-Hermitian matrices by identifying the underlying Burgers dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Burda, Zdzislaw, E-mail: zdzislaw.burda@agh.edu.pl [AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, al. Mickiewicza 30, PL-30059 Kraków (Poland); Grela, Jacek, E-mail: jacekgrela@gmail.com [M. Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Centre, Jagiellonian University, PL-30348 Kraków (Poland); Nowak, Maciej A., E-mail: nowak@th.if.uj.edu.pl [M. Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Centre, Jagiellonian University, PL-30348 Kraków (Poland); Tarnowski, Wojciech, E-mail: wojciech.tarnowski@uj.edu.pl [M. Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Centre, Jagiellonian University, PL-30348 Kraków (Poland); Warchoł, Piotr, E-mail: piotr.warchol@uj.edu.pl [M. Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Centre, Jagiellonian University, PL-30348 Kraków (Poland)

    2015-08-15

    Following our recent letter, we study in detail an entry-wise diffusion of non-hermitian complex matrices. We obtain an exact partial differential equation (valid for any matrix size N and arbitrary initial conditions) for evolution of the averaged extended characteristic polynomial. The logarithm of this polynomial has an interpretation of a potential which generates a Burgers dynamics in quaternionic space. The dynamics of the ensemble in the large N limit is completely determined by the coevolution of the spectral density and a certain eigenvector correlation function. This coevolution is best visible in an electrostatic potential of a quaternionic argument built of two complex variables, the first of which governs standard spectral properties while the second unravels the hidden dynamics of eigenvector correlation function. We obtain general formulas for the spectral density and the eigenvector correlation function for large N and for any initial conditions. We exemplify our studies by solving three examples, and we verify the analytic form of our solutions with numerical simulations.

  13. An exploration of diffusion tensor eigenvector variability within human calf muscles.

    Science.gov (United States)

    Rockel, Conrad; Noseworthy, Michael D

    2016-01-01

    To explore the effect of diffusion tensor imaging (DTI) acquisition parameters on principal and minor eigenvector stability within human lower leg skeletal muscles. Lower leg muscles were evaluated in seven healthy subjects at 3T using an 8-channel transmit/receive coil. Diffusion-encoding was performed with nine signal averages (NSA) using 6, 15, and 25 directions (NDD). Individual DTI volumes were combined into aggregate volumes of 3, 2, and 1 NSA according to number of directions. Tensor eigenvalues (λ1 , λ2 , λ3 ), eigenvectors (ε1 , ε2 , ε3 ), and DTI metrics (fractional anisotropy [FA] and mean diffusivity [MD]) were calculated for each combination of NSA and NDD. Spatial maps of signal-to-noise ratio (SNR), λ3 :λ2 ratio, and zenith angle were also calculated for region of interest (ROI) analysis of vector orientation consistency. ε1 variability was only moderately related to ε2 variability (r = 0.4045). Variation of ε1 was affected by NDD, not NSA (P < 0.0002), while variation of ε2 was affected by NSA, not NDD (P < 0.0003). In terms of tensor shape, vector variability was weakly related to FA (ε1 :r = -0.1854, ε2 : ns), but had a stronger relation to the λ3 :λ2 ratio (ε1 :r = -0.5221, ε2 :r = -0.1771). Vector variability was also weakly related to SNR (ε1 :r = -0.2873, ε2 :r = -0.3483). Zenith angle was found to be strongly associated with variability of ε1 (r = 0.8048) but only weakly with that of ε2 (r = 0.2135). The second eigenvector (ε2 ) displayed higher directional variability relative to ε1 , and was only marginally affected by experimental conditions that impacted ε1 variability. © 2015 Wiley Periodicals, Inc.

  14. On the Eigenvalues and Eigenvectors of Block Triangular Preconditioned Block Matrices

    KAUST Repository

    Pestana, Jennifer

    2014-01-01

    Block lower triangular matrices and block upper triangular matrices are popular preconditioners for 2×2 block matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned matrices are related. © 2014 Society for Industrial and Applied Mathematics.

  15. On the raising and lowering difference operators for eigenvectors of the finite Fourier transform

    International Nuclear Information System (INIS)

    Atakishiyeva, M K; Atakishiyev, N M

    2015-01-01

    We construct explicit forms of raising and lowering difference operators that govern eigenvectors of the finite (discrete) Fourier transform. Some of the algebraic properties of these operators are also examined. (paper)

  16. Quasars in the 4D Eigenvector 1 Context: a stroll down memory lane

    Science.gov (United States)

    Sulentic, Jack; Marziani, Paola

    2015-10-01

    Recently some pessimism has been expressed about our lack of progress in understanding quasars over more than fifty year since their discovery. It is worthwhile to look back at some of the progress that has been made - but still lies under the radar - perhaps because few people are working on optical/UV spectroscopy in this field. Great advances in understanding quasar phenomenology have emerged using eigenvector techniques. The 4D eigenvector 1 context provides a surrogate H-R Diagram for quasars with a source main sequence driven by Eddington ratio convolved with line-of-sight orientation. Appreciating the striking differences between quasars at opposite ends of the main sequence (so-called population A and B sources) opens the door towards a unified model of quasar physics, geometry and kinematics. We present a review of some of the progress that has been made over the past 15 years, and point out unsolved issues.

  17. Quasars in the 4D Eigenvector 1 Context: a stroll down memory lane

    Directory of Open Access Journals (Sweden)

    Jack W. Sulentic

    2015-10-01

    Full Text Available Recently some pessimism has been expressed about our lack of progress in understanding quasars over more than fifty year since their discovery. It is worthwhile to look back at some of the progress that has been made – but still lies under the radar – perhaps because few people are working on optical/UV spectroscopy in this field. Great advances in understanding quasar phenomenology have emerged using eigenvector techniques. The 4D eigenvector 1 context provides a surrogate H-R Diagram for quasars with a source main sequence driven by Eddington ratio convolved with line-of-sight orientation. Appreciating the striking differences between quasars at opposite ends of the main sequence (so-called population A and B sources opens the door towards a unified model of quasar physics, geometry and kinematics. We present a review of some of the progress that has been made over the past 15 years, and point out unsolved issues.

  18. Quasars in the 4D eigenvector 1 context: a stroll down memory lane

    International Nuclear Information System (INIS)

    Sulentic, Jack W.; Marziani, Paola

    2015-01-01

    Recently some pessimism has been expressed about our lack of progress in understanding quasars over the 50+ year since their discovery (Antonucci, 2013). It is worthwhile to look back at some of the progress that has been made—but still lies under the radar—perhaps because few people are working on optical/UV spectroscopy in this field. Great advances in understanding quasar phenomenology have emerged using eigenvector techniques. The 4D eigenvector 1 context provides a surrogate H-R Diagram for quasars with a source main sequence driven by Eddington ratio convolved with line-of-sight orientation. Appreciating the striking differences between quasars at opposite ends of the main sequence (so-called population A and B sources) opens the door toward a unified model of quasar physics, geometry and kinematics. We present a review of some of the progress that has been made over the past 15 years, and point out unsolved issues.

  19. Quasars in the 4D eigenvector 1 context: a stroll down memory lane

    Energy Technology Data Exchange (ETDEWEB)

    Sulentic, Jack W. [Instituto de Astrofísica de Andalucía-Consejo Superior de Investigaciones Científicas, Granada (Spain); Marziani, Paola, E-mail: paola.marziani@oapd.inaf.it [Istituto Nazionale di Astrofisica, Osservatorio Astronomico di Padova, Padova (Italy)

    2015-10-13

    Recently some pessimism has been expressed about our lack of progress in understanding quasars over the 50+ year since their discovery (Antonucci, 2013). It is worthwhile to look back at some of the progress that has been made—but still lies under the radar—perhaps because few people are working on optical/UV spectroscopy in this field. Great advances in understanding quasar phenomenology have emerged using eigenvector techniques. The 4D eigenvector 1 context provides a surrogate H-R Diagram for quasars with a source main sequence driven by Eddington ratio convolved with line-of-sight orientation. Appreciating the striking differences between quasars at opposite ends of the main sequence (so-called population A and B sources) opens the door toward a unified model of quasar physics, geometry and kinematics. We present a review of some of the progress that has been made over the past 15 years, and point out unsolved issues.

  20. Geometric and topological characterization of porous media: insights from eigenvector centrality

    Science.gov (United States)

    Jimenez-Martinez, J.; Negre, C.

    2017-12-01

    Solving flow and transport through complex geometries such as porous media involves an extreme computational cost. Simplifications such as pore networks, where the pores are represented by nodes and the pore throats by edges connecting pores, have been proposed. These models have the ability to preserve the connectivity of the medium. However, they have difficulties capturing preferential paths (high velocity) and stagnation zones (low velocity), as they do not consider the specific relations between nodes. Network theory approaches, where the complex network is conceptualized like a graph, can help to simplify and better understand fluid dynamics and transport in porous media. To address this issue, we propose a method based on eigenvector centrality. It has been corrected to overcome the centralization problem and modified to introduce a bias in the centrality distribution along a particular direction which allows considering the flow and transport anisotropy in porous media. The model predictions are compared with millifluidic transport experiments, showing that this technique is computationally efficient and has potential for predicting preferential paths and stagnation zones for flow and transport in porous media. Entropy computed from the eigenvector centrality probability distribution is proposed as an indicator of the "mixing capacity" of the system.

  1. Eigenvector centrality for geometric and topological characterization of porous media

    Science.gov (United States)

    Jimenez-Martinez, Joaquin; Negre, Christian F. A.

    2017-07-01

    Solving flow and transport through complex geometries such as porous media is computationally difficult. Such calculations usually involve the solution of a system of discretized differential equations, which could lead to extreme computational cost depending on the size of the domain and the accuracy of the model. Geometric simplifications like pore networks, where the pores are represented by nodes and the pore throats by edges connecting pores, have been proposed. These models, despite their ability to preserve the connectivity of the medium, have difficulties capturing preferential paths (high velocity) and stagnation zones (low velocity), as they do not consider the specific relations between nodes. Nonetheless, network theory approaches, where a complex network is a graph, can help to simplify and better understand fluid dynamics and transport in porous media. Here we present an alternative method to address these issues based on eigenvector centrality, which has been corrected to overcome the centralization problem and modified to introduce a bias in the centrality distribution along a particular direction to address the flow and transport anisotropy in porous media. We compare the model predictions with millifluidic transport experiments, which shows that, albeit simple, this technique is computationally efficient and has potential for predicting preferential paths and stagnation zones for flow and transport in porous media. We propose to use the eigenvector centrality probability distribution to compute the entropy as an indicator of the "mixing capacity" of the system.

  2. Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices

    Science.gov (United States)

    Böttcher, A.; Bogoya, J. M.; Grudsky, S. M.; Maximenko, E. A.

    2017-11-01

    Analysis of the asymptotic behaviour of the spectral characteristics of Toeplitz matrices as the dimension of the matrix tends to infinity has a history of over 100 years. For instance, quite a number of versions of Szegő's theorem on the asymptotic behaviour of eigenvalues and of the so-called strong Szegő theorem on the asymptotic behaviour of the determinants of Toeplitz matrices are known. Starting in the 1950s, the asymptotics of the maximum and minimum eigenvalues were actively investigated. However, investigation of the individual asymptotics of all the eigenvalues and eigenvectors of Toeplitz matrices started only quite recently: the first papers on this subject were published in 2009-2010. A survey of this new field is presented here. Bibliography: 55 titles.

  3. Analysis of the characteristics of the global virtual water trade network using degree and eigenvector centrality, with a focus on food and feed crops

    Directory of Open Access Journals (Sweden)

    S.-H. Lee

    2016-10-01

    Full Text Available This study aims to analyze the characteristics of global virtual water trade (GVWT, such as the connectivity of each trader, vulnerable importers, and influential countries, using degree and eigenvector centrality during the period 2006–2010. The degree centrality was used to measure the connectivity, and eigenvector centrality was used to measure the influence on the entire GVWT network. Mexico, Egypt, China, the Republic of Korea, and Japan were classified as vulnerable importers, because they imported large quantities of virtual water with low connectivity. In particular, Egypt had a 15.3 Gm3 year−1 blue water saving effect through GVWT: the vulnerable structure could cause a water shortage problem for the importer. The entire GVWT network could be changed by a few countries, termed "influential traders". We used eigenvector centrality to identify those influential traders. In GVWT for food crops, the USA, Russian Federation, Thailand, and Canada had high eigenvector centrality with large volumes of green water trade. In the case of blue water trade, western Asia, Pakistan, and India had high eigenvector centrality. For feed crops, the green water trade in the USA, Brazil, and Argentina was the most influential. However, Argentina and Pakistan used high proportions of internal water resources for virtual water export (32.9 and 25.1 %; thus other traders should carefully consider water resource management in these exporters.

  4. Analysis of the characteristics of the global virtual water trade network using degree and eigenvector centrality, with a focus on food and feed crops

    Science.gov (United States)

    Lee, Sang-Hyun; Mohtar, Rabi H.; Choi, Jin-Yong; Yoo, Seung-Hwan

    2016-10-01

    This study aims to analyze the characteristics of global virtual water trade (GVWT), such as the connectivity of each trader, vulnerable importers, and influential countries, using degree and eigenvector centrality during the period 2006-2010. The degree centrality was used to measure the connectivity, and eigenvector centrality was used to measure the influence on the entire GVWT network. Mexico, Egypt, China, the Republic of Korea, and Japan were classified as vulnerable importers, because they imported large quantities of virtual water with low connectivity. In particular, Egypt had a 15.3 Gm3 year-1 blue water saving effect through GVWT: the vulnerable structure could cause a water shortage problem for the importer. The entire GVWT network could be changed by a few countries, termed "influential traders". We used eigenvector centrality to identify those influential traders. In GVWT for food crops, the USA, Russian Federation, Thailand, and Canada had high eigenvector centrality with large volumes of green water trade. In the case of blue water trade, western Asia, Pakistan, and India had high eigenvector centrality. For feed crops, the green water trade in the USA, Brazil, and Argentina was the most influential. However, Argentina and Pakistan used high proportions of internal water resources for virtual water export (32.9 and 25.1 %); thus other traders should carefully consider water resource management in these exporters.

  5. Eigenvector Subset Selection Using Bayesian Optimization Algorithm%基于贝叶斯优化算法的脸面特征向量子集选择

    Institute of Scientific and Technical Information of China (English)

    郭卫锋; 林亚平; 罗光平

    2002-01-01

    Eigenvector subset selection is the key to face recognition. In this paper ,we propose ESS-BOA, a newrandomized, population-based evolutionary algorithm which deals with the Eigenvector Subset Selection (ESS)prob-lem on face recognition application. In ESS-BOA ,the ESS problem, stated as a search problem ,uses the BayesianOptimization Algorithm (BOA) as searching engine and the distance degree as the object function to select eigenvec-tor. Experimental results show that ESS-BOA outperforms the traditional the eigenface selection algorithm.

  6. Computation of dominant eigenvalues and eigenvectors: A comparative study of algorithms

    International Nuclear Information System (INIS)

    Nightingale, M.P.; Viswanath, V.S.; Mueller, G.

    1993-01-01

    We investigate two widely used recursive algorithms for the computation of eigenvectors with extreme eigenvalues of large symmetric matrices---the modified Lanczoes method and the conjugate-gradient method. The goal is to establish a connection between their underlying principles and to evaluate their performance in applications to Hamiltonian and transfer matrices of selected model systems of interest in condensed matter physics and statistical mechanics. The conjugate-gradient method is found to converge more rapidly for understandable reasons, while storage requirements are the same for both methods

  7. Eigenvector Weighting Function in Face Recognition

    Directory of Open Access Journals (Sweden)

    Pang Ying Han

    2011-01-01

    Full Text Available Graph-based subspace learning is a class of dimensionality reduction technique in face recognition. The technique reveals the local manifold structure of face data that hidden in the image space via a linear projection. However, the real world face data may be too complex to measure due to both external imaging noises and the intra-class variations of the face images. Hence, features which are extracted by the graph-based technique could be noisy. An appropriate weight should be imposed to the data features for better data discrimination. In this paper, a piecewise weighting function, known as Eigenvector Weighting Function (EWF, is proposed and implemented in two graph based subspace learning techniques, namely Locality Preserving Projection and Neighbourhood Preserving Embedding. Specifically, the computed projection subspace of the learning approach is decomposed into three partitions: a subspace due to intra-class variations, an intrinsic face subspace, and a subspace which is attributed to imaging noises. Projected data features are weighted differently in these subspaces to emphasize the intrinsic face subspace while penalizing the other two subspaces. Experiments on FERET and FRGC databases are conducted to show the promising performance of the proposed technique.

  8. Protein structure recognition: From eigenvector analysis to structural threading method

    Science.gov (United States)

    Cao, Haibo

    In this work, we try to understand the protein folding problem using pair-wise hydrophobic interaction as the dominant interaction for the protein folding process. We found a strong correlation between amino acid sequence and the corresponding native structure of the protein. Some applications of this correlation were discussed in this dissertation include the domain partition and a new structural threading method as well as the performance of this method in the CASP5 competition. In the first part, we give a brief introduction to the protein folding problem. Some essential knowledge and progress from other research groups was discussed. This part include discussions of interactions among amino acids residues, lattice HP model, and the designablity principle. In the second part, we try to establish the correlation between amino acid sequence and the corresponding native structure of the protein. This correlation was observed in our eigenvector study of protein contact matrix. We believe the correlation is universal, thus it can be used in automatic partition of protein structures into folding domains. In the third part, we discuss a threading method based on the correlation between amino acid sequence and ominant eigenvector of the structure contact-matrix. A mathematically straightforward iteration scheme provides a self-consistent optimum global sequence-structure alignment. The computational efficiency of this method makes it possible to search whole protein structure databases for structural homology without relying on sequence similarity. The sensitivity and specificity of this method is discussed, along with a case of blind test prediction. In the appendix, we list the overall performance of this threading method in CASP5 blind test in comparison with other existing approaches.

  9. Protein Structure Recognition: From Eigenvector Analysis to Structural Threading Method

    Energy Technology Data Exchange (ETDEWEB)

    Cao, Haibo [Iowa State Univ., Ames, IA (United States)

    2003-01-01

    In this work, they try to understand the protein folding problem using pair-wise hydrophobic interaction as the dominant interaction for the protein folding process. They found a strong correlation between amino acid sequences and the corresponding native structure of the protein. Some applications of this correlation were discussed in this dissertation include the domain partition and a new structural threading method as well as the performance of this method in the CASP5 competition. In the first part, they give a brief introduction to the protein folding problem. Some essential knowledge and progress from other research groups was discussed. This part includes discussions of interactions among amino acids residues, lattice HP model, and the design ability principle. In the second part, they try to establish the correlation between amino acid sequence and the corresponding native structure of the protein. This correlation was observed in the eigenvector study of protein contact matrix. They believe the correlation is universal, thus it can be used in automatic partition of protein structures into folding domains. In the third part, they discuss a threading method based on the correlation between amino acid sequences and ominant eigenvector of the structure contact-matrix. A mathematically straightforward iteration scheme provides a self-consistent optimum global sequence-structure alignment. The computational efficiency of this method makes it possible to search whole protein structure databases for structural homology without relying on sequence similarity. The sensitivity and specificity of this method is discussed, along with a case of blind test prediction. In the appendix, they list the overall performance of this threading method in CASP5 blind test in comparison with other existing approaches.

  10. Protein Structure Recognition: From Eigenvector Analysis to Structural Threading Method

    International Nuclear Information System (INIS)

    Haibo Cao

    2003-01-01

    In this work, they try to understand the protein folding problem using pair-wise hydrophobic interaction as the dominant interaction for the protein folding process. They found a strong correlation between amino acid sequences and the corresponding native structure of the protein. Some applications of this correlation were discussed in this dissertation include the domain partition and a new structural threading method as well as the performance of this method in the CASP5 competition. In the first part, they give a brief introduction to the protein folding problem. Some essential knowledge and progress from other research groups was discussed. This part includes discussions of interactions among amino acids residues, lattice HP model, and the design ability principle. In the second part, they try to establish the correlation between amino acid sequence and the corresponding native structure of the protein. This correlation was observed in the eigenvector study of protein contact matrix. They believe the correlation is universal, thus it can be used in automatic partition of protein structures into folding domains. In the third part, they discuss a threading method based on the correlation between amino acid sequences and ominant eigenvector of the structure contact-matrix. A mathematically straightforward iteration scheme provides a self-consistent optimum global sequence-structure alignment. The computational efficiency of this method makes it possible to search whole protein structure databases for structural homology without relying on sequence similarity. The sensitivity and specificity of this method is discussed, along with a case of blind test prediction. In the appendix, they list the overall performance of this threading method in CASP5 blind test in comparison with other existing approaches

  11. Investigation, development and application of optimal output feedback theory. Vol. 4: Measures of eigenvalue/eigenvector sensitivity to system parameters and unmodeled dynamics

    Science.gov (United States)

    Halyo, Nesim

    1987-01-01

    Some measures of eigenvalue and eigenvector sensitivity applicable to both continuous and discrete linear systems are developed and investigated. An infinite series representation is developed for the eigenvalues and eigenvectors of a system. The coefficients of the series are coupled, but can be obtained recursively using a nonlinear coupled vector difference equation. A new sensitivity measure is developed by considering the effects of unmodeled dynamics. It is shown that the sensitivity is high when any unmodeled eigenvalue is near a modeled eigenvalue. Using a simple example where the sensor dynamics have been neglected, it is shown that high feedback gains produce high eigenvalue/eigenvector sensitivity. The smallest singular value of the return difference is shown not to reflect eigenvalue sensitivity since it increases with the feedback gains. Using an upper bound obtained from the infinite series, a procedure to evaluate whether the sensitivity to parameter variations is within given acceptable bounds is developed and demonstrated by an example.

  12. q-Extension of Mehta's eigenvectors of the finite Fourier transform for q, a root of unity

    NARCIS (Netherlands)

    Atakishiyeva, M.K.; Atakishiyev, N.M.; Koornwinder, T.H.

    2009-01-01

    It is shown that the continuous q-Hermite polynomials for q, a root of unity, have simple transformation properties with respect to the classical Fourier transform. This result is then used to construct q-extended eigenvectors of the finite Fourier transform in terms of these polynomials.

  13. Recursive Principal Components Analysis Using Eigenvector Matrix Perturbation

    Directory of Open Access Journals (Sweden)

    Deniz Erdogmus

    2004-10-01

    Full Text Available Principal components analysis is an important and well-studied subject in statistics and signal processing. The literature has an abundance of algorithms for solving this problem, where most of these algorithms could be grouped into one of the following three approaches: adaptation based on Hebbian updates and deflation, optimization of a second-order statistical criterion (like reconstruction error or output variance, and fixed point update rules with deflation. In this paper, we take a completely different approach that avoids deflation and the optimization of a cost function using gradients. The proposed method updates the eigenvector and eigenvalue matrices simultaneously with every new sample such that the estimates approximately track their true values as would be calculated from the current sample estimate of the data covariance matrix. The performance of this algorithm is compared with that of traditional methods like Sanger's rule and APEX, as well as a structurally similar matrix perturbation-based method.

  14. Detection of multiple damages employing best achievable eigenvectors under Bayesian inference

    Science.gov (United States)

    Prajapat, Kanta; Ray-Chaudhuri, Samit

    2018-05-01

    A novel approach is presented in this work to localize simultaneously multiple damaged elements in a structure along with the estimation of damage severity for each of the damaged elements. For detection of damaged elements, a best achievable eigenvector based formulation has been derived. To deal with noisy data, Bayesian inference is employed in the formulation wherein the likelihood of the Bayesian algorithm is formed on the basis of errors between the best achievable eigenvectors and the measured modes. In this approach, the most probable damage locations are evaluated under Bayesian inference by generating combinations of various possible damaged elements. Once damage locations are identified, damage severities are estimated using a Bayesian inference Markov chain Monte Carlo simulation. The efficiency of the proposed approach has been demonstrated by carrying out a numerical study involving a 12-story shear building. It has been found from this study that damage scenarios involving as low as 10% loss of stiffness in multiple elements are accurately determined (localized and severities quantified) even when 2% noise contaminated modal data are utilized. Further, this study introduces a term parameter impact (evaluated based on sensitivity of modal parameters towards structural parameters) to decide the suitability of selecting a particular mode, if some idea about the damaged elements are available. It has been demonstrated here that the accuracy and efficiency of the Bayesian quantification algorithm increases if damage localization is carried out a-priori. An experimental study involving a laboratory scale shear building and different stiffness modification scenarios shows that the proposed approach is efficient enough to localize the stories with stiffness modification.

  15. Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz

    Directory of Open Access Journals (Sweden)

    Samuel Belliard

    2013-11-01

    Full Text Available We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this result for the chains with small length. We obtain also an off-shell equation (i.e. satisfied without the Bethe equations formally similar to the ones obtained in the periodic case or with diagonal boundaries.

  16. On a q-extension of Mehta's eigenvectors of the finite Fourier transform for q a root of unity

    OpenAIRE

    Atakishiyeva, Mesuma K.; Atakishiyev, Natig M.; Koornwinder, Tom H.

    2008-01-01

    It is shown that the continuous q-Hermite polynomials for q a root of unity have simple transformation properties with respect to the classical Fourier transform. This result is then used to construct q-extended eigenvectors of the finite Fourier transform in terms of these polynomials.

  17. Application Research of the Sparse Representation of Eigenvector on the PD Positioning in the Transformer Oil

    Directory of Open Access Journals (Sweden)

    Qing Xie

    2016-01-01

    Full Text Available The partial discharge (PD detection of electrical equipment is important for the safe operation of power system. The ultrasonic signal generated by the PD in the oil is a broadband signal. However, most methods of the array signal processing are used for the narrowband signal at present, and the effect of some methods for processing wideband signals is not satisfactory. Therefore, it is necessary to find new broadband signal processing methods to improve detection ability of the PD source. In this paper, the direction of arrival (DOA estimation method based on sparse representation of eigenvector is proposed, and this method can further reduce the noise interference. Moreover, the simulation results show that this direction finding method is feasible for broadband signal and thus improve the following positioning accuracy of the three-array localization method. And experimental results verify that the direction finding method based on sparse representation of eigenvector is feasible for the ultrasonic array, which can achieve accurate estimation of direction of arrival and improve the following positioning accuracy. This can provide important guidance information for the equipment maintenance in the practical application.

  18. Eigenvectors and fixed point of non-linear operators

    Directory of Open Access Journals (Sweden)

    Giulio Trombetta

    2007-12-01

    Full Text Available Let X be a real infinite-dimensional Banach space and ψ a measure of noncompactness on X. Let Ω be a bounded open subset of X and A : Ω → X a ψ-condensing operator, which has no fixed points on ∂Ω.Then the fixed point index, ind(A,Ω, of A on Ω is defined (see, for example, ([1] and [18]. In particular, if A is a compact operator ind(A,Ω agrees with the classical Leray-Schauder degree of I −A on Ω relative to the point 0, deg(I −A,Ω,0. The main aim of this note is to investigate boundary conditions, under which the fixed point index of strict- ψ-contractive or ψ-condensing operators A : Ω → X is equal to zero. Correspondingly, results on eigenvectors and nonzero fixed points of k-ψ-contractive and ψ-condensing operators are obtained. In particular we generalize the Birkhoff-Kellog theorem [4] and Guo’s domain compression and expansion theorem [17]. The note is based mainly on the results contained in [7] and [8].

  19. Multivariate analysis of eigenvalues and eigenvectors in tensor based morphometry

    Science.gov (United States)

    Rajagopalan, Vidya; Schwartzman, Armin; Hua, Xue; Leow, Alex; Thompson, Paul; Lepore, Natasha

    2015-01-01

    We develop a new algorithm to compute voxel-wise shape differences in tensor-based morphometry (TBM). As in standard TBM, we non-linearly register brain T1-weighed MRI data from a patient and control group to a template, and compute the Jacobian of the deformation fields. In standard TBM, the determinants of the Jacobian matrix at each voxel are statistically compared between the two groups. More recently, a multivariate extension of the statistical analysis involving the deformation tensors derived from the Jacobian matrices has been shown to improve statistical detection power.7 However, multivariate methods comprising large numbers of variables are computationally intensive and may be subject to noise. In addition, the anatomical interpretation of results is sometimes difficult. Here instead, we analyze the eigenvalues and the eigenvectors of the Jacobian matrices. Our method is validated on brain MRI data from Alzheimer's patients and healthy elderly controls from the Alzheimer's Disease Neuro Imaging Database.

  20. Eigenvalue-eigenvector decomposition (EED) analysis of dissimilarity and covariance matrix obtained from total synchronous fluorescence spectral (TSFS) data sets of herbal preparations: Optimizing the classification approach

    Science.gov (United States)

    Tarai, Madhumita; Kumar, Keshav; Divya, O.; Bairi, Partha; Mishra, Kishor Kumar; Mishra, Ashok Kumar

    2017-09-01

    The present work compares the dissimilarity and covariance based unsupervised chemometric classification approaches by taking the total synchronous fluorescence spectroscopy data sets acquired for the cumin and non-cumin based herbal preparations. The conventional decomposition method involves eigenvalue-eigenvector analysis of the covariance of the data set and finds the factors that can explain the overall major sources of variation present in the data set. The conventional approach does this irrespective of the fact that the samples belong to intrinsically different groups and hence leads to poor class separation. The present work shows that classification of such samples can be optimized by performing the eigenvalue-eigenvector decomposition on the pair-wise dissimilarity matrix.

  1. Joint eigenvector estimation from mutually anisotropic tensors improves susceptibility tensor imaging of the brain, kidney, and heart.

    Science.gov (United States)

    Dibb, Russell; Liu, Chunlei

    2017-06-01

    To develop a susceptibility-based MRI technique for probing microstructure and fiber architecture of magnetically anisotropic tissues-such as central nervous system white matter, renal tubules, and myocardial fibers-in three dimensions using susceptibility tensor imaging (STI) tools. STI can probe tissue microstructure, but is limited by reconstruction artifacts because of absent phase information outside the tissue and noise. STI accuracy may be improved by estimating a joint eigenvector from mutually anisotropic susceptibility and relaxation tensors. Gradient-recalled echo image data were simulated using a numerical phantom and acquired from the ex vivo mouse brain, kidney, and heart. Susceptibility tensor data were reconstructed using STI, regularized STI, and the proposed algorithm of mutually anisotropic and joint eigenvector STI (MAJESTI). Fiber map and tractography results from each technique were compared with diffusion tensor data. MAJESTI reduced the estimated susceptibility tensor orientation error by 30% in the phantom, 36% in brain white matter, 40% in the inner medulla of the kidney, and 45% in myocardium. This improved the continuity and consistency of susceptibility-based fiber tractography in each tissue. MAJESTI estimation of the susceptibility tensors yields lower orientation errors for susceptibility-based fiber mapping and tractography in the intact brain, kidney, and heart. Magn Reson Med 77:2331-2346, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

  2. Eigenvalue-eigenvector decomposition (EED) analysis of dissimilarity and covariance matrix obtained from total synchronous fluorescence spectral (TSFS) data sets of herbal preparations: Optimizing the classification approach.

    Science.gov (United States)

    Tarai, Madhumita; Kumar, Keshav; Divya, O; Bairi, Partha; Mishra, Kishor Kumar; Mishra, Ashok Kumar

    2017-09-05

    The present work compares the dissimilarity and covariance based unsupervised chemometric classification approaches by taking the total synchronous fluorescence spectroscopy data sets acquired for the cumin and non-cumin based herbal preparations. The conventional decomposition method involves eigenvalue-eigenvector analysis of the covariance of the data set and finds the factors that can explain the overall major sources of variation present in the data set. The conventional approach does this irrespective of the fact that the samples belong to intrinsically different groups and hence leads to poor class separation. The present work shows that classification of such samples can be optimized by performing the eigenvalue-eigenvector decomposition on the pair-wise dissimilarity matrix. Copyright © 2017 Elsevier B.V. All rights reserved.

  3. Experimentation of Eigenvector Dynamics in a Multiple Input Multiple Output Channel in the 5GHz Band

    DEFF Research Database (Denmark)

    Brown, Tim; Eggers, Patrick Claus F.; Katz, Marcos

    2005-01-01

    Much research has been carried out on the production of both physical and non physical Multiple Input Multiple Output channel models with regard to increased channel capacity as well as analysis of eigenvalues through the use of singular value decomposition. Little attention has been paid...... to the analysis of vector dynamics in terms of how the state of eigenvectors will change as a mobile is moving through a changing physical environment. This is important in terms of being able to track the orthogonal eigenmodes at system level, while also relieving the burden of tracking of the full channel...

  4. AMDLIBF, IBM 360 Subroutine Library, Eigenvalues, Eigenvectors, Matrix Inversion

    International Nuclear Information System (INIS)

    Wang, Jesse Y.

    1980-01-01

    Description of problem or function: AMDLIBF is a subset of the IBM 360 Subroutine Library at the Applied Mathematics Division at Argonne. This subset includes library category F: Identification/Description: F152S F SYMINV: Invert sym. matrices, solve lin. systems; F154S A DOTP: Double plus precision accum. inner prod.; F156S F RAYCOR: Rayleigh corrections for eigenvalues; F161S F XTRADP: A fast extended precision inner product; F162S A XTRADP: Inner product of two DP real vectors; F202S F1 EIGEN: Eigen-system for real symmetric matrix; F203S F: Driver for F202S; F248S F RITZIT: Largest eigenvalue and vec. real sym. matrix; F261S F EIGINV: Inverse eigenvalue problem; F313S F CQZHES: Reduce cmplx matrices to upper Hess and tri; F314S F CQZVAL: Reduce complex matrix to upper Hess. form; F315S F CQZVEC: Eigenvectors of cmplx upper triang. syst.; F316S F CGG: Driver for complex general Eigen-problem; F402S F MATINV: Matrix inversion and sol. of linear eqns.; F403S F: Driver for F402S; F452S F CHOLLU,CHOLEQ: Sym. decomp. of pos. def. band matrices; F453S F MATINC: Inversion of complex matrices; F454S F CROUT: Solution of simultaneous linear equations; F455S F CROUTC: Sol. of simultaneous complex linear eqns.; F456S F1 DIAG: Integer preserving Gaussian elimination

  5. Spin-orbit splitted excited states using explicitly-correlated equation-of-motion coupled-cluster singles and doubles eigenvectors

    Science.gov (United States)

    Bokhan, Denis; Trubnikov, Dmitrii N.; Perera, Ajith; Bartlett, Rodney J.

    2018-04-01

    An explicitly-correlated method of calculation of excited states with spin-orbit couplings, has been formulated and implemented. Developed approach utilizes left and right eigenvectors of equation-of-motion coupled-cluster model, which is based on the linearly approximated explicitly correlated coupled-cluster singles and doubles [CCSD(F12)] method. The spin-orbit interactions are introduced by using the spin-orbit mean field (SOMF) approximation of the Breit-Pauli Hamiltonian. Numerical tests for several atoms and molecules show good agreement between explicitly-correlated results and the corresponding values, calculated in complete basis set limit (CBS); the highly-accurate excitation energies can be obtained already at triple- ζ level.

  6. Decaying states as complex energy eigenvectors in generalized quantum mechanics

    International Nuclear Information System (INIS)

    Sudarshan, E.C.G.; Chiu, C.B.; Gorini, V.

    1977-04-01

    The problem of particle decay is reexamined within the Hamiltonian formalism. By deforming contours of integration, the survival amplitude is expressed as a sum of purely exponential contributions arising from the simple poles of the resolvent on the second sheet plus a background integral along a complex contour GAMMA running below the location of the poles. One observes that the time dependence of the survival amplitude in the small time region is strongly correlated to the asymptotic behaviour of the energy spectrum of the system; one computes the small time behavior of the survival amplitude for a wide variety of asymptotic behaviors. In the special case of the Lee model, using a formal procedure of analytic continuation, it is shown that a complete set of complex energy eigenvectors of the Hamiltonian can be associated with the poles of the resolvent of the background contour GAMMA. These poles and points along GAMMA correspond to the discrete and the continuum states respectively. In this context, each unstable particle is associated with a well defined object, which is a discrete generalized eigenstate of the Hamiltonian having a complex eigenvalue, with its real and negative imaginary parts being the mass and half width of the particle respectively. Finally, one briefly discusses the analytic continuation of the scattering amplitude within this generalized scheme, and notes the appearance of ''redundant poles'' which do not correspond to discrete solutions of the modified eigenvalue problem

  7. The Application of Principal Component Analysis Using Fixed Eigenvectors to the Infrared Thermographic Inspection of the Space Shuttle Thermal Protection System

    Science.gov (United States)

    Cramer, K. Elliott; Winfree, William P.

    2006-01-01

    The Nondestructive Evaluation Sciences Branch at NASA s Langley Research Center has been actively involved in the development of thermographic inspection techniques for more than 15 years. Since the Space Shuttle Columbia accident, NASA has focused on the improvement of advanced NDE techniques for the Reinforced Carbon-Carbon (RCC) panels that comprise the orbiter s wing leading edge. Various nondestructive inspection techniques have been used in the examination of the RCC, but thermography has emerged as an effective inspection alternative to more traditional methods. Thermography is a non-contact inspection method as compared to ultrasonic techniques which typically require the use of a coupling medium between the transducer and material. Like radiographic techniques, thermography can be used to inspect large areas, but has the advantage of minimal safety concerns and the ability for single-sided measurements. Principal Component Analysis (PCA) has been shown effective for reducing thermographic NDE data. A typical implementation of PCA is when the eigenvectors are generated from the data set being analyzed. Although it is a powerful tool for enhancing the visibility of defects in thermal data, PCA can be computationally intense and time consuming when applied to the large data sets typical in thermography. Additionally, PCA can experience problems when very large defects are present (defects that dominate the field-of-view), since the calculation of the eigenvectors is now governed by the presence of the defect, not the good material. To increase the processing speed and to minimize the negative effects of large defects, an alternative method of PCA is being pursued when a fixed set of eigenvectors is used to process the thermal data from the RCC materials. These eigen vectors can be generated either from an analytic model of the thermal response of the material under examination, or from a large cross section of experimental data. This paper will provide the

  8. Eigenvector/eigenvalue analysis of a 3D current referential fault detection and diagnosis of an induction motor

    International Nuclear Information System (INIS)

    Pires, V. Fernao; Martins, J.F.; Pires, A.J.

    2010-01-01

    In this paper an integrated approach for on-line induction motor fault detection and diagnosis is presented. The need to insure a continuous and safety operation for induction motors involves preventive maintenance procedures combined with fault diagnosis techniques. The proposed approach uses an automatic three step algorithm. Firstly, the induction motor stator currents are measured which will give typical patterns that can be used to identify the fault. Secondly, the eigenvectors/eigenvalues of the 3D current referential are computed. Finally the proposed algorithm will discern if the motor is healthy or not and report the extent of the fault. Furthermore this algorithm is able to identify distinct faults (stator winding faults or broken bars). The proposed approach was experimentally implemented and its performance verified on various types of working conditions.

  9. EISPACK, Subroutines for Eigenvalues, Eigenvectors, Matrix Operations

    International Nuclear Information System (INIS)

    Garbow, Burton S.; Cline, A.K.; Meyering, J.

    1993-01-01

    1 - Description of problem or function: EISPACK3 is a collection of 75 FORTRAN subroutines, both single- and double-precision, that compute the eigenvalues and eigenvectors of nine classes of matrices. The package can determine the Eigen-system of complex general, complex Hermitian, real general, real symmetric, real symmetric band, real symmetric tridiagonal, special real tridiagonal, generalized real, and generalized real symmetric matrices. In addition, there are two routines which use the singular value decomposition to solve certain least squares problem. The individual subroutines are - Identification/Description: BAKVEC: Back transform vectors of matrix formed by FIGI; BALANC: Balance a real general matrix; BALBAK: Back transform vectors of matrix formed by BALANC; BANDR: Reduce sym. band matrix to sym. tridiag. matrix; BANDV: Find some vectors of sym. band matrix; BISECT: Find some values of sym. tridiag. matrix; BQR: Find some values of sym. band matrix; CBABK2: Back transform vectors of matrix formed by CBAL; CBAL: Balance a complex general matrix; CDIV: Perform division of two complex quantities; CG: Driver subroutine for a complex general matrix; CH: Driver subroutine for a complex Hermitian matrix; CINVIT: Find some vectors of complex Hess. matrix; COMBAK: Back transform vectors of matrix formed by COMHES; COMHES: Reduce complex matrix to complex Hess. (elementary); COMLR: Find all values of complex Hess. matrix (LR); COMLR2: Find all values/vectors of cmplx Hess. matrix (LR); CCMQR: Find all values of complex Hessenberg matrix (QR); COMQR2: Find all values/vectors of cmplx Hess. matrix (QR); CORTB: Back transform vectors of matrix formed by CORTH; CORTH: Reduce complex matrix to complex Hess. (unitary); CSROOT: Find square root of complex quantity; ELMBAK: Back transform vectors of matrix formed by ELMHES; ELMHES: Reduce real matrix to real Hess. (elementary); ELTRAN: Accumulate transformations from ELMHES (for HQR2); EPSLON: Estimate unit roundoff

  10. Disrupted Brain Network in Progressive Mild Cognitive Impairment Measured by Eigenvector Centrality Mapping is Linked to Cognition and Cerebrospinal Fluid Biomarkers.

    Science.gov (United States)

    Qiu, Tiantian; Luo, Xiao; Shen, Zhujing; Huang, Peiyu; Xu, Xiaojun; Zhou, Jiong; Zhang, Minming

    2016-10-18

    Mild cognitive impairment (MCI) is a heterogeneous condition associated with a high risk of progressing to Alzheimer's disease (AD). Although functional brain network alterations have been observed in progressive MCI (pMCI), the underlying pathological mechanisms of network alterations remain unclear. In the present study, we evaluated neuropsychological, imaging, and cerebrospinal fluid (CSF) data at baseline across a cohort of: 21 pMCI patients, 33 stable MCI (sMCI) patients, and 29 normal controls. Fast eigenvector centrality mapping (fECM) based on resting-state functional MRI (rsfMRI) was used to investigate brain network organization differences among these groups, and we further assessed its relation to cognition and AD-related pathology. Our results demonstrated that pMCI had decreased eigenvector centrality (EC) in left temporal pole and parahippocampal gyrus, and increased EC in left middle frontal gyrus compared to sMCI. In addition, compared to normal controls, patients with pMCI showed decreased EC in right hippocampus and bilateral parahippocampal gyrus, and sMCI had decreased EC in right middle frontal gyrus and superior parietal lobule. Correlation analysis showed that EC in the left temporal pole was related to Wechsler Memory Scale-Revised Logical Memory (WMS-LM) delay score (r = 0.467, p = 0.044) and total tau (t-tau) level in CSF (r = -0.509, p = 0.026) in pMCI. Our findings implicate EC changes of different brain network nodes in the prognosis of pMCI and sMCI. Importantly, the association between decreased EC of brain network node and pathological changes may provide a deeper understanding of the underlying pathophysiology of pMCI.

  11. Analysis of structural correlations in a model binary 3D liquid through the eigenvalues and eigenvectors of the atomic stress tensors

    International Nuclear Information System (INIS)

    Levashov, V. A.

    2016-01-01

    It is possible to associate with every atom or molecule in a liquid its own atomic stress tensor. These atomic stress tensors can be used to describe liquids’ structures and to investigate the connection between structural and dynamic properties. In particular, atomic stresses allow to address atomic scale correlations relevant to the Green-Kubo expression for viscosity. Previously correlations between the atomic stresses of different atoms were studied using the Cartesian representation of the stress tensors or the representation based on spherical harmonics. In this paper we address structural correlations in a 3D model binary liquid using the eigenvalues and eigenvectors of the atomic stress tensors. This approach allows to interpret correlations relevant to the Green-Kubo expression for viscosity in a simple geometric way. On decrease of temperature the changes in the relevant stress correlation function between different atoms are significantly more pronounced than the changes in the pair density function. We demonstrate that this behaviour originates from the orientational correlations between the eigenvectors of the atomic stress tensors. We also found correlations between the eigenvalues of the same atomic stress tensor. For the studied system, with purely repulsive interactions between the particles, the eigenvalues of every atomic stress tensor are positive and they can be ordered: λ 1 ≥ λ 2 ≥ λ 3 ≥ 0. We found that, for the particles of a given type, the probability distributions of the ratios (λ 2 /λ 1 ) and (λ 3 /λ 2 ) are essentially identical to each other in the liquids state. We also found that λ 2 tends to be equal to the geometric average of λ 1 and λ 3 . In our view, correlations between the eigenvalues may represent “the Poisson ratio effect” at the atomic scale.

  12. Analysis of structural correlations in a model binary 3D liquid through the eigenvalues and eigenvectors of the atomic stress tensors

    Energy Technology Data Exchange (ETDEWEB)

    Levashov, V. A. [Technological Design Institute of Scientific Instrument Engineering, Novosibirsk 630058 (Russian Federation)

    2016-03-07

    It is possible to associate with every atom or molecule in a liquid its own atomic stress tensor. These atomic stress tensors can be used to describe liquids’ structures and to investigate the connection between structural and dynamic properties. In particular, atomic stresses allow to address atomic scale correlations relevant to the Green-Kubo expression for viscosity. Previously correlations between the atomic stresses of different atoms were studied using the Cartesian representation of the stress tensors or the representation based on spherical harmonics. In this paper we address structural correlations in a 3D model binary liquid using the eigenvalues and eigenvectors of the atomic stress tensors. This approach allows to interpret correlations relevant to the Green-Kubo expression for viscosity in a simple geometric way. On decrease of temperature the changes in the relevant stress correlation function between different atoms are significantly more pronounced than the changes in the pair density function. We demonstrate that this behaviour originates from the orientational correlations between the eigenvectors of the atomic stress tensors. We also found correlations between the eigenvalues of the same atomic stress tensor. For the studied system, with purely repulsive interactions between the particles, the eigenvalues of every atomic stress tensor are positive and they can be ordered: λ{sub 1} ≥ λ{sub 2} ≥ λ{sub 3} ≥ 0. We found that, for the particles of a given type, the probability distributions of the ratios (λ{sub 2}/λ{sub 1}) and (λ{sub 3}/λ{sub 2}) are essentially identical to each other in the liquids state. We also found that λ{sub 2} tends to be equal to the geometric average of λ{sub 1} and λ{sub 3}. In our view, correlations between the eigenvalues may represent “the Poisson ratio effect” at the atomic scale.

  13. The Physical Driver of the Optical Eigenvector 1 in Quasar Main Sequence

    Energy Technology Data Exchange (ETDEWEB)

    Panda, Swayamtrupta; Czerny, Bożena [Center for Theoretical Physics, Polish Academy of Sciences, Warsaw (Poland); Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, Warsaw (Poland); Wildy, Conor, E-mail: panda@cft.edu.pl [Center for Theoretical Physics, Polish Academy of Sciences, Warsaw (Poland)

    2017-11-07

    Quasars are complex sources, characterized by broad band spectra from radio through optical to X-ray band, with numerous emission and absorption features. This complexity leads to rich diagnostics. However, Boroson and Green (1992) used Principal Component Analysis (PCA), and with this analysis they were able to show significant correlations between the measured parameters. The leading component, related to Eigenvector 1 (EV1) was dominated by the anticorrelation between the FeII optical emission and [OIII] line and EV1 alone contained 30% of the total variance. It opened a way in defining a quasar main sequence, in close analogy to the stellar main sequence on the Hertzsprung-Russel (HR) diagram (Sulentic et al., 2001). The question still remains which of the basic theoretically motivated parameters of an active nucleus (Eddington ratio, black hole mass, accretion rate, spin, and viewing angle) is the main driver behind the EV1. Here we limit ourselves to the optical waveband, and concentrate on theoretical modeling the FeII to Hβ ratio, and we test the hypothesis that the physical driver of EV1 is the maximum of the accretion disk temperature, reflected in the shape of the spectral energy distribution (SED). We performed computations of the Hβ and optical FeII for a broad range of SED peak position using CLOUDY photoionisation code. We assumed that both Hβ and FeII emission come from the Broad Line Region represented as a constant density cloud in a plane-parallel geometry. We expected that a hotter disk continuum will lead to more efficient production of FeII but our computations show that the FeII to Hβ ratio actually drops with the rise of the disk temperature. Thus either hypothesis is incorrect, or approximations used in our paper for the description of the line emissivity is inadequate.

  14. The Physical Driver of the Optical Eigenvector 1 in Quasar Main Sequence

    Directory of Open Access Journals (Sweden)

    Swayamtrupta Panda

    2017-11-01

    Full Text Available Quasars are complex sources, characterized by broad band spectra from radio through optical to X-ray band, with numerous emission and absorption features. This complexity leads to rich diagnostics. However, Boroson and Green (1992 used Principal Component Analysis (PCA, and with this analysis they were able to show significant correlations between the measured parameters. The leading component, related to Eigenvector 1 (EV1 was dominated by the anticorrelation between the FeII optical emission and [OIII] line and EV1 alone contained 30% of the total variance. It opened a way in defining a quasar main sequence, in close analogy to the stellar main sequence on the Hertzsprung-Russel (HR diagram (Sulentic et al., 2001. The question still remains which of the basic theoretically motivated parameters of an active nucleus (Eddington ratio, black hole mass, accretion rate, spin, and viewing angle is the main driver behind the EV1. Here we limit ourselves to the optical waveband, and concentrate on theoretical modeling the FeII to Hβ ratio, and we test the hypothesis that the physical driver of EV1 is the maximum of the accretion disk temperature, reflected in the shape of the spectral energy distribution (SED. We performed computations of the Hβ and optical FeII for a broad range of SED peak position using CLOUDY photoionisation code. We assumed that both Hβ and FeII emission come from the Broad Line Region represented as a constant density cloud in a plane-parallel geometry. We expected that a hotter disk continuum will lead to more efficient production of FeII but our computations show that the FeII to Hβ ratio actually drops with the rise of the disk temperature. Thus either hypothesis is incorrect, or approximations used in our paper for the description of the line emissivity is inadequate.

  15. Eigenvector Spatial Filtering Regression Modeling of Ground PM2.5 Concentrations Using Remotely Sensed Data

    Directory of Open Access Journals (Sweden)

    Jingyi Zhang

    2018-06-01

    Full Text Available This paper proposes a regression model using the Eigenvector Spatial Filtering (ESF method to estimate ground PM2.5 concentrations. Covariates are derived from remotely sensed data including aerosol optical depth, normal differential vegetation index, surface temperature, air pressure, relative humidity, height of planetary boundary layer and digital elevation model. In addition, cultural variables such as factory densities and road densities are also used in the model. With the Yangtze River Delta region as the study area, we constructed ESF-based Regression (ESFR models at different time scales, using data for the period between December 2015 and November 2016. We found that the ESFR models effectively filtered spatial autocorrelation in the OLS residuals and resulted in increases in the goodness-of-fit metrics as well as reductions in residual standard errors and cross-validation errors, compared to the classic OLS models. The annual ESFR model explained 70% of the variability in PM2.5 concentrations, 16.7% more than the non-spatial OLS model. With the ESFR models, we performed detail analyses on the spatial and temporal distributions of PM2.5 concentrations in the study area. The model predictions are lower than ground observations but match the general trend. The experiment shows that ESFR provides a promising approach to PM2.5 analysis and prediction.

  16. Eigenvector Spatial Filtering Regression Modeling of Ground PM2.5 Concentrations Using Remotely Sensed Data.

    Science.gov (United States)

    Zhang, Jingyi; Li, Bin; Chen, Yumin; Chen, Meijie; Fang, Tao; Liu, Yongfeng

    2018-06-11

    This paper proposes a regression model using the Eigenvector Spatial Filtering (ESF) method to estimate ground PM 2.5 concentrations. Covariates are derived from remotely sensed data including aerosol optical depth, normal differential vegetation index, surface temperature, air pressure, relative humidity, height of planetary boundary layer and digital elevation model. In addition, cultural variables such as factory densities and road densities are also used in the model. With the Yangtze River Delta region as the study area, we constructed ESF-based Regression (ESFR) models at different time scales, using data for the period between December 2015 and November 2016. We found that the ESFR models effectively filtered spatial autocorrelation in the OLS residuals and resulted in increases in the goodness-of-fit metrics as well as reductions in residual standard errors and cross-validation errors, compared to the classic OLS models. The annual ESFR model explained 70% of the variability in PM 2.5 concentrations, 16.7% more than the non-spatial OLS model. With the ESFR models, we performed detail analyses on the spatial and temporal distributions of PM 2.5 concentrations in the study area. The model predictions are lower than ground observations but match the general trend. The experiment shows that ESFR provides a promising approach to PM 2.5 analysis and prediction.

  17. Algebraic Bethe ansatz for the quantum group invariant open XXZ chain at roots of unity

    Directory of Open Access Journals (Sweden)

    Azat M. Gainutdinov

    2016-08-01

    Full Text Available For generic values of q, all the eigenvectors of the transfer matrix of the Uqsl(2-invariant open spin-1/2 XXZ chain with finite length N can be constructed using the algebraic Bethe ansatz (ABA formalism of Sklyanin. However, when q is a root of unity (q=eiπ/p with integer p≥2, the Bethe equations acquire continuous solutions, and the transfer matrix develops Jordan cells. Hence, there appear eigenvectors of two new types: eigenvectors corresponding to continuous solutions (exact complete p-strings, and generalized eigenvectors. We propose general ABA constructions for these two new types of eigenvectors. We present many explicit examples, and we construct complete sets of (generalized eigenvectors for various values of p and N.

  18. An object recognition method based on fuzzy theory and BP networks

    Science.gov (United States)

    Wu, Chuan; Zhu, Ming; Yang, Dong

    2006-01-01

    It is difficult to choose eigenvectors when neural network recognizes object. It is possible that the different object eigenvectors is similar or the same object eigenvectors is different under scaling, shifting, rotation if eigenvectors can not be chosen appropriately. In order to solve this problem, the image is edged, the membership function is reconstructed and a new threshold segmentation method based on fuzzy theory is proposed to get the binary image. Moment invariant of binary image is extracted and normalized. Some time moment invariant is too small to calculate effectively so logarithm of moment invariant is taken as input eigenvectors of BP network. The experimental results demonstrate that the proposed approach could recognize the object effectively, correctly and quickly.

  19. Learning Eigenvectors for Free

    NARCIS (Netherlands)

    W.M. Koolen-Wijkstra (Wouter); W.T. Kotlowski (Wojciech); M.K. Warmuth

    2011-01-01

    htmlabstractWe extend the classical problem of predicting a sequence of outcomes from a finite alphabet to the matrix domain. In this extension, the alphabet of n outcomes is replaced by the set of all dyads, i.e. outer products uu^T where u is a vector in R^n of unit length. Whereas in the

  20. Resonances, scattering theory and rigged Hilbert spaces

    International Nuclear Information System (INIS)

    Parravicini, G.; Gorini, V.; Sudarshan, E.C.G.

    1979-01-01

    The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free, in, and out eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian; the singularities of the out eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of complete sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the out eigenvectors. The free, in and out eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee-Friedrichs model. 48 references

  1. Acceleration techniques for the discrete ordinate method

    International Nuclear Information System (INIS)

    Efremenko, Dmitry; Doicu, Adrian; Loyola, Diego; Trautmann, Thomas

    2013-01-01

    In this paper we analyze several acceleration techniques for the discrete ordinate method with matrix exponential and the small-angle modification of the radiative transfer equation. These techniques include the left eigenvectors matrix approach for computing the inverse of the right eigenvectors matrix, the telescoping technique, and the method of false discrete ordinate. The numerical simulations have shown that on average, the relative speedup of the left eigenvector matrix approach and the telescoping technique are of about 15% and 30%, respectively. -- Highlights: ► We presented the left eigenvector matrix approach. ► We analyzed the method of false discrete ordinate. ► The telescoping technique is applied for matrix operator method. ► Considered techniques accelerate the computations by 20% in average.

  2. Spectral Bisection with Two Eigenvectors

    Czech Academy of Sciences Publication Activity Database

    Rocha, Israel

    2017-01-01

    Roč. 61, August (2017), s. 1019-1025 ISSN 1571-0653 Institutional support: RVO:67985807 Keywords : graph partitioning * Laplacian matrix * Fiedler vector Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics

  3. SU-C-BRA-07: Variability of Patient-Specific Motion Models Derived Using Different Deformable Image Registration Algorithms for Lung Cancer Stereotactic Body Radiotherapy (SBRT) Patients

    Energy Technology Data Exchange (ETDEWEB)

    Dhou, S; Williams, C [Brigham and Women’s Hospital / Harvard Medical School, Boston, MA (United States); Ionascu, D [William Beaumont Hospital, Royal Oak, MI (United States); Lewis, J [University of California at Los Angeles, Los Angeles, CA (United States)

    2016-06-15

    Purpose: To study the variability of patient-specific motion models derived from 4-dimensional CT (4DCT) images using different deformable image registration (DIR) algorithms for lung cancer stereotactic body radiotherapy (SBRT) patients. Methods: Motion models are derived by 1) applying DIR between each 4DCT image and a reference image, resulting in a set of displacement vector fields (DVFs), and 2) performing principal component analysis (PCA) on the DVFs, resulting in a motion model (a set of eigenvectors capturing the variations in the DVFs). Three DIR algorithms were used: 1) Demons, 2) Horn-Schunck, and 3) iterative optical flow. The motion models derived were compared using patient 4DCT scans. Results: Motion models were derived and the variations were evaluated according to three criteria: 1) the average root mean square (RMS) difference which measures the absolute difference between the components of the eigenvectors, 2) the dot product between the eigenvectors which measures the angular difference between the eigenvectors in space, and 3) the Euclidean Model Norm (EMN), which is calculated by summing the dot products of an eigenvector with the first three eigenvectors from the reference motion model in quadrature. EMN measures how well an eigenvector can be reconstructed using another motion model derived using a different DIR algorithm. Results showed that comparing to a reference motion model (derived using the Demons algorithm), the eigenvectors of the motion model derived using the iterative optical flow algorithm has smaller RMS, larger dot product, and larger EMN values than those of the motion model derived using Horn-Schunck algorithm. Conclusion: The study showed that motion models vary depending on which DIR algorithms were used to derive them. The choice of a DIR algorithm may affect the accuracy of the resulting model, and it is important to assess the suitability of the algorithm chosen for a particular application. This project was supported

  4. SU-C-BRA-07: Variability of Patient-Specific Motion Models Derived Using Different Deformable Image Registration Algorithms for Lung Cancer Stereotactic Body Radiotherapy (SBRT) Patients

    International Nuclear Information System (INIS)

    Dhou, S; Williams, C; Ionascu, D; Lewis, J

    2016-01-01

    Purpose: To study the variability of patient-specific motion models derived from 4-dimensional CT (4DCT) images using different deformable image registration (DIR) algorithms for lung cancer stereotactic body radiotherapy (SBRT) patients. Methods: Motion models are derived by 1) applying DIR between each 4DCT image and a reference image, resulting in a set of displacement vector fields (DVFs), and 2) performing principal component analysis (PCA) on the DVFs, resulting in a motion model (a set of eigenvectors capturing the variations in the DVFs). Three DIR algorithms were used: 1) Demons, 2) Horn-Schunck, and 3) iterative optical flow. The motion models derived were compared using patient 4DCT scans. Results: Motion models were derived and the variations were evaluated according to three criteria: 1) the average root mean square (RMS) difference which measures the absolute difference between the components of the eigenvectors, 2) the dot product between the eigenvectors which measures the angular difference between the eigenvectors in space, and 3) the Euclidean Model Norm (EMN), which is calculated by summing the dot products of an eigenvector with the first three eigenvectors from the reference motion model in quadrature. EMN measures how well an eigenvector can be reconstructed using another motion model derived using a different DIR algorithm. Results showed that comparing to a reference motion model (derived using the Demons algorithm), the eigenvectors of the motion model derived using the iterative optical flow algorithm has smaller RMS, larger dot product, and larger EMN values than those of the motion model derived using Horn-Schunck algorithm. Conclusion: The study showed that motion models vary depending on which DIR algorithms were used to derive them. The choice of a DIR algorithm may affect the accuracy of the resulting model, and it is important to assess the suitability of the algorithm chosen for a particular application. This project was supported

  5. Computational analysis of chain flexibility and fluctuations in Rhizomucor miehei lipase

    DEFF Research Database (Denmark)

    Peters, Günther H.J.; Bywater, R. P.

    1999-01-01

    We have performed molecular dynamics simulation of Rhizomucor miehei lipase (Rml) with explicit water molecules present. The simulation was carried out in periodic boundary conditions and conducted for 1.2 ns in order to determine the concerted protein dynamics and to examine how well the essential...... motions are preserved along the trajectory. Protein motions are extracted by means of the essential dynamics analysis method for different lengths of the trajectory. Motions described by eigenvector 1 converge after approximately 200 ps and only small changes are observed with increasing simulation time....... Protein dynamics along eigenvectors with larger indices, however, change with simulation time and generally, with increasing eigenvector index, longer simulation times are required for observing similar protein motions (along a particular eigenvector). Several regions in the protein show relatively large...

  6. Fukunaga-Koontz transform based dimensionality reduction for hyperspectral imagery

    Science.gov (United States)

    Ochilov, S.; Alam, M. S.; Bal, A.

    2006-05-01

    Fukunaga-Koontz Transform based technique offers some attractive properties for desired class oriented dimensionality reduction in hyperspectral imagery. In FKT, feature selection is performed by transforming into a new space where feature classes have complimentary eigenvectors. Dimensionality reduction technique based on these complimentary eigenvector analysis can be described under two classes, desired class and background clutter, such that each basis function best represent one class while carrying the least amount of information from the second class. By selecting a few eigenvectors which are most relevant to desired class, one can reduce the dimension of hyperspectral cube. Since the FKT based technique reduces data size, it provides significant advantages for near real time detection applications in hyperspectral imagery. Furthermore, the eigenvector selection approach significantly reduces computation burden via the dimensionality reduction processes. The performance of the proposed dimensionality reduction algorithm has been tested using real-world hyperspectral dataset.

  7. Deflation of Eigenvalues for GMRES in Lattice QCD

    International Nuclear Information System (INIS)

    Morgan, Ronald B.; Wilcox, Walter

    2002-01-01

    Versions of GMRES with deflation of eigenvalues are applied to lattice QCD problems. Approximate eigenvectors corresponding to the smallest eigenvalues are generated at the same time that linear equations are solved. The eigenvectors improve convergence for the linear equations, and they help solve other right-hand sides

  8. The Statistics and Mathematics of High Dimension Low Sample Size Asymptotics.

    Science.gov (United States)

    Shen, Dan; Shen, Haipeng; Zhu, Hongtu; Marron, J S

    2016-10-01

    The aim of this paper is to establish several deep theoretical properties of principal component analysis for multiple-component spike covariance models. Our new results reveal an asymptotic conical structure in critical sample eigendirections under the spike models with distinguishable (or indistinguishable) eigenvalues, when the sample size and/or the number of variables (or dimension) tend to infinity. The consistency of the sample eigenvectors relative to their population counterparts is determined by the ratio between the dimension and the product of the sample size with the spike size. When this ratio converges to a nonzero constant, the sample eigenvector converges to a cone, with a certain angle to its corresponding population eigenvector. In the High Dimension, Low Sample Size case, the angle between the sample eigenvector and its population counterpart converges to a limiting distribution. Several generalizations of the multi-spike covariance models are also explored, and additional theoretical results are presented.

  9. A robust multilevel simultaneous eigenvalue solver

    Science.gov (United States)

    Costiner, Sorin; Taasan, Shlomo

    1993-01-01

    Multilevel (ML) algorithms for eigenvalue problems are often faced with several types of difficulties such as: the mixing of approximated eigenvectors by the solution process, the approximation of incomplete clusters of eigenvectors, the poor representation of solution on coarse levels, and the existence of close or equal eigenvalues. Algorithms that do not treat appropriately these difficulties usually fail, or their performance degrades when facing them. These issues motivated the development of a robust adaptive ML algorithm which treats these difficulties, for the calculation of a few eigenvectors and their corresponding eigenvalues. The main techniques used in the new algorithm include: the adaptive completion and separation of the relevant clusters on different levels, the simultaneous treatment of solutions within each cluster, and the robustness tests which monitor the algorithm's efficiency and convergence. The eigenvectors' separation efficiency is based on a new ML projection technique generalizing the Rayleigh Ritz projection, combined with a technique, the backrotations. These separation techniques, when combined with an FMG formulation, in many cases lead to algorithms of O(qN) complexity, for q eigenvectors of size N on the finest level. Previously developed ML algorithms are less focused on the mentioned difficulties. Moreover, algorithms which employ fine level separation techniques are of O(q(sub 2)N) complexity and usually do not overcome all these difficulties. Computational examples are presented where Schrodinger type eigenvalue problems in 2-D and 3-D, having equal and closely clustered eigenvalues, are solved with the efficiency of the Poisson multigrid solver. A second order approximation is obtained in O(qN) work, where the total computational work is equivalent to only a few fine level relaxations per eigenvector.

  10. Low complexity non-iterative coordinated beamforming in 2-user broadcast channels

    KAUST Repository

    Park, Kihong

    2010-10-01

    We propose a new non-iterative coordinated beamforming scheme to obtain full multiplexing gain in 2-user MIMO systems. In order to find the beamforming and combining matrices, we solve a generalized eigenvector problem and describe how to find generalized eigenvectors according to the Gaussian broadcast channels. Selected simulation results show that the proposed method yields the same sum-rate performance as the iterative coordinated beamforming method, while maintaining lower complexity by non-iterative computation of the beamforming and combining matrices. We also show that the proposed method can easily exploit selective gain by choosing the best combination of generalized eigenvectors. © 2006 IEEE.

  11. Low complexity non-iterative coordinated beamforming in 2-user broadcast channels

    KAUST Repository

    Park, Kihong; Ko, Youngchai; Alouini, Mohamed-Slim

    2010-01-01

    We propose a new non-iterative coordinated beamforming scheme to obtain full multiplexing gain in 2-user MIMO systems. In order to find the beamforming and combining matrices, we solve a generalized eigenvector problem and describe how to find generalized eigenvectors according to the Gaussian broadcast channels. Selected simulation results show that the proposed method yields the same sum-rate performance as the iterative coordinated beamforming method, while maintaining lower complexity by non-iterative computation of the beamforming and combining matrices. We also show that the proposed method can easily exploit selective gain by choosing the best combination of generalized eigenvectors. © 2006 IEEE.

  12. Riesz basis for strongly continuous groups.

    NARCIS (Netherlands)

    Zwart, Heiko J.

    Given a Hilbert space and the generator of a strongly continuous group on this Hilbert space. If the eigenvalues of the generator have a uniform gap, and if the span of the corresponding eigenvectors is dense, then these eigenvectors form a Riesz basis (or unconditional basis) of the Hilbert space.

  13. Multiscale finite element methods for high-contrast problems using local spectral basis functions

    KAUST Repository

    Efendiev, Yalchin

    2011-02-01

    In this paper we study multiscale finite element methods (MsFEMs) using spectral multiscale basis functions that are designed for high-contrast problems. Multiscale basis functions are constructed using eigenvectors of a carefully selected local spectral problem. This local spectral problem strongly depends on the choice of initial partition of unity functions. The resulting space enriches the initial multiscale space using eigenvectors of local spectral problem. The eigenvectors corresponding to small, asymptotically vanishing, eigenvalues detect important features of the solutions that are not captured by initial multiscale basis functions. Multiscale basis functions are constructed such that they span these eigenfunctions that correspond to small, asymptotically vanishing, eigenvalues. We present a convergence study that shows that the convergence rate (in energy norm) is proportional to (H/Λ*)1/2, where Λ* is proportional to the minimum of the eigenvalues that the corresponding eigenvectors are not included in the coarse space. Thus, we would like to reach to a larger eigenvalue with a smaller coarse space. This is accomplished with a careful choice of initial multiscale basis functions and the setup of the eigenvalue problems. Numerical results are presented to back-up our theoretical results and to show higher accuracy of MsFEMs with spectral multiscale basis functions. We also present a hierarchical construction of the eigenvectors that provides CPU savings. © 2010.

  14. Perfect observables for the hierarchical non-linear O(N)-invariant σ-model

    International Nuclear Information System (INIS)

    Wieczerkowski, C.; Xylander, Y.

    1995-05-01

    We compute moving eigenvalues and the eigenvectors of the linear renormalization group transformation for observables along the renormalized trajectory of the hierarchical non-linear O(N)-invariant σ-model by means of perturbation theory in the running coupling constant. Moving eigenvectors are defined as solutions to a Callan-Symanzik type equation. (orig.)

  15. Estimation and calibration of observation impact signals using the Lanczos method in NOAA/NCEP data assimilation system

    Directory of Open Access Journals (Sweden)

    M. Wei

    2012-09-01

    Full Text Available Despite the tremendous progress that has been made in data assimilation (DA methodology, observing systems that reduce observation errors, and model improvements that reduce background errors, the analyses produced by the best available DA systems are still different from the truth. Analysis error and error covariance are important since they describe the accuracy of the analyses, and are directly related to the future forecast errors, i.e., the forecast quality. In addition, analysis error covariance is critically important in building an efficient ensemble forecast system (EFS.

    Estimating analysis error covariance in an ensemble-based Kalman filter DA is straightforward, but it is challenging in variational DA systems, which have been in operation at most NWP (Numerical Weather Prediction centers. In this study, we use the Lanczos method in the NCEP (the National Centers for Environmental Prediction Gridpoint Statistical Interpolation (GSI DA system to look into other important aspects and properties of this method that were not exploited before. We apply this method to estimate the observation impact signals (OIS, which are directly related to the analysis error variances. It is found that the smallest eigenvalue of the transformed Hessian matrix converges to one as the number of minimization iterations increases. When more observations are assimilated, the convergence becomes slower and more eigenvectors are needed to retrieve the observation impacts. It is also found that the OIS over data-rich regions can be represented by the eigenvectors with dominant eigenvalues.

    Since only a limited number of eigenvectors can be computed due to computational expense, the OIS is severely underestimated, and the analysis error variance is consequently overestimated. It is found that the mean OIS values for temperature and wind components at typical model levels are increased by about 1.5 times when the number of eigenvectors is doubled

  16. Homogenization of the critically spectral equation in neutron transport

    International Nuclear Information System (INIS)

    Allaire, G.; Paris-6 Univ., 75; Bal, G.

    1998-01-01

    We address the homogenization of an eigenvalue problem for the neutron transport equation in a periodic heterogeneous domain, modeling the criticality study of nuclear reactor cores. We prove that the neutron flux, corresponding to the first and unique positive eigenvector, can be factorized in the product of two terms, up to a remainder which goes strongly to zero with the period. On terms is the first eigenvector of the transport equation in the periodicity cell. The other term is the first eigenvector of a diffusion equation in the homogenized domain. Furthermore, the corresponding eigenvalue gives a second order corrector for the eigenvalue of the heterogeneous transport problem. This result justifies and improves the engineering procedure used in practice for nuclear reactor cores computations. (author)

  17. Homogenization of the critically spectral equation in neutron transport

    Energy Technology Data Exchange (ETDEWEB)

    Allaire, G. [CEA Saclay, 91 - Gif-sur-Yvette (France). Dept. de Mecanique et de Technologie]|[Paris-6 Univ., 75 (France). Lab. d' Analyse Numerique; Bal, G. [Electricite de France (EDF), 92 - Clamart (France). Direction des Etudes et Recherches

    1998-07-01

    We address the homogenization of an eigenvalue problem for the neutron transport equation in a periodic heterogeneous domain, modeling the criticality study of nuclear reactor cores. We prove that the neutron flux, corresponding to the first and unique positive eigenvector, can be factorized in the product of two terms, up to a remainder which goes strongly to zero with the period. On terms is the first eigenvector of the transport equation in the periodicity cell. The other term is the first eigenvector of a diffusion equation in the homogenized domain. Furthermore, the corresponding eigenvalue gives a second order corrector for the eigenvalue of the heterogeneous transport problem. This result justifies and improves the engineering procedure used in practice for nuclear reactor cores computations. (author)

  18. Estimation of genetic parameters for test day records of dairy traits in the first three lactations

    Directory of Open Access Journals (Sweden)

    Ducrocq Vincent

    2005-05-01

    Full Text Available Abstract Application of test-day models for the genetic evaluation of dairy populations requires the solution of large mixed model equations. The size of the (covariance matrices required with such models can be reduced through the use of its first eigenvectors. Here, the first two eigenvectors of (covariance matrices estimated for dairy traits in first lactation were used as covariables to jointly estimate genetic parameters of the first three lactations. These eigenvectors appear to be similar across traits and have a biological interpretation, one being related to the level of production and the other to persistency. Furthermore, they explain more than 95% of the total genetic variation. Variances and heritabilities obtained with this model were consistent with previous studies. High correlations were found among production levels in different lactations. Persistency measures were less correlated. Genetic correlations between second and third lactations were close to one, indicating that these can be considered as the same trait. Genetic correlations within lactation were high except between extreme parts of the lactation. This study shows that the use of eigenvectors can reduce the rank of (covariance matrices for the test-day model and can provide consistent genetic parameters.

  19. The Perron-Frobenius Theorem for Markov Semigroups

    OpenAIRE

    Hijab, Omar

    2014-01-01

    Let $P^V_t$, $t\\ge0$, be the Schrodinger semigroup associated to a potential $V$ and Markov semigroup $P_t$, $t\\ge0$, on $C(X)$. Existence is established of a left eigenvector and right eigenvector corresponding to the spectral radius $e^{\\lambda_0t}$ of $P^V_t$, simultaneously for all $t\\ge0$. This is derived with no compactness assumption on the semigroup operators.

  20. A Spectral Algorithm for Envelope Reduction of Sparse Matrices

    Science.gov (United States)

    Barnard, Stephen T.; Pothen, Alex; Simon, Horst D.

    1993-01-01

    The problem of reordering a sparse symmetric matrix to reduce its envelope size is considered. A new spectral algorithm for computing an envelope-reducing reordering is obtained by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. This Laplacian eigenvector solves a continuous relaxation of a discrete problem related to envelope minimization called the minimum 2-sum problem. The permutation vector computed by the spectral algorithm is a closest permutation vector to the specified Laplacian eigenvector. Numerical results show that the new reordering algorithm usually computes smaller envelope sizes than those obtained from the current standard algorithms such as Gibbs-Poole-Stockmeyer (GPS) or SPARSPAK reverse Cuthill-McKee (RCM), in some cases reducing the envelope by more than a factor of two.

  1. Semi-supervised Eigenvectors for Locally-biased Learning

    DEFF Research Database (Denmark)

    Hansen, Toke Jansen; Mahoney, Michael W.

    2012-01-01

    In many applications, one has side information, e.g., labels that are provided in a semi-supervised manner, about a specific target region of a large data set, and one wants to perform machine learning and data analysis tasks "nearby" that pre-specified target region. Locally-biased problems of t...

  2. Drawing Space: Mathematicians' Kinetic Conceptions of Eigenvectors

    Science.gov (United States)

    Sinclair, Nathalie; Gol Tabaghi, Shiva

    2010-01-01

    This paper explores how mathematicians build meaning through communicative activity involving talk, gesture and diagram. In the course of describing mathematical concepts, mathematicians use these semiotic resources in ways that blur the distinction between the mathematical and physical world. We shall argue that mathematical meaning of…

  3. Random matrix approach to cross correlations in financial data

    Science.gov (United States)

    Plerou, Vasiliki; Gopikrishnan, Parameswaran; Rosenow, Bernd; Amaral, Luís A.; Guhr, Thomas; Stanley, H. Eugene

    2002-06-01

    We analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate cross-correlation matrices C of returns constructed from (i) 30-min returns of 1000 US stocks for the 2-yr period 1994-1995, (ii) 30-min returns of 881 US stocks for the 2-yr period 1996-1997, and (iii) 1-day returns of 422 US stocks for the 35-yr period 1962-1996. We test the statistics of the eigenvalues λi of C against a ``null hypothesis'' - a random correlation matrix constructed from mutually uncorrelated time series. We find that a majority of the eigenvalues of C fall within the RMT bounds [λ-,λ+] for the eigenvalues of random correlation matrices. We test the eigenvalues of C within the RMT bound for universal properties of random matrices and find good agreement with the results for the Gaussian orthogonal ensemble of random matrices-implying a large degree of randomness in the measured cross-correlation coefficients. Further, we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the RMT bound display systematic deviations from the RMT prediction. In addition, we find that these ``deviating eigenvectors'' are stable in time. We analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks. Our analysis of the remaining deviating eigenvectors shows distinct groups, whose identities correspond to conventionally identified business sectors. Finally, we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return.

  4. Molecular Mechanics and Quantum Chemistry Based Study of Nickel-N-Allyl Urea and N-Allyl Thiourea Complexes

    Directory of Open Access Journals (Sweden)

    P. D. Sharma

    2009-01-01

    Full Text Available Eigenvalue, eigenvector and overlap matrix of nickel halide complex of N-allyl urea and N-allyl thiourea have been evaluated. Our results indicate that ligand field parameters (Dq, B’ and β evaluated earlier by electronic spectra are very close to values evaluated with the help of eigenvalues and eigenvectors. Eigenvector analysis and population analysis shows that in bonding 4s, 4p, and 3dx2-y2, 3dyz orbitals of nickel are involved but the coefficient values differ in different complexes. Out of 4px, 4py, 4pz the involvement of either 4pz or 4py, is noticeable. The theoretically evaluated positions of infrared bands indicate that N-allyl urea is coordinated to nickel through its oxygen and N-allyl thiourea is coordinated to nickel through its sulphur which is in conformity with the experimental results.

  5. Collective Correlations of Brodmann Areas fMRI Study with RMT-Denoising

    Science.gov (United States)

    Burda, Z.; Kornelsen, J.; Nowak, M. A.; Porebski, B.; Sboto-Frankenstein, U.; Tomanek, B.; Tyburczyk, J.

    We study collective behavior of Brodmann regions of human cerebral cortex using functional Magnetic Resonance Imaging (fMRI) and Random Matrix Theory (RMT). The raw fMRI data is mapped onto the cortex regions corresponding to the Brodmann areas with the aid of the Talairach coordinates. Principal Component Analysis (PCA) of the Pearson correlation matrix for 41 different Brodmann regions is carried out to determine their collective activity in the idle state and in the active state stimulated by tapping. The collective brain activity is identified through the statistical analysis of the eigenvectors to the largest eigenvalues of the Pearson correlation matrix. The leading eigenvectors have a large participation ratio. This indicates that several Broadmann regions collectively give rise to the brain activity associated with these eigenvectors. We apply random matrix theory to interpret the underlying multivariate data.

  6. A Quantum Implementation Model for Artificial Neural Networks

    OpenAIRE

    Ammar Daskin

    2018-01-01

    The learning process for multilayered neural networks with many nodes makes heavy demands on computational resources. In some neural network models, the learning formulas, such as the Widrow–Hoff formula, do not change the eigenvectors of the weight matrix while flatting the eigenvalues. In infinity, these iterative formulas result in terms formed by the principal components of the weight matrix, namely, the eigenvectors corresponding to the non-zero eigenvalues. In quantum computing, the pha...

  7. Hints on the Broad Line Region Structure of Quasars at High and Low Luminosities

    Directory of Open Access Journals (Sweden)

    Marziani Paola

    2011-09-01

    Full Text Available Quasars show a considerable spectroscopic diversity. However, the variety of quasar spectra at low redshifts is non-random: a principal component analysis applied to large samples customarily identifies two main eigenvectors. In this contribution we show that the range of quasar optical spectral properties observed at low-z and associated with the first eigenvector is preserved up to z ≈ 2 in a sample of high luminosity quasars. We also describe two major luminosity effects.

  8. Mathematical methods linear algebra normed spaces distributions integration

    CERN Document Server

    Korevaar, Jacob

    1968-01-01

    Mathematical Methods, Volume I: Linear Algebra, Normed Spaces, Distributions, Integration focuses on advanced mathematical tools used in applications and the basic concepts of algebra, normed spaces, integration, and distributions.The publication first offers information on algebraic theory of vector spaces and introduction to functional analysis. Discussions focus on linear transformations and functionals, rectangular matrices, systems of linear equations, eigenvalue problems, use of eigenvectors and generalized eigenvectors in the representation of linear operators, metric and normed vector

  9. Quantum damped oscillator I: Dissipation and resonances

    International Nuclear Information System (INIS)

    Chruscinski, Dariusz; Jurkowski, Jacek

    2006-01-01

    Quantization of a damped harmonic oscillator leads to so called Bateman's dual system. The corresponding Bateman's Hamiltonian, being a self-adjoint operator, displays the discrete family of complex eigenvalues. We show that they correspond to the poles of energy eigenvectors and the corresponding resolvent operator when continued to the complex energy plane. Therefore, the corresponding generalized eigenvectors may be interpreted as resonant states which are responsible for the irreversible quantum dynamics of a damped harmonic oscillator

  10. A Quantum Implementation Model for Artificial Neural Networks

    OpenAIRE

    Daskin, Ammar

    2016-01-01

    The learning process for multi layered neural networks with many nodes makes heavy demands on computational resources. In some neural network models, the learning formulas, such as the Widrow-Hoff formula, do not change the eigenvectors of the weight matrix while flatting the eigenvalues. In infinity, this iterative formulas result in terms formed by the principal components of the weight matrix: i.e., the eigenvectors corresponding to the non-zero eigenvalues. In quantum computing, the phase...

  11. Algebraic structure of general electromagnetic fields and energy flow

    International Nuclear Information System (INIS)

    Hacyan, Shahen

    2011-01-01

    Highlights: → Algebraic structure of general electromagnetic fields in stationary spacetime. → Eigenvalues and eigenvectors of the electomagnetic field tensor. → Energy-momentum in terms of eigenvectors and Killing vector. → Explicit form of reference frame with vanishing Poynting vector. → Application of formalism to Bessel beams. - Abstract: The algebraic structures of a general electromagnetic field and its energy-momentum tensor in a stationary space-time are analyzed. The explicit form of the reference frame in which the energy of the field appears at rest is obtained in terms of the eigenvectors of the electromagnetic tensor and the existing Killing vector. The case of a stationary electromagnetic field is also studied and a comparison is made with the standard short-wave approximation. The results can be applied to the general case of a structured light beams, in flat or curved spaces. Bessel beams are worked out as example.

  12. Seismic network based detection, classification and location of volcanic tremors

    Science.gov (United States)

    Nikolai, S.; Soubestre, J.; Seydoux, L.; de Rosny, J.; Droznin, D.; Droznina, S.; Senyukov, S.; Gordeev, E.

    2017-12-01

    Volcanic tremors constitute an important attribute of volcanic unrest in many volcanoes, and their detection and characterization is a challenging issue of volcano monitoring. The main goal of the present work is to develop a network-based method to automatically classify volcanic tremors, to locate their sources and to estimate the associated wave speed. The method is applied to four and a half years of seismic data continuously recorded by 19 permanent seismic stations in the vicinity of the Klyuchevskoy volcanic group (KVG) in Kamchatka (Russia), where five volcanoes were erupting during the considered time period. The method is based on the analysis of eigenvalues and eigenvectors of the daily array covariance matrix. As a first step, following Seydoux et al. (2016), most coherent signals corresponding to dominating tremor sources are detected based on the width of the covariance matrix eigenvalues distribution. With this approach, the volcanic tremors of the two volcanoes known as most active during the considered period, Klyuchevskoy and Tolbachik, are efficiently detected. As a next step, we consider the array covariance matrix's first eigenvectors computed every day. The main hypothesis of our analysis is that these eigenvectors represent the principal component of the daily seismic wavefield and, for days with tremor activity, characterize the dominant tremor sources. Those first eigenvectors can therefore be used as network-based fingerprints of tremor sources. A clustering process is developed to analyze this collection of first eigenvectors, using correlation coefficient as a measure of their similarity. Then, we locate tremor sources based on cross-correlations amplitudes. We characterize seven tremor sources associated with different periods of activity of four volcanoes: Tolbachik, Klyuchevskoy, Shiveluch, and Kizimen. The developed method does not require a priori knowledge, is fully automatic and the database of network-based tremor fingerprints

  13. Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares

    Science.gov (United States)

    Orr, Jeb S.

    2012-01-01

    A technique is presented for initializing multiple discrete finite element model (FEM) mode sets for certain types of flight dynamics formulations that rely on superposition of orthogonal modes for modeling the elastic response. Such approaches are commonly used for modeling launch vehicle dynamics, and challenges arise due to the rapidly time-varying nature of the rigid-body and elastic characteristics. By way of an energy argument, a quadratic inequality constrained least squares (LSQI) algorithm is employed to e ect a smooth transition from one set of FEM eigenvectors to another with no requirement that the models be of similar dimension or that the eigenvectors be correlated in any particular way. The physically unrealistic and controversial method of eigenvector interpolation is completely avoided, and the discrete solution approximates that of the continuously varying system. The real-time computational burden is shown to be negligible due to convenient features of the solution method. Simulation results are presented, and applications to staging and other discontinuous mass changes are discussed

  14. Inverse Problem for Two-Dimensional Discrete Schr`dinger Equation

    CERN Document Server

    Serdyukova, S I

    2000-01-01

    For two-dimensional discrete Schroedinger equation the boundary-value problem in rectangle M times N with zero boundary conditions is solved. It's stated in this work, that inverse problem reduces to reconstruction of C symmetric five-diagonal matrix with given spectrum and given first k(M,N), 1<-keigenvectors. C matrix has lacuna between the second and (N+1)-th diagonals. As a result the first N components of basic eigenvectors must satisfy (N-1)^2 (M-1) additional conditions and N conditions of compatibility. The elements of C together with "lacking" (N-k) components can be determined by solving the system of the additional conditions, the compatibility conditions and the orthonormality conditions coupled with relations determining elements of C matrix by eigenvalues and components of basic eigenvectors. We succeeded to clear the statement of the problem to the end in the process of concrete calculations. Deriving and solving the huge polynomial systems had been perfor...

  15. Functional brain connectivity is predictable from anatomic network's Laplacian eigen-structure.

    Science.gov (United States)

    Abdelnour, Farras; Dayan, Michael; Devinsky, Orrin; Thesen, Thomas; Raj, Ashish

    2018-05-15

    How structural connectivity (SC) gives rise to functional connectivity (FC) is not fully understood. Here we mathematically derive a simple relationship between SC measured from diffusion tensor imaging, and FC from resting state fMRI. We establish that SC and FC are related via (structural) Laplacian spectra, whereby FC and SC share eigenvectors and their eigenvalues are exponentially related. This gives, for the first time, a simple and analytical relationship between the graph spectra of structural and functional networks. Laplacian eigenvectors are shown to be good predictors of functional eigenvectors and networks based on independent component analysis of functional time series. A small number of Laplacian eigenmodes are shown to be sufficient to reconstruct FC matrices, serving as basis functions. This approach is fast, and requires no time-consuming simulations. It was tested on two empirical SC/FC datasets, and was found to significantly outperform generative model simulations of coupled neural masses. Copyright © 2018. Published by Elsevier Inc.

  16. On the convex closed set-valued operators in Banach spaces and their applications in control problems

    International Nuclear Information System (INIS)

    Vu Ngoc Phat; Jong Yeoul Park

    1995-10-01

    The paper studies a class of set-values operators with emphasis on properties of their adjoints and existence of eigenvalues and eigenvectors of infinite-dimensional convex closed set-valued operators. Sufficient conditions for existence of eigenvalues and eigenvectors of set-valued convex closed operators are derived. These conditions specify possible features of control problems. The results are applied to some constrained control problems of infinite-dimensional systems described by discrete-time inclusions whose right-hand-sides are convex closed set- valued functions. (author). 8 refs

  17. The Rabi Oscillation in Subdynamic System for Quantum Computing

    Directory of Open Access Journals (Sweden)

    Bi Qiao

    2015-01-01

    Full Text Available A quantum computation for the Rabi oscillation based on quantum dots in the subdynamic system is presented. The working states of the original Rabi oscillation are transformed to the eigenvectors of subdynamic system. Then the dissipation and decoherence of the system are only shown in the change of the eigenvalues as phase errors since the eigenvectors are fixed. This allows both dissipation and decoherence controlling to be easier by only correcting relevant phase errors. This method can be extended to general quantum computation systems.

  18. A Note on the Eigensystem of the Covariance Matrix of Dichotomous Guttman Items.

    Science.gov (United States)

    Davis-Stober, Clintin P; Doignon, Jean-Paul; Suck, Reinhard

    2015-01-01

    We consider the covariance matrix for dichotomous Guttman items under a set of uniformity conditions, and obtain closed-form expressions for the eigenvalues and eigenvectors of the matrix. In particular, we describe the eigenvalues and eigenvectors of the matrix in terms of trigonometric functions of the number of items. Our results parallel those of Zwick (1987) for the correlation matrix under the same uniformity conditions. We provide an explanation for certain properties of principal components under Guttman scalability which have been first reported by Guttman (1950).

  19. Noise Reduction in the Time Domain using Joint Diagonalization

    DEFF Research Database (Denmark)

    Nørholm, Sidsel Marie; Benesty, Jacob; Jensen, Jesper Rindom

    2014-01-01

    , an estimate of the desired signal is found by subtraction of the noise estimate from the observed signal. The filter can be designed to obtain a desired trade-off between noise reduction and signal distortion, depending on the number of eigenvectors included in the filter design. This is explored through...... simulations using a speech signal corrupted by car noise, and the results confirm that the output signal-to-noise ratio and speech distortion index both increase when more eigenvectors are included in the filter design....

  20. Low-lying eigenmodes of the Wilson-Dirac operator and correlations with topological objects

    International Nuclear Information System (INIS)

    Kusterer, Daniel-Jens; Hedditch, John; Kamleh, Waseem; Leinweber, D.B.; Williams, Anthony G.

    2002-01-01

    The probability density of low-lying eigenvectors of the hermitian Wilson-Dirac operator H(κ)=γ 5 D W (κ) is examined. Comparisons in position and size between eigenvectors, topological charge and action density are made. We do this for standard Monte-Carlo generated SU(3) background fields and for single instanton background fields. Both hot and cooled SU(3) background fields are considered. An instanton model is fitted to eigenmodes and topological charge density and the sizes and positions of these are compared

  1. On the discrete Frobenius-Perron operator of the Bernoulli map

    International Nuclear Information System (INIS)

    Bai Zaiqiao

    2006-01-01

    We study the spectra of a finite-dimensional Frobenius-Perron operator (matrix) of the Bernoulli map derived from phase space discretization. The eigenvalues and (right and left) eigenvectors are analytically calculated, which are closely related to periodic orbits on the partition points. In the degenerate case, Jordan decomposition of the matrix is explicitly constructed. Except for the isolated eigenvalue 1, there is no definite limit with respect to eigenvalues when n → ∞. The behaviour of the eigenvectors is discussed in the limit of large n

  2. A note on the eigensystem of the covariance matrix of dichotomous Guttman items

    Directory of Open Access Journals (Sweden)

    Clintin P Davis-Stober

    2015-12-01

    Full Text Available We consider the sample covariance matrix for dichotomous Guttman items under a set of uniformity conditions, and obtain closed-form expressions for the eigenvalues and eigenvectors of the matrix. In particular, we describe the eigenvalues and eigenvectors of the matrix in terms of trigonometric functions of the number of items. Our results parallel those of Zwick (1987 for the correlation matrix under the same uniformity conditions. We provide an explanation for certain properties of principal components under Guttman scalability which have been first reported by Guttman (1950.

  3. Spectral Analysis Methods of Social Networks

    Directory of Open Access Journals (Sweden)

    P. G. Klyucharev

    2017-01-01

    Full Text Available Online social networks (such as Facebook, Twitter, VKontakte, etc. being an important channel for disseminating information are often used to arrange an impact on the social consciousness for various purposes - from advertising products or services to the full-scale information war thereby making them to be a very relevant object of research. The paper reviewed the analysis methods of social networks (primarily, online, based on the spectral theory of graphs. Such methods use the spectrum of the social graph, i.e. a set of eigenvalues of its adjacency matrix, and also the eigenvectors of the adjacency matrix.Described measures of centrality (in particular, centrality based on the eigenvector and PageRank, which reflect a degree of impact one or another user of the social network has. A very popular PageRank measure uses, as a measure of centrality, the graph vertices, the final probabilities of the Markov chain, whose matrix of transition probabilities is calculated on the basis of the adjacency matrix of the social graph. The vector of final probabilities is an eigenvector of the matrix of transition probabilities.Presented a method of dividing the graph vertices into two groups. It is based on maximizing the network modularity by computing the eigenvector of the modularity matrix.Considered a method for detecting bots based on the non-randomness measure of a graph to be computed using the spectral coordinates of vertices - sets of eigenvector components of the adjacency matrix of a social graph.In general, there are a number of algorithms to analyse social networks based on the spectral theory of graphs. These algorithms show very good results, but their disadvantage is the relatively high (albeit polynomial computational complexity for large graphs.At the same time it is obvious that the practical application capacity of the spectral graph theory methods is still underestimated, and it may be used as a basis to develop new methods.The work

  4. Maxwell meets Reeh–Schlieder: The quantum mechanics of neutral bosons

    Energy Technology Data Exchange (ETDEWEB)

    Hawton, Margaret, E-mail: margaret.hawton@lakeheadu.ca [Department of Physics, Lakehead University, Thunder Bay, ON, P7B 5E1 (Canada); Debierre, Vincent, E-mail: debierrev@mpi-hd.mpg.de [Max Planck Institute for Nuclear Physics, Saupfercheckweg 1, 69117, Heidelberg (Germany)

    2017-06-21

    We find that biorthogonal quantum mechanics with a scalar product that counts both absorbed and emitted particles leads to covariant position operators with localized eigenvectors. In this manifestly covariant formulation the probability for a transition from a one-photon state to a position eigenvector is the first order Glauber correlation function, bridging the gap between photon counting and the sensitivity of light detectors to electromagnetic energy density. The position eigenvalues are identified as the spatial parameters in the canonical quantum field operators and the position basis describes an array of localized devices that instantaneously absorb and re-emit bosons. - Highlights: • In biorthogonal quantum mechanics position operators are manifestly covariant and their eigenvectors are localized. • By including negative frequencies to give real fields our formalism escapes the no-go theorems. • Positive definite probability density exists locally but particles should be counted globally. • Relationships amongst photon probability, energy and current densities are local. • Use of the Newton Wigner basis should be limited to the calculation of expectation values.

  5. Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory

    Energy Technology Data Exchange (ETDEWEB)

    Vecharynski, Eugene [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Brabec, Jiri [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Shao, Meiyue [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Govind, Niranjan [Pacific Northwest National Lab. (PNNL), Richland, WA (United States). Environmental Molecular Sciences Lab.; Yang, Chao [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division

    2017-12-01

    We present two efficient iterative algorithms for solving the linear response eigen- value problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into a product eigenvalue problem that is self-adjoint with respect to a K-inner product. This product eigenvalue problem can be solved efficiently by a modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the K-inner product. The solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. However, the other component of the eigenvector can be easily recovered in a postprocessing procedure. Therefore, the algorithms we present here are more efficient than existing algorithms that try to approximate both components of the eigenvectors simultaneously. The efficiency of the new algorithms is demonstrated by numerical examples.

  6. Maxwell meets Reeh–Schlieder: The quantum mechanics of neutral bosons

    International Nuclear Information System (INIS)

    Hawton, Margaret; Debierre, Vincent

    2017-01-01

    We find that biorthogonal quantum mechanics with a scalar product that counts both absorbed and emitted particles leads to covariant position operators with localized eigenvectors. In this manifestly covariant formulation the probability for a transition from a one-photon state to a position eigenvector is the first order Glauber correlation function, bridging the gap between photon counting and the sensitivity of light detectors to electromagnetic energy density. The position eigenvalues are identified as the spatial parameters in the canonical quantum field operators and the position basis describes an array of localized devices that instantaneously absorb and re-emit bosons. - Highlights: • In biorthogonal quantum mechanics position operators are manifestly covariant and their eigenvectors are localized. • By including negative frequencies to give real fields our formalism escapes the no-go theorems. • Positive definite probability density exists locally but particles should be counted globally. • Relationships amongst photon probability, energy and current densities are local. • Use of the Newton Wigner basis should be limited to the calculation of expectation values.

  7. Network-Based Detection and Classification of Seismovolcanic Tremors: Example From the Klyuchevskoy Volcanic Group in Kamchatka

    Science.gov (United States)

    Soubestre, Jean; Shapiro, Nikolai M.; Seydoux, Léonard; de Rosny, Julien; Droznin, Dmitry V.; Droznina, Svetlana Ya.; Senyukov, Sergey L.; Gordeev, Evgeniy I.

    2018-01-01

    We develop a network-based method for detecting and classifying seismovolcanic tremors. The proposed approach exploits the coherence of tremor signals across the network that is estimated from the array covariance matrix. The method is applied to four and a half years of continuous seismic data recorded by 19 permanent seismic stations in the vicinity of the Klyuchevskoy volcanic group in Kamchatka (Russia), where five volcanoes were erupting during the considered time period. We compute and analyze daily covariance matrices together with their eigenvalues and eigenvectors. As a first step, most coherent signals corresponding to dominating tremor sources are detected based on the width of the covariance matrix eigenvalues distribution. Thus, volcanic tremors of the two volcanoes known as most active during the considered period, Klyuchevskoy and Tolbachik, are efficiently detected. As a next step, we consider the daily array covariance matrix's first eigenvector. Our main hypothesis is that these eigenvectors represent the principal components of the daily seismic wavefield and, for days with tremor activity, characterize dominant tremor sources. Those daily first eigenvectors, which can be used as network-based fingerprints of tremor sources, are then grouped into clusters using correlation coefficient as a measure of the vector similarity. As a result, we identify seven clusters associated with different periods of activity of four volcanoes: Tolbachik, Klyuchevskoy, Shiveluch, and Kizimen. The developed method does not require a priori knowledge and is fully automatic; and the database of the network-based tremor fingerprints can be continuously enriched with newly available data.

  8. Diffusion Forecasting Model with Basis Functions from QR-Decomposition

    Science.gov (United States)

    Harlim, John; Yang, Haizhao

    2017-12-01

    The diffusion forecasting is a nonparametric approach that provably solves the Fokker-Planck PDE corresponding to Itô diffusion without knowing the underlying equation. The key idea of this method is to approximate the solution of the Fokker-Planck equation with a discrete representation of the shift (Koopman) operator on a set of basis functions generated via the diffusion maps algorithm. While the choice of these basis functions is provably optimal under appropriate conditions, computing these basis functions is quite expensive since it requires the eigendecomposition of an N× N diffusion matrix, where N denotes the data size and could be very large. For large-scale forecasting problems, only a few leading eigenvectors are computationally achievable. To overcome this computational bottleneck, a new set of basis functions constructed by orthonormalizing selected columns of the diffusion matrix and its leading eigenvectors is proposed. This computation can be carried out efficiently via the unpivoted Householder QR factorization. The efficiency and effectiveness of the proposed algorithm will be shown in both deterministically chaotic and stochastic dynamical systems; in the former case, the superiority of the proposed basis functions over purely eigenvectors is significant, while in the latter case forecasting accuracy is improved relative to using a purely small number of eigenvectors. Supporting arguments will be provided on three- and six-dimensional chaotic ODEs, a three-dimensional SDE that mimics turbulent systems, and also on the two spatial modes associated with the boreal winter Madden-Julian Oscillation obtained from applying the Nonlinear Laplacian Spectral Analysis on the measured Outgoing Longwave Radiation.

  9. Compact versus noncompact quantum dynamics of time-dependent su(1,1)-valued Hamiltonians

    International Nuclear Information System (INIS)

    Penna, V.

    1996-01-01

    We consider the Schroedinger problem for time-dependent (TD) Hamiltonians represented by a linear combination of the compact generator and the hyperbolic generator of su(1,1). Several types of transitions, characterized by different time initial conditions on the generator coefficients, are analyzed by resorting to the harmonic oscillator model with a frequency vanishing for t→+∞. We provide examples that point out how the TD states of the transitions can be constructed either by the compact eigenvector basis or by the noncompact eigenvector basis depending on the initial conditions characterizing the frequency time behavior. Copyright copyright 1996 Academic Press, Inc

  10. Relationships between the Definition of the Hyperplane Width to the Fidelity of Principal Component Loading Patterns.

    Science.gov (United States)

    Richman, Michael B.; Gong, Xiaofeng

    1999-06-01

    When applying eigenanalysis, one decision analysts make is the determination of what magnitude an eigenvector coefficient (e.g., principal component (PC) loading) must achieve to be considered as physically important. Such coefficients can be displayed on maps or in a time series or tables to gain a fuller understanding of a large array of multivariate data. Previously, such a decision on what value of loading designates a useful signal (hereafter called the loading `cutoff') for each eigenvector has been purely subjective. The importance of selecting such a cutoff is apparent since those loading elements in the range of zero to the cutoff are ignored in the interpretation and naming of PCs since only the absolute values of loadings greater than the cutoff are physically analyzed. This research sets out to objectify the problem of best identifying the cutoff by application of matching between known correlation/covariance structures and their corresponding eigenpatterns, as this cutoff point (known as the hyperplane width) is varied.A Monte Carlo framework is used to resample at five sample sizes. Fourteen different hyperplane cutoff widths are tested, bootstrap resampled 50 times to obtain stable results. The key findings are that the location of an optimal hyperplane cutoff width (one which maximized the information content match between the eigenvector and the parent dispersion matrix from which it was derived) is a well-behaved unimodal function. On an individual eigenvector, this enables the unique determination of a hyperplane cutoff value to be used to separate those loadings that best reflect the relationships from those that do not. The effects of sample size on the matching accuracy are dramatic as the values for all solutions (i.e., unrotated, rotated) rose steadily from 25 through 250 observations and then weakly thereafter. The specific matching coefficients are useful to assess the penalties incurred when one analyzes eigenvector coefficients of a

  11. Targeting functional motifs of a protein family

    Science.gov (United States)

    Bhadola, Pradeep; Deo, Nivedita

    2016-10-01

    The structural organization of a protein family is investigated by devising a method based on the random matrix theory (RMT), which uses the physiochemical properties of the amino acid with multiple sequence alignment. A graphical method to represent protein sequences using physiochemical properties is devised that gives a fast, easy, and informative way of comparing the evolutionary distances between protein sequences. A correlation matrix associated with each property is calculated, where the noise reduction and information filtering is done using RMT involving an ensemble of Wishart matrices. The analysis of the eigenvalue statistics of the correlation matrix for the β -lactamase family shows the universal features as observed in the Gaussian orthogonal ensemble (GOE). The property-based approach captures the short- as well as the long-range correlation (approximately following GOE) between the eigenvalues, whereas the previous approach (treating amino acids as characters) gives the usual short-range correlations, while the long-range correlations are the same as that of an uncorrelated series. The distribution of the eigenvector components for the eigenvalues outside the bulk (RMT bound) deviates significantly from RMT observations and contains important information about the system. The information content of each eigenvector of the correlation matrix is quantified by introducing an entropic estimate, which shows that for the β -lactamase family the smallest eigenvectors (low eigenmodes) are highly localized as well as informative. These small eigenvectors when processed gives clusters involving positions that have well-defined biological and structural importance matching with experiments. The approach is crucial for the recognition of structural motifs as shown in β -lactamase (and other families) and selectively identifies the important positions for targets to deactivate (activate) the enzymatic actions.

  12. Optimized Large-scale CMB Likelihood and Quadratic Maximum Likelihood Power Spectrum Estimation

    Science.gov (United States)

    Gjerløw, E.; Colombo, L. P. L.; Eriksen, H. K.; Górski, K. M.; Gruppuso, A.; Jewell, J. B.; Plaszczynski, S.; Wehus, I. K.

    2015-11-01

    We revisit the problem of exact cosmic microwave background (CMB) likelihood and power spectrum estimation with the goal of minimizing computational costs through linear compression. This idea was originally proposed for CMB purposes by Tegmark et al., and here we develop it into a fully functioning computational framework for large-scale polarization analysis, adopting WMAP as a working example. We compare five different linear bases (pixel space, harmonic space, noise covariance eigenvectors, signal-to-noise covariance eigenvectors, and signal-plus-noise covariance eigenvectors) in terms of compression efficiency, and find that the computationally most efficient basis is the signal-to-noise eigenvector basis, which is closely related to the Karhunen-Loeve and Principal Component transforms, in agreement with previous suggestions. For this basis, the information in 6836 unmasked WMAP sky map pixels can be compressed into a smaller set of 3102 modes, with a maximum error increase of any single multipole of 3.8% at ℓ ≤ 32 and a maximum shift in the mean values of a joint distribution of an amplitude-tilt model of 0.006σ. This compression reduces the computational cost of a single likelihood evaluation by a factor of 5, from 38 to 7.5 CPU seconds, and it also results in a more robust likelihood by implicitly regularizing nearly degenerate modes. Finally, we use the same compression framework to formulate a numerically stable and computationally efficient variation of the Quadratic Maximum Likelihood implementation, which requires less than 3 GB of memory and 2 CPU minutes per iteration for ℓ ≤ 32, rendering low-ℓ QML CMB power spectrum analysis fully tractable on a standard laptop.

  13. Exploration of the forbidden regions of the Ramachandran plot (ϕ-ψ) with QTAIM.

    Science.gov (United States)

    Momen, Roya; Azizi, Alireza; Wang, Lingling; Ping, Yang; Xu, Tianlv; Kirk, Steven R; Li, Wenxuan; Manzhos, Sergei; Jenkins, Samantha

    2017-10-04

    A new QTAIM interpretation of the Ramachandran plot is formulated from the most and least facile eigenvectors of the second-derivative matrix of the electron density with a set of 29 magainin-2 peptide conformers. The presence of QTAIM eigenvectors associated with the most and least preferred directions of electronic charge density explained the role of hydrogen bonding, HH contacts and the glycine amino acid monomer in peptide folding. The highest degree of occupation of the QTAIM interpreted Ramachandran plot was found for the glycine amino acid monomer compared with the remaining backbone peptide bonds. The mobility of the QTAIM eigenvectors of the glycine amino acid monomer was higher than for the other amino acids and was comparable to that of the hydrogen bonding, explaining the flexibility of the magainin-2 backbone. We experimented with a variety of hybrid QTAIM-Ramachandran plots to highlight and explain why the glycine amino acid monomer largely occupies the 'forbidden' region on the Ramachandran plot. In addition, the new hybrid QTAIM-Ramachandran plots contained recognizable regions that can be associated with concepts familiar from the conventional Ramachandran plot whilst retaining the character of the QTAIM most and least preferred regions.

  14. Principal component analysis of solar flares in the soft X-ray flux

    International Nuclear Information System (INIS)

    Teuber, D.L.; Reichmann, E.J.; Wilson, R.M.; National Aeronautics and Space Administration, Huntsville, AL

    1979-01-01

    Principal component analysis is a technique for extracting the salient features from a mass of data. It applies, in particular, to the analysis of nonstationary ensembles. Computational schemes for this task require the evaluation of eigenvalues of matrices. We have used EISPACK Matrix Eigen System Routines on an IBM 360-75 to analyze full-disk proportional-counter data from the X-ray event analyzer (X-REA) which was part of the Skylab ATM/S-056 experiment. Empirical orthogonal functions have been derived for events in the soft X-ray spectrum between 2.5 and 20 A during different time frames between June 1973 and January 1974. Results indicate that approximately 90% of the cumulative power of each analyzed flare is contained in the largest eigenvector. The first two largest eigenvectors are sufficient for an empirical curve-fit through the raw data and a characterization of solar flares in the soft X-ray flux. Power spectra of the two largest eigenvectors reveal a previously reported periodicity of approximately 5 min. Similar signatures were also obtained from flares that are synchronized on maximum pulse-height when subjected to a principal component analysis. (orig.)

  15. The diversity of quasars unified by accretion and orientation.

    Science.gov (United States)

    Shen, Yue; Ho, Luis C

    2014-09-11

    Quasars are rapidly accreting supermassive black holes at the centres of massive galaxies. They display a broad range of properties across all wavelengths, reflecting the diversity in the physical conditions of the regions close to the central engine. These properties, however, are not random, but form well-defined trends. The dominant trend is known as 'Eigenvector 1', in which many properties correlate with the strength of optical iron and [O III] emission. The main physical driver of Eigenvector 1 has long been suspected to be the quasar luminosity normalized by the mass of the hole (the 'Eddington ratio'), which is an important parameter of the black hole accretion process. But a definitive proof has been missing. Here we report an analysis of archival data that reveals that the Eddington ratio indeed drives Eigenvector 1. We also find that orientation plays a significant role in determining the observed kinematics of the gas in the broad-line region, implying a flattened, disk-like geometry for the fast-moving clouds close to the black hole. Our results show that most of the diversity of quasar phenomenology can be unified using two simple quantities: Eddington ratio and orientation.

  16. Unstable quantum states and rigged Hilbert spaces

    International Nuclear Information System (INIS)

    Gorini, V.; Parravicini, G.

    1978-10-01

    Rigged Hilbert space techniques are applied to the quantum mechanical treatment of unstable states in nonrelativistic scattering theory. A method is discussed which is based on representations of decay amplitudes in terms of expansions over complete sets of generalized eigenvectors of the interacting Hamiltonian, corresponding to complex eigenvalues. These expansions contain both a discrete and a continuum contribution. The former corresponds to eigenvalues located at the second sheet poles of the S matrix, and yields the exponential terms in the survival amplitude. The latter arises from generalized eigenvectors associated to complex eigenvalues on background contours in the complex plane, and gives the corrections to the exponential law. 27 references

  17. A Spectral Analysis of Discrete-Time Quantum Walks Related to the Birth and Death Chains

    Science.gov (United States)

    Ho, Choon-Lin; Ide, Yusuke; Konno, Norio; Segawa, Etsuo; Takumi, Kentaro

    2018-04-01

    In this paper, we consider a spectral analysis of discrete time quantum walks on the path. For isospectral coin cases, we show that the time averaged distribution and stationary distributions of the quantum walks are described by the pair of eigenvalues of the coins as well as the eigenvalues and eigenvectors of the corresponding random walks which are usually referred as the birth and death chains. As an example of the results, we derive the time averaged distribution of so-called Szegedy's walk which is related to the Ehrenfest model. It is represented by Krawtchouk polynomials which is the eigenvectors of the model and includes the arcsine law.

  18. A Perron–Frobenius theory for block matrices associated to a multiplex network

    International Nuclear Information System (INIS)

    Romance, Miguel; Solá, Luis; Flores, Julio; García, Esther; García del Amo, Alejandro; Criado, Regino

    2015-01-01

    The uniqueness of the Perron vector of a nonnegative block matrix associated to a multiplex network is discussed. The conclusions come from the relationships between the irreducibility of some nonnegative block matrix associated to a multiplex network and the irreducibility of the corresponding matrices to each layer as well as the irreducibility of the adjacency matrix of the projection network. In addition the computation of that Perron vector in terms of the Perron vectors of the blocks is also addressed. Finally we present the precise relations that allow to express the Perron eigenvector of the multiplex network in terms of the Perron eigenvectors of its layers

  19. A Perron-Frobenius theory for block matrices associated to a multiplex network

    Science.gov (United States)

    Romance, Miguel; Solá, Luis; Flores, Julio; García, Esther; García del Amo, Alejandro; Criado, Regino

    2015-03-01

    The uniqueness of the Perron vector of a nonnegative block matrix associated to a multiplex network is discussed. The conclusions come from the relationships between the irreducibility of some nonnegative block matrix associated to a multiplex network and the irreducibility of the corresponding matrices to each layer as well as the irreducibility of the adjacency matrix of the projection network. In addition the computation of that Perron vector in terms of the Perron vectors of the blocks is also addressed. Finally we present the precise relations that allow to express the Perron eigenvector of the multiplex network in terms of the Perron eigenvectors of its layers.

  20. Violating Bell inequalities maximally for two d-dimensional systems

    International Nuclear Information System (INIS)

    Chen Jingling; Wu Chunfeng; Oh, C. H.; Kwek, L. C.; Ge Molin

    2006-01-01

    We show the maximal violation of Bell inequalities for two d-dimensional systems by using the method of the Bell operator. The maximal violation corresponds to the maximal eigenvalue of the Bell operator matrix. The eigenvectors corresponding to these eigenvalues are described by asymmetric entangled states. We estimate the maximum value of the eigenvalue for large dimension. A family of elegant entangled states |Ψ> app that violate Bell inequality more strongly than the maximally entangled state but are somewhat close to these eigenvectors is presented. These approximate states can potentially be useful for quantum cryptography as well as many other important fields of quantum information

  1. Instanton dominance of topological charge fluctuations in QCD?

    International Nuclear Information System (INIS)

    Hip, I.; Lippert, Th.; Schilling, K.; Schroers, W.; Neff, H.

    2002-01-01

    We consider the local chirality of near-zero eigenvectors from Wilson-Dirac and clover improved Wilson-Dirac lattice operators as proposed recently by Horvath et al. We study finer lattices and repair for the loss of orthogonality due to the non-normality of the Wilson-Dirac matrix. As a result we do see a clear double peak structure on lattices with resolutions higher than 0.1 fm. We find that the lattice artifacts can be considerably reduced by exploiting the biorthogonal system of left and right eigenvectors. We conclude that the dominance of instantons in topological charge fluctuations is not ruled out by local chirality measurements

  2. Spatio-temporal Eigenvector Filtering: Application on Bioenergy Crop Impacts

    Science.gov (United States)

    Wang, M.; Kamarianakis, Y.; Georgescu, M.

    2017-12-01

    A suite of 10-year ensemble-based simulations was conducted to investigate the hydroclimatic impacts due to large-scale deployment of perennial bioenergy crops across the continental United States. Given the large size of the simulated dataset (about 60Tb), traditional hierarchical spatio-temporal statistical modelling cannot be implemented for the evaluation of physics parameterizations and biofuel impacts. In this work, we propose a filtering algorithm that takes into account the spatio-temporal autocorrelation structure of the data while avoiding spatial confounding. This method is used to quantify the robustness of simulated hydroclimatic impacts associated with bioenergy crops to alternative physics parameterizations and observational datasets. Results are evaluated against those obtained from three alternative Bayesian spatio-temporal specifications.

  3. Eigenvector decomposition of full-spectrum x-ray computed tomography.

    Science.gov (United States)

    Gonzales, Brian J; Lalush, David S

    2012-03-07

    Energy-discriminated x-ray computed tomography (CT) data were projected onto a set of basis functions to suppress the noise in filtered back-projection (FBP) reconstructions. The x-ray CT data were acquired using a novel x-ray system which incorporated a single-pixel photon-counting x-ray detector to measure the x-ray spectrum for each projection ray. A matrix of the spectral response of different materials was decomposed using eigenvalue decomposition to form the basis functions. Projection of FBP onto basis functions created a de facto image segmentation of multiple contrast agents. Final reconstructions showed significant noise suppression while preserving important energy-axis data. The noise suppression was demonstrated by a marked improvement in the signal-to-noise ratio (SNR) along the energy axis for multiple regions of interest in the reconstructed images. Basis functions used on a more coarsely sampled energy axis still showed an improved SNR. We conclude that the noise-resolution trade off along the energy axis was significantly improved using the eigenvalue decomposition basis functions.

  4. The Topology of Symmetric Tensor Fields

    Science.gov (United States)

    Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval

    1997-01-01

    Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.

  5. Nonlinear signaling on biological networks: The role of stochasticity and spectral clustering

    Science.gov (United States)

    Hernandez-Hernandez, Gonzalo; Myers, Jesse; Alvarez-Lacalle, Enrique; Shiferaw, Yohannes

    2017-03-01

    Signal transduction within biological cells is governed by networks of interacting proteins. Communication between these proteins is mediated by signaling molecules which bind to receptors and induce stochastic transitions between different conformational states. Signaling is typically a cooperative process which requires the occurrence of multiple binding events so that reaction rates have a nonlinear dependence on the amount of signaling molecule. It is this nonlinearity that endows biological signaling networks with robust switchlike properties which are critical to their biological function. In this study we investigate how the properties of these signaling systems depend on the network architecture. Our main result is that these nonlinear networks exhibit bistability where the network activity can switch between states that correspond to a low and high activity level. We show that this bistable regime emerges at a critical coupling strength that is determined by the spectral structure of the network. In particular, the set of nodes that correspond to large components of the leading eigenvector of the adjacency matrix determines the onset of bistability. Above this transition the eigenvectors of the adjacency matrix determine a hierarchy of clusters, defined by its spectral properties, which are activated sequentially with increasing network activity. We argue further that the onset of bistability occurs either continuously or discontinuously depending upon whether the leading eigenvector is localized or delocalized. Finally, we show that at low network coupling stochastic transitions to the active branch are also driven by the set of nodes that contribute more strongly to the leading eigenvector. However, at high coupling, transitions are insensitive to network structure since the network can be activated by stochastic transitions of a few nodes. Thus this work identifies important features of biological signaling networks that may underlie their biological

  6. Coupling coefficients for tensor product representations of quantum SU(2)

    International Nuclear Information System (INIS)

    Groenevelt, Wolter

    2014-01-01

    We study tensor products of infinite dimensional irreducible * -representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometric orthogonal polynomials and q-Bessel-type functions

  7. Coupling coefficients for tensor product representations of quantum SU(2)

    Science.gov (United States)

    Groenevelt, Wolter

    2014-10-01

    We study tensor products of infinite dimensional irreducible *-representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometric orthogonal polynomials and q-Bessel-type functions.

  8. Finite-lattice form factors in free-fermion models

    International Nuclear Information System (INIS)

    Iorgov, N; Lisovyy, O

    2011-01-01

    We consider the general Z 2 -symmetric free-fermion model on the finite periodic lattice, which includes as special cases the Ising model on the square and triangular lattices and the Z n -symmetric BBS τ (2) -model with n = 2. Translating Kaufman's fermionic approach to diagonalization of Ising-like transfer matrices into the language of Grassmann integrals, we determine the transfer matrix eigenvectors and observe that they coincide with the eigenvectors of a square lattice Ising transfer matrix. This allows us to find exact finite-lattice form factors of spin operators for the statistical model and the associated finite-length quantum chains, of which the most general is equivalent to the XY chain in a transverse field

  9. Calculations of transient fields in the Felix experiments at Argonne using null field integrated techniques

    International Nuclear Information System (INIS)

    Han, H.C.; Davey, K.R.; Turner, L.

    1985-08-01

    The transient eddy current problem is characteristically computationally intensive. The motivation for this research was to realize an efficient, accurate, solution technique involving small matrices via an eigenvalue approach. Such a technique is indeed realized and tested using the null field integral technique. Using smart (i.e., efficient, global) basis functions to represent unknowns in terms of a minimum number of unknowns, homogeneous eigenvectors and eigenvalues are first determined. The general excitatory response is then represented in terms of these eigenvalues/eigenvectors. Excellent results are obtained for the Argonne Felix cylinder experiments using a 4 x 4 matrix. Extension to the 3-D problem (short cylinder) is set up in terms of an 8 x 8 matrix

  10. Optical spectra and lattice dynamics of molecular crystals

    CERN Document Server

    Zhizhin, GN

    1995-01-01

    The current volume is a single topic volume on the optical spectra and lattice dynamics of molecular crystals. The book is divided into two parts. Part I covers both the theoretical and experimental investigations of organic crystals. Part II deals with the investigation of the structure, phase transitions and reorientational motion of molecules in organic crystals. In addition appendices are given which provide the parameters for the calculation of the lattice dynamics of molecular crystals, procedures for the calculation of frequency eigenvectors of utilizing computers, and the frequencies and eigenvectors of lattice modes for several organic crystals. Quite a large amount of Russian literature is cited, some of which has previously not been available to scientists in the West.

  11. An improved V-Lambda solution of the matrix Riccati equation

    Science.gov (United States)

    Bar-Itzhack, Itzhack Y.; Markley, F. Landis

    1988-01-01

    The authors present an improved algorithm for computing the V-Lambda solution of the matrix Riccati equation. The improvement is in the reduction of the computational load, results from the orthogonality of the eigenvector matrix that has to be solved for. The orthogonality constraint reduces the number of independent parameters which define the matrix from n-squared to n (n - 1)/2. The authors show how to specify the parameters, how to solve for them and how to form from them the needed eigenvector matrix. In the search for suitable parameters, the analogy between the present problem and the problem of attitude determination is exploited, resulting in the choice of Rodrigues parameters.

  12. Method of locating related items in a geometric space for data mining

    Science.gov (United States)

    Hendrickson, Bruce A.

    1999-01-01

    A method for locating related items in a geometric space transforms relationships among items to geometric locations. The method locates items in the geometric space so that the distance between items corresponds to the degree of relatedness. The method facilitates communication of the structure of the relationships among the items. The method is especially beneficial for communicating databases with many items, and with non-regular relationship patterns. Examples of such databases include databases containing items such as scientific papers or patents, related by citations or keywords. A computer system adapted for practice of the present invention can include a processor, a storage subsystem, a display device, and computer software to direct the location and display of the entities. The method comprises assigning numeric values as a measure of similarity between each pairing of items. A matrix is constructed, based on the numeric values. The eigenvectors and eigenvalues of the matrix are determined. Each item is located in the geometric space at coordinates determined from the eigenvectors and eigenvalues. Proper construction of the matrix and proper determination of coordinates from eigenvectors can ensure that distance between items in the geometric space is representative of the numeric value measure of the items' similarity.

  13. Imaging Arterial Fibres Using Diffusion Tensor Imaging—Feasibility Study and Preliminary Results

    Directory of Open Access Journals (Sweden)

    Kerskens Christian

    2010-01-01

    Full Text Available Abstract MR diffusion tensor imaging (DTI was used to analyze the fibrous structure of aortic tissue. A fresh porcine aorta was imaged at 7T using a spin echo sequence with the following parameters: matrix 128 128 pixel; slice thickness 0.5 mm; interslice spacing 0.1 mm; number of slices 16; echo time 20.3 s; field of view 28 mm 28 mm. Eigenvectors from the diffusion tensor images were calculated for the central image slice and the averaged tensors and the eigenvector corresponding to the largest eigenvalue showed two distinct angles corresponding to near and to the transverse plane of the aorta. Fibre tractography within the aortic volume imaged confirmed that fibre angles were oriented helically with lead angles of and . The findings correspond to current histological and microscopy data on the fibrous structure of aortic tissue, and therefore the eigenvector maps and fibre tractography appear to reflect the alignment of the fibers in the aorta. In view of current efforts to develop noninvasive diagnostic tools for cardiovascular diseases, DTI may offer a technique to assess the structural properties of arterial tissue and hence any changes or degradation in arterial tissue.

  14. Volatility of an Indian stock market: A random matrix approach

    International Nuclear Information System (INIS)

    Kulkarni, V.; Deo, N.

    2006-07-01

    We examine volatility of an Indian stock market in terms of aspects like participation, synchronization of stocks and quantification of volatility using the random matrix approach. Volatility pattern of the market is found using the BSE index for the three-year period 2000- 2002. Random matrix analysis is carried out using daily returns of 70 stocks for several time windows of 85 days in 2001 to (i) do a brief comparative analysis with statistics of eigenvalues and eigenvectors of the matrix C of correlations between price fluctuations, in time regimes of different volatilities. While a bulk of eigenvalues falls within RMT bounds in all the time periods, we see that the largest (deviating) eigenvalue correlates well with the volatility of the index, the corresponding eigenvector clearly shows a shift in the distribution of its components from volatile to less volatile periods and verifies the qualitative association between participation and volatility (ii) observe that the Inverse participation ratio for the last eigenvector is sensitive to market fluctuations (the two quantities are observed to anti correlate significantly) (iii) set up a variability index, V whose temporal evolution is found to be significantly correlated with the volatility of the overall market index. MIRAMAR (author)

  15. Spectral decomposition of single-tone-driven quantum phase modulation

    International Nuclear Information System (INIS)

    Capmany, Jose; Fernandez-Pousa, Carlos R

    2011-01-01

    Electro-optic phase modulators driven by a single radio-frequency tone Ω can be described at the quantum level as scattering devices where input single-mode radiation undergoes energy changes in multiples of ℎΩ. In this paper, we study the spectral representation of the unitary, multimode scattering operator describing these devices. The eigenvalue equation, phase modulation being a process preserving the photon number, is solved at each subspace with definite number of photons. In the one-photon subspace F 1 , the problem is equivalent to the computation of the continuous spectrum of the Susskind-Glogower cosine operator of the harmonic oscillator. Using this analogy, the spectral decomposition in F 1 is constructed and shown to be equivalent to the usual Fock-space representation. The result is then generalized to arbitrary N-photon subspaces, where eigenvectors are symmetrized combinations of N one-photon eigenvectors and the continuous spectrum spans the entire unit circle. Approximate normalizable one-photon eigenstates are constructed in terms of London phase states truncated to optical bands. Finally, we show that synchronous ultrashort pulse trains represent classical field configurations with the same structure as these approximate eigenstates, and that they can be considered as approximate eigenvectors of the classical formulation of phase modulation.

  16. Spectral decomposition of single-tone-driven quantum phase modulation

    Energy Technology Data Exchange (ETDEWEB)

    Capmany, Jose [ITEAM Research Institute, Univ. Politecnica de Valencia, 46022 Valencia (Spain); Fernandez-Pousa, Carlos R, E-mail: c.pousa@umh.es [Signal Theory and Communications, Department of Physics and Computer Science, Univ. Miguel Hernandez, 03202 Elche (Spain)

    2011-02-14

    Electro-optic phase modulators driven by a single radio-frequency tone {Omega} can be described at the quantum level as scattering devices where input single-mode radiation undergoes energy changes in multiples of {h_bar}{Omega}. In this paper, we study the spectral representation of the unitary, multimode scattering operator describing these devices. The eigenvalue equation, phase modulation being a process preserving the photon number, is solved at each subspace with definite number of photons. In the one-photon subspace F{sub 1}, the problem is equivalent to the computation of the continuous spectrum of the Susskind-Glogower cosine operator of the harmonic oscillator. Using this analogy, the spectral decomposition in F{sub 1} is constructed and shown to be equivalent to the usual Fock-space representation. The result is then generalized to arbitrary N-photon subspaces, where eigenvectors are symmetrized combinations of N one-photon eigenvectors and the continuous spectrum spans the entire unit circle. Approximate normalizable one-photon eigenstates are constructed in terms of London phase states truncated to optical bands. Finally, we show that synchronous ultrashort pulse trains represent classical field configurations with the same structure as these approximate eigenstates, and that they can be considered as approximate eigenvectors of the classical formulation of phase modulation.

  17. Conduction mechanism studies on electron transfer of disordered system

    Institute of Scientific and Technical Information of China (English)

    徐慧; 宋祎璞; 李新梅

    2002-01-01

    Using the negative eigenvalue theory and the infinite order perturbation theory, a new method was developed to solve the eigenvectors of disordered systems. The result shows that eigenvectors change from the extended state to the localized state with the increase of the site points and the disordered degree of the system. When electric field is exerted, the electrons transfer from one localized state to another one. The conductivity is induced by the electron transfer. The authors derive the formula of electron conductivity and find the electron hops between localized states whose energies are close to each other, whereas localized positions differ from each other greatly. At low temperature the disordered system has the character of the negative differential dependence of resistivity and temperature.

  18. Symmetries of the second-difference matrix and the finite Fourier transform

    International Nuclear Information System (INIS)

    Aguilar, A.; Wolf, K.B.

    1979-01-01

    The finite Fourier transformation is well known to diagonalize the second-difference matrix and has been thus applied extensively to describe finite crystal lattices and electric networks. In setting out to find all transformations having this property, we obtain a multiparameter class of them. While permutations and unitary scaling of the eigenvectors constitute the trivial freedom of choice common to all diagonalization processes, the second-difference matrix has a larger symmetry group among whose elements we find the dihedral manifest symmetry transformations of the lattice. The latter are nevertheless sufficient for the unique specification of eigenvectors in various symmetry-adapted bases for the constrained lattice. The free symmetry parameters are shown to lead to a complete set of conserved quantities for the physical lattice motion. (author)

  19. Calculation of degenerated Eigenmodes with modified power method

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Peng; Lee, Hyun Suk; Lee, Deok Jung [School of Mechanical and Nuclear Engineering, Ulsan National Institute of Science and Technology, Ulsan (Korea, Republic of)

    2017-02-15

    The modified power method has been studied by many researchers to calculate the higher Eigenmodes and accelerate the convergence of the fundamental mode. Its application to multidimensional problems may be unstable due to degenerated or near-degenerated Eigenmodes. Complex Eigenmode solutions are occasionally encountered in such cases, and the shapes of the corresponding eigenvectors may change during the simulation. These issues must be addressed for the successful implementation of the modified power method. Complex components are examined and an approximation method to eliminate the usage of the complex numbers is provided. A technique to fix the eigenvector shapes is also provided. The performance of the methods for dealing with those aforementioned problems is demonstrated with two dimensional one group and three dimensional one group homogeneous diffusion problems.

  20. On the structure of acceleration in turbulence

    DEFF Research Database (Denmark)

    Liberzon, A.; Lüthi, B.; Holzner, M.

    2012-01-01

    Acceleration and spatial velocity gradients are obtained simultaneously in an isotropic turbulent flow via three dimensional particle tracking velocimetry. We observe two distinct populations of intense acceleration events: one in flow regions of strong strain and another in regions of strong...... vorticity. Geometrical alignments with respect to vorticity vector and to the strain eigenvectors, curvature of Lagrangian trajectories and of streamlines for total acceleration, and for its convective part, , are studied in detail. We discriminate the alignment features of total and convective acceleration...... statistics, which are genuine features of turbulent nature from those of kinematic nature. We find pronounced alignment of acceleration with vorticity. Similarly, and especially are predominantly aligned at 45°with the most stretching and compressing eigenvectors of the rate of the strain tensor...

  1. Tailoring three-point functions and integrability IV. Θ-morphism

    Energy Technology Data Exchange (ETDEWEB)

    Gromov, Nikolay [Department of Mathematics WC2R 2LS, King’s College London,London (United Kingdom); St. Petersburg INP,St. Petersburg (Russian Federation); Vieira, Pedro [Perimeter Institute for Theoretical Physics,Waterloo, Ontario N2L 2Y5 (Canada)

    2014-04-09

    We compute structure constants in N=4 SYM at one loop using Integrability. This requires having full control over the two loop eigenvectors of the dilatation operator for operators of arbitrary size. To achieve this, we develop an algebraic description called the Θ-morphism. In this approach we introduce impurities at each spin chain site, act with particular differential operators on the standard algebraic Bethe ansatz vectors and generate in this way higher loop eigenvectors. The final results for the structure constants take a surprisingly simple form, recently reported by us in the short note http://arxiv.org/abs/1202.4103. These are based on the tree level and one loop patterns together and also on some higher loop experiments involving simple operators.

  2. A Slater parameter optimisation interface for the CIV3 atomic structure code and its possible use with the R-matrix close coupling collision code

    International Nuclear Information System (INIS)

    Fawcett, B.C.; Hibbert, A.

    1989-11-01

    Details are here provided of amendments to the atomic structure code CIV3 which allow the optional adjustment of Slater parameters and average energies of configurations so that they result in improved energy levels and eigenvectors. It is also indicated how, in principle, the resultant improved eigenvectors can be utilised by the R-matrix collision code, thus providing an optimised target for close coupling collision strength calculations. An analogous computational method was recently reported for distorted wave collision strength calculations and applied to Fe XIII. The general method is suitable for the computation of collision strengths for complex ions and in some cases can then provide a basis for collision strength calculations in ions where ab initio computations break down or result in unnecessarily large errors. (author)

  3. Comparison of (e,2e), photoelectron and conventional spectroscopies for the Ar2 ion

    International Nuclear Information System (INIS)

    McCarthy, I.E.; Uylings, P.; Poppe, R.

    1978-05-01

    States of the Ar2 ion whose eigenvectors contain large components of single-hole configurations are observed in the (e,2e) and (γ,e) reactions on the Ar1 atom. The cross section is regarded as being proportional to the spectroscopic factor, that is the state expectation value of the single-hole configuration in the eigenvector. State expectation values obtained from these reactions for 1/2 + states are compared with ones obtained by diagonalizing an effective hamiltonian in a model space, with radial matrix elememts determined by fitting spectra for bound states. (e,2e) and conventional spectroscopy are compatible and provide complementary information about structure. Simple analysis of present (γ,e) data does not lead to compatible information on spectroscopic factors

  4. Algorithm 589. SICEDR: a FORTRAN subroutine for improving the accuracy of computed matrix eigenvalues

    International Nuclear Information System (INIS)

    Dongarra, J.J.

    1982-01-01

    SICEDR is a FORTRAN subroutine for improving the accuracy of a computed real eigenvalue and improving or computing the associated eigenvector. It is first used to generate information during the determination of the eigenvalues by the Schur decomposition technique. In particular, the Schur decomposition technique results in an orthogonal matrix Q and an upper quasi-triangular matrix T, such that A = QTQ/sup T/. Matrices A, Q, and T and the approximate eigenvalue, say lambda, are then used in the improvement phase. SICEDR uses an iterative method similar to iterative improvement for linear systems to improve the accuracy of lambda and improve or compute the eigenvector x in O(n 2 ) work, where n is the order of the matrix A

  5. Tailoring three-point functions and integrability IV. Θ-morphism

    International Nuclear Information System (INIS)

    Gromov, Nikolay; Vieira, Pedro

    2014-01-01

    We compute structure constants in N=4 SYM at one loop using Integrability. This requires having full control over the two loop eigenvectors of the dilatation operator for operators of arbitrary size. To achieve this, we develop an algebraic description called the Θ-morphism. In this approach we introduce impurities at each spin chain site, act with particular differential operators on the standard algebraic Bethe ansatz vectors and generate in this way higher loop eigenvectors. The final results for the structure constants take a surprisingly simple form, recently reported by us in the short note http://arxiv.org/abs/1202.4103. These are based on the tree level and one loop patterns together and also on some higher loop experiments involving simple operators

  6. Linear algebra

    CERN Document Server

    Berberian, Sterling K

    2014-01-01

    Introductory treatment covers basic theory of vector spaces and linear maps - dimension, determinants, eigenvalues, and eigenvectors - plus more advanced topics such as the study of canonical forms for matrices. 1992 edition.

  7. (WRFDA) for WRF non-hydrostatic mesoscale model

    Indian Academy of Sciences (India)

    Sujata Pattanayak

    2018-05-22

    May 22, 2018 ... Keywords. WRF-NMM; WRFDA; single observation test; eigenvalues; eigenvector; correlation; tropical .... The per- turbation variables here are defined as deviations ..... Synop, Sound, Metar, Pilot, Buoy, Ships, Airep,. Geoamv ...

  8. Spectral segmentation of polygonized images with normalized cuts

    Energy Technology Data Exchange (ETDEWEB)

    Matsekh, Anna [Los Alamos National Laboratory; Skurikhin, Alexei [Los Alamos National Laboratory; Rosten, Edward [UNIV OF CAMBRIDGE

    2009-01-01

    We analyze numerical behavior of the eigenvectors corresponding to the lowest eigenvalues of the generalized graph Laplacians arising in the Normalized Cuts formulations of the image segmentation problem on coarse polygonal grids.

  9. Target oriented dimensionality reduction of hyperspectral data by Kernel Fukunaga-Koontz Transform

    Science.gov (United States)

    Binol, Hamidullah; Ochilov, Shuhrat; Alam, Mohammad S.; Bal, Abdullah

    2017-02-01

    Principal component analysis (PCA) is a popular technique in remote sensing for dimensionality reduction. While PCA is suitable for data compression, it is not necessarily an optimal technique for feature extraction, particularly when the features are exploited in supervised learning applications (Cheriyadat and Bruce, 2003) [1]. Preserving features belonging to the target is very crucial to the performance of target detection/recognition techniques. Fukunaga-Koontz Transform (FKT) based supervised band reduction technique can be used to provide this requirement. FKT achieves feature selection by transforming into a new space in where feature classes have complimentary eigenvectors. Analysis of these eigenvectors under two classes, target and background clutter, can be utilized for target oriented band reduction since each basis functions best represent target class while carrying least information of the background class. By selecting few eigenvectors which are the most relevant to the target class, dimension of hyperspectral data can be reduced and thus, it presents significant advantages for near real time target detection applications. The nonlinear properties of the data can be extracted by kernel approach which provides better target features. Thus, we propose constructing kernel FKT (KFKT) to present target oriented band reduction. The performance of the proposed KFKT based target oriented dimensionality reduction algorithm has been tested employing two real-world hyperspectral data and results have been reported consequently.

  10. Exact solution of corner-modified banded block-Toeplitz eigensystems

    International Nuclear Information System (INIS)

    Cobanera, Emilio; Alase, Abhijeet; Viola, Lorenza; Ortiz, Gerardo

    2017-01-01

    Motivated by the challenge of seeking a rigorous foundation for the bulk-boundary correspondence for free fermions, we introduce an algorithm for determining exactly the spectrum and a generalized-eigenvector basis of a class of banded block quasi-Toeplitz matrices that we call corner-modified . Corner modifications of otherwise arbitrary banded block-Toeplitz matrices capture the effect of boundary conditions and the associated breakdown of translational invariance. Our algorithm leverages the interplay between a non-standard, projector-based method of kernel determination (physically, a bulk-boundary separation) and families of linear representations of the algebra of matrix Laurent polynomials. Thanks to the fact that these representations act on infinite-dimensional carrier spaces in which translation symmetry is restored, it becomes possible to determine the eigensystem of an auxiliary projected block-Laurent matrix. This results in an analytic eigenvector Ansatz , independent of the system size, which we prove is guaranteed to contain the full solution of the original finite-dimensional problem. The actual solution is then obtained by imposing compatibility with a boundary matrix , whose shape is also independent of system size. As an application, we show analytically that eigenvectors of short-ranged fermionic tight-binding models may display power-law corrections to exponential behavior, and demonstrate the phenomenon for the paradigmatic Majorana chain of Kitaev. (paper)

  11. Imaging Arterial Fibres Using Diffusion Tensor Imaging—Feasibility Study and Preliminary Results

    Directory of Open Access Journals (Sweden)

    Ciaran K. Simms

    2010-01-01

    Full Text Available MR diffusion tensor imaging (DTI was used to analyze the fibrous structure of aortic tissue. A fresh porcine aorta was imaged at 7T using a spin echo sequence with the following parameters: matrix 128 × 128 pixel; slice thickness 0.5 mm; interslice spacing 0.1 mm; number of slices 16; echo time 20.3 s; field of view 28 mm × 28 mm. Eigenvectors from the diffusion tensor images were calculated for the central image slice and the averaged tensors and the eigenvector corresponding to the largest eigenvalue showed two distinct angles corresponding to near 0∘ and 180∘ to the transverse plane of the aorta. Fibre tractography within the aortic volume imaged confirmed that fibre angles were oriented helically with lead angles of 15±2.5∘ and 175±2.5∘. The findings correspond to current histological and microscopy data on the fibrous structure of aortic tissue, and therefore the eigenvector maps and fibre tractography appear to reflect the alignment of the fibers in the aorta. In view of current efforts to develop noninvasive diagnostic tools for cardiovascular diseases, DTI may offer a technique to assess the structural properties of arterial tissue and hence any changes or degradation in arterial tissue.

  12. Possibility of modifying the growth trajectory in Raeini Cashmere goat.

    Science.gov (United States)

    Ghiasi, Heydar; Mokhtari, M S

    2018-03-27

    The objective of this study was to investigate the possibility of modifying the growth trajectory in Raeini Cashmere goat breed. In total, 13,193 records on live body weight collected from 4788 Raeini Cashmere goats were used. According to Akanke's information criterion (AIC), the sing-trait random regression model included fourth-order Legendre polynomial for direct and maternal genetic effect; maternal and individual permanent environmental effect was the best model for estimating (co)variance components. The matrices of eigenvectors for (co)variances between random regression coefficients of direct additive genetic were used to calculate eigenfunctions, and different eigenvector indices were also constructed. The obtained results showed that the first eigenvalue explained 79.90% of total genetic variance. Therefore, changing the body weights applying the first eigenfunction will be obtained rapidly. Selection based on the first eigenvector will cause favorable positive genetic gains for all body weight considered from birth to 12 months of age. For modifying the growth trajectory in Raeini Cashmere goat, the selection should be based on the second eigenfunction. The second eigenvalue accounted for 14.41% of total genetic variance for body weights that is low in comparison with genetic variance explained by the first eigenvalue. The complex patterns of genetic change in growth trajectory observed under the third and fourth eigenfunction and low amount of genetic variance explained by the third and fourth eigenvalues.

  13. Detecting, anticipating, and predicting critical transitions in spatially extended systems.

    Science.gov (United States)

    Kwasniok, Frank

    2018-03-01

    A data-driven linear framework for detecting, anticipating, and predicting incipient bifurcations in spatially extended systems based on principal oscillation pattern (POP) analysis is discussed. The dynamics are assumed to be governed by a system of linear stochastic differential equations which is estimated from the data. The principal modes of the system together with corresponding decay or growth rates and oscillation frequencies are extracted as the eigenvectors and eigenvalues of the system matrix. The method can be applied to stationary datasets to identify the least stable modes and assess the proximity to instability; it can also be applied to nonstationary datasets using a sliding window approach to track the changing eigenvalues and eigenvectors of the system. As a further step, a genuinely nonstationary POP analysis is introduced. Here, the system matrix of the linear stochastic model is time-dependent, allowing for extrapolation and prediction of instabilities beyond the learning data window. The methods are demonstrated and explored using the one-dimensional Swift-Hohenberg equation as an example, focusing on the dynamics of stochastic fluctuations around the homogeneous stable state prior to the first bifurcation. The POP-based techniques are able to extract and track the least stable eigenvalues and eigenvectors of the system; the nonstationary POP analysis successfully predicts the timing of the first instability and the unstable mode well beyond the learning data window.

  14. Identifying the structure of group correlation in the Korean financial market

    Science.gov (United States)

    Ahn, Sanghyun; Choi, Jaewon; Lim, Gyuchang; Cha, Kil Young; Kim, Sooyong; Kim, Kyungsik

    2011-06-01

    We investigate the structure of the cross-correlation in the Korean stock market. We analyze daily cross-correlations between price fluctuations of 586 different Korean stock entities for the 6-year time period from 2003 to 2008. The main purpose is to investigate the structure of group correlation and its stability by undressing the market-wide effect using the Markowitz multi-factor model and the network-based approach. We find the explicit list of significant firms in the few largest eigenvectors from the undressed correlation matrix. We also observe that each contributor is involved in the same business sectors. The structure of group correlation can not remain constant during each 1-year time period with different starting points, whereas only two largest eigenvectors are stable for 6 years 8-9 eigenvectors remain stable for half-year. The structure of group correlation in the Korean financial market is disturbed during a sufficiently short time period even though the group correlation exists as an ensemble for the 6-year time period in the evolution of the system. We verify the structure of group correlation by applying a network-based approach. In addition, we examine relations between market capitalization and businesses. The Korean stock market shows a different behavior compared to mature markets, implying that the KOSPI is a target for short-positioned investors.

  15. Matrices and transformations

    CERN Document Server

    Pettofrezzo, Anthony J

    1978-01-01

    Elementary, concrete approach: fundamentals of matrix algebra, linear transformation of the plane, application of properties of eigenvalues and eigenvectors to study of conics. Includes proofs of most theorems. Answers to odd-numbered exercises.

  16. Use of eigenvectors in the solution of the flutter equation

    CSIR Research Space (South Africa)

    Van Zyl, Lourens H

    1993-07-01

    Full Text Available stream_source_info Van Zyl_1993.pdf.txt stream_content_type text/plain stream_size 2 Content-Encoding ISO-8859-1 stream_name Van Zyl_1993.pdf.txt Content-Type text/plain; charset=ISO-8859-1 ...

  17. Morphological covariance in anatomical MRI scans can identify discrete neural pathways in the brain and their disturbances in persons with neuropsychiatric disorders.

    Science.gov (United States)

    Bansal, Ravi; Hao, Xuejun; Peterson, Bradley S

    2015-05-01

    We hypothesize that coordinated functional activity within discrete neural circuits induces morphological organization and plasticity within those circuits. Identifying regions of morphological covariation that are independent of morphological covariation in other regions therefore may therefore allow us to identify discrete neural systems within the brain. Comparing the magnitude of these variations in individuals who have psychiatric disorders with the magnitude of variations in healthy controls may allow us to identify aberrant neural pathways in psychiatric illnesses. We measured surface morphological features by applying nonlinear, high-dimensional warping algorithms to manually defined brain regions. We transferred those measures onto the surface of a unit sphere via conformal mapping and then used spherical wavelets and their scaling coefficients to simplify the data structure representing these surface morphological features of each brain region. We used principal component analysis (PCA) to calculate covariation in these morphological measures, as represented by their scaling coefficients, across several brain regions. We then assessed whether brain subregions that covaried in morphology, as identified by large eigenvalues in the PCA, identified specific neural pathways of the brain. To do so, we spatially registered the subnuclei for each eigenvector into the coordinate space of a Diffusion Tensor Imaging dataset; we used these subnuclei as seed regions to track and compare fiber pathways with known fiber pathways identified in neuroanatomical atlases. We applied these procedures to anatomical MRI data in a cohort of 82 healthy participants (42 children, 18 males, age 10.5 ± 2.43 years; 40 adults, 22 males, age 32.42 ± 10.7 years) and 107 participants with Tourette's Syndrome (TS) (71 children, 59 males, age 11.19 ± 2.2 years; 36 adults, 21 males, age 37.34 ± 10.9 years). We evaluated the construct validity of the identified covariation in morphology

  18. Complex correlation approach for high frequency financial data

    Science.gov (United States)

    Wilinski, Mateusz; Ikeda, Yuichi; Aoyama, Hideaki

    2018-02-01

    We propose a novel approach that allows the calculation of a Hilbert transform based complex correlation for unevenly spaced data. This method is especially suitable for high frequency trading data, which are of a particular interest in finance. Its most important feature is the ability to take into account lead-lag relations on different scales, without knowing them in advance. We also present results obtained with this approach while working on Tokyo Stock Exchange intraday quotations. We show that individual sectors and subsectors tend to form important market components which may follow each other with small but significant delays. These components may be recognized by analysing eigenvectors of complex correlation matrix for Nikkei 225 stocks. Interestingly, sectorial components are also found in eigenvectors corresponding to the bulk eigenvalues, traditionally treated as noise.

  19. High values of disorder-generated multifractals and logarithmically correlated processes

    International Nuclear Information System (INIS)

    Fyodorov, Yan V.; Giraud, Olivier

    2015-01-01

    In the introductory section of the article we give a brief account of recent insights into statistics of high and extreme values of disorder-generated multifractals following a recent work by the first author with P. Le Doussal and A. Rosso (FLR) employing a close relation between multifractality and logarithmically correlated random fields. We then substantiate some aspects of the FLR approach analytically for multifractal eigenvectors in the Ruijsenaars–Schneider ensemble (RSE) of random matrices introduced by E. Bogomolny and the second author by providing an ab initio calculation that reveals hidden logarithmic correlations at the background of the disorder-generated multifractality. In the rest we investigate numerically a few representative models of that class, including the study of the highest component of multifractal eigenvectors in the Ruijsenaars–Schneider ensemble

  20. Nature of complex time eigenvalues of the one speed transport equation in a homogeneous sphere

    International Nuclear Information System (INIS)

    Dahl, E.B.; Sahni, D.C.

    1990-01-01

    The complex time eigenvalues of the transport equation have been studied for one speed neutrons, scattered isotropically in a homogeneous sphere with vacuum boundary conditions. It is shown that the complex decay constants vary continuously with the radius of the sphere. Our earlier conjecture (Dahl and Sahni (1983-84)) regarding disjoint arcs is thus shown to be true. We also indicate that complex decay constants exist even for large assemblies, though with rapid oscillations in the corresponding eigenvectors. These modes cannot be predicted by the diffusion equation as this behaviour of the eigenvectors contradicts the assumption of 'slowly varying flux' needed to derive the diffusion approximation from the transport equation. For an infinite system, the existence of complex modes is related to the solution of a homogeneous equation. (author)

  1. Parameter estimation for an expanding universe

    Directory of Open Access Journals (Sweden)

    Jieci Wang

    2015-03-01

    Full Text Available We study the parameter estimation for excitations of Dirac fields in the expanding Robertson–Walker universe. We employ quantum metrology techniques to demonstrate the possibility for high precision estimation for the volume rate of the expanding universe. We show that the optimal precision of the estimation depends sensitively on the dimensionless mass m˜ and dimensionless momentum k˜ of the Dirac particles. The optimal precision for the ratio estimation peaks at some finite dimensionless mass m˜ and momentum k˜. We find that the precision of the estimation can be improved by choosing the probe state as an eigenvector of the hamiltonian. This occurs because the largest quantum Fisher information is obtained by performing projective measurements implemented by the projectors onto the eigenvectors of specific probe states.

  2. Scale dependence of the alignment between strain rate and rotation in turbulent shear flow

    KAUST Repository

    Fiscaletti, D.

    2016-10-24

    The scale dependence of the statistical alignment tendencies of the eigenvectors of the strain-rate tensor e(i), with the vorticity vector omega, is examined in the self-preserving region of a planar turbulent mixing layer. Data from a direct numerical simulation are filtered at various length scales and the probability density functions of the magnitude of the alignment cosines between the two unit vectors vertical bar e(i) . (omega) over cap vertical bar are examined. It is observed that the alignment tendencies are insensitive to the concurrent large-scale velocity fluctuations, but are quantitatively affected by the nature of the concurrent large-scale velocity-gradient fluctuations. It is confirmed that the small-scale (local) vorticity vector is preferentially aligned in parallel with the large-scale (background) extensive strain-rate eigenvector e(1), in contrast to the global tendency for omega to be aligned in parallelwith the intermediate strain-rate eigenvector [Hamlington et al., Phys. Fluids 20, 111703 (2008)]. When only data from regions of the flow that exhibit strong swirling are included, the so-called high-enstrophy worms, the alignment tendencies are exaggerated with respect to the global picture. These findings support the notion that the production of enstrophy, responsible for a net cascade of turbulent kinetic energy from large scales to small scales, is driven by vorticity stretching due to the preferential parallel alignment between omega and nonlocal e(1) and that the strongly swirling worms are kinematically significant to this process.

  3. Scale dependence of the alignment between strain rate and rotation in turbulent shear flow

    KAUST Repository

    Fiscaletti, D.; Elsinga, G. E.; Attili, Antonio; Bisetti, Fabrizio; Buxton, O. R. H.

    2016-01-01

    The scale dependence of the statistical alignment tendencies of the eigenvectors of the strain-rate tensor e(i), with the vorticity vector omega, is examined in the self-preserving region of a planar turbulent mixing layer. Data from a direct numerical simulation are filtered at various length scales and the probability density functions of the magnitude of the alignment cosines between the two unit vectors vertical bar e(i) . (omega) over cap vertical bar are examined. It is observed that the alignment tendencies are insensitive to the concurrent large-scale velocity fluctuations, but are quantitatively affected by the nature of the concurrent large-scale velocity-gradient fluctuations. It is confirmed that the small-scale (local) vorticity vector is preferentially aligned in parallel with the large-scale (background) extensive strain-rate eigenvector e(1), in contrast to the global tendency for omega to be aligned in parallelwith the intermediate strain-rate eigenvector [Hamlington et al., Phys. Fluids 20, 111703 (2008)]. When only data from regions of the flow that exhibit strong swirling are included, the so-called high-enstrophy worms, the alignment tendencies are exaggerated with respect to the global picture. These findings support the notion that the production of enstrophy, responsible for a net cascade of turbulent kinetic energy from large scales to small scales, is driven by vorticity stretching due to the preferential parallel alignment between omega and nonlocal e(1) and that the strongly swirling worms are kinematically significant to this process.

  4. Impact of Bone Marrow Radiation Dose on Acute Hematologic Toxicity in Cervical Cancer: Principal Component Analysis on High Dimensional Data

    International Nuclear Information System (INIS)

    Yun Liang; Messer, Karen; Rose, Brent S.; Lewis, John H.; Jiang, Steve B.; Yashar, Catheryn M.; Mundt, Arno J.; Mell, Loren K.

    2010-01-01

    Purpose: To study the effects of increasing pelvic bone marrow (BM) radiation dose on acute hematologic toxicity in patients undergoing chemoradiotherapy, using a novel modeling approach to preserve the local spatial dose information. Methods and Materials: The study included 37 cervical cancer patients treated with concurrent weekly cisplatin and pelvic radiation therapy. The white blood cell count nadir during treatment was used as the indicator for acute hematologic toxicity. Pelvic BM radiation dose distributions were standardized across patients by registering the pelvic BM volumes to a common template, followed by dose remapping using deformable image registration, resulting in a dose array. Principal component (PC) analysis was applied to the dose array, and the significant eigenvectors were identified by linear regression on the PCs. The coefficients for PC regression and significant eigenvectors were represented in three dimensions to identify critical BM subregions where dose accumulation is associated with hematologic toxicity. Results: We identified five PCs associated with acute hematologic toxicity. PC analysis regression modeling explained a high proportion of the variation in acute hematologicity (adjusted R 2 , 0.49). Three-dimensional rendering of a linear combination of the significant eigenvectors revealed patterns consistent with anatomical distributions of hematopoietically active BM. Conclusions: We have developed a novel approach that preserves spatial dose information to model effects of radiation dose on toxicity, which may be useful in optimizing radiation techniques to avoid critical subregions of normal tissues. Further validation of this approach in a large cohort is ongoing.

  5. Perron–Frobenius theorem for nonnegative multilinear forms and extensions

    OpenAIRE

    Friedland, S.; Gaubert, S.; Han, L.

    2013-01-01

    We prove an analog of Perron-Frobenius theorem for multilinear forms with nonnegative coefficients, and more generally, for polynomial maps with nonnegative coefficients. We determine the geometric convergence rate of the power algorithm to the unique normalized eigenvector.

  6. Analysis of Heavy-Tailed Time Series

    DEFF Research Database (Denmark)

    Xie, Xiaolei

    This thesis is about analysis of heavy-tailed time series. We discuss tail properties of real-world equity return series and investigate the possibility that a single tail index is shared by all return series of actively traded equities in a market. Conditions for this hypothesis to be true...... are identified. We study the eigenvalues and eigenvectors of sample covariance and sample auto-covariance matrices of multivariate heavy-tailed time series, and particularly for time series with very high dimensions. Asymptotic approximations of the eigenvalues and eigenvectors of such matrices are found...... and expressed in terms of the parameters of the dependence structure, among others. Furthermore, we study an importance sampling method for estimating rare-event probabilities of multivariate heavy-tailed time series generated by matrix recursion. We show that the proposed algorithm is efficient in the sense...

  7. Deflation for inversion with multiple right-hand sides in QCD

    International Nuclear Information System (INIS)

    Stathopoulos, A; Abdel-Rehim, A M; Orginos, K

    2009-01-01

    Most calculations in lattice Quantum Chromodynamics (QCD) involve the solution of a series of linear systems of equations with exceedingly large matrices and a large number of right hand sides. Iterative methods for these problems can be sped up significantly if we deflate approximations of appropriate invariant spaces from the initial guesses. Recently we have developed eigCG, a modification of the Conjugate Gradient (CG) method, which while solving a linear system can reuse a window of the CG vectors to compute eigenvectors almost as accurately as the Lanczos method. The number of approximate eigenvectors can increase as more systems are solved. In this paper we review some of the characteristics of eigCG and show how it helps remove the critical slowdown in QCD calculations. Moreover, we study scaling with lattice volume and an extension of the technique to nonsymmetric problems.

  8. Impact of sample size on principal component analysis ordination of an environmental data set: effects on eigenstructure

    Directory of Open Access Journals (Sweden)

    Shaukat S. Shahid

    2016-06-01

    Full Text Available In this study, we used bootstrap simulation of a real data set to investigate the impact of sample size (N = 20, 30, 40 and 50 on the eigenvalues and eigenvectors resulting from principal component analysis (PCA. For each sample size, 100 bootstrap samples were drawn from environmental data matrix pertaining to water quality variables (p = 22 of a small data set comprising of 55 samples (stations from where water samples were collected. Because in ecology and environmental sciences the data sets are invariably small owing to high cost of collection and analysis of samples, we restricted our study to relatively small sample sizes. We focused attention on comparison of first 6 eigenvectors and first 10 eigenvalues. Data sets were compared using agglomerative cluster analysis using Ward’s method that does not require any stringent distributional assumptions.

  9. Predictive error dependencies when using pilot points and singular value decomposition in groundwater model calibration

    DEFF Research Database (Denmark)

    Christensen, Steen; Doherty, John

    2008-01-01

    A significant practical problem with the pilot point method is to choose the location of the pilot points. We present a method that is intended to relieve the modeler from much of this responsibility. The basic idea is that a very large number of pilot points are distributed more or less uniformly...... over the model area. Singular value decomposition (SVD) of the (possibly weighted) sensitivity matrix of the pilot point based model produces eigenvectors of which we pick a small number corresponding to significant eigenvalues. Super parameters are defined as factors through which parameter...... combinations corresponding to the chosen eigenvectors are multiplied to obtain the pilot point values. The model can thus be transformed from having many-pilot-point parameters to having a few super parameters that can be estimated by nonlinear regression on the basis of the available observations. (This...

  10. Cross-correlation matrix analysis of Chinese and American bank stocks in subprime crisis

    International Nuclear Information System (INIS)

    Zhu Shi-Zhao; Li Xin-Li; Zhang Wen-Qing; Wang Bing-Hong; Nie Sen; Yu Gao-Feng; Han Xiao-Pu

    2015-01-01

    In order to study the universality of the interactions among different markets, we analyze the cross-correlation matrix of the price of the Chinese and American bank stocks. We then find that the stock prices of the emerging market are more correlated than that of the developed market. Considering that the values of the components for the eigenvector may be positive or negative, we analyze the differences between two markets in combination with the endogenous and exogenous events which influence the financial markets. We find that the sparse pattern of components of eigenvectors out of the threshold value has no change in American bank stocks before and after the subprime crisis. However, it changes from sparse to dense for Chinese bank stocks. By using the threshold value to exclude the external factors, we simulate the interactions in financial markets. (paper)

  11. Introduction to the mathematics of inversion in remote sensing and indirect measurements

    CERN Document Server

    Twomey, S

    2013-01-01

    Developments in Geomathematics, 3: Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements focuses on the application of the mathematics of inversion in remote sensing and indirect measurements, including vectors and matrices, eigenvalues and eigenvectors, and integral equations. The publication first examines simple problems involving inversion, theory of large linear systems, and physical and geometric aspects of vectors and matrices. Discussions focus on geometrical view of matrix operations, eigenvalues and eigenvectors, matrix products, inverse of a matrix, transposition and rules for product inversion, and algebraic elimination. The manuscript then tackles the algebraic and geometric aspects of functions and function space and linear inversion methods, as well as the algebraic and geometric nature of constrained linear inversion, least squares solution, approximation by sums of functions, and integral equations. The text examines information content of indirect sensing m...

  12. Transfer matrix method for dynamics modeling and independent modal space vibration control design of linear hybrid multibody system

    Science.gov (United States)

    Rong, Bao; Rui, Xiaoting; Lu, Kun; Tao, Ling; Wang, Guoping; Ni, Xiaojun

    2018-05-01

    In this paper, an efficient method of dynamics modeling and vibration control design of a linear hybrid multibody system (MS) is studied based on the transfer matrix method. The natural vibration characteristics of a linear hybrid MS are solved by using low-order transfer equations. Then, by constructing the brand-new body dynamics equation, augmented operator and augmented eigenvector, the orthogonality of augmented eigenvector of a linear hybrid MS is satisfied, and its state space model expressed in each independent model space is obtained easily. According to this dynamics model, a robust independent modal space-fuzzy controller is designed for vibration control of a general MS, and the genetic optimization of some critical control parameters of fuzzy tuners is also presented. Two illustrative examples are performed, which results show that this method is computationally efficient and with perfect control performance.

  13. Baroclinic wave configurations evolution at European scale in the period 1948-2013

    Science.gov (United States)

    Carbunaru, Daniel; Burcea, Sorin; Carbunaru, Felicia

    2016-04-01

    The main aim of the study was to investigate the dynamic characteristics of synoptic configurations at European scale and especially in south-eastern part of Europe for the period 1948-2013. Using the empirical orthogonal functions analysis, simultaneously applied to daily average geopotential field at different pressure levels (200 hPa, 300 hPa, 500 hPa and 850 hPa) during warm (April-September) and cold (October-March) seasons, on a synoptic spatial domain centered on Europe (-27.5o lon V to 45o lon E and 32.5o lat N to 72.5o lat N), the main mode of oscillation characteristic to vertical shift of mean baroclinic waves was obtained. The analysis independently applied on 66 years showed that the first eigenvectors in warms periods describe about 60% of the data and in cold season 40% of the data for each year. In comparison secondary eigenvectors describe up to 20% and 10% of the data. Thus, the analysis was focused on the complex evolution of the first eigenvector in 66 years, during the summer period. On average, this eigenvector describes a small vertical phase shift in the west part of the domain and a large one in the eastern part. Because the spatial extent of the considered synoptic domain incorporates in the west part AMO (Atlantic Multidecadal Oscillation) and NAO (North Atlantic Oscillation) oscillations, and in the north part being sensitive to AO (Arctic Oscillation) oscillation, these three oscillations were considered as modulating dynamic factors at hemispherical scale. The preliminary results show that in the summer seasons AMO and NAO oscillations modulated vertical phase shift of baroclinic wave in the west of the area (Northwestern Europe), and the relationship between AO and NAO oscillations modulated vertical phase shift in the southeast area (Southeast Europe). Second, it was shown the way in which this vertical phase shift modulates the overall behavior of cyclonic activity, particularly in Southeastern Europe. This work has been developed

  14. Shock and Rarefaction Waves in a Heterogeneous Mantle

    Science.gov (United States)

    Jordan, J.; Hesse, M. A.

    2012-12-01

    We explore the effect of heterogeneities on partial melting and melt migration during active upwelling in the Earth's mantle. We have constructed simple, explicit nonlinear models in one dimension to examine heterogeneity and its dynamic affects on porosity, temperature and the magnesium number in a partially molten, porous medium comprised of olivine. The composition of the melt and solid are defined by a closed, binary phase diagram for a simplified, two-component olivine system. The two-component solid solution is represented by a phase loop where concentrations 0 and 1 to correspond to fayalite and forsterite, respectively. For analysis, we examine an advective system with a Riemann initial condition. Chromatographic tools and theory have primarily been used to track large, rare earth elements as tracers. In our case, we employ these theoretical tools to highlight the importance of the magnesium number, enthalpy and overall heterogeneity in the dynamics of melt migration. We calculate the eigenvectors and eigenvalues in the concentration-enthalpy space in order to glean the characteristics of the waves emerging the Riemann step. Analysis on Riemann problems of this nature shows us that the composition-enthalpy waves can be represented by self-similar solutions. The eigenvalues of the composition-enthalpy system represent the characteristic wave propagation speeds of the compositions and enthalpy through the domain. Furthermore, the corresponding eigenvectors are the directions of variation, or ``pathways," in concentration-enthalpy space that the characteristic waves follow. In the two-component system, the Riemann problem yields two waves connected by an intermediate concentration-enthalpy state determined by the intersections of the integral curves of the eigenvectors emanating from both the initial and boundary states. The first wave, ``slow path," and second wave, ``fast path," follow the aformentioned pathways set by the eigenvectors. The slow path wave

  15. A classification system for one Killing vector solutions of Einstein's equations

    International Nuclear Information System (INIS)

    Hoenselaers, C.

    1978-01-01

    A double classification system for one Killing vector solutions in terms of the eigenvectors and eigenvalues of the Ricci and Bach tensor of the associated three manifold is proposed. The calculations of the Bach tensor are carried out for special cases. (author)

  16. Fiber crossing in human brain depicted with diffusion tensor MR imaging

    DEFF Research Database (Denmark)

    Wiegell, M.R.; Larsson, H.B.; Wedeen, V.J.

    2000-01-01

    Human white matter fiber crossings were investigated with use of the full eigenstructure of the magnetic resonance diffusion tensor. Intravoxel fiber dispersions were characterized by the plane spanned by the major and medium eigenvectors and depicted with three-dimensional graphics. This method...

  17. Feature extraction for classification in the data mining process

    NARCIS (Netherlands)

    Pechenizkiy, M.; Puuronen, S.; Tsymbal, A.

    2003-01-01

    Dimensionality reduction is a very important step in the data mining process. In this paper, we consider feature extraction for classification tasks as a technique to overcome problems occurring because of "the curse of dimensionality". Three different eigenvector-based feature extraction approaches

  18. Performance Analysis of the Decentralized Eigendecomposition and ESPRIT Algorithm

    Science.gov (United States)

    Suleiman, Wassim; Pesavento, Marius; Zoubir, Abdelhak M.

    2016-05-01

    In this paper, we consider performance analysis of the decentralized power method for the eigendecomposition of the sample covariance matrix based on the averaging consensus protocol. An analytical expression of the second order statistics of the eigenvectors obtained from the decentralized power method which is required for computing the mean square error (MSE) of subspace-based estimators is presented. We show that the decentralized power method is not an asymptotically consistent estimator of the eigenvectors of the true measurement covariance matrix unless the averaging consensus protocol is carried out over an infinitely large number of iterations. Moreover, we introduce the decentralized ESPRIT algorithm which yields fully decentralized direction-of-arrival (DOA) estimates. Based on the performance analysis of the decentralized power method, we derive an analytical expression of the MSE of DOA estimators using the decentralized ESPRIT algorithm. The validity of our asymptotic results is demonstrated by simulations.

  19. A Quantum Implementation Model for Artificial Neural Networks

    Directory of Open Access Journals (Sweden)

    Ammar Daskin

    2018-02-01

    Full Text Available The learning process for multilayered neural networks with many nodes makes heavy demands on computational resources. In some neural network models, the learning formulas, such as the Widrow–Hoff formula, do not change the eigenvectors of the weight matrix while flatting the eigenvalues. In infinity, these iterative formulas result in terms formed by the principal components of the weight matrix, namely, the eigenvectors corresponding to the non-zero eigenvalues. In quantum computing, the phase estimation algorithm is known to provide speedups over the conventional algorithms for the eigenvalue-related problems. Combining the quantum amplitude amplification with the phase estimation algorithm, a quantum implementation model for artificial neural networks using the Widrow–Hoff learning rule is presented. The complexity of the model is found to be linear in the size of the weight matrix. This provides a quadratic improvement over the classical algorithms. Quanta 2018; 7: 7–18.

  20. Pore Fluid Effects on Shear Modulus for Sandstones with Soft Anisotropy

    International Nuclear Information System (INIS)

    Berryman, J G

    2004-01-01

    A general analysis of poroelasticity for vertical transverse isotropy (VTI) shows that four eigenvectors are pure shear modes with no coupling to the pore-fluidmechanics. The remaining two eigenvectors are linear combinations of pure compression and uniaxial shear, both of which are coupled to the fluid mechanics. After reducing the problem to a 2x2 system, the analysis shows in a relatively elementary fashion how a poroelastic system with isotropic solid elastic frame, but with anisotropy introduced through the poroelastic coefficients, interacts with the mechanics of the pore fluid and produces shear dependence on fluid properties in the overall mechanical system. The analysis shows, for example, that this effect is always present (though sometimes small in magnitude) in the systems studied, and can be quite large (up to a definite maximum increase of 20 per cent) in some rocks--including Spirit River sandstone and Schuler-Cotton Valley sandstone

  1. Efficient GW calculations using eigenvalue-eigenvector decomposition of the dielectric matrix

    Science.gov (United States)

    Nguyen, Huy-Viet; Pham, T. Anh; Rocca, Dario; Galli, Giulia

    2011-03-01

    During the past 25 years, the GW method has been successfully used to compute electronic quasi-particle excitation spectra of a variety of materials. It is however a computationally intensive technique, as it involves summations over occupied and empty electronic states, to evaluate both the Green function (G) and the dielectric matrix (DM) entering the expression of the screened Coulomb interaction (W). Recent developments have shown that eigenpotentials of DMs can be efficiently calculated without any explicit evaluation of empty states. In this work, we will present a computationally efficient approach to the calculations of GW spectra by combining a representation of DMs in terms of its eigenpotentials and a recently developed iterative algorithm. As a demonstration of the efficiency of the method, we will present calculations of the vertical ionization potentials of several systems. Work was funnded by SciDAC-e DE-FC02-06ER25777.

  2. Using Solar Radiation Pressure to Control L2 Orbits

    Science.gov (United States)

    Tene, Noam; Richon, Karen; Folta, David

    1998-01-01

    The main perturbations at the Sun-Earth Lagrange points L1 and L2 are from solar radiation pressure (SRP), the Moon and the planets. Traditional approaches to trajectory design for Lagrange-point orbits use maneuvers every few months to correct for these perturbations. The gravitational effects of the Moon and the planets are small and periodic. However, they cannot be neglected because small perturbations in the direction of the unstable eigenvector are enough to cause exponential growth within a few months. The main effect of a constant SRP is to shift the center of the orbit by a small distance. For spacecraft with large sun-shields like the Microwave Anisotropy Probe (MAP) and the Next Generation Space Telescope (NGST), the SRP effect is larger than all other perturbations and depends mostly on spacecraft attitude. Small variations in the spacecraft attitude are large enough to excite or control the exponential eigenvector. A closed-loop linear controller based on the SRP variations would eliminate one of the largest errors to the orbit and provide a continuous acceleration for use in controlling other disturbances. It is possible to design reference trajectories that account for the periodic lunar and planetary perturbations and still satisfy mission requirements. When such trajectories are used the acceleration required to control the unstable eigenvector is well within the capabilities of a continuous linear controller. Initial estimates show that by using attitude control it should be possible to minimize and even eliminate thruster maneuvers for station keeping.

  3. Linear algebra of the permutation invariant Crow-Kimura model of prebiotic evolution.

    Science.gov (United States)

    Bratus, Alexander S; Novozhilov, Artem S; Semenov, Yuri S

    2014-10-01

    A particular case of the famous quasispecies model - the Crow-Kimura model with a permutation invariant fitness landscape - is investigated. Using the fact that the mutation matrix in the case of a permutation invariant fitness landscape has a special tridiagonal form, a change of the basis is suggested such that in the new coordinates a number of analytical results can be obtained. In particular, using the eigenvectors of the mutation matrix as the new basis, we show that the quasispecies distribution approaches a binomial one and give simple estimates for the speed of convergence. Another consequence of the suggested approach is a parametric solution to the system of equations determining the quasispecies. Using this parametric solution we show that our approach leads to exact asymptotic results in some cases, which are not covered by the existing methods. In particular, we are able to present not only the limit behavior of the leading eigenvalue (mean population fitness), but also the exact formulas for the limit quasispecies eigenvector for special cases. For instance, this eigenvector has a geometric distribution in the case of the classical single peaked fitness landscape. On the biological side, we propose a mathematical definition, based on the closeness of the quasispecies to the binomial distribution, which can be used as an operational definition of the notorious error threshold. Using this definition, we suggest two approximate formulas to estimate the critical mutation rate after which the quasispecies delocalization occurs. Copyright © 2014 Elsevier Inc. All rights reserved.

  4. SU-E-I-58: Objective Models of Breast Shape Undergoing Mammography and Tomosynthesis Using Principal Component Analysis.

    Science.gov (United States)

    Feng, Ssj; Sechopoulos, I

    2012-06-01

    To develop an objective model of the shape of the compressed breast undergoing mammographic or tomosynthesis acquisition. Automated thresholding and edge detection was performed on 984 anonymized digital mammograms (492 craniocaudal (CC) view mammograms and 492 medial lateral oblique (MLO) view mammograms), to extract the edge of each breast. Principal Component Analysis (PCA) was performed on these edge vectors to identify a limited set of parameters and eigenvectors that. These parameters and eigenvectors comprise a model that can be used to describe the breast shapes present in acquired mammograms and to generate realistic models of breasts undergoing acquisition. Sample breast shapes were then generated from this model and evaluated. The mammograms in the database were previously acquired for a separate study and authorized for use in further research. The PCA successfully identified two principal components and their corresponding eigenvectors, forming the basis for the breast shape model. The simulated breast shapes generated from the model are reasonable approximations of clinically acquired mammograms. Using PCA, we have obtained models of the compressed breast undergoing mammographic or tomosynthesis acquisition based on objective analysis of a large image database. Up to now, the breast in the CC view has been approximated as a semi-circular tube, while there has been no objectively-obtained model for the MLO view breast shape. Such models can be used for various breast imaging research applications, such as x-ray scatter estimation and correction, dosimetry estimates, and computer-aided detection and diagnosis. © 2012 American Association of Physicists in Medicine.

  5. The Faddeev equation and essential spectrum of a Hamiltonian in Fock space

    International Nuclear Information System (INIS)

    Muminov, M.I.; Rasulov, T.H.

    2008-05-01

    A model operator H associated to a quantum system with non conserved number of particles is studied. The Faddeev type system of equation for eigenvectors of H is constructed. The essential spectrum of H is described by the spectrum of the channel operator. (author)

  6. A computational approach for fluid queues driven by truncated birth-death processes.

    NARCIS (Netherlands)

    Lenin, R.B.; Parthasarathy, P.R.

    2000-01-01

    In this paper, we analyze fluid queues driven by truncated birth-death processes with general birth and death rates. We compute the equilibrium distribution of the content of the fluid buffer by providing efficient numerical procedures to compute the eigenvalues and the eigenvectors of the

  7. Random matrix theory and acoustic resonances in plates with an approximate symmetry

    DEFF Research Database (Denmark)

    Andersen, Anders Peter; Ellegaard, C.; Jackson, A.D.

    2001-01-01

    We discuss a random matrix model of systems with an approximate symmetry and present the spectral fluctuation statistics and eigenvector characteristics for the model. An acoustic resonator like, e.g., an aluminum plate may have an approximate symmetry. We have measured the frequency spectrum and...

  8. Sensor scheme design for active structural acoustic control

    NARCIS (Netherlands)

    Berkhoff, Arthur P.

    Efficient sensing schemes for the active reduction of sound radiation from plates are presented based on error signals derived from spatially weighted plate velocity or near-field pressure. The schemes result in near-optimal reductions as compared to weighting procedures derived from eigenvector or

  9. A Brief Historical Introduction to Determinants with Applications

    Science.gov (United States)

    Debnath, L.

    2013-01-01

    This article deals with a short historical introduction to determinants with applications to the theory of equations, geometry, multiple integrals, differential equations and linear algebra. Included are some properties of determinants with proofs, eigenvalues, eigenvectors and characteristic equations with examples of applications to simple…

  10. Lineární algebra ukrytá v internetovém vyhledávači Google

    Czech Academy of Sciences Publication Activity Database

    Brandts, J.; Křížek, Michal

    2007-01-01

    Roč. 52, č. 3 (2007), s. 195-204 ISSN 0032-2423 R&D Projects: GA MŠk 1P05ME749 Institutional research plan: CEZ:AV0Z10190503 Keywords : data structures * teleportation matrix * eigenvalues and eigenvectors Subject RIV: BA - General Mathematics

  11. Self-averaging correlation functions in the mean field theory of spin glasses

    International Nuclear Information System (INIS)

    Mezard, M.; Parisi, G.

    1984-01-01

    In the infinite range spin glass model, we consider the staggered spin σsub(lambda)associated with a given eigenvector of the interaction matrix. We show that the thermal average of sub(lambda)sup(2) is a self-averaging quantity and we compute it

  12. More evidence of localization in the low-lying Dirac spectrum

    CERN Document Server

    Bernard, C; Gottlieb, Steven; Levkova, L.; Heller, U.M.; Hetrick, J.E.; Jahn, O.; Maresca, F.; Renner, Dru Bryant; Toussaint, D.; Sugar, R.; Forcrand, Ph. de; Gottlieb, Steven

    2006-01-01

    We have extended our computation of the inverse participation ratio of low-lying (asqtad) Dirac eigenvectors in quenched SU(3). The scaling dimension of the confining manifold is clearer and very near 3. We have also computed the 2-point correlator which further characterizes the localization.

  13. Mode repulsion of ultrasonic guided waves in rails

    CSIR Research Space (South Africa)

    Loveday, Philip W

    2018-03-01

    Full Text Available . The modes can therefore be numbered in the same way that Lamb waves in plates are numbered, making it easier to communicate results. The derivative of the eigenvectors with respect to wavenumber contains the same repulsion term and shows how the mode shapes...

  14. Using many pilot points and singular value decomposition in groundwater model calibration

    DEFF Research Database (Denmark)

    Christensen, Steen; Doherty, John

    2008-01-01

    over the model area. Singular value decomposition (SVD) of the normal matrix is used to reduce the large number of pilot point parameters to a smaller number of so-called super parameters that can be estimated by nonlinear regression from the available observations. A number of eigenvectors...

  15. Neutral evolution of mutational robustness

    NARCIS (Netherlands)

    Nimwegen, Erik van; Crutchfield, James P.; Huynen, Martijn

    1999-01-01

    We introduce and analyze a general model of a population evolving over a network of selectively neutral genotypes. We show that the population s limit distribution on the neutral network is solely determined by the network topology and given by the principal eigenvector of the network

  16. Power Grid Modelling From Wind Turbine Perspective Using Principal Componenet Analysis

    DEFF Research Database (Denmark)

    Farajzadehbibalan, Saber; Ramezani, Mohammad Hossein; Nielsen, Peter

    2015-01-01

    In this study, we derive an eigenvector-based multivariate model of a power grid from the wind farm's standpoint using dynamic principal component analysis (DPCA). The main advantages of our model over previously developed models are being more realistic and having low complexity. We show that th...

  17. Extended Park's transformation for 2×3-phase synchronous machine and converter phasor model with representation of AC harmonics

    DEFF Research Database (Denmark)

    Knudsen, Hans

    1995-01-01

    A model of the 2×3-phase synchronous machine is presented using a new transformation based on the eigenvectors of the stator inductance matrix. The transformation fully decouples the stator inductance matrix, and this leads to an equivalent diagram of the machine with no mutual couplings...

  18. Bone histology, phylogeny, and palaeognathous birds (Aves, Palaeognathae)

    DEFF Research Database (Denmark)

    Legendre, Lucas; Bourdon, Estelle; Scofield, Paul

    2014-01-01

    a comprehensive study in which we quantify the phylogenetic signal on 62 osteohistological features in an exhaustive sample of palaeognathous birds. We used four different estimators to measure phylogenetic signal – Pagel’s λ, Abouheif’s Cmean, Blomberg’s K, and Diniz-Filho’s phylogenetic eigenvector regressions...

  19. Minute splitting of magnetic excitations in CsFeCl{sub 3} due to dipolar interaction observed by polarised neutrons

    Energy Technology Data Exchange (ETDEWEB)

    Dorner, B [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France); Baehr, M [HMI, Berlin (Germany); Petitgrand, D [Laboratoire Leon Brillouin (LLB) - Centre d` Etudes de Saclay, 91 - Gif-sur-Yvette (France)

    1997-04-01

    Using inelastic neutron scattering with polarisation analysis it was possible, for the first time, to observe simultaneously the two magnetic modes split due to dipolar interaction. This would not have been possible with energy resolution only. An analysis of eigenvectors was also performed. (author). 4 refs.

  20. Spin wave spectrum and zero spin fluctuation of antiferromagnetic solid 3He

    International Nuclear Information System (INIS)

    Roger, M.; Delrieu, J.M.

    1981-08-01

    The spin wave spectrum and eigenvectors of the uudd antiferromagnetic phase of solid 3 He are calculated; an optical mode is predicted around 150 - 180 Mc and a zero point spin deviation of 0.74 is obtained in agreement with the antiferromagnetic resonance frequency measured by Osheroff

  1. The non-linear Perron-Frobenius theorem : Perturbations and aggregation

    NARCIS (Netherlands)

    Dietzenbacher, E

    The dominant eigenvalue and the corresponding eigenvector (or Perron vector) of a non-linear eigensystem are considered. We discuss the effects upon these, of perturbations and of aggregation of the underlying mapping. The results are applied to study the sensivity of the outputs in a non-linear

  2. Jacobi-Davidson methods for generalized MHD-eigenvalue problems

    NARCIS (Netherlands)

    J.G.L. Booten; D.R. Fokkema; G.L.G. Sleijpen; H.A. van der Vorst (Henk)

    1995-01-01

    textabstractA Jacobi-Davidson algorithm for computing selected eigenvalues and associated eigenvectors of the generalized eigenvalue problem $Ax = lambda Bx$ is presented. In this paper the emphasis is put on the case where one of the matrices, say the B-matrix, is Hermitian positive definite. The

  3. Simultaneous maximization of spatial and temporal autocorrelation in spatio-temporal data

    DEFF Research Database (Denmark)

    Nielsen, Allan Aasbjerg

    2002-01-01

    . This is done by solving the generalized eigenproblem represented by the Rayleigh coefficient where is the dispersion of and is the dispersion of the difference between and spatially shifted. Hence, the new variates are obtained from the conjugate eigenvectors and the autocorrelations obtained are , i.e., high...

  4. The Modern Origin of Matrices and Their Applications

    Science.gov (United States)

    Debnath, L.

    2014-01-01

    This paper deals with the modern development of matrices, linear transformations, quadratic forms and their applications to geometry and mechanics, eigenvalues, eigenvectors and characteristic equations with applications. Included are the representations of real and complex numbers, and quaternions by matrices, and isomorphism in order to show…

  5. An expert system in medical diagnosis

    International Nuclear Information System (INIS)

    Raboanary, R.; Raoelina Andriambololona; Soffer, J.; Raboanary, J.

    2001-01-01

    Health problem is still a crucial one in some countries. It is so important that it becomes a major handicap in economic and social development. In order to solve this problem, we have conceived an expert system that we called MITSABO, which means TO HEAL, to help the physicians to diagnose tropical diseases. It is clear that by extending the data base and the knowledge base, we can extend the application of the software to more general areas. In our expert system, we used the concept of 'self organization' of neural network based on the determination of the eigenvalues and the eigenvectors associated to the correlation matrix XX t . The projection of the data on the two first eigenvectors gives a classification of the diseases which is used to get a first approach in the diagnosis of the patient. This diagnosis is improved by using an expert system which is built from the knowledge base.

  6. Cavity approach to the first eigenvalue problem in a family of symmetric random sparse matrices

    International Nuclear Information System (INIS)

    Kabashima, Yoshiyuki; Takahashi, Hisanao; Watanabe, Osamu

    2010-01-01

    A methodology to analyze the properties of the first (largest) eigenvalue and its eigenvector is developed for large symmetric random sparse matrices utilizing the cavity method of statistical mechanics. Under a tree approximation, which is plausible for infinitely large systems, in conjunction with the introduction of a Lagrange multiplier for constraining the length of the eigenvector, the eigenvalue problem is reduced to a bunch of optimization problems of a quadratic function of a single variable, and the coefficients of the first and the second order terms of the functions act as cavity fields that are handled in cavity analysis. We show that the first eigenvalue is determined in such a way that the distribution of the cavity fields has a finite value for the second order moment with respect to the cavity fields of the first order coefficient. The validity and utility of the developed methodology are examined by applying it to two analytically solvable and one simple but non-trivial examples in conjunction with numerical justification.

  7. Excitations

    International Nuclear Information System (INIS)

    Dorner, B.

    1996-01-01

    A short introduction to instrumental resolution is followed by a discussion of visibilities of phonon modes due to their eigenvectors. High precision phonon dispersion curves in GaAs are presented together with 'ab initio' calculations. Al 2 O 3 is taken as an example of selected visibility due to group theory. By careful determination of phonon intensities eigenvectors can be determined, such as in Silicon and Diamond. The investigation of magnon modes is shown for the garnet Fe 2 Ca 3 (GeO 4 ) 3 , where also a quantum gap due to zero point spin fluctuations was observed. The study of the splitting of excitons in CsFeCl 3 in an applied magnetic field demonstrates the possibilities of neutron polarisation analysis, which made it possible to observe a mode crossing. An outlook to inelastic X-ray scattering with very high energy resolution of synchrotron radiation is given with the examples of phonons in Beryllium and in water. (author) 19 figs., 36 refs

  8. Centrality metrics and localization in core-periphery networks

    International Nuclear Information System (INIS)

    Barucca, Paolo; Lillo, Fabrizio; Tantari, Daniele

    2016-01-01

    Two concepts of centrality have been defined in complex networks. The first considers the centrality of a node and many different metrics for it have been defined (e.g. eigenvector centrality, PageRank, non-backtracking centrality, etc). The second is related to large scale organization of the network, the core-periphery structure, composed by a dense core plus an outlying and loosely-connected periphery. In this paper we investigate the relation between these two concepts. We consider networks generated via the stochastic block model, or its degree corrected version, with a core-periphery structure and we investigate the centrality properties of the core nodes and the ability of several centrality metrics to identify them. We find that the three measures with the best performance are marginals obtained with belief propagation, PageRank, and degree centrality, while non-backtracking and eigenvector centrality (or MINRES [10], showed to be equivalent to the latter in the large network limit) perform worse in the investigated networks. (paper: interdisciplinary statistical mechanics )

  9. Centrality measures in temporal networks with time series analysis

    Science.gov (United States)

    Huang, Qiangjuan; Zhao, Chengli; Zhang, Xue; Wang, Xiaojie; Yi, Dongyun

    2017-05-01

    The study of identifying important nodes in networks has a wide application in different fields. However, the current researches are mostly based on static or aggregated networks. Recently, the increasing attention to networks with time-varying structure promotes the study of node centrality in temporal networks. In this paper, we define a supra-evolution matrix to depict the temporal network structure. With using of the time series analysis, the relationships between different time layers can be learned automatically. Based on the special form of the supra-evolution matrix, the eigenvector centrality calculating problem is turned into the calculation of eigenvectors of several low-dimensional matrices through iteration, which effectively reduces the computational complexity. Experiments are carried out on two real-world temporal networks, Enron email communication network and DBLP co-authorship network, the results of which show that our method is more efficient at discovering the important nodes than the common aggregating method.

  10. Predicting the impact of urban flooding using open data.

    Science.gov (United States)

    Tkachenko, Nataliya; Procter, Rob; Jarvis, Stephen

    2016-05-01

    This paper aims to explore whether there is a relationship between search patterns for flood risk information on the Web and how badly localities have been affected by flood events. We hypothesize that localities where people stay more actively informed about potential flooding experience less negative impact than localities where people make less effort to be informed. Being informed, of course, does not hold the waters back; however, it may stimulate (or serve as an indicator of) such resilient behaviours as timely use of sandbags, relocation of possessions from basements to upper floors and/or temporary evacuation from flooded homes to alternative accommodation. We make use of open data to test this relationship empirically. Our results demonstrate that although aggregated Web search reflects average rainfall patterns, its eigenvectors predominantly consist of locations with similar flood impacts during 2014-2015. These results are also consistent with statistically significant correlations of Web search eigenvectors with flood warning and incident reporting datasets.

  11. On the relationship between Gaussian stochastic blockmodels and label propagation algorithms

    International Nuclear Information System (INIS)

    Zhang, Junhao; Hu, Junfeng; Chen, Tongfei

    2015-01-01

    The problem of community detection has received great attention in recent years. Many methods have been proposed to discover communities in networks. In this paper, we propose a Gaussian stochastic blockmodel that uses Gaussian distributions to fit weight of edges in networks for non-overlapping community detection. The maximum likelihood estimation of this model has the same objective function as general label propagation with node preference. The node preference of a specific vertex turns out to be a value proportional to the intra-community eigenvector centrality (the corresponding entry in principal eigenvector of the adjacency matrix of the subgraph inside that vertex's community) under maximum likelihood estimation. Additionally, the maximum likelihood estimation of a constrained version of our model is highly related to another extension of the label propagation algorithm, namely, the label propagation algorithm under constraint. Experiments show that the proposed Gaussian stochastic blockmodel performs well on various benchmark networks. (paper)

  12. Asymptotics of empirical eigenstructure for high dimensional spiked covariance.

    Science.gov (United States)

    Wang, Weichen; Fan, Jianqing

    2017-06-01

    We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the magnitude of spiked eigenvalues, sample size, and dimensionality. This regime allows high dimensionality and diverging eigenvalues and provides new insights into the roles that the leading eigenvalues, sample size, and dimensionality play in principal component analysis. Our results are a natural extension of those in Paul (2007) to a more general setting and solve the rates of convergence problems in Shen et al. (2013). They also reveal the biases of estimating leading eigenvalues and eigenvectors by using principal component analysis, and lead to a new covariance estimator for the approximate factor model, called shrinkage principal orthogonal complement thresholding (S-POET), that corrects the biases. Our results are successfully applied to outstanding problems in estimation of risks of large portfolios and false discovery proportions for dependent test statistics and are illustrated by simulation studies.

  13. Evaluation of the synchrotron close orbit

    International Nuclear Information System (INIS)

    Bashmakov, Yu.A.; Karpov, V.A.

    1991-01-01

    The knowledge of the closed orbit position is an essential condition for the effective work of any accelerator. Therefore questions of calculations, measurements and controls have great importance. For example, during injection of particles into a synchrotron, the amplitudes of their betatron oscillations may become commensurable with the working region of the synchrotron. This makes one pay attention at the problem of formation of the optimum orbit with use of correcting optical elements. In addition, it is often necessary to calculate such an orbit at the end of the acceleration cycle when particles are deposited at internal targets or removed from the synchrotron. In this paper, the computation of the close orbit is reduced to a determination at an arbitrarily chosen azimuth of the eigenvector of the total transfer matrix of the synchrotron ring and to tracing with this vector desired orbit. The eigenvector is found as a result of an iteration

  14. Gamow-Jordan vectors and non-reducible density operators from higher-order S-matrix poles

    International Nuclear Information System (INIS)

    Bohm, A.; Loewe, M.; Maxson, S.; Patuleanu, P.; Puentmann, C.; Gadella, M.

    1997-01-01

    In analogy to Gamow vectors that are obtained from first-order resonance poles of the S-matrix, one can also define higher-order Gamow vectors which are derived from higher-order poles of the S-matrix. An S-matrix pole of r-th order at z R =E R -iΓ/2 leads to r generalized eigenvectors of order k=0,1,hor-ellipsis,r-1, which are also Jordan vectors of degree (k+1) with generalized eigenvalue (E R -iΓ/2). The Gamow-Jordan vectors are elements of a generalized complex eigenvector expansion, whose form suggests the definition of a state operator (density matrix) for the microphysical decaying state of this higher-order pole. This microphysical state is a mixture of non-reducible components. In spite of the fact that the k-th order Gamow-Jordan vectors has the polynomial time-dependence which one always associates with higher-order poles, the microphysical state obeys a purely exponential decay law. copyright 1997 American Institute of Physics

  15. Non-self-adjoint hamiltonians defined by Riesz bases

    Energy Technology Data Exchange (ETDEWEB)

    Bagarello, F., E-mail: fabio.bagarello@unipa.it [Dipartimento di Energia, Ingegneria dell' Informazione e Modelli Matematici, Facoltà di Ingegneria, Università di Palermo, I-90128 Palermo, Italy and INFN, Università di Torino, Torino (Italy); Inoue, A., E-mail: a-inoue@fukuoka-u.ac.jp [Department of Applied Mathematics, Fukuoka University, Fukuoka 814-0180 (Japan); Trapani, C., E-mail: camillo.trapani@unipa.it [Dipartimento di Matematica e Informatica, Università di Palermo, I-90123 Palermo (Italy)

    2014-03-15

    We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, we give conditions under which these Hamiltonians can be factorized in terms of generalized lowering and raising operators.

  16. Maslov indices and monodromy

    International Nuclear Information System (INIS)

    Dullin, H R; Robbins, J M; Waalkens, H; Creagh, S C; Tanner, G

    2005-01-01

    We prove that for a Hamiltonian system on a cotangent bundle that is Liouville-integrable and has monodromy the vector of Maslov indices is an eigenvector of the monodromy matrix with eigenvalue 1. As a corollary, the resulting restrictions on the monodromy matrix are derived. (letter to the editor)

  17. Certain properties of some special functions of two variables and two indices

    International Nuclear Information System (INIS)

    Khan, Subuhi

    2002-07-01

    In this paper, we derive a result concerning eigenvector and eigenvalue for a quadratic combination of four operators defined on a Lie algebra of endomorphisms of a vector space. Further, using this result, we deduce certain properties of some special functions of two variables and two indices. (author)

  18. Biological Applications in the Mathematics Curriculum

    Science.gov (United States)

    Marland, Eric; Palmer, Katrina M.; Salinas, Rene A.

    2008-01-01

    In this article we provide two detailed examples of how we incorporate biological examples into two mathematics courses: Linear Algebra and Ordinary Differential Equations. We use Leslie matrix models to demonstrate the biological properties of eigenvalues and eigenvectors. For Ordinary Differential Equations, we show how using a logistic growth…

  19. Perfect state transfer in unitary Cayley graphs over local rings

    Directory of Open Access Journals (Sweden)

    Yotsanan Meemark

    2014-12-01

    Full Text Available In this work, using eigenvalues and eigenvectors of unitary Cayley graphs over finite local rings and elementary linear algebra, we characterize which local rings allowing PST occurring in its unitary Cayley graph. Moreover, we have some developments when $R$ is a product of local rings.

  20. A computational approach for a fluid queue driven by a truncated birth-death process

    NARCIS (Netherlands)

    Lenin, R.B.; Parthasarathy, P.R.

    1999-01-01

    In this paper, we consider a fluid queue driven by a truncated birth-death process with general birth and death rates. We find the equilibrium distribution of the content of the fluid buffer by computing the eigenvalues and eigenvectors of an associated real tridiagonal matrix. We provide efficient

  1. Complex Wedge-Shaped Matrices: A Generalization of Jacobi Matrices

    Czech Academy of Sciences Publication Activity Database

    Hnětynková, Iveta; Plešinger, M.

    2015-01-01

    Roč. 487, 15 December (2015), s. 203-219 ISSN 0024-3795 R&D Projects: GA ČR GA13-06684S Keywords : eigenvalues * eigenvector * wedge-shaped matrices * generalized Jacobi matrices * band (or block) Krylov subspace methods Subject RIV: BA - General Mathematics Impact factor: 0.965, year: 2015

  2. Reducing System Artifacts in Hyperspectral Image Data Analysis with the Use of Estimates of the Error Covariance in the Data; TOPICAL

    International Nuclear Information System (INIS)

    HAALAND, DAVID M.; VAN BENTHEM, MARK H.; WEHLBURG, CHRISTINE M.; KOEHLER, IV FREDERICK W.

    2002-01-01

    Hyperspectral Fourier transform infrared images have been obtained from a neoprene sample aged in air at elevated temperatures. The massive amount of spectra available from this heterogeneous sample provides the opportunity to perform quantitative analysis of the spectral data without the need for calibration standards. Multivariate curve resolution (MCR) methods with non-negativity constraints applied to the iterative alternating least squares analysis of the spectral data has been shown to achieve the goal of quantitative image analysis without the use of standards. However, the pure-component spectra and the relative concentration maps were heavily contaminated by the presence of system artifacts in the spectral data. We have demonstrated that the detrimental effects of these artifacts can be minimized by adding an estimate of the error covariance structure of the spectral image data to the MCR algorithm. The estimate is added by augmenting the concentration and pure-component spectra matrices with scores and eigenvectors obtained from the mean-centered repeat image differences of the sample. The implementation of augmentation is accomplished by employing efficient equality constraints on the MCR analysis. Augmentation with the scores from the repeat images is found to primarily improve the pure-component spectral estimates while augmentation with the corresponding eigenvectors primarily improves the concentration maps. Augmentation with both scores and eigenvectors yielded the best result by generating less noisy pure-component spectral estimates and relative concentration maps that were largely free from a striping artifact that is present due to system errors in the FT-IR images. The MCR methods presented are general and can also be applied productively to non-image spectral data

  3. Lagrangian investigations of vorticity dynamics in compressible turbulence

    Science.gov (United States)

    Parashar, Nishant; Sinha, Sawan Suman; Danish, Mohammad; Srinivasan, Balaji

    2017-10-01

    In this work, we investigate the influence of compressibility on vorticity-strain rate dynamics. Well-resolved direct numerical simulations of compressible homogeneous isotropic turbulence performed over a cubical domain of 10243 are employed for this study. To clearly identify the influence of compressibility on the time-dependent dynamics (rather than on the one-time flow field), we employ a well-validated Lagrangian particle tracker. The tracker is used to obtain time correlations between the instantaneous vorticity vector and the strain-rate eigenvector system of an appropriately chosen reference time. In this work, compressibility is parameterized in terms of both global (turbulent Mach number) and local parameters (normalized dilatation-rate and flow field topology). Our investigations reveal that the local dilatation rate significantly influences these statistics. In turn, this observed influence of the dilatation rate is predominantly associated with rotation dominated topologies (unstable-focus-compressing, stable-focus-stretching). We find that an enhanced dilatation rate (in both contracting and expanding fluid elements) significantly enhances the tendency of the vorticity vector to align with the largest eigenvector of the strain-rate. Further, in fluid particles where the vorticity vector is maximally misaligned (perpendicular) at the reference time, vorticity does show a substantial tendency to align with the intermediate eigenvector as well. The authors make an attempt to provide physical explanations of these observations (in terms of moment of inertia and angular momentum) by performing detailed calculations following tetrads {approach of Chertkov et al. ["Lagrangian tetrad dynamics and the phenomenology of turbulence," Phys. Fluids 11(8), 2394-2410 (1999)] and Xu et al. ["The pirouette effect in turbulent flows," Nat. Phys. 7(9), 709-712 (2011)]} in a compressible flow field.

  4. Social structure of a semi-free ranging group of mandrills (Mandrillus sphinx: a social network analysis.

    Directory of Open Access Journals (Sweden)

    Céline Bret

    Full Text Available The difficulty involved in following mandrills in the wild means that very little is known about social structure in this species. Most studies initially considered mandrill groups to be an aggregation of one-male/multifemale units, with males occupying central positions in a structure similar to those observed in the majority of baboon species. However, a recent study hypothesized that mandrills form stable groups with only two or three permanent males, and that females occupy more central positions than males within these groups. We used social network analysis methods to examine how a semi-free ranging group of 19 mandrills is structured. We recorded all dyads of individuals that were in contact as a measure of association. The betweenness and the eigenvector centrality for each individual were calculated and correlated to kinship, age and dominance. Finally, we performed a resilience analysis by simulating the removal of individuals displaying the highest betweenness and eigenvector centrality values. We found that related dyads were more frequently associated than unrelated dyads. Moreover, our results showed that the cumulative distribution of individual betweenness and eigenvector centrality followed a power function, which is characteristic of scale-free networks. This property showed that some group members, mostly females, occupied a highly central position. Finally, the resilience analysis showed that the removal of the two most central females split the network into small subgroups and increased the network diameter. Critically, this study confirms that females appear to occupy more central positions than males in mandrill groups. Consequently, these females appear to be crucial for group cohesion and probably play a pivotal role in this species.

  5. Social structure of a semi-free ranging group of mandrills (Mandrillus sphinx): a social network analysis.

    Science.gov (United States)

    Bret, Céline; Sueur, Cédric; Ngoubangoye, Barthélémy; Verrier, Delphine; Deneubourg, Jean-Louis; Petit, Odile

    2013-01-01

    The difficulty involved in following mandrills in the wild means that very little is known about social structure in this species. Most studies initially considered mandrill groups to be an aggregation of one-male/multifemale units, with males occupying central positions in a structure similar to those observed in the majority of baboon species. However, a recent study hypothesized that mandrills form stable groups with only two or three permanent males, and that females occupy more central positions than males within these groups. We used social network analysis methods to examine how a semi-free ranging group of 19 mandrills is structured. We recorded all dyads of individuals that were in contact as a measure of association. The betweenness and the eigenvector centrality for each individual were calculated and correlated to kinship, age and dominance. Finally, we performed a resilience analysis by simulating the removal of individuals displaying the highest betweenness and eigenvector centrality values. We found that related dyads were more frequently associated than unrelated dyads. Moreover, our results showed that the cumulative distribution of individual betweenness and eigenvector centrality followed a power function, which is characteristic of scale-free networks. This property showed that some group members, mostly females, occupied a highly central position. Finally, the resilience analysis showed that the removal of the two most central females split the network into small subgroups and increased the network diameter. Critically, this study confirms that females appear to occupy more central positions than males in mandrill groups. Consequently, these females appear to be crucial for group cohesion and probably play a pivotal role in this species.

  6. Comparison of eigensolvers for symmetric band matrices.

    Science.gov (United States)

    Moldaschl, Michael; Gansterer, Wilfried N

    2014-09-15

    We compare different algorithms for computing eigenvalues and eigenvectors of a symmetric band matrix across a wide range of synthetic test problems. Of particular interest is a comparison of state-of-the-art tridiagonalization-based methods as implemented in Lapack or Plasma on the one hand, and the block divide-and-conquer (BD&C) algorithm as well as the block twisted factorization (BTF) method on the other hand. The BD&C algorithm does not require tridiagonalization of the original band matrix at all, and the current version of the BTF method tridiagonalizes the original band matrix only for computing the eigenvalues. Avoiding the tridiagonalization process sidesteps the cost of backtransformation of the eigenvectors. Beyond that, we discovered another disadvantage of the backtransformation process for band matrices: In several scenarios, a lot of gradual underflow is observed in the (optional) accumulation of the transformation matrix and in the (obligatory) backtransformation step. According to the IEEE 754 standard for floating-point arithmetic, this implies many operations with subnormal (denormalized) numbers, which causes severe slowdowns compared to the other algorithms without backtransformation of the eigenvectors. We illustrate that in these cases the performance of existing methods from Lapack and Plasma reaches a competitive level only if subnormal numbers are disabled (and thus the IEEE standard is violated). Overall, our performance studies illustrate that if the problem size is large enough relative to the bandwidth, BD&C tends to achieve the highest performance of all methods if the spectrum to be computed is clustered. For test problems with well separated eigenvalues, the BTF method tends to become the fastest algorithm with growing problem size.

  7. Semiclassical geometry of integrable systems

    Science.gov (United States)

    Reshetikhin, Nicolai

    2018-04-01

    The main result of this paper is a formula for the scalar product of semiclassical eigenvectors of two integrable systems on the same symplectic manifold. An important application of this formula is the Ponzano–Regge type of asymptotic of Racah–Wigner coefficients. Dedicated to the memory of P P Kulish.

  8. Algebraic Bethe ansatz for 19-vertex models with reflection conditions

    International Nuclear Information System (INIS)

    Utiel, Wagner

    2003-01-01

    In this work we solve the 19-vertex models with the use of algebraic Bethe ansatz for diagonal reflection matrices (Sklyanin K-matrices). The eigenvectors, eigenvalues and Bethe equations are given in a general form. Quantum spin chains of spin one derived from the 19-vertex models were also discussed

  9. Multi-Grid Lanczos

    Science.gov (United States)

    Clark, M. A.; Jung, Chulwoo; Lehner, Christoph

    2018-03-01

    We present a Lanczos algorithm utilizing multiple grids that reduces the memory requirements both on disk and in working memory by one order of magnitude for RBC/UKQCD's 48I and 64I ensembles at the physical pion mass. The precision of the resulting eigenvectors is on par with exact deflation.

  10. Robust periodic steady state analysis of autonomous oscillators based on generalized eigenvalues

    NARCIS (Netherlands)

    Mirzavand, R.; Maten, ter E.J.W.; Beelen, T.G.J.; Schilders, W.H.A.; Abdipour, A.

    2011-01-01

    In this paper, we present a new gauge technique for the Newton Raphson method to solve the periodic steady state (PSS) analysis of free-running oscillators in the time domain. To find the frequency a new equation is added to the system of equations. Our equation combines a generalized eigenvector

  11. Robust periodic steady state analysis of autonomous oscillators based on generalized eigenvalues

    NARCIS (Netherlands)

    Mirzavand, R.; Maten, ter E.J.W.; Beelen, T.G.J.; Schilders, W.H.A.; Abdipour, A.; Michielsen, B.; Poirier, J.R.

    2012-01-01

    In this paper, we present a new gauge technique for the Newton Raphson method to solve the periodic steady state (PSS) analysis of free-running oscillators in the time domain. To find the frequency a new equation is added to the system of equations. Our equation combines a generalized eigenvector

  12. Analysis of numerical methods

    CERN Document Server

    Isaacson, Eugene

    1994-01-01

    This excellent text for advanced undergraduates and graduate students covers norms, numerical solution of linear systems and matrix factoring, iterative solutions of nonlinear equations, eigenvalues and eigenvectors, polynomial approximation, and other topics. It offers a careful analysis and stresses techniques for developing new methods, plus many examples and problems. 1966 edition.

  13. Finite Element-Galerkin Approximation of the Eigenvalues of Eigenvectors of Selfadjoint Problems

    Science.gov (United States)

    1988-07-01

    l’ "k, + 1. Combining (3.20), (3.22), and the fact that I-Eh(Ak ) and Ph are orthogonal projections we have I(I-Eh(Xk,)) PhUB 5 Si (I-Eh(xk)) PhT(Ph-I...Its adjoint are equal. (3.23) implies Hf(I-Eh(1kI )Ph)u{1B - P(IPh)UIBI 5 I(I-Eh(Ak )) PhuB -< d i ii ( Ph- I )T II H B_--H,3 1(P h- I ) u liB , and

  14. Simultaneous multigrid techniques for nonlinear eigenvalue problems: Solutions of the nonlinear Schrödinger-Poisson eigenvalue problem in two and three dimensions

    Science.gov (United States)

    Costiner, Sorin; Ta'asan, Shlomo

    1995-07-01

    Algorithms for nonlinear eigenvalue problems (EP's) often require solving self-consistently a large number of EP's. Convergence difficulties may occur if the solution is not sought in an appropriate region, if global constraints have to be satisfied, or if close or equal eigenvalues are present. Multigrid (MG) algorithms for nonlinear problems and for EP's obtained from discretizations of partial differential EP have often been shown to be more efficient than single level algorithms. This paper presents MG techniques and a MG algorithm for nonlinear Schrödinger Poisson EP's. The algorithm overcomes the above mentioned difficulties combining the following techniques: a MG simultaneous treatment of the eigenvectors and nonlinearity, and with the global constrains; MG stable subspace continuation techniques for the treatment of nonlinearity; and a MG projection coupled with backrotations for separation of solutions. These techniques keep the solutions in an appropriate region, where the algorithm converges fast, and reduce the large number of self-consistent iterations to only a few or one MG simultaneous iteration. The MG projection makes it possible to efficiently overcome difficulties related to clusters of close and equal eigenvalues. Computational examples for the nonlinear Schrödinger-Poisson EP in two and three dimensions, presenting special computational difficulties that are due to the nonlinearity and to the equal and closely clustered eigenvalues are demonstrated. For these cases, the algorithm requires O(qN) operations for the calculation of q eigenvectors of size N and for the corresponding eigenvalues. One MG simultaneous cycle per fine level was performed. The total computational cost is equivalent to only a few Gauss-Seidel relaxations per eigenvector. An asymptotic convergence rate of 0.15 per MG cycle is attained.

  15. A robust variant of block Jacobi-Davidson for extracting a large number of eigenpairs: Application to grid-based real-space density functional theory

    Science.gov (United States)

    Lee, M.; Leiter, K.; Eisner, C.; Breuer, A.; Wang, X.

    2017-09-01

    In this work, we investigate a block Jacobi-Davidson (J-D) variant suitable for sparse symmetric eigenproblems where a substantial number of extremal eigenvalues are desired (e.g., ground-state real-space quantum chemistry). Most J-D algorithm variations tend to slow down as the number of desired eigenpairs increases due to frequent orthogonalization against a growing list of solved eigenvectors. In our specification of block J-D, all of the steps of the algorithm are performed in clusters, including the linear solves, which allows us to greatly reduce computational effort with blocked matrix-vector multiplies. In addition, we move orthogonalization against locked eigenvectors and working eigenvectors outside of the inner loop but retain the single Ritz vector projection corresponding to the index of the correction vector. Furthermore, we minimize the computational effort by constraining the working subspace to the current vectors being updated and the latest set of corresponding correction vectors. Finally, we incorporate accuracy thresholds based on the precision required by the Fermi-Dirac distribution. The net result is a significant reduction in the computational effort against most previous block J-D implementations, especially as the number of wanted eigenpairs grows. We compare our approach with another robust implementation of block J-D (JDQMR) and the state-of-the-art Chebyshev filter subspace (CheFSI) method for various real-space density functional theory systems. Versus CheFSI, for first-row elements, our method yields competitive timings for valence-only systems and 4-6× speedups for all-electron systems with up to 10× reduced matrix-vector multiplies. For all-electron calculations on larger elements (e.g., gold) where the wanted spectrum is quite narrow compared to the full spectrum, we observe 60× speedup with 200× fewer matrix-vector multiples vs. CheFSI.

  16. Electrostatic point charge fitting as an inverse problem: Revealing the underlying ill-conditioning

    International Nuclear Information System (INIS)

    Ivanov, Maxim V.; Talipov, Marat R.; Timerghazin, Qadir K.

    2015-01-01

    Atom-centered point charge (PC) model of the molecular electrostatics—a major workhorse of the atomistic biomolecular simulations—is usually parameterized by least-squares (LS) fitting of the point charge values to a reference electrostatic potential, a procedure that suffers from numerical instabilities due to the ill-conditioned nature of the LS problem. To reveal the origins of this ill-conditioning, we start with a general treatment of the point charge fitting problem as an inverse problem and construct an analytical model with the point charges spherically arranged according to Lebedev quadrature which is naturally suited for the inverse electrostatic problem. This analytical model is contrasted to the atom-centered point-charge model that can be viewed as an irregular quadrature poorly suited for the problem. This analysis shows that the numerical problems of the point charge fitting are due to the decay of the curvatures corresponding to the eigenvectors of LS sum Hessian matrix. In part, this ill-conditioning is intrinsic to the problem and is related to decreasing electrostatic contribution of the higher multipole moments, that are, in the case of Lebedev grid model, directly associated with the Hessian eigenvectors. For the atom-centered model, this association breaks down beyond the first few eigenvectors related to the high-curvature monopole and dipole terms; this leads to even wider spread-out of the Hessian curvature values. Using these insights, it is possible to alleviate the ill-conditioning of the LS point-charge fitting without introducing external restraints and/or constraints. Also, as the analytical Lebedev grid PC model proposed here can reproduce multipole moments up to a given rank, it may provide a promising alternative to including explicit multipole terms in a force field

  17. Equilibrium beam distribution in an electron storage ring near linear synchrobetatron coupling resonances

    Directory of Open Access Journals (Sweden)

    Boaz Nash

    2006-03-01

    Full Text Available Linear dynamics in a storage ring can be described by the one-turn map matrix. In the case of a resonance where two of the eigenvalues of this matrix are degenerate, a coupling perturbation causes a mixing of the uncoupled eigenvectors. A perturbation formalism is developed to find eigenvalues and eigenvectors of the one-turn map near such a linear resonance. Damping and diffusion due to synchrotron radiation can be obtained by integrating their effects over one turn, and the coupled eigenvectors can be used to find the coupled damping and diffusion coefficients. Expressions for the coupled equilibrium emittances and beam distribution moments are then derived. In addition to the conventional instabilities at the sum, integer, and half-integer resonances, it is found that the coupling can cause an instability through antidamping near a sum resonance even when the symplectic dynamics are stable. As one application of this formalism, the case of linear synchrobetatron coupling is analyzed where the coupling is caused by dispersion in the rf cavity, or by a crab cavity. Explicit closed-form expressions for the sum/difference resonances are given along with the integer/half-integer resonances. The integer and half-integer resonances caused by coupling require particular care. We find an example of this with the case of a crab cavity for the integer resonance of the synchrotron tune. Whether or not there is an instability is determined by the value of the horizontal betatron tune, a unique feature of these coupling-caused integer or half-integer resonances. Finally, the coupled damping and diffusion coefficients along with the equilibrium invariants and projected emittances are plotted as a function of the betatron and synchrotron tunes for an example storage ring based on PEP-II.

  18. Exact Finite Differences. The Derivative on Non Uniformly Spaced Partitions

    Directory of Open Access Journals (Sweden)

    Armando Martínez-Pérez

    2017-10-01

    Full Text Available We define a finite-differences derivative operation, on a non uniformly spaced partition, which has the exponential function as an exact eigenvector. We discuss some properties of this operator and we propose a definition for the components of a finite-differences momentum operator. This allows us to perform exact discrete calculations.

  19. Eigenvalue for Densely Defined Perturbations of Multivalued Maximal Monotone Operators in Reflexive Banach Spaces

    Directory of Open Access Journals (Sweden)

    Boubakari Ibrahimou

    2013-01-01

    maximal monotone with and . Using the topological degree theory developed by Kartsatos and Quarcoo we study the eigenvalue problem where the operator is a single-valued of class . The existence of continuous branches of eigenvectors of infinite length then could be easily extended to the case where the operator is multivalued and is investigated.

  20. Radioactivity computation of steady-state and pulsed fusion reactors operation

    International Nuclear Information System (INIS)

    Attaya, H.

    1994-06-01

    Different mathematical methods are used to calculate the nuclear transmutation in steady-state and pulsed neutron irradiation. These methods are the Schuer decomposition, the eigenvector decomposition, and the Pade approximation of the matrix exponential function. In the case of the linear decay chain approximation, a simple algorithm is used to evaluate the transition matrices

  1. Multi-Grid Lanczos

    Directory of Open Access Journals (Sweden)

    Clark M. A.

    2018-01-01

    Full Text Available We present a Lanczos algorithm utilizing multiple grids that reduces the memory requirements both on disk and in working memory by one order of magnitude for RBC/UKQCD’s 48I and 64I ensembles at the physical pion mass. The precision of the resulting eigenvectors is on par with exact deflation.

  2. Universal growth modes of high-elevation conifers

    Czech Academy of Sciences Publication Activity Database

    Datsenko, N. M.; Sonechkin, D. M.; Büntgen, Ulf; Yang, B.

    2016-01-01

    Roč. 38, JUN (2016), s. 38-50 ISSN 1125-7865 Institutional support: RVO:67179843 Keywords : tree-ring chronologies * summer temperature-variations * northeastern tibetan plateau * climate signal * fennoscandian summers * annual precipitation * density * variability * qinghai * Growth modes * Ring width and maximum latewood density * Eigenvector analysis Subject RIV: EF - Botanics Impact factor: 2.259, year: 2016

  3. An Application of the Vandermonde Determinant

    Science.gov (United States)

    Xu, Junqin; Zhao, Likuan

    2006-01-01

    Eigenvalue is an important concept in Linear Algebra. It is well known that the eigenvectors corresponding to different eigenvalues of a square matrix are linear independent. In most of the existing textbooks, this result is proven using mathematical induction. In this note, a new proof using Vandermonde determinant is given. It is shown that this…

  4. SU2 nonstandard bases: the case of mutually unbiased bases

    International Nuclear Information System (INIS)

    Olivier, Albouy; Kibler, Maurice R.

    2007-02-01

    This paper deals with bases in a finite-dimensional Hilbert space. Such a space can be realized as a subspace of the representation space of SU 2 corresponding to an irreducible representation of SU 2 . The representation theory of SU 2 is reconsidered via the use of two truncated deformed oscillators. This leads to replace the familiar scheme [j 2 , j z ] by a scheme [j 2 , v ra ], where the two-parameter operator v ra is defined in the universal enveloping algebra of the Lie algebra su 2 . The eigenvectors of the commuting set of operators [j 2 , v ra ] are adapted to a tower of chains SO 3 includes C 2j+1 (2j belongs to N * ), where C 2j+1 is the cyclic group of order 2j + 1. In the case where 2j + 1 is prime, the corresponding eigenvectors generate a complete set of mutually unbiased bases. Some useful relations on generalized quadratic Gauss sums are exposed in three appendices. (authors)

  5. Extending the eigCG algorithm to nonsymmetric Lanczos for linear systems with multiple right-hand sides

    Energy Technology Data Exchange (ETDEWEB)

    Abdel-Rehim, A M; Stathopoulos, Andreas; Orginos, Kostas

    2014-08-01

    The technique that was used to build the EigCG algorithm for sparse symmetric linear systems is extended to the nonsymmetric case using the BiCG algorithm. We show that, similarly to the symmetric case, we can build an algorithm that is capable of computing a few smallest magnitude eigenvalues and their corresponding left and right eigenvectors of a nonsymmetric matrix using only a small window of the BiCG residuals while simultaneously solving a linear system with that matrix. For a system with multiple right-hand sides, we give an algorithm that computes incrementally more eigenvalues while solving the first few systems and then uses the computed eigenvectors to deflate BiCGStab for the remaining systems. Our experiments on various test problems, including Lattice QCD, show the remarkable ability of EigBiCG to compute spectral approximations with accuracy comparable to that of the unrestarted, nonsymmetric Lanczos. Furthermore, our incremental EigBiCG followed by appropriately restarted and deflated BiCGStab provides a competitive method for systems with multiple right-hand sides.

  6. Tridiagonal realization of the antisymmetric Gaussian β-ensemble

    International Nuclear Information System (INIS)

    Dumitriu, Ioana; Forrester, Peter J.

    2010-01-01

    The Householder reduction of a member of the antisymmetric Gaussian unitary ensemble gives an antisymmetric tridiagonal matrix with all independent elements. The random variables permit the introduction of a positive parameter β, and the eigenvalue probability density function of the corresponding random matrices can be computed explicitly, as can the distribution of (q i ), the first components of the eigenvectors. Three proofs are given. One involves an inductive construction based on bordering of a family of random matrices which are shown to have the same distributions as the antisymmetric tridiagonal matrices. This proof uses the Dixon-Anderson integral from Selberg integral theory. A second proof involves the explicit computation of the Jacobian for the change of variables between real antisymmetric tridiagonal matrices, its eigenvalues, and (q i ). The third proof maps matrices from the antisymmetric Gaussian β-ensemble to those realizing particular examples of the Laguerre β-ensemble. In addition to these proofs, we note some simple properties of the shooting eigenvector and associated Pruefer phases of the random matrices.

  7. Color-based scale-invariant feature detection applied in robot vision

    Science.gov (United States)

    Gao, Jian; Huang, Xinhan; Peng, Gang; Wang, Min; Li, Xinde

    2007-11-01

    The scale-invariant feature detecting methods always require a lot of computation yet sometimes still fail to meet the real-time demands in robot vision fields. To solve the problem, a quick method for detecting interest points is presented. To decrease the computation time, the detector selects as interest points those whose scale normalized Laplacian values are the local extrema in the nonholonomic pyramid scale space. The descriptor is built with several subregions, whose width is proportional to the scale factor, and the coordinates of the descriptor are rotated in relation to the interest point orientation just like the SIFT descriptor. The eigenvector is computed in the original color image and the mean values of the normalized color g and b in each subregion are chosen to be the factors of the eigenvector. Compared with the SIFT descriptor, this descriptor's dimension has been reduced evidently, which can simplify the point matching process. The performance of the method is analyzed in theory in this paper and the experimental results have certified its validity too.

  8. MiRNA-TF-gene network analysis through ranking of biomolecules for multi-informative uterine leiomyoma dataset.

    Science.gov (United States)

    Mallik, Saurav; Maulik, Ujjwal

    2015-10-01

    Gene ranking is an important problem in bioinformatics. Here, we propose a new framework for ranking biomolecules (viz., miRNAs, transcription-factors/TFs and genes) in a multi-informative uterine leiomyoma dataset having both gene expression and methylation data using (statistical) eigenvector centrality based approach. At first, genes that are both differentially expressed and methylated, are identified using Limma statistical test. A network, comprising these genes, corresponding TFs from TRANSFAC and ITFP databases, and targeter miRNAs from miRWalk database, is then built. The biomolecules are then ranked based on eigenvector centrality. Our proposed method provides better average accuracy in hub gene and non-hub gene classifications than other methods. Furthermore, pre-ranked Gene set enrichment analysis is applied on the pathway database as well as GO-term databases of Molecular Signatures Database with providing a pre-ranked gene-list based on different centrality values for comparing among the ranking methods. Finally, top novel potential gene-markers for the uterine leiomyoma are provided. Copyright © 2015 Elsevier Inc. All rights reserved.

  9. Ab initio nuclear structure - the large sparse matrix eigenvalue problem

    Energy Technology Data Exchange (ETDEWEB)

    Vary, James P; Maris, Pieter [Department of Physics, Iowa State University, Ames, IA, 50011 (United States); Ng, Esmond; Yang, Chao [Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Sosonkina, Masha, E-mail: jvary@iastate.ed [Scalable Computing Laboratory, Ames Laboratory, Iowa State University, Ames, IA, 50011 (United States)

    2009-07-01

    The structure and reactions of light nuclei represent fundamental and formidable challenges for microscopic theory based on realistic strong interaction potentials. Several ab initio methods have now emerged that provide nearly exact solutions for some nuclear properties. The ab initio no core shell model (NCSM) and the no core full configuration (NCFC) method, frame this quantum many-particle problem as a large sparse matrix eigenvalue problem where one evaluates the Hamiltonian matrix in a basis space consisting of many-fermion Slater determinants and then solves for a set of the lowest eigenvalues and their associated eigenvectors. The resulting eigenvectors are employed to evaluate a set of experimental quantities to test the underlying potential. For fundamental problems of interest, the matrix dimension often exceeds 10{sup 10} and the number of nonzero matrix elements may saturate available storage on present-day leadership class facilities. We survey recent results and advances in solving this large sparse matrix eigenvalue problem. We also outline the challenges that lie ahead for achieving further breakthroughs in fundamental nuclear theory using these ab initio approaches.

  10. Ab initio nuclear structure - the large sparse matrix eigenvalue problem

    International Nuclear Information System (INIS)

    Vary, James P; Maris, Pieter; Ng, Esmond; Yang, Chao; Sosonkina, Masha

    2009-01-01

    The structure and reactions of light nuclei represent fundamental and formidable challenges for microscopic theory based on realistic strong interaction potentials. Several ab initio methods have now emerged that provide nearly exact solutions for some nuclear properties. The ab initio no core shell model (NCSM) and the no core full configuration (NCFC) method, frame this quantum many-particle problem as a large sparse matrix eigenvalue problem where one evaluates the Hamiltonian matrix in a basis space consisting of many-fermion Slater determinants and then solves for a set of the lowest eigenvalues and their associated eigenvectors. The resulting eigenvectors are employed to evaluate a set of experimental quantities to test the underlying potential. For fundamental problems of interest, the matrix dimension often exceeds 10 10 and the number of nonzero matrix elements may saturate available storage on present-day leadership class facilities. We survey recent results and advances in solving this large sparse matrix eigenvalue problem. We also outline the challenges that lie ahead for achieving further breakthroughs in fundamental nuclear theory using these ab initio approaches.

  11. Random matrix theory and fund of funds portfolio optimisation

    Science.gov (United States)

    Conlon, T.; Ruskin, H. J.; Crane, M.

    2007-08-01

    The proprietary nature of Hedge Fund investing means that it is common practise for managers to release minimal information about their returns. The construction of a fund of hedge funds portfolio requires a correlation matrix which often has to be estimated using a relatively small sample of monthly returns data which induces noise. In this paper, random matrix theory (RMT) is applied to a cross-correlation matrix C, constructed using hedge fund returns data. The analysis reveals a number of eigenvalues that deviate from the spectrum suggested by RMT. The components of the deviating eigenvectors are found to correspond to distinct groups of strategies that are applied by hedge fund managers. The inverse participation ratio is used to quantify the number of components that participate in each eigenvector. Finally, the correlation matrix is cleaned by separating the noisy part from the non-noisy part of C. This technique is found to greatly reduce the difference between the predicted and realised risk of a portfolio, leading to an improved risk profile for a fund of hedge funds.

  12. SU{sub 2} nonstandard bases: the case of mutually unbiased bases

    Energy Technology Data Exchange (ETDEWEB)

    Olivier, Albouy; Kibler, Maurice R. [Universite de Lyon, Institut de Physique Nucleaire de Lyon, Universite Lyon, CNRS/IN2P3, 43 bd du 11 novembre 1918, F-69622 Villeurbanne Cedex (France)

    2007-02-15

    This paper deals with bases in a finite-dimensional Hilbert space. Such a space can be realized as a subspace of the representation space of SU{sub 2} corresponding to an irreducible representation of SU{sub 2}. The representation theory of SU{sub 2} is reconsidered via the use of two truncated deformed oscillators. This leads to replace the familiar scheme [j{sub 2}, j{sub z}] by a scheme [j{sup 2}, v{sub ra}], where the two-parameter operator v{sub ra} is defined in the universal enveloping algebra of the Lie algebra su{sub 2}. The eigenvectors of the commuting set of operators [j{sup 2}, v{sub ra}] are adapted to a tower of chains SO{sub 3} includes C{sub 2j+1} (2j belongs to N{sup *}), where C{sub 2j+1} is the cyclic group of order 2j + 1. In the case where 2j + 1 is prime, the corresponding eigenvectors generate a complete set of mutually unbiased bases. Some useful relations on generalized quadratic Gauss sums are exposed in three appendices. (authors)

  13. Cleaning the correlation matrix with a denoising autoencoder

    OpenAIRE

    Hayou, Soufiane

    2017-01-01

    In this paper, we use an adjusted autoencoder to estimate the true eigenvalues of the population correlation matrix from the sample correlation matrix when the number of samples is small. We show that the model outperforms the Rotational Invariant Estimator (Bouchaud) which is the optimal estimator in the sample eigenvectors basis when the dimension goes to infinity.

  14. On certain properties of some generalized special functions

    International Nuclear Information System (INIS)

    Pathan, M.A.; Khan, Subuhi

    2002-06-01

    In this paper, we derive a result concerning eigenvector for the product of two operators defined on a Lie algebra of endomorphisms of a vector space. The results given by Radulescu, Mandal and authors follow as special cases of this result. Further using these results, we deduce certain properties of generalized Hermite polynomials and Hermite Tricomi functions. (author)

  15. Singularly Perturbed Equations in the Critical Case.

    Science.gov (United States)

    1980-02-01

    asymptotic properties of the differential equation (1) in the noncritical case (all ReXi (t) ɘ) . We will consider the critical case (k 0) ; the...the inequality (3), that is, ReXi (t,a) < 0 (58) The matrix ca(t,a) , consisting of the eigenvectors corresponding to w 0 , now has the form I (P -(t

  16. An algorithm to compute the square root of 3x3 positive definite matrix

    International Nuclear Information System (INIS)

    Franca, L.P.

    1988-06-01

    An efficient closed form to compute the square root of a 3 x 3 positive definite matrix is presented. The derivation employs the Cayley-Hamilton theorem avoiding calculation of eigenvectors. We show that evaluation of one eigenvalue of the square root matrix is needed and can not be circumvented. The algorithm is robust and efficient. (author) [pt

  17. Optimized Binomial Quantum States of Complex Oscillators with Real Spectrum

    International Nuclear Information System (INIS)

    Zelaya, K D; Rosas-Ortiz, O

    2016-01-01

    Classical and nonclassical states of quantum complex oscillators with real spectrum are presented. Such states are bi-orthonormal superpositions of n +1 energy eigenvectors of the system with binomial-like coefficients. For large values of n these optimized binomial states behave as photon added coherent states when the imaginary part of the potential is cancelled. (paper)

  18. Fusion And Inference From Multiple And Massive Disparate Distributed Dynamic Data Sets

    Science.gov (United States)

    2017-07-01

    computational execution together form a comprehensive, widely- applicable paradigm for statistical graph inference. Approved for Public Release; Distribution...always involve challenging empirical modeling and implementation issues. Our project has propelled the mathematical development, statistical design...D. J., and Sussman, D. L., “A limit theorem for scaled eigenvectors of random dot product graphs,” Sankhya A. Mathemat - ical Statistics and

  19. Deformed GOE for systems with a few degrees of freedom in the chaotic regime

    International Nuclear Information System (INIS)

    Hussein, M.S.; Pato, M.P.

    1990-01-01

    New distribution laws for the energy level spacings and the eigenvector amplitudes, appropriate for systems with a few degrees of freedom in the chaotic regime, are derived by conveniently deforming the GOE. The cases of 2X2 and 3X3 matrices are fully worked out. Suggestions concerning the general case of matrices with large dimensions are made. (author)

  20. Deformed GOE for systems with a few degrees of freedom in the chaotic regime

    International Nuclear Information System (INIS)

    Hussein, M.S.; Pato, M.P.

    1990-03-01

    New distribution laws for the energy level spacings and the eigenvector amplitudes, approapriate for systems with a few degrees of freedom in the chaotic regime, are derived by conveniently deforming the GOE. The cases of 2x2 and 3x3 matrices are fully worked out. Suggestions concerning the general case of matrices with large dimensions are made. (author) [pt

  1. On the rational approximation of the bidimensional potentials

    International Nuclear Information System (INIS)

    Niculescu, V.I.R; Catana, D.

    1997-01-01

    In the present letter we introduced a symmetrical bidimensional potential with Woods-Saxon tail. The potential approximation has permitted to replace in the matrix the evaluation of double integration by a product of two integrals. That implied a complexity reduction in the Hamiltonian eigenvalue and eigenvector evaluation. Also, the harmonic bidimensional basis simplifies significantly the evaluation of electric multipole operators. (authors)

  2. Using the Jacobi-Davidson method to obtain the dominant Lambda modes of a nuclear power reactor

    Energy Technology Data Exchange (ETDEWEB)

    Verdu, G. [Departamento de Ingenieria Quimica y Nuclear, Universidad Politecnica de Valencia, Camino de Vera 14, 46022 Valencia (Spain)]. E-mail: gverdu@iqn.upv.es; Ginestar, D. [Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, Camino de Vera 14, 46022 Valencia (Spain); Miro, R. [Departamento de Ingenieria Quimica y Nuclear, Universidad Politecnica de Valencia, Camino de Vera 14, 46022 Valencia (Spain); Vidal, V. [Departamento de Sistemas Informaticos y Computacion, Universidad Politecnica de Valencia, Camino de Vera 14, 46022 Valencia (Spain)

    2005-07-15

    The Jacobi-Davidson method is a modification of Davidson method, which has shown to be very effective to compute the dominant eigenvalues and their corresponding eigenvectors of a large and sparse matrix. This method has been used to compute the dominant Lambda modes of two configurations of Cofrentes nuclear power reactor, showing itself a quite effective method, especially for perturbed configurations.

  3. Direct structural parameter identification by modal test results

    Science.gov (United States)

    Chen, J.-C.; Kuo, C.-P.; Garba, J. A.

    1983-01-01

    A direct identification procedure is proposed to obtain the mass and stiffness matrices based on the test measured eigenvalues and eigenvectors. The method is based on the theory of matrix perturbation in which the correct mass and stiffness matrices are expanded in terms of analytical values plus a modification matrix. The simplicity of the procedure enables real time operation during the structural testing.

  4. Using CUDA Technology for Defining the Stiffness Matrix in the Subspace of Eigenvectors

    Directory of Open Access Journals (Sweden)

    Yu. V. Berchun

    2015-01-01

    Full Text Available The aim is to improve the performance of solving a problem of deformable solid mechanics through the use of GPGPU. The paper describes technologies for computing systems using both a central and a graphics processor and provides motivation for using CUDA technology as the efficient one.The paper also analyses methods to solve the problem of defining natural frequencies and design waveforms, i.e. an iteration method in the subspace. The method includes several stages. The paper considers the most resource-hungry stage, which defines the stiffness matrix in the subspace of eigenforms and gives the mathematical interpretation of this stage.The GPU choice as a computing device is justified. The paper presents an algorithm for calculating the stiffness matrix in the subspace of eigenforms taking into consideration the features of input data. The global stiffness matrix is very sparse, and its size can reach tens of millions. Therefore, it is represented as a set of the stiffness matrices of the single elements of a model. The paper analyses methods of data representation in the software and selects the best practices for GPU computing.It describes the software implementation using CUDA technology to calculate the stiffness matrix in the subspace of eigenforms. Due to the input data nature, it is impossible to use the universal libraries of matrix computations (cuSPARSE and cuBLAS for loading the GPU. For efficient use of GPU resources in the software implementation, the stiffness matrices of elements are built in the block matrices of a special form. The advantages of using shared memory in GPU calculations are described.The transfer to the GPU computations allowed a twentyfold increase in performance (as compared to the multithreaded CPU-implementation on the model of middle dimensions (degrees of freedom about 2 million. Such an acceleration of one stage speeds up defining the natural frequencies and waveforms by the iteration method in a subspace up to times.

  5. Spatially varying coefficient models in real estate: Eigenvector spatial filtering and alternative approaches

    NARCIS (Netherlands)

    Helbich, M; Griffith, D

    2016-01-01

    Real estate policies in urban areas require the recognition of spatial heterogeneity in housing prices to account for local settings. In response to the growing number of spatially varying coefficient models in housing applications, this study evaluated four models in terms of their spatial patterns

  6. Conjugacy classes in the Weyl group admitting a regular eigenvector and integrable hierarchies

    International Nuclear Information System (INIS)

    Delduc, F.; Feher, L.

    1994-10-01

    The classification of the integrable hierarchies in the Drinfeld-Sokolov (DS) approach is studied. The DS construction, originally based on the principal Heisenberg subalgebra of an affine Lie algebra, has been recently generalized to arbitrary graded Heisenberg subalgebras. The graded Heisenberg subalgebras of an untwisted loop algebra l(G) are classified by the conjugacy classes in the Weyl group of G, but a complete classification of the hierarchies obtained from generalized DS reductions is still missing. The main result presented here is the complete list of the graded regular elements of l(G) for G a classical Lie algebra or G 2 , extending previous results on the gl n case. (author). 9 refs., 4 tabs

  7. An EEG-Based Biometric System Using Eigenvector Centrality in Resting State Brain Networks

    NARCIS (Netherlands)

    Fraschini, M.; Hillebrand, A.; Demuru, M.; Didaci, L.; Marcialis, G.L.

    2015-01-01

    Recently, there has been a growing interest in the use of brain activity for biometric systems. However, so far these studies have focused mainly on basic features of the Electroencephalography. In this study we propose an approach based on phase synchronization, to investigate personal distinctive

  8. Eigenvector localization as a tool to study small communities in online social networks

    Czech Academy of Sciences Publication Activity Database

    Slanina, František; Konopásek, Z.

    2010-01-01

    Roč. 13, č. 6 (2010), s. 699-723 ISSN 0219-5259 R&D Projects: GA MŠk OC09078 Institutional research plan: CEZ:AV0Z10100520 Keywords : networks * localization Subject RIV: BE - Theoretical Physics Impact factor: 1.213, year: 2010 http://www.worldscinet.com/acs/13/1306/S0219525910002840.html

  9. Cross-correlation matrix analysis of Chinese and American bank stocks in subprime crisis

    Science.gov (United States)

    Zhu, Shi-Zhao; Li, Xin-Li; Nie, Sen; Zhang, Wen-Qing; Yu, Gao-Feng; Han, Xiao-Pu; Wang, Bing-Hong

    2015-05-01

    In order to study the universality of the interactions among different markets, we analyze the cross-correlation matrix of the price of the Chinese and American bank stocks. We then find that the stock prices of the emerging market are more correlated than that of the developed market. Considering that the values of the components for the eigenvector may be positive or negative, we analyze the differences between two markets in combination with the endogenous and exogenous events which influence the financial markets. We find that the sparse pattern of components of eigenvectors out of the threshold value has no change in American bank stocks before and after the subprime crisis. However, it changes from sparse to dense for Chinese bank stocks. By using the threshold value to exclude the external factors, we simulate the interactions in financial markets. Project supported by the National Natural Science Foundation of China (Grant Nos. 11275186, 91024026, and FOM2014OF001) and the University of Shanghai for Science and Technology (USST) of Humanities and Social Sciences, China (Grant Nos. USST13XSZ05 and 11YJA790231).

  10. Finite-range-scaling analysis of metastability in an Ising model with long-range interactions

    International Nuclear Information System (INIS)

    Gorman, B.M.; Rikvold, P.A.; Novotny, M.A.

    1994-01-01

    We apply both a scalar field theory and a recently developed transfer-matrix method to study the stationary properties of metastability in a two-state model with weak, long-range interactions: the Nx∞ quasi-one-dimensional Ising model. Using the field theory, we find the analytic continuation f of the free energy across the first-order transition, assuming that the system escapes the metastable state by the nucleation of noninteracting droplets. We find that corrections to the field dependence are substantial, and, by solving the Euler-Lagrange equation for the model numerically, we have verified the form of the free-energy cost of nucleation, including the first correction. In the transfer-matrix method, we associate with the subdominant eigenvectors of the transfer matrix a complex-valued ''constrained'' free-energy density f α computed directly from the matrix. For the eigenvector with an associated magnetization most strongly opposed to the applied magnetic field, f α exhibits finite-range scaling behavior in agreement with f over a wide range of temperatures and fields, extending nearly to the classical spinodal. Some implications of these results for numerical studies of metastability are discussed

  11. EvArnoldi: A New Algorithm for Large-Scale Eigenvalue Problems.

    Science.gov (United States)

    Tal-Ezer, Hillel

    2016-05-19

    Eigenvalues and eigenvectors are an essential theme in numerical linear algebra. Their study is mainly motivated by their high importance in a wide range of applications. Knowledge of eigenvalues is essential in quantum molecular science. Solutions of the Schrödinger equation for the electrons composing the molecule are the basis of electronic structure theory. Electronic eigenvalues compose the potential energy surfaces for nuclear motion. The eigenvectors allow calculation of diople transition matrix elements, the core of spectroscopy. The vibrational dynamics molecule also requires knowledge of the eigenvalues of the vibrational Hamiltonian. Typically in these problems, the dimension of Hilbert space is huge. Practically, only a small subset of eigenvalues is required. In this paper, we present a highly efficient algorithm, named EvArnoldi, for solving the large-scale eigenvalues problem. The algorithm, in its basic formulation, is mathematically equivalent to ARPACK ( Sorensen , D. C. Implicitly Restarted Arnoldi/Lanczos Methods for Large Scale Eigenvalue Calculations ; Springer , 1997 ; Lehoucq , R. B. ; Sorensen , D. C. SIAM Journal on Matrix Analysis and Applications 1996 , 17 , 789 ; Calvetti , D. ; Reichel , L. ; Sorensen , D. C. Electronic Transactions on Numerical Analysis 1994 , 2 , 21 ) (or Eigs of Matlab) but significantly simpler.

  12. An Orbit And Dispersion Correction Scheme for the PEP II

    International Nuclear Information System (INIS)

    Cai, Y.; Donald, M.; Shoaee, H.; White, G.; Yasukawa, L.A.

    2011-01-01

    To achieve optimum luminosity in a storage ring it is vital to control the residual vertical dispersion. In the original PEP storage ring, a scheme to control the residual dispersion function was implemented using the ring orbit as the controlling element. The 'best' orbit not necessarily giving the lowest vertical dispersion. A similar scheme has been implemented in both the on-line control code and in the simulation code LEGO. The method involves finding the response matrices (sensitivity of orbit/dispersion at each Beam-Position-Monitor (BPM) to each orbit corrector) and solving in a least squares sense for minimum orbit, dispersion function or both. The optimum solution is usually a subset of the full least squares solution. A scheme of simultaneously correcting the orbits and dispersion has been implemented in the simulation code and on-line control system for PEP-II. The scheme is based on the eigenvector decomposition method. An important ingredient of the scheme is to choose the optimum eigenvectors that minimize the orbit, dispersion and corrector strength. Simulations indicate this to be a very effective way to control the vertical residual dispersion.

  13. Beamforming using subspace estimation from a diagonally averaged sample covariance.

    Science.gov (United States)

    Quijano, Jorge E; Zurk, Lisa M

    2017-08-01

    The potential benefit of a large-aperture sonar array for high resolution target localization is often challenged by the lack of sufficient data required for adaptive beamforming. This paper introduces a Toeplitz-constrained estimator of the clairvoyant signal covariance matrix corresponding to multiple far-field targets embedded in background isotropic noise. The estimator is obtained by averaging along subdiagonals of the sample covariance matrix, followed by covariance extrapolation using the method of maximum entropy. The sample covariance is computed from limited data snapshots, a situation commonly encountered with large-aperture arrays in environments characterized by short periods of local stationarity. Eigenvectors computed from the Toeplitz-constrained covariance are used to construct signal-subspace projector matrices, which are shown to reduce background noise and improve detection of closely spaced targets when applied to subspace beamforming. Monte Carlo simulations corresponding to increasing array aperture suggest convergence of the proposed projector to the clairvoyant signal projector, thereby outperforming the classic projector obtained from the sample eigenvectors. Beamforming performance of the proposed method is analyzed using simulated data, as well as experimental data from the Shallow Water Array Performance experiment.

  14. An algorithm for the basis of the finite Fourier transform

    Science.gov (United States)

    Santhanam, Thalanayar S.

    1995-01-01

    The Finite Fourier Transformation matrix (F.F.T.) plays a central role in the formulation of quantum mechanics in a finite dimensional space studied by the author over the past couple of decades. An outstanding problem which still remains open is to find a complete basis for F.F.T. In this paper we suggest a simple algorithm to find the eigenvectors of F.T.T.

  15. Spectral analysis connected with suspension bridge systems

    Czech Academy of Sciences Publication Activity Database

    Malík, Josef

    2016-01-01

    Roč. 81, č. 1 (2016), s. 42-75 ISSN 0272-4960 R&D Projects: GA MŠk ED2.1.00/03.0082 Institutional support: RVO:68145535 Keywords : suspension bridge * vertical and torsional oscillation * eigenvalue * eigenvector * flutter Subject RIV: JM - Building Engineering Impact factor: 0.945, year: 2016 http://imamat.oxfordjournals.org/content/early/2015/09/16/imamat.hxv027.short?rss=1

  16. Commutator perturbation method in the study of vibrational-rotational spectra of diatomic molecules

    International Nuclear Information System (INIS)

    Matamala-Vasquez, A.; Karwowski, J.

    2000-01-01

    The commutator perturbation method, an algebraic version of the Van Vleck-Primas perturbation method, expressed in terms of ladder operators, has been applied to solving the eigenvalue problem of the Hamiltonian describing the vibrational-rotational motion of a diatomic molecule. The physical model used in this work is based on Dunham's approach. The method facilitates obtaining both energies and eigenvectors in an algebraic way

  17. Parallel Symmetric Eigenvalue Problem Solvers

    Science.gov (United States)

    2015-05-01

    Research” and the use of copyright material. Approved by Major Professor(s): Approved by: Head of the Departmental Graduate Program Date Alicia Marie... matrix . . . . . . . . . . . . . . . . . 106 8.15 Sparsity patterns for the Nastran benchmark of order 1.5 million . . . . 108 8.16 Sparsity patterns...magnitude eigenvalues of a given matrix pencil (A,B) along with their associated eigenvectors. Computing the smallest eigenvalues is more difficult

  18. Algorithms for orbit control on SPEAR

    International Nuclear Information System (INIS)

    Corbett, J.; Keeley, D.; Hettel, R.; Linscott, I.; Sebek, J.

    1994-06-01

    A global orbit feedback system has been installed on SPEAR to help stabilize the position of the photon beams. The orbit control algorithms depend on either harmonic reconstruction of the orbit or eigenvector decomposition. The orbit motion is corrected by dipole corrector kicks determined from the inverse corrector-to-bpm response matrix. This paper outlines features of these control algorithms as applied to SPEAR

  19. Low-frequency electromagnetic field in a Wigner crystal

    OpenAIRE

    Stupka, Anton

    2016-01-01

    Long-wave low-frequency oscillations are described in a Wigner crystal by generalization of the reverse continuum model for the case of electronic lattice. The internal self-consistent long-wave electromagnetic field is used to describe the collective motions in the system. The eigenvectors and eigenvalues of the obtained system of equations are derived. The velocities of longitudinal and transversal sound waves are found.

  20. Improving the sensitivity of LISA

    International Nuclear Information System (INIS)

    Nayak, K Rajesh; Pai, A; Dhurandhar, S V; Vinet, J-Y

    2003-01-01

    It has been shown in several recent papers that the six Doppler data streams obtained from a triangular LISA configuration can be combined by appropriately delaying the data streams for cancelling the laser frequency noise. Raw laser noise is several orders of magnitude above the other noises and thus it is essential to bring it down to the level of other noises such as shot, acceleration, etc. A rigorous and systematic formalism using the powerful techniques of computational commutative algebra was developed, which generates in principle all the data combinations cancelling the laser frequency noise. The relevant data combinations form a first module of syzygies. In this paper, we use this formalism to advantage for optimizing the sensitivity of LISA by analysing the noise and signal covariance matrices. The signal covariance matrix is calculated for binaries whose frequency changes at most adiabatically and the signal is averaged over polarizations and directions. We then present the extremal SNR curves for all the data combinations in the module. They correspond to the eigenvectors of the noise and signal covariance matrices. A LISA 'network' SNR is also computed by combining the outputs of the eigenvectors. We show that substantial gains in sensitivity can be obtained by employing these strategies. The maximum SNR curve can yield an improvement up to 70% over the Michelson, mainly at high frequencies, while the improvement using the network SNR ranges from 40% to over 100%. Finally, we describe a simple toy model, in which LISA rotates in a plane. In this analysis, we estimate the improvement in the LISA sensitivity, if one switches from one data combination to another as it rotates. Here the improvement in sensitivity, if one switches optimally over three cyclic data combinations of the eigenvector, is about 55% on average over the LISA bandwidth. The corresponding SNR improvement increases to 60%, if one maximizes over the module

  1. The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science.

    Science.gov (United States)

    Marek, A; Blum, V; Johanni, R; Havu, V; Lang, B; Auckenthaler, T; Heinecke, A; Bungartz, H-J; Lederer, H

    2014-05-28

    Obtaining the eigenvalues and eigenvectors of large matrices is a key problem in electronic structure theory and many other areas of computational science. The computational effort formally scales as O(N(3)) with the size of the investigated problem, N (e.g. the electron count in electronic structure theory), and thus often defines the system size limit that practical calculations cannot overcome. In many cases, more than just a small fraction of the possible eigenvalue/eigenvector pairs is needed, so that iterative solution strategies that focus only on a few eigenvalues become ineffective. Likewise, it is not always desirable or practical to circumvent the eigenvalue solution entirely. We here review some current developments regarding dense eigenvalue solvers and then focus on the Eigenvalue soLvers for Petascale Applications (ELPA) library, which facilitates the efficient algebraic solution of symmetric and Hermitian eigenvalue problems for dense matrices that have real-valued and complex-valued matrix entries, respectively, on parallel computer platforms. ELPA addresses standard as well as generalized eigenvalue problems, relying on the well documented matrix layout of the Scalable Linear Algebra PACKage (ScaLAPACK) library but replacing all actual parallel solution steps with subroutines of its own. For these steps, ELPA significantly outperforms the corresponding ScaLAPACK routines and proprietary libraries that implement the ScaLAPACK interface (e.g. Intel's MKL). The most time-critical step is the reduction of the matrix to tridiagonal form and the corresponding backtransformation of the eigenvectors. ELPA offers both a one-step tridiagonalization (successive Householder transformations) and a two-step transformation that is more efficient especially towards larger matrices and larger numbers of CPU cores. ELPA is based on the MPI standard, with an early hybrid MPI-OpenMPI implementation available as well. Scalability beyond 10,000 CPU cores for problem

  2. A unified definition of a vortex derived from vortical flow and the resulting pressure minimum

    Energy Technology Data Exchange (ETDEWEB)

    Nakayama, K [Department of Mechanical Engineering, Aichi Institute of Technology, Toyota, Aichi 470–0392 (Japan); Sugiyama, K; Takagi, S, E-mail: nakayama@aitech.ac.jp, E-mail: kazuyasu.sugiyama@riken.jp, E-mail: takagi@mech.t.u-tokyo.ac.jp [Department of Mechanical Engineering, School of Engineering, The University of Tokyo, Hongo, Tokyo 113–8656 (Japan)

    2014-10-01

    This paper presents a novel definition of a vortex that integrates the concepts of the invariant swirling motion, the pressure minimum characteristics induced by the swirling motion and the positive Laplacian of the pressure. The current definition specifies a vortex that has a swirling motion and resulting pressure minimum feature in the swirl plane, which is simply represented by the eigenvalues and eigenvectors of the velocity gradient tensor. (paper)

  3. Generalized Perron--Frobenius Theorem for Nonsquare Matrices

    OpenAIRE

    Avin, Chen; Borokhovich, Michael; Haddad, Yoram; Kantor, Erez; Lotker, Zvi; Parter, Merav; Peleg, David

    2013-01-01

    The celebrated Perron--Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. However, many real-life scenarios give rise to nonsquare matrices. A natural question is whether the...

  4. Kernel principal component analysis for change detection

    DEFF Research Database (Denmark)

    Nielsen, Allan Aasbjerg; Morton, J.C.

    2008-01-01

    region acquired at two different time points. If change over time does not dominate the scene, the projection of the original two bands onto the second eigenvector will show change over time. In this paper a kernel version of PCA is used to carry out the analysis. Unlike ordinary PCA, kernel PCA...... with a Gaussian kernel successfully finds the change observations in a case where nonlinearities are introduced artificially....

  5. Climate variations and the greenhouse effect

    International Nuclear Information System (INIS)

    Michaels, P.J.; Knappenberger, P.C.; Gay, D.A.

    1994-01-01

    A number of recent publications have established the scientific paradigm that anthropogenerated sulfate aerosols are a sufficient explanation for the lack of observed greenhouse warming that has been predicted by transient general circulation climate models. This paper tests that hypothesis by examining the observed and modeled behavior of eigenvectors of the observed temperature field at three levels: hemispheric, polar, and over the regions where sulfate aerosol is most concentrated. Without sulfates in the transient model, there is no significant difference in explanatory power between the three test regions. In all three cases, the model creates much more spurious climatic change than it is able to capture. Most damaging to the sulfate hypothesis is that the GCM most accurately represents the behavior of the first eigenvector in summer in the high sulfate regions. This is where the difference between the model and observed temperatures is supposed to be greatest. Thus while the addition of sulfate aerosol to a transient general circulation model may improve its performance over some regions, this effect is insufficient to explain the overall lack of observed warming. This failure of the aerosol hypothesis is particularly evident in polar regions that are relatively aerosol-free, but also devoid of any significant warming

  6. The genealogical decomposition of a matrix population model with applications to the aggregation of stages.

    Science.gov (United States)

    Bienvenu, François; Akçay, Erol; Legendre, Stéphane; McCandlish, David M

    2017-06-01

    Matrix projection models are a central tool in many areas of population biology. In most applications, one starts from the projection matrix to quantify the asymptotic growth rate of the population (the dominant eigenvalue), the stable stage distribution, and the reproductive values (the dominant right and left eigenvectors, respectively). Any primitive projection matrix also has an associated ergodic Markov chain that contains information about the genealogy of the population. In this paper, we show that these facts can be used to specify any matrix population model as a triple consisting of the ergodic Markov matrix, the dominant eigenvalue and one of the corresponding eigenvectors. This decomposition of the projection matrix separates properties associated with lineages from those associated with individuals. It also clarifies the relationships between many quantities commonly used to describe such models, including the relationship between eigenvalue sensitivities and elasticities. We illustrate the utility of such a decomposition by introducing a new method for aggregating classes in a matrix population model to produce a simpler model with a smaller number of classes. Unlike the standard method, our method has the advantage of preserving reproductive values and elasticities. It also has conceptually satisfying properties such as commuting with changes of units. Copyright © 2017 Elsevier Inc. All rights reserved.

  7. Functional network centrality in obesity: A resting-state and task fMRI study.

    Science.gov (United States)

    García-García, Isabel; Jurado, María Ángeles; Garolera, Maite; Marqués-Iturria, Idoia; Horstmann, Annette; Segura, Bàrbara; Pueyo, Roser; Sender-Palacios, María José; Vernet-Vernet, Maria; Villringer, Arno; Junqué, Carme; Margulies, Daniel S; Neumann, Jane

    2015-09-30

    Obesity is associated with structural and functional alterations in brain areas that are often functionally distinct and anatomically distant. This suggests that obesity is associated with differences in functional connectivity of regions distributed across the brain. However, studies addressing whole brain functional connectivity in obesity remain scarce. Here, we compared voxel-wise degree centrality and eigenvector centrality between participants with obesity (n=20) and normal-weight controls (n=21). We analyzed resting state and task-related fMRI data acquired from the same individuals. Relative to normal-weight controls, participants with obesity exhibited reduced degree centrality in the right middle frontal gyrus in the resting-state condition. During the task fMRI condition, obese participants exhibited less degree centrality in the left middle frontal gyrus and the lateral occipital cortex along with reduced eigenvector centrality in the lateral occipital cortex and occipital pole. Our results highlight the central role of the middle frontal gyrus in the pathophysiology of obesity, a structure involved in several brain circuits signaling attention, executive functions and motor functions. Additionally, our analysis suggests the existence of task-dependent reduced centrality in occipital areas; regions with a role in perceptual processes and that are profoundly modulated by attention. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

  8. Optimal Inconsistency Repairing of Pairwise Comparison Matrices Using Integrated Linear Programming and Eigenvector Methods

    Directory of Open Access Journals (Sweden)

    Haiqing Zhang

    2014-01-01

    Full Text Available Satisfying consistency requirements of pairwise comparison matrix (PCM is a critical step in decision making methodologies. An algorithm has been proposed to find a new modified consistent PCM in which it can replace the original inconsistent PCM in analytic hierarchy process (AHP or in fuzzy AHP. This paper defines the modified consistent PCM by the original inconsistent PCM and an adjustable consistent PCM combined. The algorithm adopts a segment tree to gradually approach the greatest lower bound of the distance with the original PCM to obtain the middle value of an adjustable PCM. It also proposes a theorem to obtain the lower value and the upper value of an adjustable PCM based on two constraints. The experiments for crisp elements show that the proposed approach can preserve more of the original information than previous works of the same consistent value. The convergence rate of our algorithm is significantly faster than previous works with respect to different parameters. The experiments for fuzzy elements show that our method could obtain suitable modified fuzzy PCMs.

  9. Twisting gravitational waves and eigenvector fields for SL(2,C on an infinite jet

    Directory of Open Access Journals (Sweden)

    J. D. Finley III

    2000-07-01

    Full Text Available A system of coupled vector-field-valued partial differential equations is presented, the solutions to which would determine two coupled, infinite-dimensional vector-field realizations of the group SL(2,C. While the general solution is (partially presented, the complicated nature of that solution is deplored, and the hope expressed that someone can replace it by something much more natural. The physical origins of the problem are briefly described. The problem arises out of searches for Backlund transforms of a system of PDE's that describe twisting, Petrov type N solutions of Einstein's vacuum field equations.

  10. Eigenvalues and eigenvectors of the translation matrices of spherical waves of multiple-scattering theory

    International Nuclear Information System (INIS)

    Torrini, M.

    1983-01-01

    The exponential nature of the translation matrix G of spherical free waves has been set forth in a previous paper.The explicit expression of the exponential form of the translation matrix is given here, once the eigenvectros and the eigenvalues of G have been found. In addition, the eigenproblem relative to the matrix which transforms outgoing waves scattered by a centre in a set of spherical free waves centered at a different point is solved

  11. The Adf Insurgency Network in the Eastern Democratic Republic of the Congo: Spillover Effects Into Tanzania

    Science.gov (United States)

    2014-06-01

    The funding facilitated the conduct of this study. Lastly, but not least, I thank my family and my parents . Though they were miles away from me...beginning of the end for his regime. To continue stay in power, Mobutu had to do something. He opted for a laissez-faire style of leadership. He allowed...Barahiyan (56.786). 60 Figure 19. Sociogram of Eigenvector Centrality. C. COHESIVE SUBGROUP ANALYSIS 1. Subgroups The Girvan- Newman

  12. Computation of diverging sums based on a finite number of terms

    Science.gov (United States)

    Lv, Q. Z.; Norris, S.; Pelphrey, R.; Su, Q.; Grobe, R.

    2017-10-01

    We propose a numerical method that permits us to compute the sum of a diverging series from only the first N terms by generalizing the traditional Borel technique. The method is rather robust and can be used to recover the ground state energy from the diverging perturbation theory for quantum field theoretical systems that are spatially constrained. Surprisingly, even the corresponding eigenvectors can be generated despite the intrinsic non-perturbative nature of bound state problems.

  13. Matrix theory selected topics and useful results

    CERN Document Server

    Mehta, Madan Lal

    1989-01-01

    Matrices and operations on matrices ; determinants ; elementary operations on matrices (continued) ; eigenvalues and eigenvectors, diagonalization of normal matrices ; functions of a matrix ; positive definiteness, various polar forms of a matrix ; special matrices ; matrices with quaternion elements ; inequalities ; generalised inverse of a matrix ; domain of values of a matrix, location and dispersion of eigenvalues ; symmetric functions ; integration over matrix variables ; permanents of doubly stochastic matrices ; infinite matrices ; Alexander matrices, knot polynomials, torsion numbers.

  14. Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media

    Science.gov (United States)

    Stamnes, Knut; Tsay, S.-CHEE; Jayaweera, Kolf; Wiscombe, Warren

    1988-01-01

    The transfer of monochromatic radiation in a scattering, absorbing, and emitting plane-parallel medium with a specified bidirectional reflectivity at the lower boundary is considered. The equations and boundary conditions are summarized. The numerical implementation of the theory is discussed with attention given to the reliable and efficient computation of eigenvalues and eigenvectors. Ways of avoiding fatal overflows and ill-conditioning in the matrix inversion needed to determine the integration constants are also presented.

  15. Exact analysis of the spectral properties of the anisotropic two-bosons Rabi model

    OpenAIRE

    Cui, Shuai; Cao, Jun-Peng; Fan, Heng; Amico, Luigi

    2015-01-01

    We introduce the anisotropic two-photon Rabi model in which the rotating and counter rotating terms enters along with two different coupling constants. Eigenvalues and eigenvectors are studied with exact means. We employ a variation of the Braak method based on Bogolubov rotation of the underlying $su(1,1)$ Lie algebra. Accordingly, the spectrum is provided by the analytical properties of a suitable meromorphic function. Our formalism applies to the two-modes Rabi model as well, sharing the s...

  16. Hybrid numerical calculation method for bend waveguides

    OpenAIRE

    Garnier , Lucas; Saavedra , C.; Castro-Beltran , Rigoberto; Lucio , José Luis; Bêche , Bruno

    2017-01-01

    National audience; The knowledge of how the light will behave in a waveguide with a radius of curvature becomes more and more important because of the development of integrated photonics, which include ring micro-resonators, phasars, and other devices with a radius of curvature. This work presents a numerical calculation method to determine the eigenvalues and eigenvectors of curved waveguides. This method is a hybrid method which uses at first conform transformation of the complex plane gene...

  17. Orbit control on SPEAR: a progress report

    International Nuclear Information System (INIS)

    Corbett, W.J.; Keeley, D.

    1994-01-01

    In this paper, we report work on initial studies of the global feedback system for SPEAR. In particular, we describe components of a comprehensive accelerator simulation program used to assess the performance of harmonic and eigenvector orbit control algorithms. This program has also been used to choose new bpm sites, and can simulate the interaction between global and local orbit feedback systems. A prototype on-line version used for SPEAR is discussed. copyright 1994 American Institute of Physics

  18. A pragmatic approach to including complex natural modes of vibration in aeroelastic analysis

    CSIR Research Space (South Africa)

    Van Zyl, Lourens H

    2015-09-01

    Full Text Available complex natural modes of vibration in aeroelastic analysis Louw van Zyl International Aerospace Symposium of South Africa 14 to 16 September, 2015 Stellenbosch, South Africa Slide 2 © CSIR 2006 www.csir.co.za Problem statement..., the square of the angular frequencies in radians per second) [ ]{ } [ ]{ } [ ]{ } { }fxKxCxM =++ &&& [ ]{ } [ ]{ } 0=+ xKxMs2 Slide 4 © CSIR 2006 www.csir.co.za Structural Dynamics (continued) • The corresponding eigenvectors are real...

  19. Multivariate statistical methods a primer

    CERN Document Server

    Manly, Bryan FJ

    2004-01-01

    THE MATERIAL OF MULTIVARIATE ANALYSISExamples of Multivariate DataPreview of Multivariate MethodsThe Multivariate Normal DistributionComputer ProgramsGraphical MethodsChapter SummaryReferencesMATRIX ALGEBRAThe Need for Matrix AlgebraMatrices and VectorsOperations on MatricesMatrix InversionQuadratic FormsEigenvalues and EigenvectorsVectors of Means and Covariance MatricesFurther Reading Chapter SummaryReferencesDISPLAYING MULTIVARIATE DATAThe Problem of Displaying Many Variables in Two DimensionsPlotting index VariablesThe Draftsman's PlotThe Representation of Individual Data P:ointsProfiles o

  20. Lattice Paths and the Constant Term

    International Nuclear Information System (INIS)

    Brak, R; Essam, J; Osborn, J; Owczarek, A L; Rechnitzer, A

    2006-01-01

    We firstly review the constant term method (CTM), illustrating its combinatorial connections and show how it can be used to solve a certain class of lattice path problems. We show the connection between the CTM, the transfer matrix method (eigenvectors and eigenvalues), partial difference equations, the Bethe Ansatz and orthogonal polynomials. Secondly, we solve a lattice path problem first posed in 1971. The model stated in 1971 was only solved for a special case - we solve the full model

  1. Energies and bounds from perturbative approximations to the Bloch-Horowitz effective Hamiltonian

    International Nuclear Information System (INIS)

    Darema-Rogers, F.; Vincent, C.M.

    1978-01-01

    Bloch-Horowitz perturbation theory is applied to the calculation of approximate energies and model-space eigenvectors, for the solvable large-matrix Hamiltonian H used by Pittel, Vincent, and Vergados. Two types of upper and lower bounds to the energies are discussed: moment-theory bounds, obtained by applying moment theory to the terms of perturbation theory, and norm bounds, derived from the expectation E-bar and variance sigma 2 of H with respect to an eigenvector approximated by nth order perturbation theory (n < or = 6). It is shown that lower bounds cannot be constructed unless some fourth-order quantity is known. The upper bounds are generally stricter than the lower bounds. All of the bounds apply even when back-door intruder states cause perturbation theory to diverge; but they lose their rigor and become ''quasibounds'' when there are physical intruders. The moment-theory and norm lower quasibounds always require estimation of a parameter. For the solvable Hamiltonians, it is shown that this can be done quite reliably, and that the resulting quasibounds are tight enough to have some practical utility. The energy-independent effective interaction V is constructed and its errors are displayed and discussed. Finally, a certain [1/2] pseudo-Pade approximant is empirically shown to give energies with a mean absolute error of less than 0.3 MeV in all cases

  2. SUPERPIXEL BASED FACTOR ANALYSIS AND TARGET TRANSFORMATION METHOD FOR MARTIAN MINERALS DETECTION

    Directory of Open Access Journals (Sweden)

    X. Wu

    2018-04-01

    Full Text Available The Factor analysis and target transformation (FATT is an effective method to test for the presence of particular mineral on Martian surface. It has been used both in thermal infrared (Thermal Emission Spectrometer, TES and near-infrared (Compact Reconnaissance Imaging Spectrometer for Mars, CRISM hyperspectral data. FATT derived a set of orthogonal eigenvectors from a mixed system and typically selected first 10 eigenvectors to least square fit the library mineral spectra. However, minerals present only in a limited pixels will be ignored because its weak spectral features compared with full image signatures. Here, we proposed a superpixel based FATT method to detect the mineral distributions on Mars. The simple linear iterative clustering (SLIC algorithm was used to partition the CRISM image into multiple connected image regions with spectral homogeneous to enhance the weak signatures by increasing their proportion in a mixed system. A least square fitting was used in target transformation and performed to each region iteratively. Finally, the distribution of the specific minerals in image was obtained, where fitting residual less than a threshold represent presence and otherwise absence. We validate our method by identifying carbonates in a well analysed CRISM image in Nili Fossae on Mars. Our experimental results indicate that the proposed method work well both in simulated and real data sets.

  3. Invariant Feature Matching for Image Registration Application Based on New Dissimilarity of Spatial Features

    Science.gov (United States)

    Mousavi Kahaki, Seyed Mostafa; Nordin, Md Jan; Ashtari, Amir H.; J. Zahra, Sophia

    2016-01-01

    An invariant feature matching method is proposed as a spatially invariant feature matching approach. Deformation effects, such as affine and homography, change the local information within the image and can result in ambiguous local information pertaining to image points. New method based on dissimilarity values, which measures the dissimilarity of the features through the path based on Eigenvector properties, is proposed. Evidence shows that existing matching techniques using similarity metrics—such as normalized cross-correlation, squared sum of intensity differences and correlation coefficient—are insufficient for achieving adequate results under different image deformations. Thus, new descriptor’s similarity metrics based on normalized Eigenvector correlation and signal directional differences, which are robust under local variation of the image information, are proposed to establish an efficient feature matching technique. The method proposed in this study measures the dissimilarity in the signal frequency along the path between two features. Moreover, these dissimilarity values are accumulated in a 2D dissimilarity space, allowing accurate corresponding features to be extracted based on the cumulative space using a voting strategy. This method can be used in image registration applications, as it overcomes the limitations of the existing approaches. The output results demonstrate that the proposed technique outperforms the other methods when evaluated using a standard dataset, in terms of precision-recall and corner correspondence. PMID:26985996

  4. CORRELATION ANALYSIS OF A LARGE SAMPLE OF NARROW-LINE SEYFERT 1 GALAXIES: LINKING CENTRAL ENGINE AND HOST PROPERTIES

    International Nuclear Information System (INIS)

    Xu Dawei; Komossa, S.; Wang Jing; Yuan Weimin; Zhou Hongyan; Lu Honglin; Li Cheng; Grupe, Dirk

    2012-01-01

    We present a statistical study of a large, homogeneously analyzed sample of narrow-line Seyfert 1 (NLS1) galaxies, accompanied by a comparison sample of broad-line Seyfert 1 (BLS1) galaxies. Optical emission-line and continuum properties are subjected to correlation analyses, in order to identify the main drivers of the correlation space of active galactic nuclei (AGNs), and of NLS1 galaxies in particular. For the first time, we have established the density of the narrow-line region as a key parameter in Eigenvector 1 space, as important as the Eddington ratio L/L Edd . This is important because it links the properties of the central engine with the properties of the host galaxy, i.e., the interstellar medium (ISM). We also confirm previously found correlations involving the line width of Hβ and the strength of the Fe II and [O III] λ5007 emission lines, and we confirm the important role played by L/L Edd in driving the properties of NLS1 galaxies. A spatial correlation analysis shows that large-scale environments of the BLS1 and NLS1 galaxies of our sample are similar. If mergers are rare in our sample, accretion-driven winds, on the one hand, or bar-driven inflows, on the other hand, may account for the strong dependence of Eigenvector 1 on ISM density.

  5. Prediction of partial synchronization in delay-coupled nonlinear oscillators, with application to Hindmarsh–Rose neurons

    International Nuclear Information System (INIS)

    Ünal, Hakkı Ulaş; Michiels, Wim

    2013-01-01

    The full synchronization of coupled nonlinear oscillators has been widely studied. In this paper we investigate conditions for which partial synchronization of time-delayed diffusively coupled systems arises. The coupling configuration of the systems is described by a directed graph. As a novel quantitative result we first give necessary and sufficient conditions for the presence of forward invariant sets characterized by partially synchronous motion. These conditions can easily be checked from the eigenvalues and eigenvectors of the graph Laplacian. Second, we perform stability analysis of the synchronized equilibria in a (gain,delay) parameter space. For this analysis the coupled nonlinear systems are linearized around the synchronized equilibria and then the resulting characteristic function is factorized. By such a factorization, it is shown that the relation between the behaviour of different agents at the zero of the characteristic function depends on the structure of the eigenvectors of the weighted Laplacian matrix. By determining the structure of the solutions in the unstable manifold, combined with the characterization of invariant sets, we predict which partially synchronous regimes occur and estimate the corresponding coupling gain and delay values. We apply the obtained results to networks of coupled Hindmarsh–Rose neurons and verify the occurrence of the expected partially synchronous regimes by using a numerical simulation. We also make a comparison with an existing approach based on Lyapunov functionals. (paper)

  6. An adjoint-based scheme for eigenvalue error improvement

    International Nuclear Information System (INIS)

    Merton, S.R.; Smedley-Stevenson, R.P.; Pain, C.C.; El-Sheikh, A.H.; Buchan, A.G.

    2011-01-01

    A scheme for improving the accuracy and reducing the error in eigenvalue calculations is presented. Using a rst order Taylor series expansion of both the eigenvalue solution and the residual of the governing equation, an approximation to the error in the eigenvalue is derived. This is done using a convolution of the equation residual and adjoint solution, which is calculated in-line with the primal solution. A defect correction on the solution is then performed in which the approximation to the error is used to apply a correction to the eigenvalue. The method is shown to dramatically improve convergence of the eigenvalue. The equation for the eigenvalue is shown to simplify when certain normalizations are applied to the eigenvector. Two such normalizations are considered; the rst of these is a fission-source type of normalisation and the second is an eigenvector normalisation. Results are demonstrated on a number of demanding elliptic problems using continuous Galerkin weighted nite elements. Moreover, the correction scheme may also be applied to hyperbolic problems and arbitrary discretization. This is not limited to spatial corrections and may be used throughout the phase space of the discrete equation. The applied correction not only improves fidelity of the calculation, it allows assessment of the reliability of numerical schemes to be made and could be used to guide mesh adaption algorithms or to automate mesh generation schemes. (author)

  7. Spectral biclustering of microarray data: coclustering genes and conditions.

    Science.gov (United States)

    Kluger, Yuval; Basri, Ronen; Chang, Joseph T; Gerstein, Mark

    2003-04-01

    Global analyses of RNA expression levels are useful for classifying genes and overall phenotypes. Often these classification problems are linked, and one wants to find "marker genes" that are differentially expressed in particular sets of "conditions." We have developed a method that simultaneously clusters genes and conditions, finding distinctive "checkerboard" patterns in matrices of gene expression data, if they exist. In a cancer context, these checkerboards correspond to genes that are markedly up- or downregulated in patients with particular types of tumors. Our method, spectral biclustering, is based on the observation that checkerboard structures in matrices of expression data can be found in eigenvectors corresponding to characteristic expression patterns across genes or conditions. In addition, these eigenvectors can be readily identified by commonly used linear algebra approaches, in particular the singular value decomposition (SVD), coupled with closely integrated normalization steps. We present a number of variants of the approach, depending on whether the normalization over genes and conditions is done independently or in a coupled fashion. We then apply spectral biclustering to a selection of publicly available cancer expression data sets, and examine the degree to which the approach is able to identify checkerboard structures. Furthermore, we compare the performance of our biclustering methods against a number of reasonable benchmarks (e.g., direct application of SVD or normalized cuts to raw data).

  8. Invariant Feature Matching for Image Registration Application Based on New Dissimilarity of Spatial Features.

    Directory of Open Access Journals (Sweden)

    Seyed Mostafa Mousavi Kahaki

    Full Text Available An invariant feature matching method is proposed as a spatially invariant feature matching approach. Deformation effects, such as affine and homography, change the local information within the image and can result in ambiguous local information pertaining to image points. New method based on dissimilarity values, which measures the dissimilarity of the features through the path based on Eigenvector properties, is proposed. Evidence shows that existing matching techniques using similarity metrics--such as normalized cross-correlation, squared sum of intensity differences and correlation coefficient--are insufficient for achieving adequate results under different image deformations. Thus, new descriptor's similarity metrics based on normalized Eigenvector correlation and signal directional differences, which are robust under local variation of the image information, are proposed to establish an efficient feature matching technique. The method proposed in this study measures the dissimilarity in the signal frequency along the path between two features. Moreover, these dissimilarity values are accumulated in a 2D dissimilarity space, allowing accurate corresponding features to be extracted based on the cumulative space using a voting strategy. This method can be used in image registration applications, as it overcomes the limitations of the existing approaches. The output results demonstrate that the proposed technique outperforms the other methods when evaluated using a standard dataset, in terms of precision-recall and corner correspondence.

  9. The Female Population Growth Projection Year 2021 in Trenggalek Regency by Leslie Matrix Model on the Birth Rate and Life Expectancy

    Directory of Open Access Journals (Sweden)

    Dewi Anggreini

    2017-10-01

    Full Text Available This research aims to determine the number of female residents in Trenggalek Regency in 2021 based on data on birth rate and life expectancy. The use of eigenvalues and eigenvectors aims to determine the dividing age distribution by Leslie matrix model. The eigenvectors are used to determine the number of female populations of each age interval, while the eigenvalues are used to determine population growth rates. The research method used is to determine the subject of research. The next stage is to collect research data, then analyze the data and last draw conclusions. The research data is obtained from BPS Kabupaten Trenggalek and BPS East Java Province that is data of woman population from year 2010-2015. The result of this research using Leslie matrix model for female population in Trenggalek Regency that is discrete model. The discrete model is divided into fourteen age intervals constructed using the birthrate and life expectancy. The conclusions of the study showed that the number of female population in Trenggalek Regency tended to increase with positive eigen value greater than one. In other words, the growth rate of female population in Trenggalek Regency tends to be positive. The success of Leslie's matrix model is the application of case studies in predicting the number of female populations in Trenggalek District by 2021 using the MAPLE 16 Program.

  10. Detection of ferromagnetic target based on mobile magnetic gradient tensor system

    Energy Technology Data Exchange (ETDEWEB)

    Gang, Y.I.N., E-mail: gang.gang88@163.com; Yingtang, Zhang; Zhining, Li; Hongbo, Fan; Guoquan, Ren

    2016-03-15

    Attitude change of mobile magnetic gradient tensor system critically affects the precision of gradient measurements, thereby increasing ambiguity in target detection. This paper presents a rotational invariant-based method for locating and identifying ferromagnetic targets. Firstly, unit magnetic moment vector was derived based on the geometrical invariant, such that the intermediate eigenvector of the magnetic gradient tensor is perpendicular to the magnetic moment vector and the source–sensor displacement vector. Secondly, unit source–sensor displacement vector was derived based on the characteristic that the angle between magnetic moment vector and source–sensor displacement is a rotational invariant. By introducing a displacement vector between two measurement points, the magnetic moment vector and the source–sensor displacement vector were theoretically derived. To resolve the problem of measurement noises existing in the realistic detection applications, linear equations were formulated using invariants corresponding to several distinct measurement points and least square solution of magnetic moment vector and source–sensor displacement vector were obtained. Results of simulation and principal verification experiment showed the correctness of the analytical method, along with the practicability of the least square method. - Highlights: • Ferromagnetic target detection method is proposed based on rotational invariants • Intermediate eigenvector is perpendicular to magnetic moment and displacement vector • Angle between magnetic moment and displacement vector is a rotational invariant • Magnetic moment and displacement vector are derived based on invariants of two points.

  11. A study on reducing update frequency of the forecast samples in the ensemble-based 4DVar data assimilation method

    Energy Technology Data Exchange (ETDEWEB)

    Shao, Aimei; Xu, Daosheng [Lanzhou Univ. (China). Key Lab. of Arid Climatic Changing and Reducing Disaster of Gansu Province; Chinese Academy of Meteorological Sciences, Beijing (China). State Key Lab. of Severe Weather; Qiu, Xiaobin [Lanzhou Univ. (China). Key Lab. of Arid Climatic Changing and Reducing Disaster of Gansu Province; Tianjin Institute of Meteorological Science (China); Qiu, Chongjian [Lanzhou Univ. (China). Key Lab. of Arid Climatic Changing and Reducing Disaster of Gansu Province

    2013-02-15

    In the ensemble-based four dimensional variational assimilation method (SVD-En4DVar), a singular value decomposition (SVD) technique is used to select the leading eigenvectors and the analysis variables are expressed as the orthogonal bases expansion of the eigenvectors. The experiments with a two-dimensional shallow-water equation model and simulated observations show that the truncation error and rejection of observed signals due to the reduced-dimensional reconstruction of the analysis variable are the major factors that damage the analysis when the ensemble size is not large enough. However, a larger-sized ensemble is daunting computational burden. Experiments with a shallow-water equation model also show that the forecast error covariances remain relatively constant over time. For that reason, we propose an approach that increases the members of the forecast ensemble while reducing the update frequency of the forecast error covariance in order to increase analysis accuracy and to reduce the computational cost. A series of experiments were conducted with the shallow-water equation model to test the efficiency of this approach. The experimental results indicate that this approach is promising. Further experiments with the WRF model show that this approach is also suitable for the real atmospheric data assimilation problem, but the update frequency of the forecast error covariances should not be too low. (orig.)

  12. Spectral properties of Google matrix of Wikipedia and other networks

    Science.gov (United States)

    Ermann, Leonardo; Frahm, Klaus M.; Shepelyansky, Dima L.

    2013-05-01

    We study the properties of eigenvalues and eigenvectors of the Google matrix of the Wikipedia articles hyperlink network and other real networks. With the help of the Arnoldi method, we analyze the distribution of eigenvalues in the complex plane and show that eigenstates with significant eigenvalue modulus are located on well defined network communities. We also show that the correlator between PageRank and CheiRank vectors distinguishes different organizations of information flow on BBC and Le Monde web sites.

  13. Stabilization and Riesz basis property for an overhead crane model with feedback in velocity and rotating velocity

    Directory of Open Access Journals (Sweden)

    Toure K. Augustin

    2014-06-01

    Full Text Available This paper studies a variant of an overhead crane model's problem, with a control force in velocity and rotating velocity on the platform. We obtain under certain conditions the well-posedness and the strong stabilization of the closed-loop system. We then analyze the spectrum of the system. Using a method due to Shkalikov, we prove the existence of a sequence of generalized eigenvectors of the system, which forms a Riesz basis for the state energy Hilbert space.

  14. The detection of influential subsets in linear regression using an influence matrix

    OpenAIRE

    Peña, Daniel; Yohai, Víctor J.

    1991-01-01

    This paper presents a new method to identify influential subsets in linear regression problems. The procedure uses the eigenstructure of an influence matrix which is defined as the matrix of uncentered covariance of the effect on the whole data set of deleting each observation, normalized to include the univariate Cook's statistics in the diagonal. It is shown that points in an influential subset will appear with large weight in at least one of the eigenvector linked to the largest eigenvalue...

  15. [Inelastic electron scattering from surfaces

    International Nuclear Information System (INIS)

    1993-01-01

    This program uses ab-initio and multiple scattering to study surface dynamical processes; high-resolution electron-energy loss spectroscopy is used in particular. Off-specular excitation cross sections are much larger if electron energies are in the LEED range (50--300 eV). The analyses have been extended to surfaces of ordered alloys. Phonon eigenvectors and eigenfrequencies were used as inputs to electron-energy-loss multiple scattering cross section calculations. Work on low-energy electron and positron holography is mentioned

  16. Constrained GOE for systems with few degrees of freedom in the intermediate regime between chaos and order

    International Nuclear Information System (INIS)

    Carneiro, C.E.; Hussein, M.S.; Pato, M.P.

    1990-05-01

    New distribution laws for the energy level spacings and the eigenvector amplitudes, appropriate for systems with a few degrees of freedom in the intermediate regime between chaos and order, are derived by conveniently deforming the Gaussian Orthogonal Ensemble. The cases of 2X2 and 3X3 matrices are fully worked out. The general case of matrices with large dimensions is discussed. The Hubbard-Stratonowich transformation in conjunction with the Method of Integration over Alternate Variables are employed for the purpose. (author)

  17. Are topological charge fluctuations in QCD instanton dominated?

    International Nuclear Information System (INIS)

    Edwards, Robert G.; Heller, Urs M.

    2002-01-01

    We consider a recent proposal by Horvath et al. to address the question of whether topological charge fluctuations in QCD are instanton dominated via the response of fermions using lattice fermions with exact chiral symmetry, the overlap fermions. Considering several volumes and lattice spacings, we find strong evidence for chirality of a finite density of low-lying eigenvectors of the overlap-Dirac operator in the regions where these modes are peaked. This result suggests instanton dominance of topological charge fluctuations in quenched QCD

  18. Are Topological Charge Fluctuations in QCD Instanton Dominated?

    International Nuclear Information System (INIS)

    Edwards, Robert G.; Heller, Urs M.

    2001-01-01

    We consider a recent proposal by Horvath et al. to address the question whether topological charge fluctuations in QCD are instanton dominated via the response of fermions using lattice fermions with exact chiral symmetry, the overlap fermions. Considering several volumes and lattice spacings we find strong evidence for chirality of a finite density of low-lying eigenvectors of the overlap-Dirac operator in the regions where these modes are peaked. This result suggests instanton dominance of topological charge fluctuations in quenched QCD

  19. On Optimal Feedback Control for Stationary Linear Systems

    International Nuclear Information System (INIS)

    Russell, David L.

    2010-01-01

    We study linear-quadratic optimal control problems for finite dimensional stationary linear systems AX+BU=Z with output Y=CX+DU from the viewpoint of linear feedback solution. We interpret solutions in relation to system robustness with respect to disturbances Z and relate them to nonlinear matrix equations of Riccati type and eigenvalue-eigenvector problems for the corresponding Hamiltonian system. Examples are included along with an indication of extensions to continuous, i.e., infinite dimensional, systems, primarily of elliptic type.

  20. Proceedings of the NASTRAN (Tradename) Users’ Colloquium (14th) Held in San Diego, California on 5-9 May 1986

    Science.gov (United States)

    1986-05-01

    matrix equation: MGG * X’’ + KGG * X = BMAT * U Y V where X is the state vector, U is the input vector, and Y is the output vector. If NASDS users...insert the PARAM card PARAM MODOBCL 1 116 the program will accept both matrices BMAT and CMAT via user supplied DMIG bulk data input. Normally, they are...name:number.BMATG, CLASS = ARRAY CONTENTS: Input coefficient matrix BMAT compatible with g-set eigenvector matrix PHIG DS_27 DATASTRUCTURE = name:number.CMATG

  1. The Use of Comprehensive Molecular Profiling with Network and Control Theory to Better Understand GWI and Model Therapeutic Strategies

    Science.gov (United States)

    2011-07-01

    in chronic fatigue syndrome. J Chronic Fatigue syndrome, 1:23-42, 1995 102. Von Roenn JH, Armstrong D, Kotler DP, Cohn DL, Klimas NG, Tchekmedyian...of similar size and order. For any network with order, N, and normalized principle eigenvector, bX (with a maxi- mum component, xmax = max[xi]), a...prevent the degradation of GLP-1 [42], are now marketed for the treatment of type 2 diabetes mellitus (T2DM). Considering that DPPIV/CD26 has a key role

  2. Stochastic Fixed Points and Nonlinear Perron-Frobenius Theorem

    OpenAIRE

    Babaei, E.; Evstigneev, I. V.; Pirogov, S. A.

    2016-01-01

    We provide conditions for the existence of measurable solutions to the equation $\\xi(T\\omega)=f(\\omega,\\xi(\\omega))$, where $T:\\Omega \\rightarrow\\Omega$ is an automorphism of the probability space $\\Omega$ and $f(\\omega,\\cdot)$ is a strictly non-expansive mapping. We use results of this kind to establish a stochastic nonlinear analogue of the Perron-Frobenius theorem on eigenvalues and eigenvectors of a positive matrix. We consider a random mapping $D(\\omega)$ of a random closed cone $K(\\omeg...

  3. 16TH Annual Review of Progress in Applied Computational Electromagnetics at the Naval Postgraduate School Monterey, CA, March 20-24, 2000, Volume II

    Science.gov (United States)

    2000-03-24

    simplification neglects the transportation of heat radiation from one object to another and only the emission of heat from a surface. This becomes...P D - (1i 12) where -i j i(13) Oji =E 1 a, Fj, aj T4 where at, and &, are the absorption and emission coefficient of surface A , respectively...follows: _0 = GOt + hho (27) where h, 0 is nonzero eigenvector corresponding to zero eigenvalue, and h 0 is an arbitrary nonzero vector in space {h 1

  4. Some applicationS of non-Hermitian operators in quantum mechanics and quantum field theory

    International Nuclear Information System (INIS)

    Recami, E.; Rodrigues, W.A. Jr.; Smrz, P.

    1983-01-01

    Due to the possibility of rephrasing it in terms of Lie-admissible algebras, some work done in the past in collaboration with A., Agodi, M., Baldo and V.S., Olkhovsky is here reported. Such work led to the introduction of non-Hermitian operators in (classical and relativistic) quantum theory. In particular: (i) the association of unstable states (decaying 'Resonances') with the eigenvectors of non-Hermitian hamiltonians; (ii) the problem of the four position operators for relativistic spin-zero particles are dealth with

  5. Quantum interference vs. quantum chaos in the nuclear shell model

    International Nuclear Information System (INIS)

    Fernández, Gerardo; Hautefeuille, M; Velázquez, V; Hernández, Edna M; Landa, E; Morales, I O; Frank, A; Fossion, R; Vargas, C E

    2015-01-01

    In this paper we study the complexity of the nuclear states in terms of a two body quadupole-quadrupole interaction. Energy distributions and eigenvectors composition exhibit a visible interference pattern which is dependent on the intensity of the interaction. In analogy with optics, the visibility of the interference is related to the purity of the states, therefore, we show that the fluctuations associated with quantum chaos have as their origin the remaining quantum coherence with a visibility magnitude close to 5%

  6. Energy levels of germanium, Ge I through Ge XXXII

    International Nuclear Information System (INIS)

    Sugar, J.; Musgrove, A.

    1993-01-01

    Atomic energy levels of germanium have been compiled for all stages of ionization for which experimental data are available. No data have yet been published for Ge VIII through Ge XIII and Ge XXXII. Very accurate calculated values are compiled for Ge XXXI and XXXII. Experimental g-factors and leading percentages from calculated eigenvectors of levels are given. A value for the ionization energy, either experimental when available or theoretical, is included for the neutral atom and each ion. section

  7. Integrable Hierarchy of the Quantum Benjamin-Ono Equation

    Directory of Open Access Journals (Sweden)

    Maxim Nazarov

    2013-12-01

    Full Text Available A hierarchy of pairwise commuting Hamiltonians for the quantum periodic Benjamin-Ono equation is constructed by using the Lax matrix. The eigenvectors of these Hamiltonians are Jack symmetric functions of infinitely many variables x_1,x_2,…. This construction provides explicit expressions for the Hamiltonians in terms of the power sum symmetric functions p_n=x^n_1+x^n_2+⋯ and is based on our recent results from [Comm. Math. Phys. 324 (2013, 831-849].

  8. Solving symmetric-definite quadratic lambda-matrix problems without factorization

    International Nuclear Information System (INIS)

    Scott, D.S.; Ward, R.C.

    1982-01-01

    Algorithms are presented for computing some of the eigenvalues and their associated eigenvectors of the quadratic lambda-matrix M lambda 2 C lambda + K. M, C, and K are assumed to have special symmetry-type properties which insure that theory analogous to the standard symmetric eigenproblem exists. The algorithms are based on a generalization of the Rayleigh quotient and the Lanczos method for computing eigenpairs of standard symmetric eigenproblems. Monotone quadratic convergence of the basic method is proved. Test examples are presented

  9. A unified development of several techniques for the representation of random vectors and data sets

    Science.gov (United States)

    Bundick, W. T.

    1973-01-01

    Linear vector space theory is used to develop a general representation of a set of data vectors or random vectors by linear combinations of orthonormal vectors such that the mean squared error of the representation is minimized. The orthonormal vectors are shown to be the eigenvectors of an operator. The general representation is applied to several specific problems involving the use of the Karhunen-Loeve expansion, principal component analysis, and empirical orthogonal functions; and the common properties of these representations are developed.

  10. Dynamic Eigenvalue Problem of Concrete Slab Road Surface

    Science.gov (United States)

    Pawlak, Urszula; Szczecina, Michał

    2017-10-01

    The paper presents an analysis of the dynamic eigenvalue problem of concrete slab road surface. A sample concrete slab was modelled using Autodesk Robot Structural Analysis software and calculated with Finite Element Method. The slab was set on a one-parameter elastic subsoil, for which the modulus of elasticity was separately calculated. The eigen frequencies and eigenvectors (as maximal vertical nodal displacements) were presented. On the basis of the results of calculations, some basic recommendations for designers of concrete road surfaces were offered.

  11. Modulational estimate for the maximal Lyapunov exponent in Fermi-Pasta-Ulam chains

    Science.gov (United States)

    Dauxois, Thierry; Ruffo, Stefano; Torcini, Alessandro

    1997-12-01

    In the framework of the Fermi-Pasta-Ulam (FPU) model, we show a simple method to give an accurate analytical estimation of the maximal Lyapunov exponent at high energy density. The method is based on the computation of the mean value of the modulational instability growth rates associated to unstable modes. Moreover, we show that the strong stochasticity threshold found in the β-FPU system is closely related to a transition in tangent space, the Lyapunov eigenvector being more localized in space at high energy.

  12. Linear algebra a first course with applications

    CERN Document Server

    Knop, Larry E

    2008-01-01

    Linear Algebra: A First Course with Applications explores the fundamental ideas of linear algebra, including vector spaces, subspaces, basis, span, linear independence, linear transformation, eigenvalues, and eigenvectors, as well as a variety of applications, from inventories to graphics to Google's PageRank. Unlike other texts on the subject, this classroom-tested book gives students enough time to absorb the material by focusing on vector spaces early on and using computational sections as numerical interludes. It offers introductions to Maple™, MATLAB®, and TI-83 Plus for calculating matri

  13. The Relation between Degree and Strength in the Complex Network Derived from an Individual Stock

    Directory of Open Access Journals (Sweden)

    Zelin Zhang

    2016-01-01

    Full Text Available A method based on coarse-graining to construct a directed weighted complex network which models the transformation of the trading data of an individual stock is introduced. The degree (strength distribution of derived network follows a power-law. A moderated regression equation with interaction effects of average return and out-degree (in-degree on out-strength (in-strength is established. Moreover, we found that the differences of nodes affect the network’s structure and average return level impacts nodes’ eigenvector centrality and pagerank, significantly.

  14. Killing–Yano symmetry of Kaluza–Klein black holes in five dimensions

    International Nuclear Information System (INIS)

    Houri, Tsuyoshi; Yamamoto, Kei

    2013-01-01

    Using a generalized Killing–Yano equation in the presence of torsion, spacetime metrics admitting a rank-2 generalized Killing–Yano tensor are investigated in five dimensions under the assumption that its eigenvector associated with the zero eigenvalue is a Killing vector field. It is shown that such metrics are classified into three types and the corresponding local expressions are given explicitly. It is also shown that they cover some classes of charged, rotating Kaluza–Klein black hole solutions of minimal supergravity and Abelian heterotic supergravity. (paper)

  15. Graph Theory Meets Ab Initio Molecular Dynamics: Atomic Structures and Transformations at the Nanoscale

    Science.gov (United States)

    Pietrucci, Fabio; Andreoni, Wanda

    2011-08-01

    Social permutation invariant coordinates are introduced describing the bond network around a given atom. They originate from the largest eigenvalue and the corresponding eigenvector of the contact matrix, are invariant under permutation of identical atoms, and bear a clear signature of an order-disorder transition. Once combined with ab initio metadynamics, these coordinates are shown to be a powerful tool for the discovery of low-energy isomers of molecules and nanoclusters as well as for a blind exploration of isomerization, association, and dissociation reactions.

  16. An algorithm for calculation of the Jordan canonical form of a matrix

    Science.gov (United States)

    Sridhar, B.; Jordan, D.

    1973-01-01

    Jordan canonical forms are used extensively in the literature on control systems. However, very few methods are available to compute them numerically. Most numerical methods compute a set of basis vectors in terms of which the given matrix is diagonalized when such a change of basis is possible. Here, a simple and efficient method is suggested for computing the Jordan canonical form and the corresponding transformation matrix. The method is based on the definition of a generalized eigenvector, and a natural extension of Gauss elimination techniques.

  17. Geometric transformations of optical orbital angular momentum spatial modes

    Science.gov (United States)

    He, Rui; An, Xin

    2018-02-01

    With the aid of the bosonic mode conversions in two different coordinate frames, we show that (1) the coordinate eigenstate is exactly the EPR entangled state representation, and (2) the Laguerre-Gaussian (LG) mode is exactly the wave function of the common eigenvector of the orbital angular momentum and the total photon number operator. Moreover, by using the conversion of the bosonic modes, theWigner representation of the LG mode can be obtained directly. It provides an alternative to the method of Simon and Agarwal.

  18. Symmetrical Processing of Interferogram and Spectrum Reconstruction in Interference Spectrometer

    Institute of Scientific and Technical Information of China (English)

    楚建军; 赵达尊

    2003-01-01

    Because of its all-reflective layout based on the Fresnel double-mirror interference system, the newly developed Fourier transform imaging spectrometer has a very large spectral bandwidth ranged from a cut-off wavelength (related to the cut-off wave number σmax) to far infrared. According to the signal's symmetry and wide-band characteristics, a simple method that can efficiently weaken the low frequency noise in the reconstructed spectrum is presented. Also, according to the symmetry, the eigenvector method is applied to the reconstruction of the spectrum.

  19. Analysis of and Techniques for Adaptive Equalization for Underwater Acoustic Communication

    Science.gov (United States)

    2011-09-01

    used and in (b) an averaging window of 1000 samples is used. There was an overlap length of half the averaging window. The solid black line shows the ...array processing by constraining the signal covariance matrix to be realizable when the received signal was a sum of narrowband plane waves. Their goal...u0 −u0 v(u)vH(u)du. (4.4.9) A key part of the proof in [48] uses the Poincare separation theorem to show that the eigenvectors corresponding to the

  20. Principles of quantum interference

    International Nuclear Information System (INIS)

    Jones, K.R.W.

    1990-01-01

    A new approach to quantum state determination is developed using data in the form of observed eigenvectors. An exceedingly natural inversion of such data results when the quantum probability rule is recognised as a conditional. The reversal of this conditional via Bayesian methods results in an inferred probability density over states which readily reduces to a density matrix estimator. The inclusion of concepts drawn from communication theory then defines an optimal state determination problem which is explored on Hilbert spaces of arbitrary finite dimensionality. 33 refs

  1. Topics in Bethe Ansatz

    Science.gov (United States)

    Wang, Chunguang

    Integrable quantum spin chains have close connections to integrable quantum field. theories, modern condensed matter physics, string and Yang-Mills theories. Bethe. ansatz is one of the most important approaches for solving quantum integrable spin. chains. At the heart of the algebraic structure of integrable quantum spin chains is. the quantum Yang-Baxter equation and the boundary Yang-Baxter equation. This. thesis focuses on four topics in Bethe ansatz. The Bethe equations for the isotropic periodic spin-1/2 Heisenberg chain with N. sites have solutions containing ±i/2 that are singular: both the corresponding energy and the algebraic Bethe ansatz vector are divergent. Such solutions must be carefully regularized. We consider a regularization involving a parameter that can be. determined using a generalization of the Bethe equations. These generalized Bethe. equations provide a practical way of determining which singular solutions correspond. to eigenvectors of the model. The Bethe equations for the periodic XXX and XXZ spin chains admit singular. solutions, for which the corresponding eigenvalues and eigenvectors are ill-defined. We use a twist regularization to derive conditions for such singular solutions to bephysical, in which case they correspond to genuine eigenvalues and eigenvectors of. the Hamiltonian. We analyze the ground state of the open spin-1/2 isotropic quantum spin chain. with a non-diagonal boundary term using a recently proposed Bethe ansatz solution. As the coefficient of the non-diagonal boundary term tends to zero, the Bethe roots. split evenly into two sets: those that remain finite, and those that become infinite. We. argue that the former satisfy conventional Bethe equations, while the latter satisfy a. generalization of the Richardson-Gaudin equations. We derive an expression for the. leading correction to the boundary energy in terms of the boundary parameters. We argue that the Hamiltonians for A(2) 2n open quantum spin chains

  2. An empirical orthogonal function analysis of ocean shoreline location on the Virginia barrier islands

    Science.gov (United States)

    Haluska, J. D.

    2017-12-01

    Shoreline change along the Eastern Atlantic shore of Virginia has been studied for the individual barrier islands but not as an integrated system. This study combines the Atlantic shoreline locations for eleven barrier islands obtained from LANDSAT 5, 7, and 8 images. Approximately 250 shoreline locations over a 24-year period from Jan 1990 to Dec 2014 were extracted from the digitized shoreline data at 338 transects. The resulting 338 by 250 matrix was analyzed by the empirical orthogonal function (EOF) technique. The first four principal components (PC) explained 86 percent of the sample variance. Since the data was not detrended, the first PC was the overall trend of the data with a discontinuity in 2004-2005. The 2004-2005 interval included storm events and large shoreline changes. PCs 2 to 4 reflect the effects of El Nino events and tropical and non-tropical storms. Eigenvectors 1 to 4 all show the effects of the nine inlets in the island group. Eigenvector (EV) 1 explains 59 percent of the shoreline spatial variance and shows the largest changes at the northern and southern island ends. EVs 2 to 4 reflect the pattern of EV1 but at sequentially smaller percentages of the spatial variance. As a group, the eleven islands are losing ocean side shoreline. The lone exception is Hog Island. Sea level had the strongest correlation with the shoreline loss trend of PC1. The coefficient of determination was 0.41. The NAO and MEI also correlated with PC1 with correlations of determination of 0.05 and 0.12 respectively. These confidence level for the three factors was better than 99 percent. Sea level also correlated with PC3 and PC4. The PCs as a group show that the year intervals 2004-2005 and 2009-2010 had large effects on the shoreline change pattern for the island group. EVs 1 to 4 had the highest range of shoreline change at the island ends indicating the effect the changes of the inlets have on the adjacent islands. The smaller islands as a group had a higher level

  3. Optimal reduced-rank quadratic classifiers using the Fukunaga-Koontz transform with applications to automated target recognition

    Science.gov (United States)

    Huo, Xiaoming; Elad, Michael; Flesia, Ana G.; Muise, Robert R.; Stanfill, S. Robert; Friedman, Jerome; Popescu, Bogdan; Chen, Jihong; Mahalanobis, Abhijit; Donoho, David L.

    2003-09-01

    In target recognition applications of discriminant of classification analysis, each 'feature' is a result of a convolution of an imagery with a filter, which may be derived from a feature vector. It is important to use relatively few features. We analyze an optimal reduced-rank classifier under the two-class situation. Assuming each population is Gaussian and has zero mean, and the classes differ through the covariance matrices: ∑1 and ∑2. The following matrix is considered: Λ=(∑1+∑2)-1/2∑1(∑1+∑2)-1/2. We show that the k eigenvectors of this matrix whose eigenvalues are most different from 1/2 offer the best rank k approximation to the maximum likelihood classifier. The matrix Λ and its eigenvectors have been introduced by Fukunaga and Koontz; hence this analysis gives a new interpretation of the well known Fukunaga-Koontz transform. The optimality that is promised in this method hold if the two populations are exactly Guassian with the same means. To check the applicability of this approach to real data, an experiment is performed, in which several 'modern' classifiers were used on an Infrared ATR data. In these experiments, a reduced-rank classifier-Tuned Basis Functions-outperforms others. The competitive performance of the optimal reduced-rank quadratic classifier suggests that, at least for classification purposes, the imagery data behaves in a nearly-Gaussian fashion.

  4. Spatial Mapping of Translational Diffusion Coefficients Using Diffusion Tensor Imaging: A Mathematical Description.

    Science.gov (United States)

    Shetty, Anil N; Chiang, Sharon; Maletic-Savatic, Mirjana; Kasprian, Gregor; Vannucci, Marina; Lee, Wesley

    2014-01-01

    In this article, we discuss the theoretical background for diffusion weighted imaging and diffusion tensor imaging. Molecular diffusion is a random process involving thermal Brownian motion. In biological tissues, the underlying microstructures restrict the diffusion of water molecules, making diffusion directionally dependent. Water diffusion in tissue is mathematically characterized by the diffusion tensor, the elements of which contain information about the magnitude and direction of diffusion and is a function of the coordinate system. Thus, it is possible to generate contrast in tissue based primarily on diffusion effects. Expressing diffusion in terms of the measured diffusion coefficient (eigenvalue) in any one direction can lead to errors. Nowhere is this more evident than in white matter, due to the preferential orientation of myelin fibers. The directional dependency is removed by diagonalization of the diffusion tensor, which then yields a set of three eigenvalues and eigenvectors, representing the magnitude and direction of the three orthogonal axes of the diffusion ellipsoid, respectively. For example, the eigenvalue corresponding to the eigenvector along the long axis of the fiber corresponds qualitatively to diffusion with least restriction. Determination of the principal values of the diffusion tensor and various anisotropic indices provides structural information. We review the use of diffusion measurements using the modified Stejskal-Tanner diffusion equation. The anisotropy is analyzed by decomposing the diffusion tensor based on symmetrical properties describing the geometry of diffusion tensor. We further describe diffusion tensor properties in visualizing fiber tract organization of the human brain.

  5. Normalized modes at selected points without normalization

    Science.gov (United States)

    Kausel, Eduardo

    2018-04-01

    As every textbook on linear algebra demonstrates, the eigenvectors for the general eigenvalue problem | K - λM | = 0 involving two real, symmetric, positive definite matrices K , M satisfy some well-defined orthogonality conditions. Equally well-known is the fact that those eigenvectors can be normalized so that their modal mass μ =ϕT Mϕ is unity: it suffices to divide each unscaled mode by the square root of the modal mass. Thus, the normalization is the result of an explicit calculation applied to the modes after they were obtained by some means. However, we show herein that the normalized modes are not merely convenient forms of scaling, but that they are actually intrinsic properties of the pair of matrices K , M, that is, the matrices already "know" about normalization even before the modes have been obtained. This means that we can obtain individual components of the normalized modes directly from the eigenvalue problem, and without needing to obtain either all of the modes or for that matter, any one complete mode. These results are achieved by means of the residue theorem of operational calculus, a finding that is rather remarkable inasmuch as the residues themselves do not make use of any orthogonality conditions or normalization in the first place. It appears that this obscure property connecting the general eigenvalue problem of modal analysis with the residue theorem of operational calculus may have been overlooked up until now, but which has in turn interesting theoretical implications.Á

  6. Quality Aware Compression of Electrocardiogram Using Principal Component Analysis.

    Science.gov (United States)

    Gupta, Rajarshi

    2016-05-01

    Electrocardiogram (ECG) compression finds wide application in various patient monitoring purposes. Quality control in ECG compression ensures reconstruction quality and its clinical acceptance for diagnostic decision making. In this paper, a quality aware compression method of single lead ECG is described using principal component analysis (PCA). After pre-processing, beat extraction and PCA decomposition, two independent quality criteria, namely, bit rate control (BRC) or error control (EC) criteria were set to select optimal principal components, eigenvectors and their quantization level to achieve desired bit rate or error measure. The selected principal components and eigenvectors were finally compressed using a modified delta and Huffman encoder. The algorithms were validated with 32 sets of MIT Arrhythmia data and 60 normal and 30 sets of diagnostic ECG data from PTB Diagnostic ECG data ptbdb, all at 1 kHz sampling. For BRC with a CR threshold of 40, an average Compression Ratio (CR), percentage root mean squared difference normalized (PRDN) and maximum absolute error (MAE) of 50.74, 16.22 and 0.243 mV respectively were obtained. For EC with an upper limit of 5 % PRDN and 0.1 mV MAE, the average CR, PRDN and MAE of 9.48, 4.13 and 0.049 mV respectively were obtained. For mitdb data 117, the reconstruction quality could be preserved up to CR of 68.96 by extending the BRC threshold. The proposed method yields better results than recently published works on quality controlled ECG compression.

  7. Low temperature EPR investigation of Co2+ ion doped into rutile TiO2 single crystal: Experiments and simulations

    Science.gov (United States)

    Zerentürk, A.; Açıkgöz, M.; Kazan, S.; Yıldız, F.; Aktaş, B.

    2017-02-01

    In this paper, we present the results of X-band EPR spectra of Co2+ ion doped rutile (TiO2) which is one of the most promising memristor material. We obtained the angular variation of spectra in three mutually perpendicular planes at liquid helium (7-13 K) temperatures. Since the impurity ions have ½ effective spin and 7/2 nuclear spin, a relatively simple spin Hamiltonian containing only electronic Zeeman and hyperfine terms was utilized. Two different methods were used in theoretical analysis. Firstly, a linear regression analysis of spectra based on perturbation theory was studied. However, this approach is not sufficient for analyzing Co+2 spectra and leads to complex eigenvectors for G and A tensors due to large anisotropy of eigenvalues. Therefore, all spectra were analyzed again with exact diagonalization of spin Hamiltonian and the high accuracy eigenvalues and eigenvectors of G and A tensors were obtained by taking into account the effect of small sample misalignment from the exact crystallographic planes due to experimental conditions. Our results show that eigen-axes of g and A tensors are parallel to crystallographic directions. Hence, our EPR experiments proves that Co2+ ions substitute for Ti4+ ions in lattice. The obtained principal values of g tensor are gx=2.110(6), gy=5.890(2), gz=3.725(7) and principal values of hyperfine tensor are Ax=42.4, Ay=152.7, Az=26 (in 10-4/cm).

  8. Revised analysis of singly ionized xenon, Xe II

    International Nuclear Information System (INIS)

    Hansen, J.E.; Persson, W.

    1987-01-01

    We present a revised analysis of the spectrum of singly ionized xenon, Xe II. This spectrum has been reanalyzed on the basis of the wavelength material published by Drs J. C. Boyce and C. J. Humphreys. The latter has kindly placed the original wavelength list covering the wavelength range 10220-390 A at our disposal. We report 161 energy levels which have been identified on the basis of classifications of 950 lines. We report first f and g levels in Xe II. Also a number of g-factors have been determined for the first time and we give in total 75 g-factors. We have carried out least-squares fits to the even configurations and report the resulting parameter values and eigenvector compositions. A least-squares fit to the 5p 4 6p configuration is also reported. The levels have been named in jK and for many levels also in LS coupling. The former is the better coupling scheme for Xe II. We present an analysis of the 5s photoelectron satellite spectrum of Xe based on our calculated eigenvector compositions and calculations of transition probabilities for ground state transitions as well as lifetimes for the 6p levels. The latter are compared to recent experimental measurements. A list of wavelengths for observed laser transitions showing the present classifications and a discussion of the determination of the ionization potential of Xe II concludes the paper. (orig.)

  9. Energy-weighted moments in the problems of fragmentation

    International Nuclear Information System (INIS)

    Kuz'min, V.A.

    1986-01-01

    The problem of fragmentation of simple nuclear states on the complex ones is reduced to real symmetrical matrix eigenvectors and eigenvalue problem. Based on spectral decomposition of this matrix the simple and economical from computing point of view algorithm to calculate energetically-weighted strength function moments is obtained. This permitted one to investigate the sensitivity of solving the fragmentation problem to reducing the basis of complex states. It is shown that the full width of strength function is determined only by the complex states connected directly with the simple ones

  10. Accurate Quasiparticle Spectra from the T-Matrix Self-Energy and the Particle-Particle Random Phase Approximation.

    Science.gov (United States)

    Zhang, Du; Su, Neil Qiang; Yang, Weitao

    2017-07-20

    The GW self-energy, especially G 0 W 0 based on the particle-hole random phase approximation (phRPA), is widely used to study quasiparticle (QP) energies. Motivated by the desirable features of the particle-particle (pp) RPA compared to the conventional phRPA, we explore the pp counterpart of GW, that is, the T-matrix self-energy, formulated with the eigenvectors and eigenvalues of the ppRPA matrix. We demonstrate the accuracy of the T-matrix method for molecular QP energies, highlighting the importance of the pp channel for calculating QP spectra.

  11. Numerical Algorithms for Personalized Search in Self-organizing Information Networks

    CERN Document Server

    Kamvar, Sep

    2010-01-01

    This book lays out the theoretical groundwork for personalized search and reputation management, both on the Web and in peer-to-peer and social networks. Representing much of the foundational research in this field, the book develops scalable algorithms that exploit the graphlike properties underlying personalized search and reputation management, and delves into realistic scenarios regarding Web-scale data. Sep Kamvar focuses on eigenvector-based techniques in Web search, introducing a personalized variant of Google's PageRank algorithm, and he outlines algorithms--such as the now-famous quad

  12. Shell model test of the Porter-Thomas distribution

    International Nuclear Information System (INIS)

    Grimes, S.M.; Bloom, S.D.

    1981-01-01

    Eigenvectors have been calculated for the A=18, 19, 20, 21, and 26 nuclei in an sd shell basis. The decomposition of these states into their shell model components shows, in agreement with other recent work, that this distribution is not a single Gaussian. We find that the largest amplitudes are distributed approximately in a Gaussian fashion. Thus, many experimental measurements should be consistent with the Porter-Thomas predictions. We argue that the non-Gaussian form of the complete distribution can be simply related to the structure of the Hamiltonian

  13. Acoustic and elastic properties of Sn2P2S6 crystals

    International Nuclear Information System (INIS)

    Mys, O; Martynyuk-Lototska, I; Vlokh, R; Grabar, A

    2009-01-01

    We present the results concerned with acoustic and elastic properties of Sn 2 P 2 S 6 crystals. The complete matrices of elastic stiffness and compliance coefficients are determined in both the crystallographic coordinate system and the system associated with eigenvectors of the elastic stiffness tensor. The acoustic slowness surfaces are constructed and the propagation and polarization directions of the slowest acoustic waves promising for acousto-optic interactions are determined on this basis. The acoustic obliquity angle and the deviation of polarization of the acoustic waves from purely transverse or longitudinal states are quantitatively analysed.

  14. Acoustic and elastic properties of Sn(2)P(2)S(6) crystals.

    Science.gov (United States)

    Mys, O; Martynyuk-Lototska, I; Grabar, A; Vlokh, R

    2009-07-01

    We present the results concerned with acoustic and elastic properties of Sn(2)P(2)S(6) crystals. The complete matrices of elastic stiffness and compliance coefficients are determined in both the crystallographic coordinate system and the system associated with eigenvectors of the elastic stiffness tensor. The acoustic slowness surfaces are constructed and the propagation and polarization directions of the slowest acoustic waves promising for acousto-optic interactions are determined on this basis. The acoustic obliquity angle and the deviation of polarization of the acoustic waves from purely transverse or longitudinal states are quantitatively analysed.

  15. Construction of rigged Hilbert spaces to describe resonances and virtual states

    International Nuclear Information System (INIS)

    Gadella, M.

    1983-01-01

    In the present communication we present a mathematical formalism for the description of resonances and virtual states. We start by constructing rigged Hilbert spaces of Hardy class functions restricted to the positive half of the real line. Then resonances and virtual states can be written as generalized eigenvectors of the total Hamiltonian. We also define time evolution on functionals. We see that the time evolution group U(t) splits into two semigroups, one for t > 0 and the other for t < 0, hence showing the irreversibility of the decaying process

  16. Construction of rigged Hilbert spaces to describe resonances and virtual states

    International Nuclear Information System (INIS)

    Gadella, M.

    1984-01-01

    In the present communication we present a mathematical formalism for the description of resonances and virtual states. We start by constructing rigged Hilbert spaces of Hardy class functions restricted to the positive half of the real line. Then resonances and virtual states can be written as generalized eigenvectors of the total Hamiltonian. We also define time evolution on functionals. We see that the time evolution group U(t) splits into two semigroups, one for t>0 and the other for t<0, hence showing the irreversibility of the decaying process. (orig.)

  17. Random matrix theory and portfolio optimization in Moroccan stock exchange

    Science.gov (United States)

    El Alaoui, Marwane

    2015-09-01

    In this work, we use random matrix theory to analyze eigenvalues and see if there is a presence of pertinent information by using Marčenko-Pastur distribution. Thus, we study cross-correlation among stocks of Casablanca Stock Exchange. Moreover, we clean correlation matrix from noisy elements to see if the gap between predicted risk and realized risk would be reduced. We also analyze eigenvectors components distributions and their degree of deviations by computing the inverse participation ratio. This analysis is a way to understand the correlation structure among stocks of Casablanca Stock Exchange portfolio.

  18. Single-Channel Noise Reduction using Unified Joint Diagonalization and Optimal Filtering

    DEFF Research Database (Denmark)

    Nørholm, Sidsel Marie; Benesty, Jacob; Jensen, Jesper Rindom

    2014-01-01

    consider two cases, where, respectively, no distortion and distortion are incurred on the desired signal. The former can be achieved when the covariance matrix of the desired signal is rank deficient, which is the case, for example, for voiced speech. In the latter case, the covariance matrix......In this paper, the important problem of single-channel noise reduction is treated from a new perspective. The problem is posed as a filtering problem based on joint diagonalization of the covariance matrices of the desired and noise signals. More specifically, the eigenvectors from the joint...

  19. Some results on excited hadrons in 2-flavor QCD

    Science.gov (United States)

    Engel, G.; Lang, C. B.; Limmer, M.; Mohler, D.; Schafer, A.

    Results of hadron spectroscopy with two dynamical mass-degenerate chirally improved quarks are presented. Three ensembles with pion masses of 322(5), 470(4) and 525(7) MeV, lattices of size 16^3 \\times 32, and lattice spacings close to 0.15 fm are investigated. We discuss the possible appearance of scattering states, considering masses and eigenvectors. Partially quenched results in the scalar channel suggest the presence of a 2-particle state, however, in most channels we cannot identify them. Where available, we compare to results from quenched simulations using the same action.

  20. The Lanczos method in lattice gauge theories

    International Nuclear Information System (INIS)

    Barbour, I.M.; Behilil, N.E.; Gibbs, P.E.; Teper, M.; Schierholz, G.

    1984-09-01

    We present a modified version of the Lanczos algorithm as a computational method for tridiagonalising large sparse matrices, which avoids the requirement for large amounts of storage space. It can be applied as a first step in calculating eigenvalues and eigenvectors or for obtaining the inverse of a matrix row by row. Here we describe the method and apply it to various problems in lattice gauge theories. We have found it to have excellent convergence properties. In particular it enables us to do lattice calculations at small and even zero quark mass. (orig.)

  1. On the use and computation of the Jordan canonical form in system theory

    Science.gov (United States)

    Sridhar, B.; Jordan, D.

    1974-01-01

    This paper investigates various aspects of the application of the Jordan canonical form of a matrix in system theory and develops a computational approach to determining the Jordan form for a given matrix. Applications include pole placement, controllability and observability studies, serving as an intermediate step in yielding other canonical forms, and theorem proving. The computational method developed in this paper is both simple and efficient. The method is based on the definition of a generalized eigenvector and a natural extension of Gauss elimination techniques. Examples are included for demonstration purposes.

  2. JINR rapid communications

    International Nuclear Information System (INIS)

    1999-01-01

    The present collection of rapid communications from JINR, Dubna, contains seven separate records on additional conditions on eigenvectors in solving inverse problem for two-dimensional Schroedinger equation, on an absolute calibration of deuteron beam polarization at LHE, determination of the vector component of the polarization of the JINR synchrophasotron deuteron beam, wavelet-analysis: criterion of reliable signal selection, on asymptotics in inclusive production of antinuclei and nuclear fragments, use of neutron activation analysis at the IBR-2 reactor for atmospheric monitoring and impulse method for temperature measurement of silicon detectors

  3. Two often disregarded aspects of Foucault's pendulum

    International Nuclear Information System (INIS)

    Pérez, José-Philippe; Pujol, Olivier

    2015-01-01

    This paper revisits the famous Foucault's pendulum by highlighting two often-disregarded aspects in mechanics courses. The first one concerns the existence of a local accelerated reference frame to express the law of dynamics without the Coriolis force. The second aspect deals with the geometrical phase that appears in pendulum dynamics. This last point, which could appear banal, should be related to analogous consideration in quantum physics. It is also linked to vectorial parallel transport of the pendulum angular momentum eigenvector. Numerical simulations with MATLAB are proposed. (paper)

  4. Numerical transfer-matrix study of a model with competing metastable states

    DEFF Research Database (Denmark)

    Fiig, T.; Gorman, B.M.; Rikvold, P.A.

    1994-01-01

    transition. A recently developed transfer-matrix formalism is applied to the model to obtain complex-valued ''constrained'' free-energy densities f(alpha). For particular eigenvectors of the transfer matrix, the f(alpha) exhibit finite-rangescaling behavior in agreement with the analytically continued...... 'metastable free-energy density This transfer-matrix approach gives a free-energy cost of nucleation that supports the proportionality relation for the decay rate of the metastable phase T proportional to\\Imf alpha\\, even in cases where two metastable states compete. The picture that emerges from this study...

  5. Matrix-exponential description of radiative transfer

    International Nuclear Information System (INIS)

    Waterman, P.C.

    1981-01-01

    By appling the matrix-exponential operator technique to the radiative-transfer equation in discrete form, new analytical solutions are obtained for the transmission and reflection matrices in the limiting cases x >1, where x is the optical depth of the layer. Orthongonality of the eigenvectors of the matrix exponential apparently yields new conditions for determining. Chandrasekhar's characteristic roots. The exact law of reflection for the discrete eigenfunctions is also obtained. Finally, when used in conjuction with the doubling method, the matrix exponential should result in reduction in both computation time and loss of precision

  6. Highly indefinite multigrid for eigenvalue problems

    Energy Technology Data Exchange (ETDEWEB)

    Borges, L.; Oliveira, S.

    1996-12-31

    Eigenvalue problems are extremely important in understanding dynamic processes such as vibrations and control systems. Large scale eigenvalue problems can be very difficult to solve, especially if a large number of eigenvalues and the corresponding eigenvectors need to be computed. For solving this problem a multigrid preconditioned algorithm is presented in {open_quotes}The Davidson Algorithm, preconditioning and misconvergence{close_quotes}. Another approach for solving eigenvalue problems is by developing efficient solutions for highly indefinite problems. In this paper we concentrate on the use of new highly indefinite multigrid algorithms for the eigenvalue problem.

  7. Multigroup neutron transport equation in the diffusion and P{sub 1} approximation

    Energy Technology Data Exchange (ETDEWEB)

    Obradovic, D [Boris Kidric Institute of nuclear sciences Vinca, Belgrade (Yugoslavia)

    1970-07-01

    Investigations of the properties of the multigroup transport operator, width and without delayed neutrons in the diffusion and P{sub 1} approximation, is performed using Keldis's theory of operator families as well as a technique . recently used for investigations into the properties of the general linearized Boltzmann operator. It is shown that in the case without delayed neutrons, multigroup transport operator in the diffusion and P{sub 1} approximation possesses a complete set of generalized eigenvectors. A formal solution to the initial value problem is also given. (author)

  8. Natural habitats matter: Determinants of spatial pattern in the composition of animal assemblages of the Czech Republic

    Czech Academy of Sciences Publication Activity Database

    Divíšek, Jan; Zelený, D.; Culek, M.; Šťastný, K.

    2014-01-01

    Roč. 59, August 2014 (2014), s. 7-17 ISSN 1146-609X Institutional support: RVO:68145535 Keywords : animal assemblages * habitat mapping * spatial autocorrelation * CORINE Land Cover * Moran's eigenvector maps Subject RIV: DE - Earth Magnetism, Geodesy, Geography Impact factor: 1.617, year: 2014 http://ac.els-cdn.com/S1146609X14000617/1-s2.0-S1146609X14000617-main.pdf?_tid=209d34aa-3809-11e4-832a-00000aab0f01&acdnat=1410257438_9d3ff4b5ec62fd44054f111493753231

  9. Application of covariance clouds for estimating the anisotropy ellipsoid eigenvectors, with case study in uranium deposit

    International Nuclear Information System (INIS)

    Jamali Esfahlan, D.; Madani, H.; Tahmaseb Nazemi, M. T.; Mahdavi, F.; Ghaderi, M. R.; Najafi, M.

    2010-01-01

    Various methods of Kriging and nonlinear geostatistical methods considered as acceptable methods for resource and reserve estimations have characters such as the least estimation variance in their nature, and accurate results in the acceptable confidence levels range could be achieved if the required parameters for the estimation are determined accurately. If the determined parameters don't have the sufficient accuracy, 3-D geostatistical estimations will not be reliable any more, and by this, all the quantitative parameters of the mineral deposit (e.g. grade-tonnage variations) will be misinterpreted. One of the most significant parameters for 3-D geostatistical estimation is the anisotropy ellipsoid. The anisotropy ellipsoid is important for geostatistical estimations because it determines the samples in different directions required for accomplishing the estimation. The aim of this paper is to illustrate a more simple and time preserving analytical method that can apply geophysical or geochemical analysis data from the core-length of boreholes for modeling the anisotropy ellipsoid. By this method which is based on the distribution of covariance clouds in a 3-D sampling space of a deposit, quantities, ratios, azimuth and plunge of the major-axis, semi-major axis and the minor-axis determine the ore-grade continuity within the deposit and finally the anisotropy ellipsoid of the deposit will be constructed. A case study of an uranium deposit is also analytically discussed for illustrating the application of this method.

  10. Computing Principal Eigenvectors of Large Web Graphs: Algorithms and Accelerations Related to PageRank and HITS

    Science.gov (United States)

    Nagasinghe, Iranga

    2010-01-01

    This thesis investigates and develops a few acceleration techniques for the search engine algorithms used in PageRank and HITS computations. PageRank and HITS methods are two highly successful applications of modern Linear Algebra in computer science and engineering. They constitute the essential technologies accounted for the immense growth and…

  11. Numerical tests of evolution systems, gauge conditions, and boundary conditions for 1D colliding gravitational plane waves

    International Nuclear Information System (INIS)

    Bardeen, J.M.; Buchman, L.T.

    2002-01-01

    We investigate how the accuracy and stability of numerical relativity simulations of 1D colliding plane waves depends on choices of equation formulations, gauge conditions, boundary conditions, and numerical methods, all in the context of a first-order 3+1 approach to the Einstein equations, with basic variables some combination of first derivatives of the spatial metric and components of the extrinsic curvature tensor. Hyperbolic schemes, specifically variations on schemes proposed by Bona and Masso and Anderson and York, are compared with variations of the Arnowitt-Deser-Misner formulation. Modifications of the three basic schemes include raising one index in the metric derivative and extrinsic curvature variables and adding a multiple of the energy constraint to the extrinsic curvature evolution equations. Redundant variables in the Bona-Masso formulation may be reset frequently or allowed to evolve freely. Gauge conditions which simplify the dynamical structure of the system are imposed during each time step, but the lapse and shift are reset periodically to control the evolution of the spacetime slicing and the longitudinal part of the metric. We show that physically correct boundary conditions, satisfying the energy and momentum constraint equations, generically require the presence of some ingoing eigenmodes of the characteristic matrix. Numerical methods are developed for the hyperbolic systems based on decomposing flux differences into linear combinations of eigenvectors of the characteristic matrix. These methods are shown to be second-order accurate, and in practice second-order convergent, for smooth solutions, even when the eigenvectors and eigenvalues of the characteristic matrix are spatially varying

  12. Detecting mammographically occult cancer in women with dense breasts using Radon Cumulative Distribution Transform: a preliminary analysis

    Science.gov (United States)

    Lee, Juhun; Nishikawa, Robert M.; Rohde, Gustavo K.

    2018-02-01

    We propose using novel imaging biomarkers for detecting mammographically-occult (MO) cancer in women with dense breast tissue. MO cancer indicates visually occluded, or very subtle, cancer that radiologists fail to recognize as a sign of cancer. We used the Radon Cumulative Distribution Transform (RCDT) as a novel image transformation to project the difference between left and right mammograms into a space, increasing the detectability of occult cancer. We used a dataset of 617 screening full-field digital mammograms (FFDMs) of 238 women with dense breast tissue. Among 238 women, 173 were normal with 2 - 4 consecutive screening mammograms, 552 normal mammograms in total, and the remaining 65 women had an MO cancer with a negative screening mammogram. We used Principal Component Analysis (PCA) to find representative patterns in normal mammograms in the RCDT space. We projected all mammograms to the space constructed by the first 30 eigenvectors of the RCDT of normal cases. Under 10-fold crossvalidation, we conducted quantitative feature analysis to classify normal mammograms and mammograms with MO cancer. We used receiver operating characteristic (ROC) analysis to evaluate the classifier's output using the area under the ROC curve (AUC) as the figure of merit. Four eigenvectors were selected via a feature selection method. The mean and standard deviation of the AUC of the trained classifier on the test set were 0.74 and 0.08, respectively. In conclusion, we utilized imaging biomarkers to highlight differences between left and right mammograms to detect MO cancer using novel imaging transformation.

  13. Recursive structures in the multispecies TASEP

    International Nuclear Information System (INIS)

    Arita, Chikashi; Ayyer, Arvind; Mallick, Kirone; Prolhac, Sylvain

    2011-01-01

    We consider a multispecies generalization of the totally asymmetric simple exclusion process (TASEP) with the simple hopping rule: for the α and βth-class particles (α < β), the transition αβ → βα occurs with a rate independent from the values α and β. Ferrari and Martin (2007 Ann. Prob. 35 807) obtained the stationary state of this model thanks to a combinatorial algorithm, which was subsequently interpreted as a matrix product representation by Evans et al (2009 J. Stat. Phys. 135 217). This 'matrix ansatz' shows that the stationary state of the multispecies TASEP with N classes of particles (N-TASEP) can be constructed algebraically by the action of an operator on the (N - 1)-TASEP stationary state. Besides, Arita et al (2009 J. Phys. A. Math Theor. 45 345002) analyzed the spectral structure of the Markov matrix: they showed that the set of eigenvalues of the N-TASEP contains those of the (N - 1)-TASEP and that the various spectral inclusions can be encoded in a hierarchical set-theoretic structure known as the Hasse diagram. Inspired by these works, we define nontrivial operators that allow us to construct eigenvectors of the N-TASEP by lifting the eigenvectors of the (N - 1)-TASEP. This goal is achieved by generalizing the matrix product representation and the Ferrari-Martin algorithm. In particular, we show that the matrix ansatz is not only a convenient tool to write the stationary state but in fact intertwines Markov matrices of different values of N.

  14. Eigenspaces of networks reveal the overlapping and hierarchical community structure more precisely

    International Nuclear Information System (INIS)

    Ma, Xiaoke; Gao, Lin; Yong, Xuerong

    2010-01-01

    Identifying community structure is fundamental for revealing the structure–functionality relationship in complex networks, and spectral algorithms have been shown to be powerful for this purpose. In a traditional spectral algorithm, each vertex of a network is embedded into a spectral space by making use of the eigenvectors of the adjacency matrix or Laplacian matrix of the graph. In this paper, a novel spectral approach for revealing the overlapping and hierarchical community structure of complex networks is proposed by not only using the eigenvalues and eigenvectors but also the properties of eigenspaces of the networks involved. This gives us a better characterization of community. We first show that the communicability between a pair of vertices can be rewritten in term of eigenspaces of a network. An agglomerative clustering algorithm is then presented to discover the hierarchical communities using the communicability matrix. Finally, these overlapping vertices are discovered with the corresponding eigenspaces, based on the fact that the vertices more densely connected amongst one another are more likely to be linked through short cycles. Compared with the traditional spectral algorithms, our algorithm can identify both the overlapping and hierarchical community without increasing the time complexity O(n 3 ), where n is the size of the network. Furthermore, our algorithm can also distinguish the overlapping vertices from bridges. The method is tested by applying it to some computer-generated and real-world networks. The experimental results indicate that our algorithm can reveal community structure more precisely than the traditional spectral approaches

  15. The Phylogeny of Quasars and the Ontogeny of Their Central Black Holes

    Energy Technology Data Exchange (ETDEWEB)

    Fraix-Burnet, Didier [University Grenoble Alpes, CNRS, IPAG, Grenoble (France); Marziani, Paola [INAF, Osservatorio Astronomico di Padova, Padova (Italy); D' Onofrio, Mauro [Dipartimento di Fisica and Astronomia, Università di Padova, Padova (Italy); Dultzin, Deborah, E-mail: didier.fraix-burnet@univ-grenoble-alpes.fr [Instituto de Astronomía, UNAM, Mexico City (Mexico)

    2017-02-27

    The connection between multifrequency quasar observational and physical parameters related to accretion processes is still open to debate. In the last 20 year, Eigenvector 1-based approaches developed since the early papers by Boroson and Green (1992) and Sulentic et al. (2000b) have been proven to be a remarkably powerful tool to investigate this issue, and have led to the definition of a quasar “main sequence.” In this paper we perform a cladistic analysis on two samples of 215 and 85 low-z quasars (z ≲ 0.7) which were studied in several previous works and which offer a satisfactory coverage of the Eigenvector 1-derived main sequence. The data encompass accurate measurements of observational parameters which represent key aspects associated with the structural diversity of quasars. Cladistics is able to group sources radiating at higher Eddington ratios, as well as to separate radio-quiet (RQ) and radio-loud (RL) quasars. The analysis suggests a black hole mass threshold for powerful radio emission and also properly distinguishes core-dominated and lobe-dominated quasars, in accordance with the basic tenet of RL unification schemes. Considering that black hole mass provides a sort of “arrow of time” of nuclear activity, a phylogenetic interpretation becomes possible if cladistic trees are rooted on black hole mass: the ontogeny of black holes is represented by their monotonic increase in mass. More massive radio-quiet Population B sources at low-z become a more evolved counterpart of Population A i.e., wind dominated sources to which the “local” Narrow-Line Seyfert 1s belong.

  16. Analysis the Human and Environmental Consequences of Power Pplants Using Combined Delphi and AHP Method

    International Nuclear Information System (INIS)

    Jozi, S. A.; Saffarian, Sh.; Shafiee, M.; Akbari, A.

    2016-01-01

    Power plants, due to the nature of their processes and activities and also by producing the effluents, emitting the air pollutants and hazardous wastes, have the potential to cause negative human and environmental consequences. Given the importance of the issue, for determining the most important consequences of Abadan Gas Power Plant and also their impact on the human and natural environment, as a case study, a questionnaire was developed with Delphi method. This questionnaire was distributed within the environmentalists and experts of power plant. The human and environmental consequences of Power Plant were analyzed by Multiple Criteria Decision-Making methods including AHP and eigenvector technique. For this purpose, with applying of AHP method, the hierarchical structure of the human and environmental consequences of Abadan Gas Power Plant was constructed and then the decision making matrix was formed. The pair wise matrices were formed separately for criteria pair wise comparisons with respect to severity and occurrence probability of indoor and outdoor environment of power plant .With entering the data in EXPERT CHOICE software, criteria weights were computed with applying the eigenvector method. Then the final weights of consequences in terms of severity and occurrence probability of risk were computed. The results from the compution of Abadan Gas Power Plant consequences indicate that in human consequences, shallow wounds with a .105 weight and in environmental consequences, air pollution by weighing 0.66 are the most important consequences of power plant. Finally, the most important executable strategies and actions for mitigation of negative human and environmental consequences were presented.

  17. Estimation of the false discovery proportion with unknown dependence.

    Science.gov (United States)

    Fan, Jianqing; Han, Xu

    2017-09-01

    Large-scale multiple testing with correlated test statistics arises frequently in many scientific research. Incorporating correlation information in approximating false discovery proportion has attracted increasing attention in recent years. When the covariance matrix of test statistics is known, Fan, Han & Gu (2012) provided an accurate approximation of False Discovery Proportion (FDP) under arbitrary dependence structure and some sparsity assumption. However, the covariance matrix is often unknown in many applications and such dependence information has to be estimated before approximating FDP. The estimation accuracy can greatly affect FDP approximation. In the current paper, we aim to theoretically study the impact of unknown dependence on the testing procedure and establish a general framework such that FDP can be well approximated. The impacts of unknown dependence on approximating FDP are in the following two major aspects: through estimating eigenvalues/eigenvectors and through estimating marginal variances. To address the challenges in these two aspects, we firstly develop general requirements on estimates of eigenvalues and eigenvectors for a good approximation of FDP. We then give conditions on the structures of covariance matrices that satisfy such requirements. Such dependence structures include banded/sparse covariance matrices and (conditional) sparse precision matrices. Within this framework, we also consider a special example to illustrate our method where data are sampled from an approximate factor model, which encompasses most practical situations. We provide a good approximation of FDP via exploiting this specific dependence structure. The results are further generalized to the situation where the multivariate normality assumption is relaxed. Our results are demonstrated by simulation studies and some real data applications.

  18. Cucheb: A GPU implementation of the filtered Lanczos procedure

    Science.gov (United States)

    Aurentz, Jared L.; Kalantzis, Vassilis; Saad, Yousef

    2017-11-01

    This paper describes the software package Cucheb, a GPU implementation of the filtered Lanczos procedure for the solution of large sparse symmetric eigenvalue problems. The filtered Lanczos procedure uses a carefully chosen polynomial spectral transformation to accelerate convergence of the Lanczos method when computing eigenvalues within a desired interval. This method has proven particularly effective for eigenvalue problems that arise in electronic structure calculations and density functional theory. We compare our implementation against an equivalent CPU implementation and show that using the GPU can reduce the computation time by more than a factor of 10. Program Summary Program title: Cucheb Program Files doi:http://dx.doi.org/10.17632/rjr9tzchmh.1 Licensing provisions: MIT Programming language: CUDA C/C++ Nature of problem: Electronic structure calculations require the computation of all eigenvalue-eigenvector pairs of a symmetric matrix that lie inside a user-defined real interval. Solution method: To compute all the eigenvalues within a given interval a polynomial spectral transformation is constructed that maps the desired eigenvalues of the original matrix to the exterior of the spectrum of the transformed matrix. The Lanczos method is then used to compute the desired eigenvectors of the transformed matrix, which are then used to recover the desired eigenvalues of the original matrix. The bulk of the operations are executed in parallel using a graphics processing unit (GPU). Runtime: Variable, depending on the number of eigenvalues sought and the size and sparsity of the matrix. Additional comments: Cucheb is compatible with CUDA Toolkit v7.0 or greater.

  19. Recursive structures in the multispecies TASEP

    Energy Technology Data Exchange (ETDEWEB)

    Arita, Chikashi [Faculty of Mathematics, Kyushu University, Fukuoka 819-0395 (Japan); Ayyer, Arvind [University of California Davis, One Shields Avenue Davis, CA 95616 (United States); Mallick, Kirone [Institut de Physique Theorique CEA, F-91191 Gif-sur-Yvette (France); Prolhac, Sylvain, E-mail: arita@math.kyushu-u.ac.jp, E-mail: ayyer@math.ucdavis.edu, E-mail: kirone.mallick@cea.fr, E-mail: prolhac@ma.tum.de [Zentrum Mathematik, Technische Universitaet Muenchen (Germany)

    2011-08-19

    We consider a multispecies generalization of the totally asymmetric simple exclusion process (TASEP) with the simple hopping rule: for the {alpha} and {beta}th-class particles ({alpha} < {beta}), the transition {alpha}{beta} {yields} {beta}{alpha} occurs with a rate independent from the values {alpha} and {beta}. Ferrari and Martin (2007 Ann. Prob. 35 807) obtained the stationary state of this model thanks to a combinatorial algorithm, which was subsequently interpreted as a matrix product representation by Evans et al (2009 J. Stat. Phys. 135 217). This 'matrix ansatz' shows that the stationary state of the multispecies TASEP with N classes of particles (N-TASEP) can be constructed algebraically by the action of an operator on the (N - 1)-TASEP stationary state. Besides, Arita et al (2009 J. Phys. A. Math Theor. 45 345002) analyzed the spectral structure of the Markov matrix: they showed that the set of eigenvalues of the N-TASEP contains those of the (N - 1)-TASEP and that the various spectral inclusions can be encoded in a hierarchical set-theoretic structure known as the Hasse diagram. Inspired by these works, we define nontrivial operators that allow us to construct eigenvectors of the N-TASEP by lifting the eigenvectors of the (N - 1)-TASEP. This goal is achieved by generalizing the matrix product representation and the Ferrari-Martin algorithm. In particular, we show that the matrix ansatz is not only a convenient tool to write the stationary state but in fact intertwines Markov matrices of different values of N.

  20. Breeding description for fast reactors and symbiotic reactor systems

    International Nuclear Information System (INIS)

    Hanan, N.A.

    1979-01-01

    A mathematical model was developed to provide a breeding description for fast reactors and symbiotic reactor systems by means of figures of merit type quantities. The model was used to investigate the effect of several parameters and different fuel usage strategies on the figures of merit which provide the breeding description. The integrated fuel cycle model for a single-reactor is reviewed. The excess discharge is automatically used to fuel identical reactors. The resulting model describes the accumulation of fuel in a system of identical reactors. Finite burnup and out-of-pile delays and losses are treated in the model. The model is then extended from fast breeder park to symbiotic reactor systems. The asymptotic behavior of the fuel accumulation is analyzed. The asymptotic growth rate appears as the largest eigenvalue in the solution of the characteristic equations of the time dependent differential balance equations for the system. The eigenvector corresponding to the growth rate is the core equilibrium composition. The analogy of the long-term fuel cycle equations, in the framework of this model, and the neutron balance equations is explored. An eigenvalue problem adjoint to the one generated by the characteristic equations of the system is defined. The eigenvector corresponding to the largest eigenvalue, i.e. to the growth rate, represents the ''isotopic breeding worths.'' Analogously to the neutron adjoint flux it is shown that the isotopic breeding worths represent the importance of an isotope for breeding, i.e. for the growth rate of a system

  1. The phylogeny of quasars and the ontogeny of their central black holes

    Science.gov (United States)

    Fraix-Burnet, Didier; Marziani, Paola; D'Onofrio, Mauro; Dultzin, Deborah

    2017-02-01

    The connection between multifrequency quasar observational and physical parameters related to accretion processes is still open to debate. In the last 20 year, Eigenvector 1-based approaches developed since the early papers by Boroson and Green (1992) and Sulentic et al. (2000b) have been proved to be a remarkably powerful tool to investigate this issue, and have led to the definition of a quasar "main sequence". In this paper we perform a cladistic analysis on two samples of 215 and 85 low-z quasars (z ~ 0.7) which were studied in several previous works and which offer a satisfactory coverage of the Eigenvector 1-derived main sequence. The data encompass accurate measurements of observational parameters which represents key aspects associated with the structural diversity of quasars. Cladistics is able to group sources radiating at higher Eddington ratios, as well as to separate radio-quiet (RQ) and radio-loud (RL) quasars. The analysis suggests a black hole mass threshold for powerful radio emission and also properly distinguishes core-dominated and lobe-dominated quasars, in accordance with the basic tenet of RL unification schemes. Considering that black hole mass provides a sort of "arrow of time" of nuclear activity, a phylogenetic interpretation becomes possible if cladistic trees are rooted on black hole mass: the ontogeny of black holes is represented by their monotonic increase in mass. More massive radio-quiet Population B sources at low-z become a more evolved counterpart of Population A i.e., wind dominated sources to which the "local" Narrow-Line Seyfert 1s belong.

  2. The Phylogeny of Quasars and the Ontogeny of Their Central Black Holes

    International Nuclear Information System (INIS)

    Fraix-Burnet, Didier; Marziani, Paola; D'Onofrio, Mauro; Dultzin, Deborah

    2017-01-01

    The connection between multifrequency quasar observational and physical parameters related to accretion processes is still open to debate. In the last 20 year, Eigenvector 1-based approaches developed since the early papers by Boroson and Green (1992) and Sulentic et al. (2000b) have been proven to be a remarkably powerful tool to investigate this issue, and have led to the definition of a quasar “main sequence.” In this paper we perform a cladistic analysis on two samples of 215 and 85 low-z quasars (z ≲ 0.7) which were studied in several previous works and which offer a satisfactory coverage of the Eigenvector 1-derived main sequence. The data encompass accurate measurements of observational parameters which represent key aspects associated with the structural diversity of quasars. Cladistics is able to group sources radiating at higher Eddington ratios, as well as to separate radio-quiet (RQ) and radio-loud (RL) quasars. The analysis suggests a black hole mass threshold for powerful radio emission and also properly distinguishes core-dominated and lobe-dominated quasars, in accordance with the basic tenet of RL unification schemes. Considering that black hole mass provides a sort of “arrow of time” of nuclear activity, a phylogenetic interpretation becomes possible if cladistic trees are rooted on black hole mass: the ontogeny of black holes is represented by their monotonic increase in mass. More massive radio-quiet Population B sources at low-z become a more evolved counterpart of Population A i.e., wind dominated sources to which the “local” Narrow-Line Seyfert 1s belong.

  3. Dynamic evolution of cross-correlations in the Chinese stock market.

    Directory of Open Access Journals (Sweden)

    Fei Ren

    Full Text Available The analysis of cross-correlations is extensively applied for the understanding of interconnections in stock markets and the portfolio risk estimation. Current studies of correlations in Chinese market mainly focus on the static correlations between return series, and this calls for an urgent need to investigate their dynamic correlations. Our study aims to reveal the dynamic evolution of cross-correlations in the Chinese stock market, and offer an exact interpretation for the evolution behavior. The correlation matrices constructed from the return series of 367 A-share stocks traded on the Shanghai Stock Exchange from January 4, 1999 to December 30, 2011 are calculated over a moving window with a size of 400 days. The evolutions of the statistical properties of the correlation coefficients, eigenvalues, and eigenvectors of the correlation matrices are carefully analyzed. We find that the stock correlations are significantly increased in the periods of two market crashes in 2001 and 2008, during which only five eigenvalues significantly deviate from the random correlation matrix, and the systemic risk is higher in these volatile periods than calm periods. By investigating the significant contributors of the deviating eigenvectors in different time periods, we observe a dynamic evolution behavior in business sectors such as IT, electronics, and real estate, which lead the rise (drop before (after the crashes. Our results provide new perspectives for the understanding of the dynamic evolution of cross-correlations in the Chines stock markets, and the result of risk estimation is valuable for the application of risk management.

  4. Dynamic evolution of cross-correlations in the Chinese stock market.

    Science.gov (United States)

    Ren, Fei; Zhou, Wei-Xing

    2014-01-01

    The analysis of cross-correlations is extensively applied for the understanding of interconnections in stock markets and the portfolio risk estimation. Current studies of correlations in Chinese market mainly focus on the static correlations between return series, and this calls for an urgent need to investigate their dynamic correlations. Our study aims to reveal the dynamic evolution of cross-correlations in the Chinese stock market, and offer an exact interpretation for the evolution behavior. The correlation matrices constructed from the return series of 367 A-share stocks traded on the Shanghai Stock Exchange from January 4, 1999 to December 30, 2011 are calculated over a moving window with a size of 400 days. The evolutions of the statistical properties of the correlation coefficients, eigenvalues, and eigenvectors of the correlation matrices are carefully analyzed. We find that the stock correlations are significantly increased in the periods of two market crashes in 2001 and 2008, during which only five eigenvalues significantly deviate from the random correlation matrix, and the systemic risk is higher in these volatile periods than calm periods. By investigating the significant contributors of the deviating eigenvectors in different time periods, we observe a dynamic evolution behavior in business sectors such as IT, electronics, and real estate, which lead the rise (drop) before (after) the crashes. Our results provide new perspectives for the understanding of the dynamic evolution of cross-correlations in the Chines stock markets, and the result of risk estimation is valuable for the application of risk management.

  5. Google matrix analysis of C.elegans neural network

    Energy Technology Data Exchange (ETDEWEB)

    Kandiah, V., E-mail: kandiah@irsamc.ups-tlse.fr; Shepelyansky, D.L., E-mail: dima@irsamc.ups-tlse.fr

    2014-05-01

    We study the structural properties of the neural network of the C.elegans (worm) from a directed graph point of view. The Google matrix analysis is used to characterize the neuron connectivity structure and node classifications are discussed and compared with physiological properties of the cells. Our results are obtained by a proper definition of neural directed network and subsequent eigenvector analysis which recovers some results of previous studies. Our analysis highlights particular sets of important neurons constituting the core of the neural system. The applications of PageRank, CheiRank and ImpactRank to characterization of interdependency of neurons are discussed.

  6. Google matrix and Ulam networks of intermittency maps.

    Science.gov (United States)

    Ermann, L; Shepelyansky, D L

    2010-03-01

    We study the properties of the Google matrix of an Ulam network generated by intermittency maps. This network is created by the Ulam method which gives a matrix approximant for the Perron-Frobenius operator of dynamical map. The spectral properties of eigenvalues and eigenvectors of this matrix are analyzed. We show that the PageRank of the system is characterized by a power law decay with the exponent beta dependent on map parameters and the Google damping factor alpha . Under certain conditions the PageRank is completely delocalized so that the Google search in such a situation becomes inefficient.

  7. Acoustic and elastic properties of Sn{sub 2}P{sub 2}S{sub 6} crystals

    Energy Technology Data Exchange (ETDEWEB)

    Mys, O; Martynyuk-Lototska, I; Vlokh, R [Institute of Physical Optics of the Ministry of Education and Science of Ukraine, 23 Dragomanov Street, 79005 Lviv (Ukraine); Grabar, A [Istitute for Solid State Physics and Chemistry, Uzhgorod National University, 54 Voloshyn Street, 88000 Uzhgorod (Ukraine)], E-mail: vlokh@ifo.lviv.ua

    2009-07-01

    We present the results concerned with acoustic and elastic properties of Sn{sub 2}P{sub 2}S{sub 6} crystals. The complete matrices of elastic stiffness and compliance coefficients are determined in both the crystallographic coordinate system and the system associated with eigenvectors of the elastic stiffness tensor. The acoustic slowness surfaces are constructed and the propagation and polarization directions of the slowest acoustic waves promising for acousto-optic interactions are determined on this basis. The acoustic obliquity angle and the deviation of polarization of the acoustic waves from purely transverse or longitudinal states are quantitatively analysed.

  8. SLOWNESS SURFACE CALCULATION FOR DIFFERENT MEDIA USING THE SYMBOLIC MATHEMATICS LANGUAGE MAPLE®

    Directory of Open Access Journals (Sweden)

    Piedrahita Carlos

    2004-06-01

    Full Text Available Starting from the equation in different media, we obtain the different type of waves that can exists in such media. The evaluation of the eigenvalues and eigenvectors let us construct the slowness surfaces. In general complex calculations case have to be made. In this work, routines were implemented in the symbolic language MAPLE® and the slowness surfaces were plotted. This work is relevant for the modelling of equivalent media that simulates natural fractured reservoirs, like those common in the Colombian foothills. It is important to understand the seismic response of this reservoirs for exploration of this areas.

  9. Manual for JSSL (JAERI Scientific Subroutine Library)

    International Nuclear Information System (INIS)

    Fujimura, Toichiro; Tsutsui, Tsuneo

    1991-09-01

    JSSL (JAERI Scientific Subroutine Library) is a library of scientific subroutines developed or modified in JAERI. They are classified into sixteen fields (Special Functions, Linear Problems, Eigenvalue and Eigenvector Problems, Non Linear Problems, Mathematical Programming, Extreme Value Problems, Transformations, Functional Approximation Methods, Numerical Differential and Integral Methods, Numerical Differential and Integral Equations, Statistical Functions, Physical Problems, I/O Routines, Plotter Routines, Computer System Functions and Others). This report is the user manual for the revised version of JSSL which involves evaluated subroutines selected from the previous compilation of JSSL, applied in almost all the fields. (author)

  10. Anti-correlation and subsector structure in financial systems

    Science.gov (United States)

    Jiang, X. F.; Zheng, B.

    2012-02-01

    With the random matrix theory, we study the spatial structure of the Chinese stock market, the American stock market and global market indices. After taking into account the signs of the components in the eigenvectors of the cross-correlation matrix, we detect the subsector structure of the financial systems. The positive and negative subsectors are anti-correlated with respect to each other in the corresponding eigenmode. The subsector structure is strong in the Chinese stock market, while somewhat weaker in the American stock market and global market indices. Characteristics of the subsector structures in different markets are revealed.

  11. Graph-drawing algorithms geometries versus molecular mechanics in fullereness

    Science.gov (United States)

    Kaufman, M.; Pisanski, T.; Lukman, D.; Borštnik, B.; Graovac, A.

    1996-09-01

    The algorithms of Kamada-Kawai (KK) and Fruchterman-Reingold (FR) have been recently generalized (Pisanski et al., Croat. Chem. Acta 68 (1995) 283) in order to draw molecular graphs in three-dimensional space. The quality of KK and FR geometries is studied here by comparing them with the molecular mechanics (MM) and the adjacency matrix eigenvectors (AME) algorithm geometries. In order to compare different layouts of the same molecule, an appropriate method has been developed. Its application to a series of experimentally detected fullerenes indicates that the KK, FR and AME algorithms are able to reproduce plausible molecular geometries.

  12. Quantum algorithms for topological and geometric analysis of data

    Science.gov (United States)

    Lloyd, Seth; Garnerone, Silvano; Zanardi, Paolo

    2016-01-01

    Extracting useful information from large data sets can be a daunting task. Topological methods for analysing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifying topological features and for determining how such features persist as the data is viewed at different scales. Here we present quantum machine learning algorithms for calculating Betti numbers—the numbers of connected components, holes and voids—in persistent homology, and for finding eigenvectors and eigenvalues of the combinatorial Laplacian. The algorithms provide an exponential speed-up over the best currently known classical algorithms for topological data analysis. PMID:26806491

  13. On characteristic polynomials for a generalized chiral random matrix ensemble with a source

    Science.gov (United States)

    Fyodorov, Yan V.; Grela, Jacek; Strahov, Eugene

    2018-04-01

    We evaluate averages involving characteristic polynomials, inverse characteristic polynomials and ratios of characteristic polynomials for a N× N random matrix taken from a L-deformed chiral Gaussian Unitary Ensemble with an external source Ω. Relation to a recently studied statistics of bi-orthogonal eigenvectors in the complex Ginibre ensemble, see Fyodorov (2017 arXiv:1710.04699), is briefly discussed as a motivation to study asymptotics of these objects in the case of external source proportional to the identity matrix. In particular, for an associated complex bulk/chiral edge scaling regime we retrieve the kernel related to Bessel/Macdonald functions.

  14. Tensor Decompositions for Learning Latent Variable Models

    Science.gov (United States)

    2012-12-08

    and eigenvectors of tensors is generally significantly more complicated than their matrix counterpart (both algebraically [Qi05, CS11, Lim05] and...The reduction First, let W ∈ Rd×k be a linear transformation such that M2(W,W ) = W M2W = I where I is the k × k identity matrix (i.e., W whitens ...approximate the whitening matrix W ∈ Rd×k from second-moment matrix M2 ∈ Rd×d. To do this, one first multiplies M2 by a random matrix R ∈ Rd×k′ for some k′ ≥ k

  15. A General Algorithm for Reusing Krylov Subspace Information. I. Unsteady Navier-Stokes

    Science.gov (United States)

    Carpenter, Mark H.; Vuik, C.; Lucas, Peter; vanGijzen, Martin; Bijl, Hester

    2010-01-01

    A general algorithm is developed that reuses available information to accelerate the iterative convergence of linear systems with multiple right-hand sides A x = b (sup i), which are commonly encountered in steady or unsteady simulations of nonlinear equations. The algorithm is based on the classical GMRES algorithm with eigenvector enrichment but also includes a Galerkin projection preprocessing step and several novel Krylov subspace reuse strategies. The new approach is applied to a set of test problems, including an unsteady turbulent airfoil, and is shown in some cases to provide significant improvement in computational efficiency relative to baseline approaches.

  16. On middle cube graphs

    Directory of Open Access Journals (Sweden)

    C. Dalfo

    2015-10-01

    Full Text Available We study a family of graphs related to the $n$-cube. The middle cube graph of parameter k is the subgraph of $Q_{2k-1}$ induced by the set of vertices whose binary representation has either $k-1$ or $k$ number of ones. The middle cube graphs can be obtained from the well-known odd graphs by doubling their vertex set. Here we study some of the properties of the middle cube graphs in the light of the theory of distance-regular graphs. In particular, we completely determine their spectra (eigenvalues and their multiplicities, and associated eigenvectors.

  17. Calculating luminosity for a coupled Tevatron lattice

    International Nuclear Information System (INIS)

    Holt, J.A.; Martens, M.A.; Michelotti, L.; Goderre, G.

    1995-05-01

    The traditional formula for calculating luminosity assumes an uncoupled lattice and makes use of one-degree-of-freedom lattice functions, β H and β v , for relating transverse beam widths to emittances. Strong coupling requires changing this approach. It is simplest to employ directly the linear normal form coordinates of the one turn map. An equilibrium distribution in phase space is expressed as a function of the Jacobian's eigenvectors and beam size parameters or emittances. Using the equilibrium distributions an expression for the luminosity was derived and applied to the Tevatron lattice, which was coupled due to a quadrupole roll

  18. An accelerated conjugate gradient algorithm to compute low-lying eigenvalues - a study for the Dirac operator in SU(2) lattice QCD

    International Nuclear Information System (INIS)

    Kalkreuter, T.; Simma, H.

    1995-07-01

    The low-lying eigenvalues of a (sparse) hermitian matrix can be computed with controlled numerical errors by a conjugate gradient (CG) method. This CG algorithm is accelerated by alternating it with exact diagonalizations in the subspace spanned by the numerically computed eigenvectors. We study this combined algorithm in case of the Dirac operator with (dynamical) Wilson fermions in four-dimensional SU(2) gauge fields. The algorithm is numerically very stable and can be parallelized in an efficient way. On lattices of sizes 4 4 - 16 4 an acceleration of the pure CG method by a factor of 4 - 8 is found. (orig.)

  19. A digital feedback system for transverse orbit stabilization in the NSLS rings

    International Nuclear Information System (INIS)

    Friedman, A.; Bozoki, E.

    1993-01-01

    We are reporting on the design and preliminary results of a prototype digital feedback system for the storage rings at the NSLS. the system will use a nolinear eigenvector decomposition algorithm. It will have a wide dynamic range and will be able to correct noise in the orbit over a bandwidth in excess of 60 Hz. A Motorola-162 CPU board is used to sample the PUE's at a minimum rate of 200 Hz and an HP-742rt board is used to read the sampled signals and to generate a correction signal for the orbit correctors

  20. Incommensurate phase transitions

    Energy Technology Data Exchange (ETDEWEB)

    Currat, R [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)

    1996-11-01

    We review the characteristic aspects of modulated crystals from the point of view of inelastic neutron scattering. We discuss the phenomenological Landau theory of the normal-to-incommensurate displacive instability and its predictions concerning the fluctuation spectrum of the modulated phase. General results on the form of the normal-mode eigenvectors and on the inelastic scattering channels through which they couple to the probe are established using the superspace approach. We illustrate these results on a simple discrete model symmetry and we review available inelastic neutron scattering data on several displacively modulated compounds. (author) 21 figs., 73 refs.

  1. Fourier Transform Spectroscopy of Carbonyl Sulfide from 3700 to 4800 cm -1and Selection of a Line-Pointing Program

    Science.gov (United States)

    Naı̈m, S.; Fayt, A.; Bredohl, H.; Blavier, J.-F.; Dubois, I.

    1998-11-01

    We have measured the Fourier transform spectrum of natural OCS from 3700 to 4800 cm-1with a near Doppler resolution and a line-position accuracy between 4 and 8 × 10-5cm-1. For the normal isotopic species, 37 vibrational transitions have been analyzed for both frequencies and intensities. We also report 15 bands of OC34S, eight bands of O13CS, nine bands of OC33S, and two bands of18OCS. Important effective Herman-Wallis terms are explained on the basis of eigenvectors. A comparison of different line-pointing programs is also presented.

  2. Nested Bethe Ansatz for Spin Ladder Model with Open Boundary Conditions

    International Nuclear Information System (INIS)

    Wu Junfang; Zhang Chunmin; Yue Ruihong; Li Runling

    2005-01-01

    The nested Bethe ansatz (BA) method is applied to find the eigenvalues and the eigenvectors of the transfer matrix for spin-ladder model with open boundary conditions. Based on the reflection equation, we find the general diagonal solution, which determines the general boundary interaction in the Hamiltonian. We introduce the spin-ladder model with open boundary conditions. By finding the solution K ± of the reflection equation which determines the nontrivial boundary terms in the Hamiltonian, we diagonalize the transfer matrix of the spin-ladder model with open boundary conditions in the framework of nested BA.

  3. Characteristics of group networks in the KOSPI and the KOSDAQ

    Science.gov (United States)

    Kim, Kyungsik; Ko, Jeung-Su; Yi, Myunggi

    2012-02-01

    We investigate the main feature of group networks in the KOSPI and KOSDAQ of Korean financial markets and analyze daily cross-correlations between price fluctuations for the 5-year time period from 2006 to 2010. We discuss the stabilities by undressing the market-wide effect using the Markowitz multi-factor model and the network-based approach. In particular we ascertain the explicit list of significant firms in the few largest eigenvectors from the undressed correlation matrix. Finally, we show the structure of group correlation by applying a network-based approach. In addition, the relation between market capitalizations and businesses is examined.

  4. Correlation of financial markets in times of crisis

    Science.gov (United States)

    Sandoval, Leonidas; Franca, Italo De Paula

    2012-01-01

    Using the eigenvalues and eigenvectors of correlations matrices of some of the main financial market indices in the world, we show that high volatility of markets is directly linked with strong correlations between them. This means that markets tend to behave as one during great crashes. In order to do so, we investigate financial market crises that occurred in the years 1987 (Black Monday), 1998 (Russian crisis), 2001 (Burst of the dot-com bubble and September 11), and 2008 (Subprime Mortgage Crisis), which mark some of the largest downturns of financial markets in the last three decades.

  5. Numerical solution of the unsteady diffusion-convection-reaction equation based on improved spectral Galerkin method

    Science.gov (United States)

    Zhong, Jiaqi; Zeng, Cheng; Yuan, Yupeng; Zhang, Yuzhe; Zhang, Ye

    2018-04-01

    The aim of this paper is to present an explicit numerical algorithm based on improved spectral Galerkin method for solving the unsteady diffusion-convection-reaction equation. The principal characteristics of this approach give the explicit eigenvalues and eigenvectors based on the time-space separation method and boundary condition analysis. With the help of Fourier series and Galerkin truncation, we can obtain the finite-dimensional ordinary differential equations which facilitate the system analysis and controller design. By comparing with the finite element method, the numerical solutions are demonstrated via two examples. It is shown that the proposed method is effective.

  6. Google matrix analysis of C.elegans neural network

    International Nuclear Information System (INIS)

    Kandiah, V.; Shepelyansky, D.L.

    2014-01-01

    We study the structural properties of the neural network of the C.elegans (worm) from a directed graph point of view. The Google matrix analysis is used to characterize the neuron connectivity structure and node classifications are discussed and compared with physiological properties of the cells. Our results are obtained by a proper definition of neural directed network and subsequent eigenvector analysis which recovers some results of previous studies. Our analysis highlights particular sets of important neurons constituting the core of the neural system. The applications of PageRank, CheiRank and ImpactRank to characterization of interdependency of neurons are discussed.

  7. Beyond the spectral theorem: Spectrally decomposing arbitrary functions of nondiagonalizable operators

    Science.gov (United States)

    Riechers, Paul M.; Crutchfield, James P.

    2018-06-01

    Nonlinearities in finite dimensions can be linearized by projecting them into infinite dimensions. Unfortunately, the familiar linear operator techniques that one would then hope to use often fail since the operators cannot be diagonalized. The curse of nondiagonalizability also plays an important role even in finite-dimensional linear operators, leading to analytical impediments that occur across many scientific domains. We show how to circumvent it via two tracks. First, using the well-known holomorphic functional calculus, we develop new practical results about spectral projection operators and the relationship between left and right generalized eigenvectors. Second, we generalize the holomorphic calculus to a meromorphic functional calculus that can decompose arbitrary functions of nondiagonalizable linear operators in terms of their eigenvalues and projection operators. This simultaneously simplifies and generalizes functional calculus so that it is readily applicable to analyzing complex physical systems. Together, these results extend the spectral theorem of normal operators to a much wider class, including circumstances in which poles and zeros of the function coincide with the operator spectrum. By allowing the direct manipulation of individual eigenspaces of nonnormal and nondiagonalizable operators, the new theory avoids spurious divergences. As such, it yields novel insights and closed-form expressions across several areas of physics in which nondiagonalizable dynamics arise, including memoryful stochastic processes, open nonunitary quantum systems, and far-from-equilibrium thermodynamics. The technical contributions include the first full treatment of arbitrary powers of an operator, highlighting the special role of the zero eigenvalue. Furthermore, we show that the Drazin inverse, previously only defined axiomatically, can be derived as the negative-one power of singular operators within the meromorphic functional calculus and we give a new general

  8. Describing three-class task performance: three-class linear discriminant analysis and three-class ROC analysis

    Science.gov (United States)

    He, Xin; Frey, Eric C.

    2007-03-01

    Binary ROC analysis has solid decision-theoretic foundations and a close relationship to linear discriminant analysis (LDA). In particular, for the case of Gaussian equal covariance input data, the area under the ROC curve (AUC) value has a direct relationship to the Hotelling trace. Many attempts have been made to extend binary classification methods to multi-class. For example, Fukunaga extended binary LDA to obtain multi-class LDA, which uses the multi-class Hotelling trace as a figure-of-merit, and we have previously developed a three-class ROC analysis method. This work explores the relationship between conventional multi-class LDA and three-class ROC analysis. First, we developed a linear observer, the three-class Hotelling observer (3-HO). For Gaussian equal covariance data, the 3- HO provides equivalent performance to the three-class ideal observer and, under less strict conditions, maximizes the signal to noise ratio for classification of all pairs of the three classes simultaneously. The 3-HO templates are not the eigenvectors obtained from multi-class LDA. Second, we show that the three-class Hotelling trace, which is the figureof- merit in the conventional three-class extension of LDA, has significant limitations. Third, we demonstrate that, under certain conditions, there is a linear relationship between the eigenvectors obtained from multi-class LDA and 3-HO templates. We conclude that the 3-HO based on decision theory has advantages both in its decision theoretic background and in the usefulness of its figure-of-merit. Additionally, there exists the possibility of interpreting the two linear features extracted by the conventional extension of LDA from a decision theoretic point of view.

  9. More SPECTRA! a Lot MORE! Better TOO! now What?

    Science.gov (United States)

    Field, Robert W.

    2017-06-01

    I have been a card-carrying spectroscopist for 52 years. I began my career studying spectroscopic perturbations in CS and CO. I eventually graduated to vibrational polyads in acetylene and Multichannel Quantum Defect Theory (MQDT) models for Rydberg states of CaF. My experimental arsenal evolved from atomic resonance lamps to finicky cw dye lasers to user-friendly Nd:YAG pumped dye lasers, ending up with Chirped Pulse Millimeter Waves, non-finicky solid state cw lasers, and death-defying dreams about Stimulated Raman Adiabatic Passage (STIRAP). It has become possible to record an enormous quantity of unimaginably high quality spectra quickly. Increases by factors of 10^{6} in spectral velocity have been claimed. Yet everything rests on assigning the spectrum. But the assignment game has changed. Instead of looking for patterns, we deal with meta-patterns. Our goal is to build a complex model that represents all of the energy levels and associates a multi-component eigenvector with each observed eigenstate. Eigenvectors can reveal what a molecule is thinking about doing when it grows up. Spectroscopy becomes a form of molecular psychoanalysis. A spectroscopist can observe the emergence and describe the mechanistic origin of new classes of large-amplitude intramolecular motions. This makes it possible to directly characterize things, such as transition states, which dogma has labeled "spectroscopically unobservable." Where is 21st century spectroscopy headed? I will discuss examples that include: spectroscopic perturbations of the S_{2} B^{3}Σ^{-}_{u} state, the SO_{2} C state with its unequal SO bond-lengths, and the transition state for trans-cis isomerization in the S_{1} state of acetylene.

  10. Finite-temperature stress calculations in atomic models using moments of position

    Science.gov (United States)

    Parthasarathy, Ranganathan; Misra, Anil; Ouyang, Lizhi

    2018-07-01

    Continuum modeling of finite temperature mechanical behavior of atomic systems requires refined description of atomic motions. In this paper, we identify additional kinematical quantities that are relevant for a more accurate continuum description as the system is subjected to step-wise loading. The presented formalism avoids the necessity for atomic trajectory mapping with deformation, provides the definitions of the kinematic variables and their conjugates in real space, and simplifies local work conjugacy. The total work done on an atom under deformation is decomposed into the work corresponding to changing its equilibrium position and work corresponding to changing its second moment about equilibrium position. Correspondingly, we define two kinematic variables: a deformation gradient tensor and a vibration tensor, and derive their stress conjugates, termed here as static and vibration stresses, respectively. The proposed approach is validated using MD simulation in NVT ensembles for fcc aluminum subjected to uniaxial extension. The observed evolution of second moments in the MD simulation with macroscopic deformation is not directly related to the transformation of atomic trajectories through the deformation gradient using generator functions. However, it is noteworthy that deformation leads to a change in the second moment of the trajectories. Correspondingly, the vibration part of the Piola stress becomes particularly significant at high temperature and high tensile strain as the crystal approaches the softening limit. In contrast to the eigenvectors of the deformation gradient, the eigenvectors of the vibration tensor show strong spatial heterogeneity in the vicinity of softening. More importantly, the elliptic distribution of local atomic density transitions to a dumbbell shape, before significant non-affinity in equilibrium positions has occurred.

  11. Generation of realistic scene using illuminant estimation and mixed chromatic adaptation

    Science.gov (United States)

    Kim, Jae-Chul; Hong, Sang-Gi; Kim, Dong-Ho; Park, Jong-Hyun

    2003-12-01

    The algorithm of combining a real image with a virtual model was proposed to increase the reality of synthesized images. Currently, synthesizing a real image with a virtual model facilitated the surface reflection model and various geometric techniques. In the current methods, the characteristics of various illuminants in the real image are not sufficiently considered. In addition, despite the chromatic adaptation plays a vital role for accommodating different illuminants in the two media viewing conditions, it is not taken into account in the existing methods. Thus, it is hardly to get high-quality synthesized images. In this paper, we proposed the two-phase image synthesis algorithm. First, the surface reflectance of the maximum high-light region (MHR) was estimated using the three eigenvectors obtained from the principal component analysis (PCA) applied to the surface reflectances of 1269 Munsell samples. The combined spectral value, i.e., the product of surface reflectance and the spectral power distributions (SPDs) of an illuminant, of MHR was then estimated using the three eigenvectors obtained from PCA applied to the products of surface reflectances of Munsell 1269 samples and the SPDs of four CIE Standard Illuminants (A, C, D50, D65). By dividing the average combined spectral values of MHR by the average surface reflectances of MHR, we could estimate the illuminant of a real image. Second, the mixed chromatic adaptation (S-LMS) using an estimated and an external illuminants was applied to the virtual-model image. For evaluating the proposed algorithm, experiments with synthetic and real scenes were performed. It was shown that the proposed method was effective in synthesizing the real and the virtual scenes under various illuminants.

  12. Exact analysis of the spectral properties of the anisotropic two-bosons Rabi model

    International Nuclear Information System (INIS)

    Cui, Shuai; Cao, Jun-Peng; Fan, Heng; Amico, Luigi

    2017-01-01

    We introduce the anisotropic two-photon Rabi model in which the rotating and counter rotating terms enters the Hamiltonian with two different coupling constants. Eigenvalues and eigenvectors are studied with exact means. We employ a variation of the Braak method based on Bogolubov rotation of the underlying su (1, 1) Lie algebra. Accordingly, the spectrum is provided by the analytical properties of a suitable meromorphic function. Our formalism applies to the two-modes Rabi model as well, sharing the same algebraic structure of the two-photon model. Through the analysis of the spectrum, we discover that the model displays close analogies to many-body systems undergoing quantum phase transitions. (paper)

  13. Exact analysis of the spectral properties of the anisotropic two-bosons Rabi model

    Science.gov (United States)

    Cui, Shuai; Cao, Jun-Peng; Fan, Heng; Amico, Luigi

    2017-05-01

    We introduce the anisotropic two-photon Rabi model in which the rotating and counter rotating terms enters the Hamiltonian with two different coupling constants. Eigenvalues and eigenvectors are studied with exact means. We employ a variation of the Braak method based on Bogolubov rotation of the underlying su(1, 1) Lie algebra. Accordingly, the spectrum is provided by the analytical properties of a suitable meromorphic function. Our formalism applies to the two-modes Rabi model as well, sharing the same algebraic structure of the two-photon model. Through the analysis of the spectrum, we discover that the model displays close analogies to many-body systems undergoing quantum phase transitions.

  14. Recovering four-component solutions by the inverse transformation of the infinite-order two-component wave functions

    International Nuclear Information System (INIS)

    Barysz, Maria; Mentel, Lukasz; Leszczynski, Jerzy

    2009-01-01

    The two-component Hamiltonian of the infinite-order two-component (IOTC) theory is obtained by a unitary block-diagonalizing transformation of the Dirac-Hamiltonian. Once the IOTC spin orbitals are calculated, they can be back transformed into four-component solutions. The transformed four component solutions are then used to evaluate different moments of the electron density distribution. This formally exact method may, however, suffer from certain approximations involved in its numerical implementation. As shown by the present study, with sufficiently large basis set of Gaussian functions, the Dirac values of these moments are fully recovered in spite of using the approximate identity resolution into eigenvectors of the p 2 operator.

  15. Essential uncontrollability of discrete linear, time-invariant, dynamical systems

    Science.gov (United States)

    Cliff, E. M.

    1975-01-01

    The concept of a 'best approximating m-dimensional subspace' for a given set of vectors in n-dimensional whole space is introduced. Such a subspace is easily described in terms of the eigenvectors of an associated Gram matrix. This technique is used to approximate an achievable set for a discrete linear time-invariant dynamical system. This approximation characterizes the part of the state space that may be reached using modest levels of control. If the achievable set can be closely approximated by a proper subspace of the whole space then the system is 'essentially uncontrollable'. The notion finds application in studies of failure-tolerant systems, and in decoupling.

  16. H3+-WZNW correlators from Liouville theory

    International Nuclear Information System (INIS)

    Ribault, Sylvain; Teschner, Joerg

    2005-01-01

    We prove that arbitrary correlation functions of the H 3 + -WZNW model on a sphere have a simple expression in terms of Liouville theory correlation functions. This is based on the correspondence between the KZ and BPZ equations, and on relations between the structure constants of Liouville theory and the H 3 + -WZNW model. In the critical level limit, these results imply a direct link between eigenvectors of the Gaudin hamiltonians and the problem of uniformization of Riemann surfaces. We also present an expression for correlation functions of the SL(2)/U(1) gauged WZNW model in terms of correlation functions in Liouville theory

  17. The Topology of Three-Dimensional Symmetric Tensor Fields

    Science.gov (United States)

    Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus

    1994-01-01

    We study the topology of 3-D symmetric tensor fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the tensor field. Finally, we demonstrate the use of tensor field topology for the interpretation of the two-force Boussinesq problem.

  18. A first-order spectral phase transition in a class of periodically modulated Hermitian Jacobi matrices

    Directory of Open Access Journals (Sweden)

    Irina Pchelintseva

    2008-01-01

    Full Text Available We consider self-adjoint unbounded Jacobi matrices with diagonal \\(q_n = b_{n}n\\ and off-diagonal entries \\(\\lambda_n = n\\, where \\(b_{n}\\ is a \\(2\\-periodical sequence of real numbers. The parameter space is decomposed into several separate regions, where the spectrum of the operator is either purely absolutely continuous or discrete. We study the situation where the spectral phase transition occurs, namely the case of \\(b_{1}b_{2} = 4\\. The main motive of the paper is the investigation of asymptotics of generalized eigenvectors of the Jacobi matrix. The pure point part of the spectrum is analyzed in detail.

  19. Singular perturbation of simple eigenvalues

    International Nuclear Information System (INIS)

    Greenlee, W.M.

    1976-01-01

    Two operator theoretic theorems which generalize those of asymptotic regular perturbation theory and which apply to singular perturbation problems are proved. Application of these theorems to concrete problems is involved, but the perturbation expansions for eigenvalues and eigenvectors are developed in terms of solutions of linear operator equations. The method of correctors, as well as traditional boundary layer techniques, can be used to apply these theorems. The current formulation should be applicable to highly singular ''hard core'' potential perturbations of the radial equation of quantum mechanics. The theorems are applied to a comparatively simple model problem whose analysis is basic to that of the quantum mechanical problem

  20. Impact of the inherent separation of scales in the Navier-Stokes- alphabeta equations.

    Science.gov (United States)

    Kim, Tae-Yeon; Cassiani, Massimo; Albertson, John D; Dolbow, John E; Fried, Eliot; Gurtin, Morton E

    2009-04-01

    We study the effect of the length scales alpha and beta in the Navier-Stokes- alphabeta equations on the energy spectrum and the alignment between the vorticity and the eigenvectors of the stretching tensor in three-dimensional homogeneous and isotropic turbulent flows in a periodic cubic domain, including the limiting cases of the Navier-Stokes- alpha and Navier-Stokes equations. A significant increase in the accuracy of the energy spectrum at large wave numbers arises for betaNavier-Stokes- alphabeta equations also improve as beta decreases away from alpha . However, optimal choices for alpha and beta depend not only on the problem of interest but also on the grid resolution.

  1. Genome-wide meta-analysis identifies regions on 7p21 (AHR and 15q24 (CYP1A2 as determinants of habitual caffeine consumption.

    Directory of Open Access Journals (Sweden)

    Marilyn C Cornelis

    2011-04-01

    Full Text Available We report the first genome-wide association study of habitual caffeine intake. We included 47,341 individuals of European descent based on five population-based studies within the United States. In a meta-analysis adjusted for age, sex, smoking, and eigenvectors of population variation, two loci achieved genome-wide significance: 7p21 (P = 2.4 × 10(-19, near AHR, and 15q24 (P = 5.2 × 10(-14, between CYP1A1 and CYP1A2. Both the AHR and CYP1A2 genes are biologically plausible candidates as CYP1A2 metabolizes caffeine and AHR regulates CYP1A2.

  2. Fault Diagnosis for Engine Based on Single-Stage Extreme Learning Machine

    Directory of Open Access Journals (Sweden)

    Fei Gao

    2016-01-01

    Full Text Available Single-Stage Extreme Learning Machine (SS-ELM is presented to dispose of the mechanical fault diagnosis in this paper. Based on it, the traditional mapping type of extreme learning machine (ELM has been changed and the eigenvectors extracted from signal processing methods are directly regarded as outputs of the network’s hidden layer. Then the uncertainty that training data transformed from the input space to the ELM feature space with the ELM mapping and problem of the selection of the hidden nodes are avoided effectively. The experiment results of diesel engine fault diagnosis show good performance of the SS-ELM algorithm.

  3. A Fast Enhanced Secure Image Chaotic Cryptosystem Based on Hybrid Chaotic Magic Transform

    Directory of Open Access Journals (Sweden)

    Srinivas Koppu

    2017-01-01

    Full Text Available An enhanced secure image chaotic cryptosystem has been proposed based on hybrid CMT-Lanczos algorithm. We have achieved fast encryption and decryption along with privacy of images. The pseudorandom generator has been used along with Lanczos algorithm to generate root characteristics and eigenvectors. Using hybrid CMT image, pixels are shuffled to accomplish excellent randomness. Compared with existing methods, the proposed method had more robustness to various attacks: brute-force attack, known cipher plaintext, chosen-plaintext, security key space, key sensitivity, correlation analysis and information entropy, and differential attacks. Simulation results show that the proposed methods give better result in protecting images with low-time complexity.

  4. An application of the discrete-time Toda lattice to the progressive algorithm by Lanczos and related problems

    Science.gov (United States)

    Nakamura, Yoshimasa; Sekido, Hiroto

    2018-04-01

    The finite or the semi-infinite discrete-time Toda lattice has many applications to various areas in applied mathematics. The purpose of this paper is to review how the Toda lattice appears in the Lanczos algorithm through the quotient-difference algorithm and its progressive form (pqd). Then a multistep progressive algorithm (MPA) for solving linear systems is presented. The extended Lanczos parameters can be given not by computing inner products of the extended Lanczos vectors but by using the pqd algorithm with highly relative accuracy in a lower cost. The asymptotic behavior of the pqd algorithm brings us some applications of MPA related to eigenvectors.

  5. Representations of U(2∞ and the Value of the Fine Structure Constant

    Directory of Open Access Journals (Sweden)

    William H. Klink

    2005-12-01

    Full Text Available A relativistic quantum mechanics is formulated in which all of the interactions are in the four-momentum operator and Lorentz transformations are kinematic. Interactions are introduced through vertices, which are bilinear in fermion and antifermion creation and annihilation operators, and linear in boson creation and annihilation operators. The fermion-antifermion operators generate a unitary Lie algebra, whose representations are fixed by a first order Casimir operator (corresponding to baryon number or charge. Eigenvectors and eigenvalues of the four-momentum operator are analyzed and exact solutions in the strong coupling limit are sketched. A simple model shows how the fine structure constant might be determined for the QED vertex.

  6. Atomic energy levels of the iron-period elements: potassium through nickel

    International Nuclear Information System (INIS)

    Sugar, J.; Corliss, C.

    1985-01-01

    Experimentally derived energy levels of the elements from potassium to nickel in all stages of ionization are critically compiled. The data for each level include its position in /cm (relative to the ground state), configuration, term designation, J-value, and, where available, the g-value and two leading percentages of the eigenvector composition in the most appropriate coupling scheme. For the He I and H I isoelectronic sequences, calculated level positions are given because they are considered more accurate than the measurements presently available. Ionization energies for each ion are derived either from Rydberg series, extrapolation, or calculation. Complete references are given for the compiled data

  7. Simulation study of negative thermal expansion in yttrium tungstate Y2W3O12.

    Science.gov (United States)

    Rimmer, Leila H N; Dove, Martin T

    2015-05-13

    A simulation study of negative thermal expansion in Y2W3O12 was carried out using calculations of phonon dispersion curves through the application of density functional perturbation theory. The mode eigenvectors were mapped onto flexibility models and results compared with calculations of the mode Grüneisen parameters. It was found that many lower-frequency phonons contribute to negative thermal expansion in Y2W3O12, all of which can be described in terms of rotations of effectively rigid WO4 tetrahedra and Y-O rods. The results are strikingly different from previous phonon studies of higher-symmetry materials that show negative thermal expansion.

  8. Closure of the squared Zakharov--Shabat eigenstates

    International Nuclear Information System (INIS)

    Kaup, D.J.

    1976-01-01

    By solution of the inverse scattering problem for a third-order (degenerate) eigenvalue problem, the closure of the squared eigenfunctions of the Zakharov--Shabat equations is found. The question of the completeness of squared eigenstates occurs in many aspects of ''inverse scattering transforms'' (solving nonlinear evolution equations exactly by inverse scattering techniques), as well as in various aspects of the inverse scattering problem. The method used here is quite suggestive as to how one might find the closure of the squared eigenfunctions of other eigenvalue equations, and the strong analogy between these results and the problem of finding the closure of the eigenvectors of a nonself-adjoint matrix is pointed out

  9. Dependence of the fundamental time eigenvalue of linear transport operator on the system size and other parameters - An application of the Perron-Frobenius theorem

    International Nuclear Information System (INIS)

    Sahni, D.C.

    1991-01-01

    Many papers have been devoted to the study of the spectral properties of the linear (neutron) transport equation. Most of the theoretical investigations have concentrated on the existence (or otherwise) of a continuous spectrum, point spectrum, a leading/dominant eigenvalue, and a corresponding positive eigenvector. It is shown that the fundamental time eigenvalue of the linear transport operator increases with the size of the system. This follows from the increase in the largest eigenvalue of a non-negative irreducible matrix whenever any matrix element his increased. This result of matrix analysis is generalized to more general Krein-Rutman operators that leave a cone of vectors invariant

  10. Diagonalization of the symmetrized discrete i th right shift operator

    Science.gov (United States)

    Fuentes, Marc

    2007-01-01

    In this paper, we consider the symmetric part of the so-called ith right shift operator. We determine its eigenvalues as also the associated eigenvectors in a complete and closed form. The proposed proof is elementary, using only basical skills such as Trigonometry, Arithmetic and Linear algebra. The first section is devoted to the introduction of the tackled problem. Second and third parts contain almost all the ?technical? stuff of the proofE Afterwards, we continue with the end of the proof, provide a graphical illustration of the results, as well as an application on the polyhedral ?sandwiching? of a special compact of arising in Signal theory.

  11. Emission Line Correlations as Diagnostics of Quasar Winds

    Science.gov (United States)

    Sheldon, Keziah; Richards, Gordon

    2018-01-01

    We investigate correlations between UV and optical emission line properties for a sample of z~0.5 SDSS (Sloan Digital Sky Survey) quasars that have recently been observed by HST. The sample is designed to be comparable in luminosity to the existing reverberation mapping (RM) sample, but less biased in terms of their "eigenvector 1" properties. We seek to understand the conditions under which high-ionization emission lines become dominated by a wind. Our analysis takes advantage of spectral decomposition through Independent Component Analysis (ICA) and archival UV HST spectroscopy of SDSS quasars. With these data we will clarify the needs for RM analysis of quasars with wind-dominated emission features.

  12. A method for the calculation of collision strengths for complex atomic structures based on Slater parameter optimisation

    International Nuclear Information System (INIS)

    Fawcett, B.C.; Mason, H.E.

    1989-02-01

    This report presents details of a new method to enable the computation of collision strengths for complex ions which is adapted from long established optimisation techniques previously applied to the calculation of atomic structures and oscillator strengths. The procedure involves the adjustment of Slater parameters so that they determine improved energy levels and eigenvectors. They provide a basis for collision strength calculations in ions where ab initio computations break down or result in reducible errors. This application is demonstrated through modifications of the DISTORTED WAVE collision code and SUPERSTRUCTURE atomic-structure code which interface via a transformation code JAJOM which processes their output. (author)

  13. Solving complex band structure problems with the FEAST eigenvalue algorithm

    Science.gov (United States)

    Laux, S. E.

    2012-08-01

    With straightforward extension, the FEAST eigenvalue algorithm [Polizzi, Phys. Rev. B 79, 115112 (2009)] is capable of solving the generalized eigenvalue problems representing traveling-wave problems—as exemplified by the complex band-structure problem—even though the matrices involved are complex, non-Hermitian, and singular, and hence outside the originally stated range of applicability of the algorithm. The obtained eigenvalues/eigenvectors, however, contain spurious solutions which must be detected and removed. The efficiency and parallel structure of the original algorithm are unaltered. The complex band structures of Si layers of varying thicknesses and InAs nanowires of varying radii are computed as test problems.

  14. Applicability of the Galerkin method to the approximate solution of the multigroup diffusion equation

    International Nuclear Information System (INIS)

    Obradovic, D.

    1970-04-01

    In the study of the nuclear reactors space-time behaviour the modal analysis is very often used though some basic mathematical problems connected with application of this methods are still unsolved. In this paper the modal analysis is identified as a set of the methods in the mathematical literature known as the Galerkin methods (or projection methods, or sometimes direct methods). Using the results of the mathematical investigations of these methods the applicability of the Galerkin type methods to the calculations of the eigenvalue and eigenvectors of the stationary and non-stationary diffusion operator, as well as for the solutions of the corresponding functional equations, is established (author)

  15. Utilizing Problem Structure in Optimization of Radiation Therapy

    International Nuclear Information System (INIS)

    Carlsson, Fredrik

    2008-04-01

    In this thesis, optimization approaches for intensity-modulated radiation therapy are developed and evaluated with focus on numerical efficiency and treatment delivery aspects. The first two papers deal with strategies for solving fluence map optimization problems efficiently while avoiding solutions with jagged fluence profiles. The last two papers concern optimization of step-and-shoot parameters with emphasis on generating treatment plans that can be delivered efficiently and accurately. In the first paper, the problem dimension of a fluence map optimization problem is reduced through a spectral decomposition of the Hessian of the objective function. The weights of the eigenvectors corresponding to the p largest eigenvalues are introduced as optimization variables, and the impact on the solution of varying p is studied. Including only a few eigenvector weights results in faster initial decrease of the objective value, but with an inferior solution, compared to optimization of the bixel weights. An approach combining eigenvector weights and bixel weights produces improved solutions, but at the expense of the pre-computational time for the spectral decomposition. So-called iterative regularization is performed on fluence map optimization problems in the second paper. The idea is to find regular solutions by utilizing an optimization method that is able to find near-optimal solutions with non-jagged fluence profiles in few iterations. The suitability of a quasi-Newton sequential quadratic programming method is demonstrated by comparing the treatment quality of deliverable step-and-shoot plans, generated through leaf sequencing with a fixed number of segments, for different number of bixel-weight iterations. A conclusion is that over-optimization of the fluence map optimization problem prior to leaf sequencing should be avoided. An approach for dynamically generating multileaf collimator segments using a column generation approach combined with optimization of

  16. Palaeohistological Evidence for Ancestral High Metabolic Rate in Archosaurs.

    Science.gov (United States)

    Legendre, Lucas J; Guénard, Guillaume; Botha-Brink, Jennifer; Cubo, Jorge

    2016-11-01

    Metabolic heat production in archosaurs has played an important role in their evolutionary radiation during the Mesozoic, and their ancestral metabolic condition has long been a matter of debate in systematics and palaeontology. The study of fossil bone histology provides crucial information on bone growth rate, which has been used to indirectly investigate the evolution of thermometabolism in archosaurs. However, no quantitative estimation of metabolic rate has ever been performed on fossils using bone histological features. Moreover, to date, no inference model has included phylogenetic information in the form of predictive variables. Here we performed statistical predictive modeling using the new method of phylogenetic eigenvector maps on a set of bone histological features for a sample of extant and extinct vertebrates, to estimate metabolic rates of fossil archosauromorphs. This modeling procedure serves as a case study for eigenvector-based predictive modeling in a phylogenetic context, as well as an investigation of the poorly known evolutionary patterns of metabolic rate in archosaurs. Our results show that Mesozoic theropod dinosaurs exhibit metabolic rates very close to those found in modern birds, that archosaurs share a higher ancestral metabolic rate than that of extant ectotherms, and that this derived high metabolic rate was acquired at a much more inclusive level of the phylogenetic tree, among non-archosaurian archosauromorphs. These results also highlight the difficulties of assigning a given heat production strategy (i.e., endothermy, ectothermy) to an estimated metabolic rate value, and confirm findings of previous studies that the definition of the endotherm/ectotherm dichotomy may be ambiguous. © The Author(s) 2016. Published by Oxford University Press, on behalf of the Society of Systematic Biologists. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

  17. DiffSLC: A graph centrality method to detect essential proteins of a protein-protein interaction network.

    Science.gov (United States)

    Mistry, Divya; Wise, Roger P; Dickerson, Julie A

    2017-01-01

    Identification of central genes and proteins in biomolecular networks provides credible candidates for pathway analysis, functional analysis, and essentiality prediction. The DiffSLC centrality measure predicts central and essential genes and proteins using a protein-protein interaction network. Network centrality measures prioritize nodes and edges based on their importance to the network topology. These measures helped identify critical genes and proteins in biomolecular networks. The proposed centrality measure, DiffSLC, combines the number of interactions of a protein and the gene coexpression values of genes from which those proteins were translated, as a weighting factor to bias the identification of essential proteins in a protein interaction network. Potentially essential proteins with low node degree are promoted through eigenvector centrality. Thus, the gene coexpression values are used in conjunction with the eigenvector of the network's adjacency matrix and edge clustering coefficient to improve essentiality prediction. The outcome of this prediction is shown using three variations: (1) inclusion or exclusion of gene co-expression data, (2) impact of different coexpression measures, and (3) impact of different gene expression data sets. For a total of seven networks, DiffSLC is compared to other centrality measures using Saccharomyces cerevisiae protein interaction networks and gene expression data. Comparisons are also performed for the top ranked proteins against the known essential genes from the Saccharomyces Gene Deletion Project, which show that DiffSLC detects more essential proteins and has a higher area under the ROC curve than other compared methods. This makes DiffSLC a stronger alternative to other centrality methods for detecting essential genes using a protein-protein interaction network that obeys centrality-lethality principle. DiffSLC is implemented using the igraph package in R, and networkx package in Python. The python package can be

  18. A Family of Algorithms for Computing Consensus about Node State from Network Data

    Science.gov (United States)

    Brush, Eleanor R.; Krakauer, David C.; Flack, Jessica C.

    2013-01-01

    Biological and social networks are composed of heterogeneous nodes that contribute differentially to network structure and function. A number of algorithms have been developed to measure this variation. These algorithms have proven useful for applications that require assigning scores to individual nodes–from ranking websites to determining critical species in ecosystems–yet the mechanistic basis for why they produce good rankings remains poorly understood. We show that a unifying property of these algorithms is that they quantify consensus in the network about a node's state or capacity to perform a function. The algorithms capture consensus by either taking into account the number of a target node's direct connections, and, when the edges are weighted, the uniformity of its weighted in-degree distribution (breadth), or by measuring net flow into a target node (depth). Using data from communication, social, and biological networks we find that that how an algorithm measures consensus–through breadth or depth– impacts its ability to correctly score nodes. We also observe variation in sensitivity to source biases in interaction/adjacency matrices: errors arising from systematic error at the node level or direct manipulation of network connectivity by nodes. Our results indicate that the breadth algorithms, which are derived from information theory, correctly score nodes (assessed using independent data) and are robust to errors. However, in cases where nodes “form opinions” about other nodes using indirect information, like reputation, depth algorithms, like Eigenvector Centrality, are required. One caveat is that Eigenvector Centrality is not robust to error unless the network is transitive or assortative. In these cases the network structure allows the depth algorithms to effectively capture breadth as well as depth. Finally, we discuss the algorithms' cognitive and computational demands. This is an important consideration in systems in which

  19. Neural correlates of emotional personality: a structural and functional magnetic resonance imaging study.

    Directory of Open Access Journals (Sweden)

    Stefan Koelsch

    Full Text Available Studies addressing brain correlates of emotional personality have remained sparse, despite the involvement of emotional personality in health and well-being. This study investigates structural and functional brain correlates of psychological and physiological measures related to emotional personality. Psychological measures included neuroticism, extraversion, and agreeableness scores, as assessed using a standard personality questionnaire. As a physiological measure we used a cardiac amplitude signature, the so-called E κ value (computed from the electrocardiogram which has previously been related to tender emotionality. Questionnaire scores and E κ values were related to both functional (eigenvector centrality mapping, ECM and structural (voxel-based morphometry, VBM neuroimaging data. Functional magnetic resonance imaging (fMRI data were obtained from 22 individuals (12 females while listening to music (joy, fear, or neutral music. ECM results showed that agreeableness scores correlated with centrality values in the dorsolateral prefrontal cortex, the anterior cingulate cortex, and the ventral striatum (nucleus accumbens. Individuals with higher E κ values (indexing higher tender emotionality showed higher centrality values in the subiculum of the right hippocampal formation. Structural MRI data from an independent sample of 59 individuals (34 females showed that neuroticism scores correlated with volume of the left amygdaloid complex. In addition, individuals with higher E κ showed larger gray matter volume in the same portion of the subiculum in which individuals with higher E κ showed higher centrality values. Our results highlight a role of the amygdala in neuroticism. Moreover, they indicate that a cardiac signature related to emotionality (E κ correlates with both function (increased network centrality and structure (grey matter volume of the subiculum of the hippocampal formation, suggesting a role of the hippocampal formation for

  20. Neural correlates of emotional personality: a structural and functional magnetic resonance imaging study.

    Science.gov (United States)

    Koelsch, Stefan; Skouras, Stavros; Jentschke, Sebastian

    2013-01-01

    Studies addressing brain correlates of emotional personality have remained sparse, despite the involvement of emotional personality in health and well-being. This study investigates structural and functional brain correlates of psychological and physiological measures related to emotional personality. Psychological measures included neuroticism, extraversion, and agreeableness scores, as assessed using a standard personality questionnaire. As a physiological measure we used a cardiac amplitude signature, the so-called E κ value (computed from the electrocardiogram) which has previously been related to tender emotionality. Questionnaire scores and E κ values were related to both functional (eigenvector centrality mapping, ECM) and structural (voxel-based morphometry, VBM) neuroimaging data. Functional magnetic resonance imaging (fMRI) data were obtained from 22 individuals (12 females) while listening to music (joy, fear, or neutral music). ECM results showed that agreeableness scores correlated with centrality values in the dorsolateral prefrontal cortex, the anterior cingulate cortex, and the ventral striatum (nucleus accumbens). Individuals with higher E κ values (indexing higher tender emotionality) showed higher centrality values in the subiculum of the right hippocampal formation. Structural MRI data from an independent sample of 59 individuals (34 females) showed that neuroticism scores correlated with volume of the left amygdaloid complex. In addition, individuals with higher E κ showed larger gray matter volume in the same portion of the subiculum in which individuals with higher E κ showed higher centrality values. Our results highlight a role of the amygdala in neuroticism. Moreover, they indicate that a cardiac signature related to emotionality (E κ) correlates with both function (increased network centrality) and structure (grey matter volume) of the subiculum of the hippocampal formation, suggesting a role of the hippocampal formation for

  1. Spectral embedding based active contour (SEAC): application to breast lesion segmentation on DCE-MRI

    Science.gov (United States)

    Agner, Shannon C.; Xu, Jun; Rosen, Mark; Karthigeyan, Sudha; Englander, Sarah; Madabhushi, Anant

    2011-03-01

    Spectral embedding (SE), a graph-based manifold learning method, has previously been shown to be useful in high dimensional data classification. In this work, we present a novel SE based active contour (SEAC) segmentation scheme and demonstrate its applications in lesion segmentation on breast dynamic contrast enhance magnetic resonance imaging (DCE-MRI). In this work, we employ SE on DCE-MRI on a per voxel basis to embed the high dimensional time series intensity vector into a reduced dimensional space, where the reduced embedding space is characterized by the principal eigenvectors. The orthogonal eigenvector-based data representation allows for computation of strong tensor gradients in the spectrally embedded space and also yields improved region statistics that serve as optimal stopping criteria for SEAC. We demonstrate both analytically and empirically that the tensor gradients in the spectrally embedded space are stronger than the corresponding gradients in the original grayscale intensity space. On a total of 50 breast DCE-MRI studies, SEAC yielded a mean absolute difference (MAD) of 3.2+/-2.1 pixels and mean Dice similarity coefficient (DSC) of 0.74+/-0.13 compared to manual ground truth segmentation. An active contour in conjunction with fuzzy c-means (FCM+AC), a commonly used segmentation method for breast DCE-MRI, produced a corresponding MAD of 7.2+/-7.4 pixels and mean DSC of 0.58+/-0.32. In conjunction with a set of 6 quantitative morphological features automatically extracted from the SEAC derived lesion boundary, a support vector machine (SVM) classifier yielded an area under the curve (AUC) of 0.73, for discriminating between 10 benign and 30 malignant lesions; the corresponding SVM classifier with the FCM+AC derived morphological features yielded an AUC of 0.65.

  2. SpectralNET – an application for spectral graph analysis and visualization

    Directory of Open Access Journals (Sweden)

    Schreiber Stuart L

    2005-10-01

    Full Text Available Abstract Background Graph theory provides a computational framework for modeling a variety of datasets including those emerging from genomics, proteomics, and chemical genetics. Networks of genes, proteins, small molecules, or other objects of study can be represented as graphs of nodes (vertices and interactions (edges that can carry different weights. SpectralNET is a flexible application for analyzing and visualizing these biological and chemical networks. Results Available both as a standalone .NET executable and as an ASP.NET web application, SpectralNET was designed specifically with the analysis of graph-theoretic metrics in mind, a computational task not easily accessible using currently available applications. Users can choose either to upload a network for analysis using a variety of input formats, or to have SpectralNET generate an idealized random network for comparison to a real-world dataset. Whichever graph-generation method is used, SpectralNET displays detailed information about each connected component of the graph, including graphs of degree distribution, clustering coefficient by degree, and average distance by degree. In addition, extensive information about the selected vertex is shown, including degree, clustering coefficient, various distance metrics, and the corresponding components of the adjacency, Laplacian, and normalized Laplacian eigenvectors. SpectralNET also displays several graph visualizations, including a linear dimensionality reduction for uploaded datasets (Principal Components Analysis and a non-linear dimensionality reduction that provides an elegant view of global graph structure (Laplacian eigenvectors. Conclusion SpectralNET provides an easily accessible means of analyzing graph-theoretic metrics for data modeling and dimensionality reduction. SpectralNET is publicly available as both a .NET application and an ASP.NET web application from http://chembank.broad.harvard.edu/resources/. Source code is

  3. Delocalization transition for the Google matrix.

    Science.gov (United States)

    Giraud, Olivier; Georgeot, Bertrand; Shepelyansky, Dima L

    2009-08-01

    We study the localization properties of eigenvectors of the Google matrix, generated both from the world wide web and from the Albert-Barabási model of networks. We establish the emergence of a delocalization phase for the PageRank vector when network parameters are changed. For networks with localized PageRank, eigenvalues of the matrix in the complex plane with a modulus above a certain threshold correspond to localized eigenfunctions while eigenvalues below this threshold are associated with delocalized relaxation modes. We argue that, for networks with delocalized PageRank, the efficiency of information retrieval by Google-type search is strongly affected since the PageRank values have no clear hierarchical structure in this case.

  4. Measuring the Influence of Efficient Ports using Social Network Metrics

    Directory of Open Access Journals (Sweden)

    Byung-Hak Leem

    2015-02-01

    Full Text Available Data envelopment analysis (DEA is known as a useful tool that produces many efficient decision-making units (DMUs. Traditional DEA provides relative efficient scores and reference sets, but does not influence and rank the efficient DMUs. This paper suggests a method that provides influence and ranking information by using PageRank as a centrality of Social Network analysis (SNA based on reference sets and their lambda values. The social network structure expresses the DMU as a node, reference sets as link, and lambda as connection strengths or weights. This paper, with PageRank, compares the Eigenvector centrality suggested by Liu, et al. in 2009, and shows that PageRank centrality is more accurate.

  5. The Kustaanheimo-Stiefel transformation and certain special functions

    International Nuclear Information System (INIS)

    Kibler, M.; Negadi, T.; Ronveaux, A.

    1984-10-01

    The Kustaanheimo-Stiefel transformation is briefly described in various frameworks. This transformation is used to convert the R 3 harmonics into R 4 harmonics. Then, the Schroedinger equation for an hydrogen-like atom is transformed into the set of a coupled pair of Schroedinger equations for two R 2 isotropic harmonic oscillators and a coupled pair of constraint relations. This connection between two famous quantization cases is tackled in terms of both eigenvalues and eigenvectors corresponding to the discrete spectrum of the hydrogen atom. This leads to an integral involving Laguerre, Legendre, and Hermite polynomials. A program has been realized in the algebraic and symbolic programming system macsyma to cover the various computing aspects of this work

  6. Synchronization and Control of Linearly Coupled Singular Systems

    Directory of Open Access Journals (Sweden)

    Fang Qingxiang

    2013-01-01

    Full Text Available The synchronization and control problem of linearly coupled singular systems is investigated. The uncoupled dynamical behavior at each node is general and can be chaotic or, otherwise the coupling matrix is not assumed to be symmetrical. Some sufficient conditions for globally exponential synchronization are derived based on Lyapunov stability theory. These criteria, which are in terms of linear matrix inequality (LMI, indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold. The controllers are designed for state feedback control and pinning control, respectively. Finally, a numerical example is provided to illustrate the effectiveness of the proposed conditions.

  7. Reflection and transmission of electromagnetic waves in planarly stratified media

    International Nuclear Information System (INIS)

    Caviglia, G.

    1999-01-01

    Propagation of time-harmonic electromagnetic waves in planarly stratified multilayers is investigated. Each layer is allowed to be inhomogeneous and the layers are separated by interfaces. The procedure is based on the representation of the electromagnetic field in the basis of the eigenvectors of the matrix characterizing the first-order system. Hence the local reflection and transmission matrices are defined and the corresponding differential equations, in the pertinent space variable are determined. The jump conditions at interfaces are also established. The present model incorporates dissipative materials and the procedure holds without any restrictions to material symmetries. Differential equations appeared in the literature are shown to hold in particular (one-dimensional) cases or to represent homogeneous layers only

  8. Symmetry and group theory throughout physics

    Directory of Open Access Journals (Sweden)

    Villain J.

    2012-03-01

    Full Text Available As noticed in 1884 by Pierre Curie [1], physical properties of matter are tightly related to the kind of symmetry of the medium. Group theory is a systematic tool, though not always easy to handle, to exploit symmetry properties, for instance to find the eigenvectors and eigenvalues of an operator. Certain properties (optical activity, piezoelectricity are forbidden in molecules or crystals of high symmetry. A few theorems (Noether, Goldstone establish general relations between physical properties and symmetry. Applications of group theory to condensed matter physics, elementary particle physics, quantum mechanics, electromagnetism are reviewed. Group theory is not only a tool, but also a beautiful construction which casts insight into natural phenomena.

  9. Face recognition by combining eigenface method with different wavelet subbands

    Institute of Scientific and Technical Information of China (English)

    MA Yan; LI Shun-bao

    2006-01-01

    @@ A method combining eigenface with different wavelet subbands for face recognition is proposed.Each training image is decomposed into multi-subbands for extracting their eigenvector sets and projection vectors.In the recognition process,the inner product distance between the projection vectors of the test image and that of the training image are calculated.The training image,corresponding to the maximum distance under the given threshold condition,is considered as the final result.The experimental results on the ORL and YALE face database show that,compared with the eigenface method directly on the image domain or on a single wavelet subband,the recognition accuracy using the proposed method is improved by 5% without influencing the recognition speed.

  10. Implementation of QR-decomposition based on CORDIC for unitary MUSIC algorithm

    Science.gov (United States)

    Lounici, Merwan; Luan, Xiaoming; Saadi, Wahab

    2013-07-01

    The DOA (Direction Of Arrival) estimation with subspace methods such as MUSIC (MUltiple SIgnal Classification) and ESPRIT (Estimation of Signal Parameters via Rotational Invariance Technique) is based on an accurate estimation of the eigenvalues and eigenvectors of covariance matrix. QR decomposition is implemented with the Coordinate Rotation DIgital Computer (CORDIC) algorithm. QRD requires only additions and shifts [6], so it is faster and more regular than other methods. In this article the hardware architecture of an EVD (Eigen Value Decomposition) processor based on TSA (triangular systolic array) for QR decomposition is proposed. Using Xilinx System Generator (XSG), the design is implemented and the estimated logic device resource values are presented for different matrix sizes.

  11. Lattice Dynamics of Magnesium Stannide and Zinc Blende. An experimental study by means of inelastic neutron scattering. RCN Report

    International Nuclear Information System (INIS)

    Bergsma, J.

    1970-06-01

    Phonon dispersion relations in Mg 2 Sn and ZnS along the directions [001] , [110] and [111] are presented. Inelastic neutron scattering experiments were carried out by means of a triple-axis crystal spectrometer; for some optic branches the inverse beryllium-filter method was applied. A graphical method of focusing and calculations of inelastic structure factors were helpful in designing experiments. Group theory was employed for the block diagonalization of the dynamical matrices and the determination of eigenvectors. The dispersion relations are described by simple shell models allowing polarization of only one of the ions in each crystal. Zinc blende was found to be mainly covalent and magnesium stannide has an appreciable ionicity. (author)

  12. A numerical algorithm for optimal feedback gains in high dimensional linear quadratic regulator problems

    Science.gov (United States)

    Banks, H. T.; Ito, K.

    1991-01-01

    A hybrid method for computing the feedback gains in linear quadratic regulator problem is proposed. The method, which combines use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite-dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantages of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed, and numerical evidence of the efficacy of these ideas is presented.

  13. Linear stability theory as an early warning sign for transitions in high dimensional complex systems

    International Nuclear Information System (INIS)

    Piovani, Duccio; Grujić, Jelena; Jensen, Henrik Jeldtoft

    2016-01-01

    We analyse in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems by application to the Tangled Nature model of evolutionary ecology and high dimensional replicator systems with a stochastic element. A high dimensional stability matrix is derived in the mean field approximation to the stochastic dynamics. This allows us to determine the stability spectrum about the observed quasi-stable configurations. From overlap of the instantaneous configuration vector of the full stochastic system with the eigenvectors of the unstable directions of the deterministic mean field approximation, we are able to construct a good early-warning indicator of the transitions occurring intermittently. (paper)

  14. Quasars as Cosmological Standard Candles

    International Nuclear Information System (INIS)

    Negrete, C. Alenka; Dultzin, Deborah; Marziani, Paola; Sulentic, Jack W.; Esparza-Arredondo, Donají; Martínez-Aldama, Mary L.; Del Olmo, Ascensión

    2017-01-01

    We propose the use of quasars with accretion rate near the Eddington ratio (extreme quasars) as standard candles. The selection criteria are based on the Eigenvector 1 (E1) formalism. Our first sample is a selection of 334 optical quasar spectra from the SDSS DR7 database with a S/N > 20. Using the E1, we define primary and secondary selection criteria in the optical spectral range. We show that it is possible to derive a redshift-independent estimate of luminosity for extreme Eddington ratio sources. Our results are consistent with concordance cosmology but we need to work with other spectral ranges to take into account the quasar orientation, among other constrains.

  15. Multigrid techniques for nonlinear eigenvalue probems: Solutions of a nonlinear Schroedinger eigenvalue problem in 2D and 3D

    Science.gov (United States)

    Costiner, Sorin; Taasan, Shlomo

    1994-01-01

    This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.

  16. Quasars as Cosmological Standard Candles

    Energy Technology Data Exchange (ETDEWEB)

    Negrete, C. Alenka [CONACYT Research Fellow - Instituto de Astronomía, UNAM, Mexico City (Mexico); Dultzin, Deborah [Instituto de Astronomía, UNAM, Mexico City (Mexico); Marziani, Paola [INAF, Osservatorio Astronomico di Padova, Padua (Italy); Sulentic, Jack W. [Instituto de Astrofísica de Andalucía, IAA-CSIC, Granada (Spain); Esparza-Arredondo, Donají [Instituto de Radioastronomía y Astrofísica, Morelia (Mexico); Martínez-Aldama, Mary L.; Del Olmo, Ascensión, E-mail: alenka@astro.unam.mx [Instituto de Astrofísica de Andalucía, IAA-CSIC, Granada (Spain)

    2017-12-15

    We propose the use of quasars with accretion rate near the Eddington ratio (extreme quasars) as standard candles. The selection criteria are based on the Eigenvector 1 (E1) formalism. Our first sample is a selection of 334 optical quasar spectra from the SDSS DR7 database with a S/N > 20. Using the E1, we define primary and secondary selection criteria in the optical spectral range. We show that it is possible to derive a redshift-independent estimate of luminosity for extreme Eddington ratio sources. Our results are consistent with concordance cosmology but we need to work with other spectral ranges to take into account the quasar orientation, among other constrains.

  17. Analysis of the spectrum of four-times-ionized lutetium (Lu V)

    International Nuclear Information System (INIS)

    Kaufman, V.; Sugar, J.

    1978-01-01

    Spectra of Lu obtained with a sliding spark discharge at peak currents of 50--500 A were recorded with a 10.7 m normal incidence spectrograph in the range of 500--2100 A. Intercomparison of spectra revealed a distinct separation of Lu III, IV, and V, the first two of which have already been anlayzed. The present work contains an interpretation of Lu V in which 419 lines are classified as transitions among 136 energy levels of the 4f 13 , 4f 12 5d, 4f 12 6s, and 4f 12 6p configurations. Calculated energy levels and eigenvectors, obtained with fitted values for the radial integrals, are given

  18. Factorizations of rational matrix functions with application to discrete isomonodromic transformations and difference Painleve equations

    International Nuclear Information System (INIS)

    Dzhamay, Anton

    2009-01-01

    We study factorizations of rational matrix functions with simple poles on the Riemann sphere. For the quadratic case (two poles) we show, using multiplicative representations of such matrix functions, that a good coordinate system on this space is given by a mix of residue eigenvectors of the matrix and its inverse. Our approach is motivated by the theory of discrete isomonodromic transformations and their relationship with difference Painleve equations. In particular, in these coordinates, basic isomonodromic transformations take the form of the discrete Euler-Lagrange equations. Secondly we show that dPV equations, previously obtained in this context by D Arinkin and A Borodin, can be understood as simple relationships between the residues of such matrices and their inverses.

  19. A nonlinear least-squares inverse analysis of strike-slip faulting with application to the San Andreas fault

    Science.gov (United States)

    Williams, Charles A.; Richardson, Randall M.

    1988-01-01

    A nonlinear weighted least-squares analysis was performed for a synthetic elastic layer over a viscoelastic half-space model of strike-slip faulting. Also, an inversion of strain rate data was attempted for the locked portions of the San Andreas fault in California. Based on an eigenvector analysis of synthetic data, it is found that the only parameter which can be resolved is the average shear modulus of the elastic layer and viscoelastic half-space. The other parameters were obtained by performing a suite of inversions for the fault. The inversions on data from the northern San Andreas resulted in predicted parameter ranges similar to those produced by inversions on data from the whole fault.

  20. Identifying the starting point of a spreading process in complex networks.

    Science.gov (United States)

    Comin, Cesar Henrique; Costa, Luciano da Fontoura

    2011-11-01

    When dealing with the dissemination of epidemics, one important question that can be asked is the location where the contamination began. In this paper, we analyze three spreading schemes and propose and validate an effective methodology for the identification of the source nodes. The method is based on the calculation of the centrality of the nodes on the sampled network, expressed here by degree, betweenness, closeness, and eigenvector centrality. We show that the source node tends to have the highest measurement values. The potential of the methodology is illustrated with respect to three theoretical complex network models as well as a real-world network, the email network of the University Rovira i Virgili.

  1. Application of shell model with the modified surface delta interaction to 42Ca and 42Sc nuclei

    International Nuclear Information System (INIS)

    Jasielska, A.; Wiktor, S.

    1975-01-01

    The shell model with MSDI residual interaction is used to investigate properties of levels in the 42 Ca and 42 Sc nuclei. The 40 Ca core with two active outer nucleons is assumed. The energy matrices are diagonalized and the calculated level schemes for both 42 Ca and 42 Sc nuclei are presented. In both nuclei the density of the calculated levels is significantly less than of the observed levels. This fact leads to the conclusion, that some core excitation modes play an important role in the formation of low-lying states in the 42 Ca and 42 Sc nuclei. The calculated eigenvalues and eigenvectors of the states below 5 MeV are given. (author)

  2. EISPACK-J: subprogram package for solving eigenvalue problems

    International Nuclear Information System (INIS)

    Fujimura, Toichiro; Tsutsui, Tsuneo

    1979-05-01

    EISPACK-J, a subprogram package for solving eigenvalue problems, has been developed and subprograms with a variety of functions have been prepared. These subprograms can solve standard problems of complex matrices, general problems of real matrices and special problems in which only the required eigenvalues and eigenvectors are calculated. They are compared to existing subprograms, showing their features through benchmark tests. Many test problems, including realistic scale problems, are provided for the benchmark tests. Discussions are made on computer core storage and computing time required for each subprogram, and accuracy of the solution. The results show that the subprograms of EISPACK-J, based on Householder, QR and inverse iteration methods, are the best in computing time and accuracy. (author)

  3. Response functions for crystals and surfaces, with applications to surface scattering

    International Nuclear Information System (INIS)

    Barker, J.A.; Steele, W.A.

    1978-01-01

    A general solution of the equations of forced motion of a harmonic crystal or other vibrating system with arbitrary time-dependent forces acting on the atoms is given. The solution is given in terms of dynamical 'response functions', for which expressions in terms of the normal mode frequencies and eigenvectors (polarization vectors) are given. Numerical calculations of the response functions are described for (111) and (100) surfaces of face-centered cubic crystals interacting with Lennard-Jones 6-12 potentials, and the qualitative features of the surface and bulk response functions are discussed. The use of these functions in problems of atomic scattering from surface is outlined, and convenient parametrized forms for this application are given. (Auth.)

  4. Search for outlying data points in multivariate solar activity data sets

    International Nuclear Information System (INIS)

    Bartkowiak, A.; Jakimiec, M.

    1989-01-01

    The aim of this paper is the investigation of outlying data points in the solar activity data sets. Two statistical methods for identifying of multivariate outliers are presented: the chi2-plot method based on the analysis of Mahalanobis distances and the method based on principal component analysis, i.e. on scatterdiagrams constructed from the first two or last two eigenvectors. We demonstrate the usefullness of these methods applying them to same data of solar activity. The methods allow to reveal quite precisely the data vectors containing some errors and also some untypical vectors, i.e. vectors with unusually large values or with values revealing untypical relations as compared with the common relations between the appropriate variables. 12 refs., 7 figs., 8 tabs. (author)

  5. Using network properties to evaluate targeted immunization algorithms

    Directory of Open Access Journals (Sweden)

    Bita Shams

    2014-09-01

    Full Text Available Immunization of complex network with minimal or limited budget is a challenging issue for research community. In spite of much literature in network immunization, no comprehensive research has been conducted for evaluation and comparison of immunization algorithms. In this paper, we propose an evaluation framework for immunization algorithms regarding available amount of vaccination resources, goal of immunization program, and time complexity. The evaluation framework is designed based on network topological metrics which is extensible to all epidemic spreading model. Exploiting evaluation framework on well-known targeted immunization algorithms shows that in general, immunization based on PageRank centrality outperforms other targeting strategies in various types of networks, whereas, closeness and eigenvector centrality exhibit the worst case performance.

  6. Localization and chiral symmetry in 2+1 flavor domain wall QCD

    Energy Technology Data Exchange (ETDEWEB)

    David J. Antonio; Kenneth C. Bowler; Peter A. Boyle; Norman H. Christ; Michael A. Clark; Saul D. Cohen; Chris Dawson; Alistair Hart; Balint Joó; Chulwoo Jung; Richard D. Kenway; Shu Li; Meifeng Lin; Robert D. Mawhinney; Christopher M. Maynard; Shigemi Ohta; Robert J. Tweedie; Azusa Yamaguchi

    2008-01-01

    We present results for the dependence of the residual mass of domain wall fermions (DWF) on the size of the fifth dimension and its relation to the density and localization properties of low-lying eigenvectors of the corresponding hermitian Wilson Dirac operator relevant to simulations of 2+1 flavor domain wall QCD. Using the DBW2 and Iwasaki gauge actions, we generate ensembles of configurations with a $16^3\\times 32$ space-time volume and an extent of 8 in the fifth dimension for the sea quarks. We demonstrate the existence of a regime where the degree of locality, the size of chiral symmetry breaking and the rate of topology change can be acceptable for inverse lattice spacings $a^{-1} \\ge 1.6$ GeV.

  7. Extending the QUDA Library with the eigCG Solver

    Energy Technology Data Exchange (ETDEWEB)

    Strelchenko, Alexei [Fermilab; Stathopoulos, Andreas [William-Mary Coll.

    2014-12-12

    While the incremental eigCG algorithm [ 1 ] is included in many LQCD software packages, its realization on GPU micro-architectures was still missing. In this session we report our experi- ence of the eigCG implementation in the QUDA library. In particular, we will focus on how to employ the mixed precision technique to accelerate solutions of large sparse linear systems with multiple right-hand sides on GPUs. Although application of mixed precision techniques is a well-known optimization approach for linear solvers, its utilization for the eigenvector com- puting within eigCG requires special consideration. We will discuss implementation aspects of the mixed precision deflation and illustrate its numerical behavior on the example of the Wilson twisted mass fermion matrix inversions

  8. Determination of Nonlinear Stiffness Coefficients for Finite Element Models with Application to the Random Vibration Problem

    Science.gov (United States)

    Muravyov, Alexander A.

    1999-01-01

    In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.

  9. The Para-Bose oscillator in a finite linear space

    International Nuclear Information System (INIS)

    Campos, R.G.

    1987-01-01

    The harmonic oscillator whose canonical variables satisfy the generalized commutation relations proposed by Wigner is studied in a finite linear space of dimension N by elementary methods. The eigenvalue problems of the Hamiltonian and position operators are worked out and it is found that, when N tends to infinity, the H-eigenvectors tend to the two solutions obtained by Ohnuki Kamefuchi evaluated in the X eigenpoints as N is odd or even. Beside this, the P-representative in the finite X-basis resembles the form that it has in the continuous case and the X-eigenvalues satisfy a minimal property. In this context, some properties of the associated Laguerre polynomials and their zeros (some of them already studied) are derived

  10. Stability and Hopf Bifurcation of a Reaction-Diffusion Neutral Neuron System with Time Delay

    Science.gov (United States)

    Dong, Tao; Xia, Linmao

    2017-12-01

    In this paper, a type of reaction-diffusion neutral neuron system with time delay under homogeneous Neumann boundary conditions is considered. By constructing a basis of phase space based on the eigenvectors of the corresponding Laplace operator, the characteristic equation of this system is obtained. Then, by selecting time delay and self-feedback strength as the bifurcating parameters respectively, the dynamic behaviors including local stability and Hopf bifurcation near the zero equilibrium point are investigated when the time delay and self-feedback strength vary. Furthermore, the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are obtained by using the normal form and the center manifold theorem for the corresponding partial differential equation. Finally, two simulation examples are given to verify the theory.

  11. Physical properties corresponding to vortical flow geometry

    Energy Technology Data Exchange (ETDEWEB)

    Nakayama, K, E-mail: nakayama@aitech.ac.jp [Department of Mechanical Engineering, Aichi Institute of Technology, Toyota, Aichi 470-0392 (Japan)

    2014-10-01

    We examine a vortical flow geometry specified by the velocity gradient tensor ∇v, and derive properties representing the symmetry (axisymmetry or skewness) of the vortical flow in the swirl plane and a property specifying inflowing (outflowing) motion in all directions around the point. We focus on the radial and azimuthal velocities in a plane nonparallel to the eigenvector corresponding to the real eigenvalue of ∇v and show that these components are expressed as specific quadratic forms. The real and imaginary parts of the complex eigenvalues of ∇v represent averages of these eigenvalues of the quadratic forms, and are inadequate to specify the detailed flow geometry uniquely. The new properties complement specifying the precise flow geometry of the vortical flow.

  12. Voxel-wise comparisons of the morphology of diffusion tensors across groups of experimental subjects

    DEFF Research Database (Denmark)

    Bansal, Ravi; Staib, Lawrence H; Plessen, Kerstin J

    2007-01-01

    method to compute their approximate covariance matrices. Our results show that the theoretically computed mean tensor (MT) eigenvectors and eigenvalues match well with their respective true values. Furthermore, a comparison of synthetically generated groups of DTs highlights the limitations of using FA...... to detect group differences. Finally, analyses of in vivo DT data using our method reveal significant between-group differences in diffusivity along fiber tracts within white matter, whereas analyses based on FA values failed to detect some of these differences....... neuropsychiatric illnesses. Comparisons of tensor morphology across groups have typically been performed on scalar measures of diffusivity, such as Fractional Anisotropy (FA) rather than directly on the complex 3D morphologies of DTs. Scalar measures, however, are related in nonlinear ways to the eigenvalues...

  13. Epidemic extinction paths in complex networks

    Science.gov (United States)

    Hindes, Jason; Schwartz, Ira B.

    2017-05-01

    We study the extinction of long-lived epidemics on finite complex networks induced by intrinsic noise. Applying analytical techniques to the stochastic susceptible-infected-susceptible model, we predict the distribution of large fluctuations, the most probable or optimal path through a network that leads to a disease-free state from an endemic state, and the average extinction time in general configurations. Our predictions agree with Monte Carlo simulations on several networks, including synthetic weighted and degree-distributed networks with degree correlations, and an empirical high school contact network. In addition, our approach quantifies characteristic scaling patterns for the optimal path and distribution of large fluctuations, both near and away from the epidemic threshold, in networks with heterogeneous eigenvector centrality and degree distributions.

  14. Analysis of an aggregation-based algebraic two-grid method for a rotated anisotropic diffusion problem

    KAUST Repository

    Chen, Meng-Huo; Greenbaum, Anne

    2015-01-01

    Summary: A two-grid convergence analysis based on the paper [Algebraic analysis of aggregation-based multigrid, by A. Napov and Y. Notay, Numer. Lin. Alg. Appl. 18 (2011), pp. 539-564] is derived for various aggregation schemes applied to a finite element discretization of a rotated anisotropic diffusion equation. As expected, it is shown that the best aggregation scheme is one in which aggregates are aligned with the anisotropy. In practice, however, this is not what automatic aggregation procedures do. We suggest approaches for determining appropriate aggregates based on eigenvectors associated with small eigenvalues of a block splitting matrix or based on minimizing a quantity related to the spectral radius of the iteration matrix. © 2015 John Wiley & Sons, Ltd.

  15. Quantum multiple scattering: Eigenmode expansion and its applications to proximity resonance

    International Nuclear Information System (INIS)

    Li Sheng; Heller, Eric J.

    2003-01-01

    We show that for a general system of N s-wave point scatterers, there are always N eigenmodes. These eigenmodes or eigenchannels play the same role as spherical harmonics for a spherically symmetric target--they give a phase shift only. In other words, the T matrix of the system is of rank N, and the eigenmodes are eigenvectors corresponding to nonzero eigenvalues of the T matrix. The eigenmode expansion approach can give insight to the total scattering cross section; the position, width, and superradiant or subradiant nature of resonance peaks; the unsymmetric Fano line shape of sharp proximity resonance peaks based on the high-energy tail of a broadband; and other properties. Off-resonant eigenmodes for identical proximate scatterers are approximately angular-momentum eigenstates

  16. FOKKER-PLANCK ANALYSIS OF TRANSVERSE COLLECTIVE INSTABILITIES IN ELECTRON STORAGE RINGS

    Energy Technology Data Exchange (ETDEWEB)

    Lindberg, R. R.

    2017-06-25

    We analyze single bunch transverse instabilities due to wakefields using a Fokker-Planck model. We expand on the work of Suzuki [1], writing out the linear matrix equation including chromaticity, both dipolar and quadrupolar transverse wakefields, and the effects of damping and diffusion due to the synchrotron radiation. The eigenvalues and eigenvectors determine the collective stability of the beam, and we show that the predicted threshold current for transverse instability and the profile of the unstable agree well with tracking simulations. In particular, we find that predicting collective stability for high energy electron beams at moderate to large values of chromaticity requires the full Fokker-Planck analysis to properly account for the effects of damping and diffusion due to synchrotron radiation.

  17. A Complete Parametric Solutions of Eigenstructure Assignment by State-Derivative Feedback for Linear Control Systems

    Directory of Open Access Journals (Sweden)

    T. H. S. Abdelaziz

    2005-01-01

    Full Text Available In this paper we introduce a complete parametric approach for solving the problem of eigenstructure assignment via state-derivative feedback for linear systems. This problem is always solvable for any controllable systems iff the open-loop system matrix is nonsingular. In this work, two parametric solutions to the feedback gain matrix are introduced that describe the available degrees of freedom offered by the state-derivative feedback in selecting the associated eigenvectors from an admissible class. These freedoms can be utilized to improve robustness of the closed-loop system. Accordingly, the sensitivity of the assigned eigenvalues to perturbations in the system and gain matrix is minimized. Numerical examples are included to show the effectiveness of the proposed approach. 

  18. MULTIPLE CRITERA METHODS WITH FOCUS ON ANALYTIC HIERARCHY PROCESS AND GROUP DECISION MAKING

    Directory of Open Access Journals (Sweden)

    Lidija Zadnik-Stirn

    2010-12-01

    Full Text Available Managing natural resources is a group multiple criteria decision making problem. In this paper the analytic hierarchy process is the chosen method for handling the natural resource problems. The one decision maker problem is discussed and, three methods: the eigenvector method, data envelopment analysis method, and logarithmic least squares method are presented for the derivation of the priority vector. Further, the group analytic hierarchy process is discussed and six methods for the aggregation of individual judgments or priorities: weighted arithmetic mean method, weighted geometric mean method, and four methods based on data envelopment analysis are compared. The case study on land use in Slovenia is applied. The conclusions review consistency, sensitivity analyses, and some future directions of research.

  19. Modal coupling procedures adapted to NASTRAN analysis of the 1/8-scale shuttle structural dynamics model. Volume 1: Technical report

    Science.gov (United States)

    Zalesak, J.

    1975-01-01

    A dynamic substructuring analysis, utilizing the component modes technique, of the 1/8 scale space shuttle orbiter finite element model is presented. The analysis was accomplished in 3 phases, using NASTRAN RIGID FORMAT 3, with appropriate Alters, on the IBM 360-370. The orbiter was divided into 5 substructures, each of which was reduced to interface degrees of freedom and generalized normal modes. The reduced substructures were coupled to yield the first 23 symmetric free-free orbiter modes, and the eigenvectors in the original grid point degree of freedom lineup were recovered. A comparison was made with an analysis which was performed with the same model using the direct coordinate elimination approach. Eigenvalues were extracted using the inverse power method.

  20. Measurement strategy for spatially encoded photonic qubits

    International Nuclear Information System (INIS)

    Solis-Prosser, M. A.; Neves, L.

    2010-01-01

    We propose a measurement strategy which can, probabilistically, reproduce the statistics of any observable for spatially encoded photonic qubits. It comprises the implementation of a two-outcome positive operator-valued measure followed by a detection in a fixed transverse position, making the displacement of the detection system unnecessary, unlike previous methods. This strategy generalizes a scheme recently demonstrated by one of us and co-workers, restricted to measurement of observables with equatorial eigenvectors only. The method presented here can be implemented with the current technology of programmable multipixel liquid-crystal displays. In addition, it can be straightforwardly extended to high-dimensional qudits and may be a valuable tool in optical implementations of quantum information protocols with spatial qubits and qudits.

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