Introduction to matrices and vectors
Schwartz, Jacob T
2001-01-01
In this concise undergraduate text, the first three chapters present the basics of matrices - in later chapters the author shows how to use vectors and matrices to solve systems of linear equations. 1961 edition.
Elements of Calculus Quaternionic Matrices And Some Applications In Vector Algebra And Kinematics
Directory of Open Access Journals (Sweden)
Pivnyak G.G.
2016-04-01
Full Text Available Quaternionic matrices are proposed to develop mathematical models and perform computational experiments. New formulae for complex vector and scalar products matrix notation, formulae of first curvature, second curvature and orientation of true trihedron tracing are demonstrated in this paper. Application of quaternionic matrices for a problem of airspace transport system trajectory selection is shown.
Accelerating Matrix-Vector Multiplication on Hierarchical Matrices Using Graphical Processing Units
Boukaram, W.
2015-03-25
Large dense matrices arise from the discretization of many physical phenomena in computational sciences. In statistics very large dense covariance matrices are used for describing random fields and processes. One can, for instance, describe distribution of dust particles in the atmosphere, concentration of mineral resources in the earth\\'s crust or uncertain permeability coefficient in reservoir modeling. When the problem size grows, storing and computing with the full dense matrix becomes prohibitively expensive both in terms of computational complexity and physical memory requirements. Fortunately, these matrices can often be approximated by a class of data sparse matrices called hierarchical matrices (H-matrices) where various sub-blocks of the matrix are approximated by low rank matrices. These matrices can be stored in memory that grows linearly with the problem size. In addition, arithmetic operations on these H-matrices, such as matrix-vector multiplication, can be completed in almost linear time. Originally the H-matrix technique was developed for the approximation of stiffness matrices coming from partial differential and integral equations. Parallelizing these arithmetic operations on the GPU has been the focus of this work and we will present work done on the matrix vector operation on the GPU using the KSPARSE library.
Directory of Open Access Journals (Sweden)
Zimmermann Karel
2010-01-01
Full Text Available Abstract Background Sequence comparisons make use of a one-letter representation for amino acids, the necessary quantitative information being supplied by the substitution matrices. This paper deals with the problem of finding a representation that provides a comprehensive description of amino acid intrinsic properties consistent with the substitution matrices. Results We present a Euclidian vector representation of the amino acids, obtained by the singular value decomposition of the substitution matrices. The substitution matrix entries correspond to the dot product of amino acid vectors. We apply this vector encoding to the study of the relative importance of various amino acid physicochemical properties upon the substitution matrices. We also characterize and compare the PAM and BLOSUM series substitution matrices. Conclusions This vector encoding introduces a Euclidian metric in the amino acid space, consistent with substitution matrices. Such a numerical description of the amino acid is useful when intrinsic properties of amino acids are necessary, for instance, building sequence profiles or finding consensus sequences, using machine learning algorithms such as Support Vector Machine and Neural Networks algorithms.
Zimmermann, Karel; Gibrat, Jean-François
2010-01-04
Sequence comparisons make use of a one-letter representation for amino acids, the necessary quantitative information being supplied by the substitution matrices. This paper deals with the problem of finding a representation that provides a comprehensive description of amino acid intrinsic properties consistent with the substitution matrices. We present a Euclidian vector representation of the amino acids, obtained by the singular value decomposition of the substitution matrices. The substitution matrix entries correspond to the dot product of amino acid vectors. We apply this vector encoding to the study of the relative importance of various amino acid physicochemical properties upon the substitution matrices. We also characterize and compare the PAM and BLOSUM series substitution matrices. This vector encoding introduces a Euclidian metric in the amino acid space, consistent with substitution matrices. Such a numerical description of the amino acid is useful when intrinsic properties of amino acids are necessary, for instance, building sequence profiles or finding consensus sequences, using machine learning algorithms such as Support Vector Machine and Neural Networks algorithms.
Directory of Open Access Journals (Sweden)
Jonas Maziero
2016-01-01
Full Text Available Coherence vectors and correlation matrices are important functions frequently used in physics. The numerical calculation of these functions directly from their definitions, which involves Kronecker products and matrix multiplications, may seem to be a reasonable option. Notwithstanding, as we demonstrate in this paper, some algebraic manipulations before programming can reduce considerably their computational complexity. Besides, we provide Fortran code to generate generalized Gell-Mann matrices and to compute the optimized and unoptimized versions of associated Bloch’s vectors and correlation matrix in the case of bipartite quantum systems. As a code test and application example, we consider the calculation of Hilbert-Schmidt quantum discords.
Groups, matrices, and vector spaces a group theoretic approach to linear algebra
Carrell, James B
2017-01-01
This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory ...
Archer, A.W.; Maples, C.G.
1989-01-01
Numerous departures from ideal relationships are revealed by Monte Carlo simulations of widely accepted binomial coefficients. For example, simulations incorporating varying levels of matrix sparseness (presence of zeros indicating lack of data) and computation of expected values reveal that not only are all common coefficients influenced by zero data, but also that some coefficients do not discriminate between sparse or dense matrices (few zero data). Such coefficients computationally merge mutually shared and mutually absent information and do not exploit all the information incorporated within the standard 2 ?? 2 contingency table; therefore, the commonly used formulae for such coefficients are more complicated than the actual range of values produced. Other coefficients do differentiate between mutual presences and absences; however, a number of these coefficients do not demonstrate a linear relationship to matrix sparseness. Finally, simulations using nonrandom matrices with known degrees of row-by-row similarities signify that several coefficients either do not display a reasonable range of values or are nonlinear with respect to known relationships within the data. Analyses with nonrandom matrices yield clues as to the utility of certain coefficients for specific applications. For example, coefficients such as Jaccard, Dice, and Baroni-Urbani and Buser are useful if correction of sparseness is desired, whereas the Russell-Rao coefficient is useful when sparseness correction is not desired. ?? 1989 International Association for Mathematical Geology.
Existence of 121 limit cycles in a perturbed planar polynomial Hamiltonian vector field of degree 11
International Nuclear Information System (INIS)
Wang, S.; Yu, P.
2006-01-01
In this article, a systematic procedure has been explored to studying general Z q -equivariant planar polynomial Hamiltonian vector fields for the maximal number of closed orbits and the maximal number of limit cycles after perturbation. Following the procedure by taking special consideration of Z 12 -equivariant vector fields of degree 11, the maximal of 99 closed orbits are obtained under a well-defined coefficient group. Consequently, perturbation parameter control in limit cycle computation leads to the existence of 121 limit cycles in the perturbed Hamiltonian vector field, which gives rise to the lower bound of Hilbert number of 11th-order systems as H(11) ≥ 11 2 . Two conjectures are proposed regarding the maximal number of closed orbits for equivariant polynomial Hamiltonian vector fields and the maximal number of limit cycles bifurcated from the well defined Hamiltonian vector fields after perturbation
Localization of periodic orbits of polynomial vector fields of even degree by linear functions
Energy Technology Data Exchange (ETDEWEB)
Starkov, Konstantin E. [CITEDI-IPN, Av. del Parque 1310, Mesa de Otay, Tijuana, BC (Mexico)] e-mail: konst@citedi.mx
2005-08-01
This paper is concerned with the localization problem of periodic orbits of polynomial vector fields of even degree by using linear functions. Conditions of the localization of all periodic orbits in sets of a simple structure are obtained. Our results are based on the solution of the conditional extremum problem and the application of homogeneous polynomial forms of even degrees. As examples, the Lanford system, the jerky system with one quadratic monomial and a quartically perturbed harmonic oscillator are considered.
Localization of periodic orbits of polynomial vector fields of even degree by linear functions
International Nuclear Information System (INIS)
Starkov, Konstantin E.
2005-01-01
This paper is concerned with the localization problem of periodic orbits of polynomial vector fields of even degree by using linear functions. Conditions of the localization of all periodic orbits in sets of a simple structure are obtained. Our results are based on the solution of the conditional extremum problem and the application of homogeneous polynomial forms of even degrees. As examples, the Lanford system, the jerky system with one quadratic monomial and a quartically perturbed harmonic oscillator are considered
The asymptotic and exact Fisher information matrices of a vector ARMA process
Klein, A.; Melard, G.; Saidi, A.
2008-01-01
The exact Fisher information matrix of a Gaussian vector autoregressive-moving average (VARMA) process has been considered for a time series of length N in relation to the exact maximum likelihood estimation method. In this paper it is shown that the Gaussian exact Fisher information matrix
International Nuclear Information System (INIS)
Cairo, Laurent; Llibre, Jaume
2007-01-01
We classify all the global phase portraits of the cubic polynomial vector fields of Lotka-Volterra type having a rational first integral of degree 2. For such vector fields there are exactly 28 different global phase portraits in the Poincare disc up to a reversal of sense of all orbits
Thrall, Robert M
2011-01-01
This volume is suitable as a primary or supplementary text for college-level courses in linear algebra. It possesses the distinct advantage of approaching the subject simultaneously at two levels, the concrete and the axiomatic. Students thus receive the benefits of axiom-based mathematical reasoning as well as a grasp of concrete formulations. 1957 edition.
Relation of the Vector Force Needed to Lift the Upper Eyelids and the Degree of Exophthalmos.
Hwang, Kun; Kim, Joo Ho; Kim, Hun; Hwang, Se Won
2015-07-01
The aim of this study was to determine the relation of the vector force needed to lift the upper eyelids and the degree of exophthalmos (EX). In the 109 magnetic resonance imaging films, the degree of EX (the shortest distance from the cornea to the line connecting both lateral orbital rims), the anterior angle (θ, an angle formed from the lower margin of the upper eyelid-superior transverse ligament (STL)--with a parallel line connecting the supraorbital rim and the infraorbital rim in the sagittal film), the length from the STL to the upper eyelid margin (levator length [LL]), the thickness of the STL (WT), and the thickness the of levator palpebrae (LT) were measured.The average EX was 14.5 ± 2.35 mm. The average θ was 33.84 ± 2.15 degrees. The vector force needed to lift the upper eyelids (cos θ) was 0.83. The average LL was 21.0 ± 1.54 mm. The average WT was 1.07 ± 0.22 mm. The average LT was 1.69 ± 0.30 mm. There was a significant positive relationship between the EX and age (P = 0.022). The EX in those younger than 20 years (12.8 ± 2.06) was significantly lesser than that of the other age groups. There was no significant relationship between the EX and cos θ. However, there was a significant positive relationship between the EX and the LL. There was a significant positive relationship between LL and LT, and between LL and WT.The farther the eyeball protrudes, the longer the LL is needed. The longer the LL is, the thicker the levator muscle and STL.
Chiorean, Vasile-Florin
2017-10-01
Matric suction is a soil parameter which influences the behaviour of unsaturated soils in both terms of shear strength and permeability. It is a necessary aspect to know the variation of matric suction in unsaturated soil zone for solving geotechnical issues like unsaturated soil slopes stability or bearing capacity for unsaturated foundation ground. Mathematical expression of the dependency between soil moisture content and it’s matric suction (soil water characteristic curve) has a powerful character of nonlinearity. This paper presents two methods to determine the variation of matric suction along the depth included between groundwater level and soil level. First method is an analytical approach to emphasize one direction steady state unsaturated infiltration phenomenon that occurs between the groundwater level and the soil level. There were simulated three different situations in terms of border conditions: precipitations (inflow conditions on ground surface), evaporation (outflow conditions on ground surface), and perfect equilibrium (no flow on ground surface). Numerical method is finite element method used for steady state, two-dimensional, unsaturated infiltration calculus. Regarding boundary conditions there were simulated identical situations as in analytical approach. For both methods, was adopted the equation proposed by van Genuchten-Mualen (1980) for mathematical expression of soil water characteristic curve. Also for the unsaturated soil permeability prediction model was adopted the equation proposed by van Genuchten-Mualen. The fitting parameters of these models were adopted according to RETC 6.02 software in function of soil type. The analyses were performed in both methods for three major soil types: clay, silt and sand. For each soil type were concluded analyses for three situations in terms of border conditions applied on soil surface: inflow, outflow, and no flow. The obtained results are presented in order to highlight the differences
Matrices and linear transformations
Cullen, Charles G
1990-01-01
""Comprehensive . . . an excellent introduction to the subject."" - Electronic Engineer's Design Magazine.This introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field. Contents include Matrices and Linear Systems; Vector Spaces; Determinants; Linear Transformations; Similarity: Part I and Part II; Polynomials and Polynomial Matrices; Matrix Analysis; and Numerical Methods. The first
Directory of Open Access Journals (Sweden)
Yaping Huang
Full Text Available The selection of seismic attributes is a key process in reservoir prediction because the prediction accuracy relies on the reliability and credibility of the seismic attributes. However, effective selection method for useful seismic attributes is still a challenge. This paper presents a novel selection method of seismic attributes for reservoir prediction based on the gray relational degree (GRD and support vector machine (SVM. The proposed method has a two-hierarchical structure. In the first hierarchy, the primary selection of seismic attributes is achieved by calculating the GRD between seismic attributes and reservoir parameters, and the GRD between the seismic attributes. The principle of the primary selection is that these seismic attributes with higher GRD to the reservoir parameters will have smaller GRD between themselves as compared to those with lower GRD to the reservoir parameters. Then the SVM is employed in the second hierarchy to perform an interactive error verification using training samples for the purpose of determining the final seismic attributes. A real-world case study was conducted to evaluate the proposed GRD-SVM method. Reliable seismic attributes were selected to predict the coalbed methane (CBM content in southern Qinshui basin, China. In the analysis, the instantaneous amplitude, instantaneous bandwidth, instantaneous frequency, and minimum negative curvature were selected, and the predicted CBM content was fundamentally consistent with the measured CBM content. This real-world case study demonstrates that the proposed method is able to effectively select seismic attributes, and improve the prediction accuracy. Thus, the proposed GRD-SVM method can be used for the selection of seismic attributes in practice.
Directory of Open Access Journals (Sweden)
Pablo Soto-Quiros
2015-01-01
Full Text Available This paper presents a parallel implementation of a kind of discrete Fourier transform (DFT: the vector-valued DFT. The vector-valued DFT is a novel tool to analyze the spectra of vector-valued discrete-time signals. This parallel implementation is developed in terms of a mathematical framework with a set of block matrix operations. These block matrix operations contribute to analysis, design, and implementation of parallel algorithms in multicore processors. In this work, an implementation and experimental investigation of the mathematical framework are performed using MATLAB with the Parallel Computing Toolbox. We found that there is advantage to use multicore processors and a parallel computing environment to minimize the high execution time. Additionally, speedup increases when the number of logical processors and length of the signal increase.
Wang, Xiaolei
2014-12-12
Background: A quantitative understanding of interactions between transcription factors (TFs) and their DNA binding sites is key to the rational design of gene regulatory networks. Recent advances in high-throughput technologies have enabled high-resolution measurements of protein-DNA binding affinity. Importantly, such experiments revealed the complex nature of TF-DNA interactions, whereby the effects of nucleotide changes on the binding affinity were observed to be context dependent. A systematic method to give high-quality estimates of such complex affinity landscapes is, thus, essential to the control of gene expression and the advance of synthetic biology. Results: Here, we propose a two-round prediction method that is based on support vector regression (SVR) with weighted degree (WD) kernels. In the first round, a WD kernel with shifts and mismatches is used with SVR to detect the importance of subsequences with different lengths at different positions. The subsequences identified as important in the first round are then fed into a second WD kernel to fit the experimentally measured affinities. To our knowledge, this is the first attempt to increase the accuracy of the affinity prediction by applying two rounds of string kernels and by identifying a small number of crucial k-mers. The proposed method was tested by predicting the binding affinity landscape of Gcn4p in Saccharomyces cerevisiae using datasets from HiTS-FLIP. Our method explicitly identified important subsequences and showed significant performance improvements when compared with other state-of-the-art methods. Based on the identified important subsequences, we discovered two surprisingly stable 10-mers and one sensitive 10-mer which were not reported before. Further test on four other TFs in S. cerevisiae demonstrated the generality of our method. Conclusion: We proposed in this paper a two-round method to quantitatively model the DNA binding affinity landscape. Since the ability to modify
DEFF Research Database (Denmark)
Boeriis, Morten; van Leeuwen, Theo
2017-01-01
should be taken into account in discussing ‘reactions’, which Kress and van Leeuwen link only to eyeline vectors. Finally, the question can be raised as to whether actions are always realized by vectors. Drawing on a re-reading of Rudolf Arnheim’s account of vectors, these issues are outlined......This article revisits the concept of vectors, which, in Kress and van Leeuwen’s Reading Images (2006), plays a crucial role in distinguishing between ‘narrative’, action-oriented processes and ‘conceptual’, state-oriented processes. The use of this concept in image analysis has usually focused...
Metcalf, Thomas R.
1994-01-01
I present a robust algorithm that resolves the 180-deg ambiguity in measurements of the solar vector magnetic field. The technique simultaneously minimizes both the divergence of the magnetic field and the electric current density using a simulated annealing algorithm. This results in the field orientation with approximately minimum free energy. The technique is well-founded physically and is simple to implement.
Wang, Xiaolei; Kuwahara, Hiroyuki; Gao, Xin
2014-01-01
high-quality estimates of such complex affinity landscapes is, thus, essential to the control of gene expression and the advance of synthetic biology. Results: Here, we propose a two-round prediction method that is based on support vector regression
Leclerc, Arnaud; Carrington, Tucker
2014-05-07
We propose an iterative method for computing vibrational spectra that significantly reduces the memory cost of calculations. It uses a direct product primitive basis, but does not require storing vectors with as many components as there are product basis functions. Wavefunctions are represented in a basis each of whose functions is a sum of products (SOP) and the factorizable structure of the Hamiltonian is exploited. If the factors of the SOP basis functions are properly chosen, wavefunctions are linear combinations of a small number of SOP basis functions. The SOP basis functions are generated using a shifted block power method. The factors are refined with a rank reduction algorithm to cap the number of terms in a SOP basis function. The ideas are tested on a 20-D model Hamiltonian and a realistic CH3CN (12 dimensional) potential. For the 20-D problem, to use a standard direct product iterative approach one would need to store vectors with about 10(20) components and would hence require about 8 × 10(11) GB. With the approach of this paper only 1 GB of memory is necessary. Results for CH3CN agree well with those of a previous calculation on the same potential.
International Nuclear Information System (INIS)
Doebner, H.; Mann, H.
1997-01-01
We consider configuration spaces of nonidentical pointlike particles. The physically motivated assumption that any two particles cannot be located at the same point in space endash time leads to nontrivial topological structure of the configuration space. For a quantum mechanical description of such a system, we classify complex vector bundles over the configuration space and obtain potentials of topological origin, similar to those that occur in the fiber bundle approach to Dirac close-quote s magnetic monopole or in Yang endash Mills theory. copyright 1997 American Institute of Physics
Stoean, Ruxandra; Stoean, Catalin; Lupsor, Monica; Stefanescu, Horia; Badea, Radu
2011-01-01
Hepatic fibrosis, the principal pointer to the development of a liver disease within chronic hepatitis C, can be measured through several stages. The correct evaluation of its degree, based on recent different non-invasive procedures, is of current major concern. The latest methodology for assessing it is the Fibroscan and the effect of its employment is impressive. However, the complex interaction between its stiffness indicator and the other biochemical and clinical examinations towards a respective degree of liver fibrosis is hard to be manually discovered. In this respect, the novel, well-performing evolutionary-powered support vector machines are proposed towards an automated learning of the relationship between medical attributes and fibrosis levels. The traditional support vector machines have been an often choice for addressing hepatic fibrosis, while the evolutionary option has been validated on many real-world tasks and proven flexibility and good performance. The evolutionary approach is simple and direct, resulting from the hybridization of the learning component within support vector machines and the optimization engine of evolutionary algorithms. It discovers the optimal coefficients of surfaces that separate instances of distinct classes. Apart from a detached manner of establishing the fibrosis degree for new cases, a resulting formula also offers insight upon the correspondence between the medical factors and the respective outcome. What is more, a feature selection genetic algorithm can be further embedded into the method structure, in order to dynamically concentrate search only on the most relevant attributes. The data set refers 722 patients with chronic hepatitis C infection and 24 indicators. The five possible degrees of fibrosis range from F0 (no fibrosis) to F4 (cirrhosis). Since the standard support vector machines are among the most frequently used methods in recent artificial intelligence studies for hepatic fibrosis staging, the
Directory of Open Access Journals (Sweden)
Neneng Neneng
2016-11-01
Full Text Available Texture is one of the most important features for image analysis, which provides informations such as the composition of texture on the surface structure, changes of the intensity, or brightness. Gray level co-occurence matrix (GLCM is a method that can be used for statistical texture analysis. GLCM has proven to be the most powerful texture descriptors used in image analysis. This study uses the four-way GLCM 0o, 45o, 90o, and 135o. Support vector machine (SVM is a machine learning that can be used for image classification. SVM has a high generalization capability without any requirement of additional knowledge, even with the high dimension of the input space. The data used in this study are the image of goat meat, buffalo meat, horse meat, and beef with shooting distance 20 cm, 30 cm and 40 cm. The result of this study shows that the best recognition rate of 87.5% was taken at a distance of 20 cm with neighboring pixels distance d = 2 in the direction GLCM 135o.
Blended 6-Hourly Sea Surface Wind Vectors and Wind Stress on a Global 0.25 Degree Grid (1987-2011)
National Oceanic and Atmospheric Administration, Department of Commerce — The Blended Global Sea Surface Winds products contain ocean surface wind vectors and wind stress on a global 0.25 degree grid, in multiple time resolutions of...
Enhancing Understanding of Transformation Matrices
Dick, Jonathan; Childrey, Maria
2012-01-01
With the Common Core State Standards' emphasis on transformations, teachers need a variety of approaches to increase student understanding. Teaching matrix transformations by focusing on row vectors gives students tools to create matrices to perform transformations. This empowerment opens many doors: Students are able to create the matrices for…
Directory of Open Access Journals (Sweden)
Kladiev Sergey N.
2017-01-01
Full Text Available In the present work we investigate the control system development of the drive simulators to train driver/operator driving skills, taking into account the ever-changing terrain. In order to meet the required response of the four degree-of-freedom motion platform servomotor current studies have been focused on the vector control of the resistance motor angular velocity from the sensor being incremental encoder. In proposed system the standard security of the frequency converter is realized. It leads to overload capacity of two times within minutes determined by servomotor inertia. Further, we represent the algorithms: positional limitation, reliable acceleration and restraint, frequency break. As well as we demonstrate the position switches implement in software. As a result, the control system commands the control of the angular position of the platform in coordinates.
Reddy, L Ram Gopal; Kuntamalla, Srinivas
2011-01-01
Heart rate variability analysis is fast gaining acceptance as a potential non-invasive means of autonomic nervous system assessment in research as well as clinical domains. In this study, a new nonlinear analysis method is used to detect the degree of nonlinearity and stochastic nature of heart rate variability signals during two forms of meditation (Chi and Kundalini). The data obtained from an online and widely used public database (i.e., MIT/BIH physionet database), is used in this study. The method used is the delay vector variance (DVV) method, which is a unified method for detecting the presence of determinism and nonlinearity in a time series and is based upon the examination of local predictability of a signal. From the results it is clear that there is a significant change in the nonlinearity and stochastic nature of the signal before and during the meditation (p value > 0.01). During Chi meditation there is a increase in stochastic nature and decrease in nonlinear nature of the signal. There is a significant decrease in the degree of nonlinearity and stochastic nature during Kundalini meditation.
Matrices in Engineering Problems
Tobias, Marvin
2011-01-01
This book is intended as an undergraduate text introducing matrix methods as they relate to engineering problems. It begins with the fundamentals of mathematics of matrices and determinants. Matrix inversion is discussed, with an introduction of the well known reduction methods. Equation sets are viewed as vector transformations, and the conditions of their solvability are explored. Orthogonal matrices are introduced with examples showing application to many problems requiring three dimensional thinking. The angular velocity matrix is shown to emerge from the differentiation of the 3-D orthogo
An introduction to vectors, vector operators and vector analysis
Joag, Pramod S
2016-01-01
Ideal for undergraduate and graduate students of science and engineering, this book covers fundamental concepts of vectors and their applications in a single volume. The first unit deals with basic formulation, both conceptual and theoretical. It discusses applications of algebraic operations, Levi-Civita notation, and curvilinear coordinate systems like spherical polar and parabolic systems and structures, and analytical geometry of curves and surfaces. The second unit delves into the algebra of operators and their types and also explains the equivalence between the algebra of vector operators and the algebra of matrices. Formulation of eigen vectors and eigen values of a linear vector operator are elaborated using vector algebra. The third unit deals with vector analysis, discussing vector valued functions of a scalar variable and functions of vector argument (both scalar valued and vector valued), thus covering both the scalar vector fields and vector integration.
Krylov, Piotr
2017-01-01
This monograph is a comprehensive account of formal matrices, examining homological properties of modules over formal matrix rings and summarising the interplay between Morita contexts and K theory. While various special types of formal matrix rings have been studied for a long time from several points of view and appear in various textbooks, for instance to examine equivalences of module categories and to illustrate rings with one-sided non-symmetric properties, this particular class of rings has, so far, not been treated systematically. Exploring formal matrix rings of order 2 and introducing the notion of the determinant of a formal matrix over a commutative ring, this monograph further covers the Grothendieck and Whitehead groups of rings. Graduate students and researchers interested in ring theory, module theory and operator algebras will find this book particularly valuable. Containing numerous examples, Formal Matrices is a largely self-contained and accessible introduction to the topic, assuming a sol...
Hierarchical matrices algorithms and analysis
Hackbusch, Wolfgang
2015-01-01
This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix. The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition. Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchical matrices is of interest to scientists ...
Averaging operations on matrices
Indian Academy of Sciences (India)
2014-07-03
Jul 3, 2014 ... Role of Positive Definite Matrices. • Diffusion Tensor Imaging: 3 × 3 pd matrices model water flow at each voxel of brain scan. • Elasticity: 6 × 6 pd matrices model stress tensors. • Machine Learning: n × n pd matrices occur as kernel matrices. Tanvi Jain. Averaging operations on matrices ...
International Nuclear Information System (INIS)
Roper, C.D.; Clegg, T.; Dunham, J.D.; Mendez, Anthony J. II; Tornow, W.; Walter, R.L.
2010-01-01
Measurements of the H-2(d, n)(3) He transverse vector polarization-transfer coefficient K-y(y)' at 0 degrees. are reported for 29 outgoing neutron energies between 3.94 and 8.47MeV. Our new results determine K-y(y)' (0 degrees) more accurately than previous data, especially for neutron energies below 5MeV. Low-energy data for this reaction are important both as a high-intensity source of highly polarized neutrons for nuclear physics studies with polarized neutron beams, and as a test of the emerging theoretical descriptions of the four-body system, where recently substantial progress has been made.
Ebrahimi, Javad; Fragouli, Christina
2010-01-01
We develop new algebraic algorithms for scalar and vector network coding. In vector network coding, the source multicasts information by transmitting vectors of length L, while intermediate nodes process and combine their incoming packets by multiplying them with L X L coding matrices that play a similar role as coding coefficients in scalar coding. Our algorithms for scalar network jointly optimize the employed field size while selecting the coding coefficients. Similarly, for vector co...
Vector Network Coding Algorithms
Ebrahimi, Javad; Fragouli, Christina
2010-01-01
We develop new algebraic algorithms for scalar and vector network coding. In vector network coding, the source multicasts information by transmitting vectors of length L, while intermediate nodes process and combine their incoming packets by multiplying them with L x L coding matrices that play a similar role as coding c in scalar coding. Our algorithms for scalar network jointly optimize the employed field size while selecting the coding coefficients. Similarly, for vector coding, our algori...
Robinson, Gilbert de B
2011-01-01
This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom
Inverse m-matrices and ultrametric matrices
Dellacherie, Claude; San Martin, Jaime
2014-01-01
The study of M-matrices, their inverses and discrete potential theory is now a well-established part of linear algebra and the theory of Markov chains. The main focus of this monograph is the so-called inverse M-matrix problem, which asks for a characterization of nonnegative matrices whose inverses are M-matrices. We present an answer in terms of discrete potential theory based on the Choquet-Deny Theorem. A distinguished subclass of inverse M-matrices is ultrametric matrices, which are important in applications such as taxonomy. Ultrametricity is revealed to be a relevant concept in linear algebra and discrete potential theory because of its relation with trees in graph theory and mean expected value matrices in probability theory. Remarkable properties of Hadamard functions and products for the class of inverse M-matrices are developed and probabilistic insights are provided throughout the monograph.
Lambda-matrices and vibrating systems
Lancaster, Peter; Stark, M; Kahane, J P
1966-01-01
Lambda-Matrices and Vibrating Systems presents aspects and solutions to problems concerned with linear vibrating systems with a finite degrees of freedom and the theory of matrices. The book discusses some parts of the theory of matrices that will account for the solutions of the problems. The text starts with an outline of matrix theory, and some theorems are proved. The Jordan canonical form is also applied to understand the structure of square matrices. Classical theorems are discussed further by applying the Jordan canonical form, the Rayleigh quotient, and simple matrix pencils with late
Spectra of sparse random matrices
International Nuclear Information System (INIS)
Kuehn, Reimer
2008-01-01
We compute the spectral density for ensembles of sparse symmetric random matrices using replica. Our formulation of the replica-symmetric ansatz shares the symmetries of that suggested in a seminal paper by Rodgers and Bray (symmetry with respect to permutation of replica and rotation symmetry in the space of replica), but uses a different representation in terms of superpositions of Gaussians. It gives rise to a pair of integral equations which can be solved by a stochastic population-dynamics algorithm. Remarkably our representation allows us to identify pure-point contributions to the spectral density related to the existence of normalizable eigenstates. Our approach is not restricted to matrices defined on graphs with Poissonian degree distribution. Matrices defined on regular random graphs or on scale-free graphs, are easily handled. We also look at matrices with row constraints such as discrete graph Laplacians. Our approach naturally allows us to unfold the total density of states into contributions coming from vertices of different local coordinations and an example of such an unfolding is presented. Our results are well corroborated by numerical diagonalization studies of large finite random matrices
Introduction into Hierarchical Matrices
Litvinenko, Alexander
2013-12-05
Hierarchical matrices allow us to reduce computational storage and cost from cubic to almost linear. This technique can be applied for solving PDEs, integral equations, matrix equations and approximation of large covariance and precision matrices.
Introduction into Hierarchical Matrices
Litvinenko, Alexander
2013-01-01
Hierarchical matrices allow us to reduce computational storage and cost from cubic to almost linear. This technique can be applied for solving PDEs, integral equations, matrix equations and approximation of large covariance and precision matrices.
Intrinsic Density Matrices of the Nuclear Shell Model
International Nuclear Information System (INIS)
Deveikis, A.; Kamuntavichius, G.
1996-01-01
A new method for calculation of shell model intrinsic density matrices, defined as two-particle density matrices integrated over the centre-of-mass position vector of two last particles and complemented with isospin variables, has been developed. The intrinsic density matrices obtained are completely antisymmetric, translation-invariant, and do not employ a group-theoretical classification of antisymmetric states. They are used for exact realistic density matrix expansion within the framework of the reduced Hamiltonian method. The procedures based on precise arithmetic for calculation of the intrinsic density matrices that involve no numerical diagonalization or orthogonalization have been developed and implemented in the computer code. (author). 11 refs., 2 tabs
Indian Academy of Sciences (India)
IAS Admin
harmonic analysis and complex analysis, in ... gebra describes not only the study of linear transforma- tions and .... special case of the Jordan canonical form of matrices. ..... Richard Bronson, Schaum's Outline Series Theory And Problems Of.
Energy Technology Data Exchange (ETDEWEB)
Wagner, C.
1996-12-31
In 1992, Wittum introduced the frequency filtering decompositions (FFD), which yield a fast method for the iterative solution of large systems of linear equations. Based on this method, the tangential frequency filtering decompositions (TFFD) have been developed. The TFFD allow the robust and efficient treatment of matrices with strongly varying coefficients. The existence and the convergence of the TFFD can be shown for symmetric and positive definite matrices. For a large class of matrices, it is possible to prove that the convergence rate of the TFFD and of the FFD is independent of the number of unknowns. For both methods, schemes for the construction of frequency filtering decompositions for unsymmetric matrices have been developed. Since, in contrast to Wittums`s FFD, the TFFD needs only one test vector, an adaptive test vector can be used. The TFFD with respect to the adaptive test vector can be combined with other iterative methods, e.g. multi-grid methods, in order to improve the robustness of these methods. The frequency filtering decompositions have been successfully applied to the problem of the decontamination of a heterogeneous porous medium by flushing.
Estimate of spin polarization for PEP using generalized transformation matrices
International Nuclear Information System (INIS)
Chao, A.W.
1978-04-01
The spin polarization for PEP has been estimated before by using simplified models. The main difficulty in the previous estimates is that the strength of depolarization effects caused by various electromagnetic field errors could not be specified accurately. To overcome this difficulty, a matrix formalism for depolarization calculation was developed recently. One basic ingredient of this theory is to represent an electron by an 8-dimensional state vector, X = (x,x',y,y',z,δ,α,β) where the first six coordinates are the usual transverse and longitudinal canonical coordinates, while α and β are the two components of the electron's spin vector perpendicular to the equilibrium direction of polarization /cflx n/. The degree of depolarization is specified by 1/2(α 2 + β 2 ). The state vector X will be transformed by an 8 x 8 matrix as the electron passes through a beam-line element such as a bending magnet or an rf cavity. From any position s, one multiplies successively the 8 x 8 matrices around one revolution of the storage ring to obtain the total transformation T(s). Any impulse perturbation ΔX to the electron's state vector occurring at s will be transformed repeatedly by T(s) as the electron circulates around the storage ring. Another basic ingredient is to decompose ΔX into 8 eigenstate components with eigenvectors determined from T(s). Six of these eigenstate components corresponding to the space states will be damped out by the usual radiation damping. The projections of ΔX onto the remaining two spin eigenstates are directly related to the loss of polarization due to the impulse perturbation ΔX. Depolarization effects can thus be calculated directly once all perturbations are specified. 7 refs., 4 figs
Information geometry of density matrices and state estimation
International Nuclear Information System (INIS)
Brody, Dorje C
2011-01-01
Given a pure state vector |x) and a density matrix ρ-hat, the function p(x|ρ-hat)= defines a probability density on the space of pure states parameterised by density matrices. The associated Fisher-Rao information measure is used to define a unitary invariant Riemannian metric on the space of density matrices. An alternative derivation of the metric, based on square-root density matrices and trace norms, is provided. This is applied to the problem of quantum-state estimation. In the simplest case of unitary parameter estimation, new higher-order corrections to the uncertainty relations, applicable to general mixed states, are derived. (fast track communication)
A Semi-Vectorization Algorithm to Synthesis of Gravitational Anomaly Quantities on the Earth
Abdollahzadeh, M.; Eshagh, M.; Najafi Alamdari, M.
2009-04-01
The Earth's gravitational potential can be expressed by the well-known spherical harmonic expansion. The computational time of summing up this expansion is an important practical issue which can be reduced by an efficient numerical algorithm. This paper proposes such a method for block-wise synthesizing the anomaly quantities on the Earth surface using vectorization. Fully-vectorization means transformation of the summations to the simple matrix and vector products. It is not a practical for the matrices with large dimensions. Here a semi-vectorization algorithm is proposed to avoid working with large vectors and matrices. It speeds up the computations by using one loop for the summation either on degrees or on orders. The former is a good option to synthesize the anomaly quantities on the Earth surface considering a digital elevation model (DEM). This approach is more efficient than the two-step method which computes the quantities on the reference ellipsoid and continues them upward to the Earth surface. The algorithm has been coded in MATLAB which synthesizes a global grid of 5â²Ã- 5â² (corresponding 9 million points) of gravity anomaly or geoid height using a geopotential model to degree 360 in 10000 seconds by an ordinary computer with 2G RAM.
Chemiluminescence in cryogenic matrices
Lotnik, S. V.; Kazakov, Valeri P.
1989-04-01
The literature data on chemiluminescence (CL) in cryogenic matrices have been classified and correlated for the first time. The role of studies on phosphorescence and CL at low temperatures in the development of cryochemistry is shown. The features of low-temperature CL in matrices of nitrogen and inert gases (fine structure of spectra, matrix effects) and the data on the mobility and reactivity of atoms and radicals at very low temperatures are examined. The trends in the development of studies on CL in cryogenic matrices, such as the search for systems involving polyatomic molecules and extending the forms of CL reactions, are followed. The reactions of active nitrogen with hydrocarbons that are accompanied by light emission and CL in the oxidation of carbenes at T >= 77 K are examined. The bibliography includes 112 references.
Equiangular tight frames and unistochastic matrices
International Nuclear Information System (INIS)
Goyeneche, Dardo; Turek, Ondřej
2017-01-01
We demonstrate that a complex equiangular tight frame composed of N vectors in dimension d , denoted ETF ( d , N ), exists if and only if a certain bistochastic matrix, univocally determined by N and d , belongs to a special class of unistochastic matrices. This connection allows us to find new complex ETFs in infinitely many dimensions and to derive a method to introduce non-trivial free parameters in ETFs. We present an explicit six-parametric family of complex ETF(6,16), which defines a family of symmetric POVMs. Minimal and maximal possible average entanglement of the vectors within this qubit–qutrit family are described. Furthermore, we propose an efficient numerical procedure to compute the unitary matrix underlying a unistochastic matrix, which we apply to find all existing classes of complex ETFs containing up to 20 vectors. (paper)
Eisenman, Richard L
2005-01-01
This outstanding text and reference applies matrix ideas to vector methods, using physical ideas to illustrate and motivate mathematical concepts but employing a mathematical continuity of development rather than a physical approach. The author, who taught at the U.S. Air Force Academy, dispenses with the artificial barrier between vectors and matrices--and more generally, between pure and applied mathematics.Motivated examples introduce each idea, with interpretations of physical, algebraic, and geometric contexts, in addition to generalizations to theorems that reflect the essential structur
Deterministic matrices matching the compressed sensing phase transitions of Gaussian random matrices
Monajemi, Hatef; Jafarpour, Sina; Gavish, Matan; Donoho, David L.; Ambikasaran, Sivaram; Bacallado, Sergio; Bharadia, Dinesh; Chen, Yuxin; Choi, Young; Chowdhury, Mainak; Chowdhury, Soham; Damle, Anil; Fithian, Will; Goetz, Georges; Grosenick, Logan
2012-01-01
In compressed sensing, one takes samples of an N-dimensional vector using an matrix A, obtaining undersampled measurements . For random matrices with independent standard Gaussian entries, it is known that, when is k-sparse, there is a precisely determined phase transition: for a certain region in the (,)-phase diagram, convex optimization typically finds the sparsest solution, whereas outside that region, it typically fails. It has been shown empirically that the same property—with the ...
Infinite matrices and sequence spaces
Cooke, Richard G
2014-01-01
This clear and correct summation of basic results from a specialized field focuses on the behavior of infinite matrices in general, rather than on properties of special matrices. Three introductory chapters guide students to the manipulation of infinite matrices, covering definitions and preliminary ideas, reciprocals of infinite matrices, and linear equations involving infinite matrices.From the fourth chapter onward, the author treats the application of infinite matrices to the summability of divergent sequences and series from various points of view. Topics include consistency, mutual consi
2014-04-01
materials, the affinity ligand would need identification , as well as chemistries that graft the affinity ligand onto the surface of magnetic...ACTIVE CAPTURE MATRICES FOR THE DETECTION/ IDENTIFICATION OF PHARMACEUTICALS...6 As shown in Figure 2.3-1a, the spectra exhibit similar baselines and the spectral peaks lineup . Under these circumstances, the spectral
Deterministic matrices matching the compressed sensing phase transitions of Gaussian random matrices
Monajemi, Hatef; Jafarpour, Sina; Gavish, Matan; Donoho, David L.; Ambikasaran, Sivaram; Bacallado, Sergio; Bharadia, Dinesh; Chen, Yuxin; Choi, Young; Chowdhury, Mainak; Chowdhury, Soham; Damle, Anil; Fithian, Will; Goetz, Georges; Grosenick, Logan; Gross, Sam; Hills, Gage; Hornstein, Michael; Lakkam, Milinda; Lee, Jason; Li, Jian; Liu, Linxi; Sing-Long, Carlos; Marx, Mike; Mittal, Akshay; Monajemi, Hatef; No, Albert; Omrani, Reza; Pekelis, Leonid; Qin, Junjie; Raines, Kevin; Ryu, Ernest; Saxe, Andrew; Shi, Dai; Siilats, Keith; Strauss, David; Tang, Gary; Wang, Chaojun; Zhou, Zoey; Zhu, Zhen
2013-01-01
In compressed sensing, one takes samples of an N-dimensional vector using an matrix A, obtaining undersampled measurements . For random matrices with independent standard Gaussian entries, it is known that, when is k-sparse, there is a precisely determined phase transition: for a certain region in the (,)-phase diagram, convex optimization typically finds the sparsest solution, whereas outside that region, it typically fails. It has been shown empirically that the same property—with the same phase transition location—holds for a wide range of non-Gaussian random matrix ensembles. We report extensive experiments showing that the Gaussian phase transition also describes numerous deterministic matrices, including Spikes and Sines, Spikes and Noiselets, Paley Frames, Delsarte-Goethals Frames, Chirp Sensing Matrices, and Grassmannian Frames. Namely, for each of these deterministic matrices in turn, for a typical k-sparse object, we observe that convex optimization is successful over a region of the phase diagram that coincides with the region known for Gaussian random matrices. Our experiments considered coefficients constrained to for four different sets , and the results establish our finding for each of the four associated phase transitions. PMID:23277588
An algorithmic characterization of P-matricity
Ben Gharbia , Ibtihel; Gilbert , Jean Charles
2013-01-01
International audience; It is shown that a matrix M is a P-matrix if and only if, whatever is the vector q, the Newton-min algorithm does not cycle between two points when it is used to solve the linear complementarity problem 0 ≤ x ⊥ (Mx+q) ≥ 0.; Nous montrons dans cet article qu'une matrice M est une P-matrice si, et seulement si, quel que soit le vecteur q, l'algorithme de Newton-min ne fait pas de cycle de deux points lorsqu'il est utilisé pour résoudre le problème de compl\\émentarité lin...
Bapat, Ravindra B
2014-01-01
This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reo...
Modeling and Forecasting Large Realized Covariance Matrices and Portfolio Choice
Callot, Laurent A.F.; Kock, Anders B.; Medeiros, Marcelo C.
2017-01-01
We consider modeling and forecasting large realized covariance matrices by penalized vector autoregressive models. We consider Lasso-type estimators to reduce the dimensionality and provide strong theoretical guarantees on the forecast capability of our procedure. We show that we can forecast
Hierarchical quark mass matrices
International Nuclear Information System (INIS)
Rasin, A.
1998-02-01
I define a set of conditions that the most general hierarchical Yukawa mass matrices have to satisfy so that the leading rotations in the diagonalization matrix are a pair of (2,3) and (1,2) rotations. In addition to Fritzsch structures, examples of such hierarchical structures include also matrices with (1,3) elements of the same order or even much larger than the (1,2) elements. Such matrices can be obtained in the framework of a flavor theory. To leading order, the values of the angle in the (2,3) plane (s 23 ) and the angle in the (1,2) plane (s 12 ) do not depend on the order in which they are taken when diagonalizing. We find that any of the Cabbibo-Kobayashi-Maskawa matrix parametrizations that consist of at least one (1,2) and one (2,3) rotation may be suitable. In the particular case when the s 13 diagonalization angles are sufficiently small compared to the product s 12 s 23 , two special CKM parametrizations emerge: the R 12 R 23 R 12 parametrization follows with s 23 taken before the s 12 rotation, and vice versa for the R 23 R 12 R 23 parametrization. (author)
M Wedderburn, J H
1934-01-01
It is the organization and presentation of the material, however, which make the peculiar appeal of the book. This is no mere compendium of results-the subject has been completely reworked and the proofs recast with the skill and elegance which come only from years of devotion. -Bulletin of the American Mathematical Society The very clear and simple presentation gives the reader easy access to the more difficult parts of the theory. -Jahrbuch über die Fortschritte der Mathematik In 1937, the theory of matrices was seventy-five years old. However, many results had only recently evolved from sp
Schneider, Hans
1989-01-01
Linear algebra is one of the central disciplines in mathematics. A student of pure mathematics must know linear algebra if he is to continue with modern algebra or functional analysis. Much of the mathematics now taught to engineers and physicists requires it.This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related t
Intermittency and random matrices
Sokoloff, Dmitry; Illarionov, E. A.
2015-08-01
A spectacular phenomenon of intermittency, i.e. a progressive growth of higher statistical moments of a physical field excited by an instability in a random medium, attracted the attention of Zeldovich in the last years of his life. At that time, the mathematical aspects underlying the physical description of this phenomenon were still under development and relations between various findings in the field remained obscure. Contemporary results from the theory of the product of independent random matrices (the Furstenberg theory) allowed the elaboration of the phenomenon of intermittency in a systematic way. We consider applications of the Furstenberg theory to some problems in cosmology and dynamo theory.
Dimension from covariance matrices.
Carroll, T L; Byers, J M
2017-02-01
We describe a method to estimate embedding dimension from a time series. This method includes an estimate of the probability that the dimension estimate is valid. Such validity estimates are not common in algorithms for calculating the properties of dynamical systems. The algorithm described here compares the eigenvalues of covariance matrices created from an embedded signal to the eigenvalues for a covariance matrix of a Gaussian random process with the same dimension and number of points. A statistical test gives the probability that the eigenvalues for the embedded signal did not come from the Gaussian random process.
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
Generalisations of Fisher Matrices
Directory of Open Access Journals (Sweden)
Alan Heavens
2016-06-01
Full Text Available Fisher matrices play an important role in experimental design and in data analysis. Their primary role is to make predictions for the inference of model parameters—both their errors and covariances. In this short review, I outline a number of extensions to the simple Fisher matrix formalism, covering a number of recent developments in the field. These are: (a situations where the data (in the form of ( x , y pairs have errors in both x and y; (b modifications to parameter inference in the presence of systematic errors, or through fixing the values of some model parameters; (c Derivative Approximation for LIkelihoods (DALI - higher-order expansions of the likelihood surface, going beyond the Gaussian shape approximation; (d extensions of the Fisher-like formalism, to treat model selection problems with Bayesian evidence.
Energy Technology Data Exchange (ETDEWEB)
Fukuma, Masafumi; Sugishita, Sotaro; Umeda, Naoya [Department of Physics, Kyoto University,Kitashirakawa Oiwake-cho, Kyoto 606-8502 (Japan)
2015-07-17
We propose a class of models which generate three-dimensional random volumes, where each configuration consists of triangles glued together along multiple hinges. The models have matrices as the dynamical variables and are characterized by semisimple associative algebras A. Although most of the diagrams represent configurations which are not manifolds, we show that the set of possible diagrams can be drastically reduced such that only (and all of the) three-dimensional manifolds with tetrahedral decompositions appear, by introducing a color structure and taking an appropriate large N limit. We examine the analytic properties when A is a matrix ring or a group ring, and show that the models with matrix ring have a novel strong-weak duality which interchanges the roles of triangles and hinges. We also give a brief comment on the relationship of our models with the colored tensor models.
VanderLaan Circulant Type Matrices
Directory of Open Access Journals (Sweden)
Hongyan Pan
2015-01-01
Full Text Available Circulant matrices have become a satisfactory tools in control methods for modern complex systems. In the paper, VanderLaan circulant type matrices are presented, which include VanderLaan circulant, left circulant, and g-circulant matrices. The nonsingularity of these special matrices is discussed by the surprising properties of VanderLaan numbers. The exact determinants of VanderLaan circulant type matrices are given by structuring transformation matrices, determinants of well-known tridiagonal matrices, and tridiagonal-like matrices. The explicit inverse matrices of these special matrices are obtained by structuring transformation matrices, inverses of known tridiagonal matrices, and quasi-tridiagonal matrices. Three kinds of norms and lower bound for the spread of VanderLaan circulant and left circulant matrix are given separately. And we gain the spectral norm of VanderLaan g-circulant matrix.
Diagonalization of the mass matrices
International Nuclear Information System (INIS)
Rhee, S.S.
1984-01-01
It is possible to make 20 types of 3x3 mass matrices which are hermitian. We have obtained unitary matrices which could diagonalize each mass matrix. Since the three elements of mass matrix can be expressed in terms of the three eigenvalues, msub(i), we can also express the unitary matrix in terms of msub(i). (Author)
Intrinsic character of Stokes matrices
Gagnon, Jean-François; Rousseau, Christiane
2017-02-01
Two germs of linear analytic differential systems x k + 1Y‧ = A (x) Y with a non-resonant irregular singularity are analytically equivalent if and only if they have the same eigenvalues and equivalent collections of Stokes matrices. The Stokes matrices are the transition matrices between sectors on which the system is analytically equivalent to its formal normal form. Each sector contains exactly one separating ray for each pair of eigenvalues. A rotation in S allows supposing that R+ lies in the intersection of two sectors. Reordering of the coordinates of Y allows ordering the real parts of the eigenvalues, thus yielding triangular Stokes matrices. However, the choice of the rotation in x is not canonical. In this paper we establish how the collection of Stokes matrices depends on this rotation, and hence on a chosen order of the projection of the eigenvalues on a line through the origin.
Newell, Homer E
2006-01-01
When employed with skill and understanding, vector analysis can be a practical and powerful tool. This text develops the algebra and calculus of vectors in a manner useful to physicists and engineers. Numerous exercises (with answers) not only provide practice in manipulation but also help establish students' physical and geometric intuition in regard to vectors and vector concepts.Part I, the basic portion of the text, consists of a thorough treatment of vector algebra and the vector calculus. Part II presents the illustrative matter, demonstrating applications to kinematics, mechanics, and e
Hoffmann, Banesh
1975-01-01
From his unusual beginning in ""Defining a vector"" to his final comments on ""What then is a vector?"" author Banesh Hoffmann has written a book that is provocative and unconventional. In his emphasis on the unresolved issue of defining a vector, Hoffmann mixes pure and applied mathematics without using calculus. The result is a treatment that can serve as a supplement and corrective to textbooks, as well as collateral reading in all courses that deal with vectors. Major topics include vectors and the parallelogram law; algebraic notation and basic ideas; vector algebra; scalars and scalar p
Perils of parsimony: properties of reduced-rank estimates of genetic covariance matrices.
Meyer, Karin; Kirkpatrick, Mark
2008-10-01
Eigenvalues and eigenvectors of covariance matrices are important statistics for multivariate problems in many applications, including quantitative genetics. Estimates of these quantities are subject to different types of bias. This article reviews and extends the existing theory on these biases, considering a balanced one-way classification and restricted maximum-likelihood estimation. Biases are due to the spread of sample roots and arise from ignoring selected principal components when imposing constraints on the parameter space, to ensure positive semidefinite estimates or to estimate covariance matrices of chosen, reduced rank. In addition, it is shown that reduced-rank estimators that consider only the leading eigenvalues and -vectors of the "between-group" covariance matrix may be biased due to selecting the wrong subset of principal components. In a genetic context, with groups representing families, this bias is inverse proportional to the degree of genetic relationship among family members, but is independent of sample size. Theoretical results are supplemented by a simulation study, demonstrating close agreement between predicted and observed bias for large samples. It is emphasized that the rank of the genetic covariance matrix should be chosen sufficiently large to accommodate all important genetic principal components, even though, paradoxically, this may require including a number of components with negligible eigenvalues. A strategy for rank selection in practical analyses is outlined.
Flexible Bayesian Dynamic Modeling of Covariance and Correlation Matrices
Lan, Shiwei
2017-11-08
Modeling covariance (and correlation) matrices is a challenging problem due to the large dimensionality and positive-definiteness constraint. In this paper, we propose a novel Bayesian framework based on decomposing the covariance matrix into variance and correlation matrices. The highlight is that the correlations are represented as products of vectors on unit spheres. We propose a variety of distributions on spheres (e.g. the squared-Dirichlet distribution) to induce flexible prior distributions for covariance matrices that go beyond the commonly used inverse-Wishart prior. To handle the intractability of the resulting posterior, we introduce the adaptive $\\\\Delta$-Spherical Hamiltonian Monte Carlo. We also extend our structured framework to dynamic cases and introduce unit-vector Gaussian process priors for modeling the evolution of correlation among multiple time series. Using an example of Normal-Inverse-Wishart problem, a simulated periodic process, and an analysis of local field potential data (collected from the hippocampus of rats performing a complex sequence memory task), we demonstrated the validity and effectiveness of our proposed framework for (dynamic) modeling covariance and correlation matrices.
Special matrices of mathematical physics stochastic, circulant and Bell matrices
Aldrovandi, R
2001-01-01
This book expounds three special kinds of matrices that are of physical interest, centering on physical examples. Stochastic matrices describe dynamical systems of many different types, involving (or not) phenomena like transience, dissipation, ergodicity, nonequilibrium, and hypersensitivity to initial conditions. The main characteristic is growth by agglomeration, as in glass formation. Circulants are the building blocks of elementary Fourier analysis and provide a natural gateway to quantum mechanics and noncommutative geometry. Bell polynomials offer closed expressions for many formulas co
Computing with linear equations and matrices
International Nuclear Information System (INIS)
Churchhouse, R.F.
1983-01-01
Systems of linear equations and matrices arise in many disciplines. The equations may accurately represent conditions satisfied by a system or, more likely, provide an approximation to a more complex system of non-linear or differential equations. The system may involve a few or many thousand unknowns and each individual equation may involve few or many of them. Over the past 50 years a vast literature on methods for solving systems of linear equations and the associated problems of finding the inverse or eigenvalues of a matrix has been produced. These lectures cover those methods which have been found to be most useful for dealing with such types of problem. References are given where appropriate and attention is drawn to the possibility of improved methods for use on vector and parallel processors. (orig.)
Wolstenholme, E Œ
1978-01-01
Elementary Vectors, Third Edition serves as an introductory course in vector analysis and is intended to present the theoretical and application aspects of vectors. The book covers topics that rigorously explain and provide definitions, principles, equations, and methods in vector analysis. Applications of vector methods to simple kinematical and dynamical problems; central forces and orbits; and solutions to geometrical problems are discussed as well. This edition of the text also provides an appendix, intended for students, which the author hopes to bridge the gap between theory and appl
Tensor Dictionary Learning for Positive Definite Matrices.
Sivalingam, Ravishankar; Boley, Daniel; Morellas, Vassilios; Papanikolopoulos, Nikolaos
2015-11-01
Sparse models have proven to be extremely successful in image processing and computer vision. However, a majority of the effort has been focused on sparse representation of vectors and low-rank models for general matrices. The success of sparse modeling, along with popularity of region covariances, has inspired the development of sparse coding approaches for these positive definite descriptors. While in earlier work, the dictionary was formed from all, or a random subset of, the training signals, it is clearly advantageous to learn a concise dictionary from the entire training set. In this paper, we propose a novel approach for dictionary learning over positive definite matrices. The dictionary is learned by alternating minimization between sparse coding and dictionary update stages, and different atom update methods are described. A discriminative version of the dictionary learning approach is also proposed, which simultaneously learns dictionaries for different classes in classification or clustering. Experimental results demonstrate the advantage of learning dictionaries from data both from reconstruction and classification viewpoints. Finally, a software library is presented comprising C++ binaries for all the positive definite sparse coding and dictionary learning approaches presented here.
The invariant theory of matrices
Concini, Corrado De
2017-01-01
This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of m\\times m matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving the first fundamental theorem that describes a set of generators in the ring of invariants, and the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case...
Degrees of polarization for a quantum field
International Nuclear Information System (INIS)
Sanchez-Soto, L L; Soederholm, J; Yustas, E C; Klimov, A B; Bjoerk, G
2006-01-01
Unpolarized light is invariant with respect to any SU(2) polarization transformation. Since this fully characterizes the set of density matrices representing unpolarized states, we introduce the degree of polarization of a quantum state as its distance to the set of unpolarized states. We discuss different candidates of distance, and show that they induce fundamentally different degrees of polarization
Quantum matrices in two dimensions
International Nuclear Information System (INIS)
Ewen, H.; Ogievetsky, O.; Wess, J.
1991-01-01
Quantum matrices in two-dimensions, admitting left and right quantum spaces, are classified: they fall into two families, the 2-parametric family GL p,q (2) and a 1-parametric family GL α J (2). Phenomena previously found for GL p,q (2) hold in this general situation: (a) powers of quantum matrices are again quantum and (b) entries of the logarithm of a two-dimensional quantum matrix form a Lie algebra. (orig.)
Directory of Open Access Journals (Sweden)
A. A. Zolotin
2015-07-01
Full Text Available Posteriori inference is one of the three kinds of probabilistic-logic inferences in the probabilistic graphical models theory and the base for processing of knowledge patterns with probabilistic uncertainty using Bayesian networks. The paper deals with a task of local posteriori inference description in algebraic Bayesian networks that represent a class of probabilistic graphical models by means of matrix-vector equations. The latter are essentially based on the use of tensor product of matrices, Kronecker degree and Hadamard product. Matrix equations for calculating posteriori probabilities vectors within posteriori inference in knowledge patterns with quanta propositions are obtained. Similar equations of the same type have already been discussed within the confines of the theory of algebraic Bayesian networks, but they were built only for the case of posteriori inference in the knowledge patterns on the ideals of conjuncts. During synthesis and development of matrix-vector equations on quanta propositions probability vectors, a number of earlier results concerning normalizing factors in posteriori inference and assignment of linear projective operator with a selector vector was adapted. We consider all three types of incoming evidences - deterministic, stochastic and inaccurate - combined with scalar and interval estimation of probability truth of propositional formulas in the knowledge patterns. Linear programming problems are formed. Their solution gives the desired interval values of posterior probabilities in the case of inaccurate evidence or interval estimates in a knowledge pattern. That sort of description of a posteriori inference gives the possibility to extend the set of knowledge pattern types that we can use in the local and global posteriori inference, as well as simplify complex software implementation by use of existing third-party libraries, effectively supporting submission and processing of matrices and vectors when
Manin matrices and Talalaev's formula
International Nuclear Information System (INIS)
Chervov, A; Falqui, G
2008-01-01
In this paper we study properties of Lax and transfer matrices associated with quantum integrable systems. Our point of view stems from the fact that their elements satisfy special commutation properties, considered by Yu I Manin some 20 years ago at the beginning of quantum group theory. These are the commutation properties of matrix elements of linear homomorphisms between polynomial rings; more explicitly these read: (1) elements of the same column commute; (2) commutators of the cross terms are equal: [M ij , M kl ] [M kj , M il ] (e.g. [M 11 , M 22 ] = [M 21 , M 12 ]). The main aim of this paper is twofold: on the one hand we observe and prove that such matrices (which we call Manin matrices in short) behave almost as well as matrices with commutative elements. Namely, the theorems of linear algebra (e.g., a natural definition of the determinant, the Cayley-Hamilton theorem, the Newton identities and so on and so forth) have a straightforward counterpart in the case of Manin matrices. On the other hand, we remark that such matrices are somewhat ubiquitous in the theory of quantum integrability. For instance, Manin matrices (and their q-analogs) include matrices satisfying the Yang-Baxter relation 'RTT=TTR' and the so-called Cartier-Foata matrices. Also, they enter Talalaev's remarkable formulae: det(∂ z -L gaudin (z)), det(1-e -∂z T Yangian (z)) for the 'quantum spectral curve', and appear in the separation of variables problem and Capelli identities. We show that theorems of linear algebra, after being established for such matrices, have various applications to quantum integrable systems and Lie algebras, e.g. in the construction of new generators in Z(U crit (gl-hat n )) (and, in general, in the construction of quantum conservation laws), in the Knizhnik-Zamolodchikov equation, and in the problem of Wick ordering. We propose, in the appendix, a construction of quantum separated variables for the XXX-Heisenberg system
Geber, Beverly
1987-01-01
The author describes the growing movement toward accreditation for human resources development professionals. She covers the issue of diversity, undergraduate versus graduate degrees, and future trends. (CH)
On reflectionless equi-transmitting matrices
Directory of Open Access Journals (Sweden)
Pavel Kurasov
2014-01-01
Full Text Available Reflectionless equi-transmitting unitary matrices are studied in connection to matching conditions in quantum graphs. All possible such matrices of size 6 are described explicitly. It is shown that such matrices form 30 six-parameter families intersected along 12 five-parameter families closely connected to conference matrices.
Brand, Louis
2006-01-01
The use of vectors not only simplifies treatments of differential geometry, mechanics, hydrodynamics, and electrodynamics, but also makes mathematical and physical concepts more tangible and easy to grasp. This text for undergraduates was designed as a short introductory course to give students the tools of vector algebra and calculus, as well as a brief glimpse into these subjects' manifold applications. The applications are developed to the extent that the uses of the potential function, both scalar and vector, are fully illustrated. Moreover, the basic postulates of vector analysis are brou
Elliptic-symmetry vector optical fields.
Pan, Yue; Li, Yongnan; Li, Si-Min; Ren, Zhi-Cheng; Kong, Ling-Jun; Tu, Chenghou; Wang, Hui-Tian
2014-08-11
We present in principle and demonstrate experimentally a new kind of vector fields: elliptic-symmetry vector optical fields. This is a significant development in vector fields, as this breaks the cylindrical symmetry and enriches the family of vector fields. Due to the presence of an additional degrees of freedom, which is the interval between the foci in the elliptic coordinate system, the elliptic-symmetry vector fields are more flexible than the cylindrical vector fields for controlling the spatial structure of polarization and for engineering the focusing fields. The elliptic-symmetry vector fields can find many specific applications from optical trapping to optical machining and so on.
DEFF Research Database (Denmark)
2012-01-01
The present invention relates to a compact, reliable and low-cost vector velocimeter for example for determining velocities of particles suspended in a gas or fluid flow, or for determining velocity, displacement, rotation, or vibration of a solid surface, the vector velocimeter comprising a laser...
Free probability and random matrices
Mingo, James A
2017-01-01
This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory. The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.
Chequered surfaces and complex matrices
International Nuclear Information System (INIS)
Morris, T.R.; Southampton Univ.
1991-01-01
We investigate a large-N matrix model involving general complex matrices. It can be reinterpreted as a model of two hermitian matrices with specific couplings, and as a model of positive definite hermitian matrices. Large-N perturbation theory generates dynamical triangulations in which the triangles can be chequered (i.e. coloured so that neighbours are opposite colours). On a sphere there is a simple relation between such triangulations and those generated by the single hermitian matrix model. For the torus (and a quartic potential) we solve the counting problem for the number of triangulations that cannot be quechered. The critical physics of chequered triangulations is the same as that of the hermitian matrix model. We show this explicitly by solving non-perturbatively pure two-dimensional ''chequered'' gravity. The interpretative framework given here applies to a number of other generalisations of the hermitian matrix model. (orig.)
Modified conjugate gradient method for diagonalizing large matrices.
Jie, Quanlin; Liu, Dunhuan
2003-11-01
We present an iterative method to diagonalize large matrices. The basic idea is the same as the conjugate gradient (CG) method, i.e, minimizing the Rayleigh quotient via its gradient and avoiding reintroducing errors to the directions of previous gradients. Each iteration step is to find lowest eigenvector of the matrix in a subspace spanned by the current trial vector and the corresponding gradient of the Rayleigh quotient, as well as some previous trial vectors. The gradient, together with the previous trial vectors, play a similar role as the conjugate gradient of the original CG algorithm. Our numeric tests indicate that this method converges significantly faster than the original CG method. And the computational cost of one iteration step is about the same as the original CG method. It is suitable for first principle calculations.
Loop diagrams without γ matrices
International Nuclear Information System (INIS)
McKeon, D.G.C.; Rebhan, A.
1993-01-01
By using a quantum-mechanical path integral to compute matrix elements of the form left-angle x|exp(-iHt)|y right-angle, radiative corrections in quantum-field theory can be evaluated without encountering loop-momentum integrals. In this paper we demonstrate how Dirac γ matrices that occur in the proper-time ''Hamiltonian'' H lead to the introduction of a quantum-mechanical path integral corresponding to a superparticle analogous to one proposed recently by Fradkin and Gitman. Direct evaluation of this path integral circumvents many of the usual algebraic manipulations of γ matrices in the computation of quantum-field-theoretical Green's functions involving fermions
Immanant Conversion on Symmetric Matrices
Directory of Open Access Journals (Sweden)
Purificação Coelho M.
2014-01-01
Full Text Available Letr Σn(C denote the space of all n χ n symmetric matrices over the complex field C. The main objective of this paper is to prove that the maps Φ : Σn(C -> Σn (C satisfying for any fixed irre- ducible characters X, X' -SC the condition dx(A +aB = dχ·(Φ(Α + αΦ(Β for all matrices A,В ε Σ„(С and all scalars a ε C are automatically linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on ΣИ(С.
Critical statistics for non-Hermitian matrices
International Nuclear Information System (INIS)
Garcia-Garcia, A.M.; Verbaarschot, J.J.M.; Nishigaki, S.M.
2002-01-01
We introduce a generalized ensemble of non-Hermitian matrices interpolating between the Gaussian Unitary Ensemble, the Ginibre ensemble, and the Poisson ensemble. The joint eigenvalue distribution of this model is obtained by means of an extension of the Itzykson-Zuber formula to general complex matrices. Its correlation functions are studied both in the case of weak non-Hermiticity and in the case of strong non-Hermiticity. In the weak non-Hermiticity limit we show that the spectral correlations in the bulk of the spectrum display critical statistics: the asymptotic linear behavior of the number variance is already approached for energy differences of the order of the eigenvalue spacing. To lowest order, its slope does not depend on the degree of non-Hermiticity. Close the edge, the spectral correlations are similar to the Hermitian case. In the strong non-Hermiticity limit the crossover behavior from the Ginibre ensemble to the Poisson ensemble first appears close to the surface of the spectrum. Our model may be relevant for the description of the spectral correlations of an open disordered system close to an Anderson transition
Hypersymmetric functions and Pochhammers of 2×2 nonautonomous matrices
Directory of Open Access Journals (Sweden)
A. F. Antippa
2004-01-01
Full Text Available We introduce the hypersymmetric functions of 2×2 nonautonomous matrices and show that they are related, by simple expressions, to the Pochhammers (factorial polynomials of these matrices. The hypersymmetric functions are generalizations of the associated elementary symmetric functions, and for a specific class of 2×2 matrices, having a high degree of symmetry, they reduce to these latter functions. This class of matrices includes rotations, Lorentz boosts, and discrete time generators for the harmonic oscillators. The hypersymmetric functions are defined over four sets of independent indeterminates using a triplet of interrelated binary partitions. We work out the algebra of this triplet of partitions and then make use of the results in order to simplify the expressions for the hypersymmetric functions for a special class of matrices. In addition to their obvious applications in matrix theory, in coupled difference equations, and in the theory of symmetric functions, the results obtained here also have useful applications in problems involving successive rotations, successive Lorentz transformations, discrete harmonic oscillators, and linear two-state systems.
Guilfoyle, Richard A.; Smith, Lloyd M.
1994-01-01
A vector comprising a filamentous phage sequence containing a first copy of filamentous phage gene X and other sequences necessary for the phage to propagate is disclosed. The vector also contains a second copy of filamentous phage gene X downstream from a promoter capable of promoting transcription in a bacterial host. In a preferred form of the present invention, the filamentous phage is M13 and the vector additionally includes a restriction endonuclease site located in such a manner as to substantially inactivate the second gene X when a DNA sequence is inserted into the restriction site.
Guilfoyle, R.A.; Smith, L.M.
1994-12-27
A vector comprising a filamentous phage sequence containing a first copy of filamentous phage gene X and other sequences necessary for the phage to propagate is disclosed. The vector also contains a second copy of filamentous phage gene X downstream from a promoter capable of promoting transcription in a bacterial host. In a preferred form of the present invention, the filamentous phage is M13 and the vector additionally includes a restriction endonuclease site located in such a manner as to substantially inactivate the second gene X when a DNA sequence is inserted into the restriction site. 2 figures.
Extended vector-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Kimura, Rampei; Naruko, Atsushi; Yoshida, Daisuke, E-mail: rampei@th.phys.titech.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: yoshida@th.phys.titech.ac.jp [Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 (Japan)
2017-01-01
Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Proca theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.
On families of anticommuting matrices
Czech Academy of Sciences Publication Activity Database
Hrubeš, Pavel
2016-01-01
Roč. 493, March 15 (2016), s. 494-507 ISSN 0024-3795 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : anticommuting matrices * sum-of-squares formulas Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016 http://www.sciencedirect.com/science/article/pii/S0024379515007296
On families of anticommuting matrices
Czech Academy of Sciences Publication Activity Database
Hrubeš, Pavel
2016-01-01
Roč. 493, March 15 (2016), s. 494-507 ISSN 0024-3795 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : anticommuting matrices * sum -of-squares formulas Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016 http://www.sciencedirect.com/science/article/pii/S0024379515007296
Levine, Robert
2004-01-01
The cross-product is a mathematical operation that is performed between two 3-dimensional vectors. The result is a vector that is orthogonal or perpendicular to both of them. Learning about this for the first time while taking Calculus-III, the class was taught that if AxB = AxC, it does not necessarily follow that B = C. This seemed baffling. The…
The modified Gauss diagonalization of polynomial matrices
International Nuclear Information System (INIS)
Saeed, K.
1982-10-01
The Gauss algorithm for diagonalization of constant matrices is modified for application to polynomial matrices. Due to this modification the diagonal elements become pure polynomials rather than rational functions. (author)
Double stochastic matrices in quantum mechanics
International Nuclear Information System (INIS)
Louck, J.D.
1997-01-01
The general set of doubly stochastic matrices of order n corresponding to ordinary nonrelativistic quantum mechanical transition probability matrices is given. Lande's discussion of the nonquantal origin of such matrices is noted. Several concrete examples are presented for elementary and composite angular momentum systems with the focus on the unitary symmetry associated with such systems in the spirit of the recent work of Bohr and Ulfbeck. Birkhoff's theorem on doubly stochastic matrices of order n is reformulated in a geometrical language suitable for application to the subset of quantum mechanical doubly stochastic matrices. Specifically, it is shown that the set of points on the unit sphere in cartesian n'-space is subjective with the set of doubly stochastic matrices of order n. The question is raised, but not answered, as to what is the subset of points of this unit sphere that correspond to the quantum mechanical transition probability matrices, and what is the symmetry group of this subset of matrices
Virial expansion for almost diagonal random matrices
Yevtushenko, Oleg; Kravtsov, Vladimir E.
2003-08-01
Energy level statistics of Hermitian random matrices hat H with Gaussian independent random entries Higeqj is studied for a generic ensemble of almost diagonal random matrices with langle|Hii|2rangle ~ 1 and langle|Hi\
Phenomenological mass matrices with a democratic warp
International Nuclear Information System (INIS)
Kleppe, A.
2018-01-01
Taking into account all available data on the mass sector, we obtain unitary rotation matrices that diagonalize the quark matrices by using a specific parametrization of the Cabibbo-Kobayashi-Maskawa mixing matrix. In this way, we find mass matrices for the up- and down-quark sectors of a specific, symmetric form, with traces of a democratic texture.
International Nuclear Information System (INIS)
Bombardelli, Diego
2016-01-01
In these notes we review the S-matrix theory in (1+1)-dimensional integrable models, focusing mainly on the relativistic case. Once the main definitions and physical properties are introduced, we discuss the factorization of scattering processes due to integrability. We then focus on the analytic properties of the two-particle scattering amplitude and illustrate the derivation of the S-matrices for all the possible bound states using the so-called bootstrap principle. General algebraic structures underlying the S-matrix theory and its relation with the form factors axioms are briefly mentioned. Finally, we discuss the S-matrices of sine-Gordon and SU (2), SU (3) chiral Gross–Neveu models. (topical review)
Synthesised standards in natural matrices
International Nuclear Information System (INIS)
Olsen, D.G.
1980-01-01
The problem of securing the most reliable standards for the accurate analysis of radionuclides is discussed in the paper and in the comment on the paper. It is contended in the paper that the best standards can be created by quantitative addition of accurately known spiking solutions into carefully selected natural matrices. On the other hand it is argued that many natural materials can be successfully standardized for numerous trace constituents. Both points of view are supported with examples. (U.K.)
Covariance matrices and applications to the field of nuclear data
International Nuclear Information System (INIS)
Smith, D.L.
1981-11-01
A student's introduction to covariance error analysis and least-squares evaluation of data is provided. It is shown that the basic formulas used in error propagation can be derived from a consideration of the geometry of curvilinear coordinates. Procedures for deriving covariances for scaler and vector functions of several variables are presented. Proper methods for reporting experimental errors and for deriving covariance matrices from these errors are indicated. The generalized least-squares method for evaluating experimental data is described. Finally, the use of least-squares techniques in data fitting applications is discussed. Specific examples of the various procedures are presented to clarify the concepts
No Eigenvalues Outside the Limiting Support of Generally Correlated Gaussian Matrices
Kammoun, Abla
2016-05-04
This paper investigates the behaviour of the spectrum of generally correlated Gaussian random matrices whose columns are zero-mean independent vectors but have different correlations, under the specific regime where the number of their columns and that of their rows grow at infinity with the same pace. Following the approach proposed in [1], we prove that under some mild conditions, there is no eigenvalue outside the limiting support of generally correlated Gaussian matrices. As an outcome of this result, we establish that the smallest singular value of these matrices is almost surely greater than zero. From a practical perspective, this control of the smallest singular value is paramount to applications from statistical signal processing and wireless communication, in which this kind of matrices naturally arise.
No Eigenvalues Outside the Limiting Support of Generally Correlated Gaussian Matrices
Kammoun, Abla; Alouini, Mohamed-Slim
2016-01-01
This paper investigates the behaviour of the spectrum of generally correlated Gaussian random matrices whose columns are zero-mean independent vectors but have different correlations, under the specific regime where the number of their columns and that of their rows grow at infinity with the same pace. Following the approach proposed in [1], we prove that under some mild conditions, there is no eigenvalue outside the limiting support of generally correlated Gaussian matrices. As an outcome of this result, we establish that the smallest singular value of these matrices is almost surely greater than zero. From a practical perspective, this control of the smallest singular value is paramount to applications from statistical signal processing and wireless communication, in which this kind of matrices naturally arise.
Fabrication of chemically cross-linked porous gelatin matrices.
Bozzini, Sabrina; Petrini, Paola; Altomare, Lina; Tanzi, Maria Cristina
2009-01-01
The aim of this study was to chemically cross-link gelatin, by reacting its free amino groups with an aliphatic diisocyanate. To produce hydrogels with controllable properties, the number of reacting amino groups was carefully determined. Porosity was introduced into the gelatin-based hydrogels through the lyophilization process. Porous and non-porous matrices were characterized with respect to their chemical structure, morphology, water uptake and mechanical properties. The physical, chemical and mechanical properties of the porous matrices are related to the extent of their cross-linking, showing that they can be controlled by varying the reaction parameters. Water uptake values (24 hours) vary between 160% and 200% as the degree of cross-linking increases. The flexibility of the samples also decreases by changing the extent of cross-linking. Young's modulus shows values between 0.188 KPa, for the highest degree, and 0.142 KPa for the lowest degree. The matrices are potential candidates for use as tissue-engineering scaffolds by modulating their physical chemical properties according to the specific application.
Thomas, E. G. F.
2012-01-01
This paper deals with the theory of integration of scalar functions with respect to a measure with values in a, not necessarily locally convex, topological vector space. It focuses on the extension of such integrals from bounded measurable functions to the class of integrable functions, proving
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
A Perron-Frobenius theory for block matrices associated to a multiplex network
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.
Study on vulnerability matrices of masonry buildings of mainland China
Sun, Baitao; Zhang, Guixin
2018-04-01
The degree and distribution of damage to buildings subjected to earthquakes is a concern of the Chinese Government and the public. Seismic damage data indicates that seismic capacities of different types of building structures in various regions throughout mainland China are different. Furthermore, the seismic capacities of the same type of structure in different regions may vary. The contributions of this research are summarized as follows: 1) Vulnerability matrices and earthquake damage matrices of masonry structures in mainland China were chosen as research samples. The aim was to analyze the differences in seismic capacities of sample matrices and to present general rules for categorizing seismic resistance. 2) Curves relating the percentage of damaged masonry structures with different seismic resistances subjected to seismic demand in different regions of seismic intensity (VI to X) have been developed. 3) A method has been proposed to build vulnerability matrices of masonry structures. The damage ratio for masonry structures under high-intensity events such as the Ms 6.1 Panzhihua earthquake in Sichuan province on 30 August 2008, was calculated to verify the applicability of this method. This research offers a significant theoretical basis for predicting seismic damage and direct loss assessment of groups of buildings, as well as for earthquake disaster insurance.
Parallelization of mathematical library for generalized eigenvalue problem for real band matrices
International Nuclear Information System (INIS)
Tanaka, Yasuhisa.
1997-05-01
This research has focused on a parallelization of the mathematical library for a generalized eigenvalue problem for real band matrices on IBM SP and Hitachi SR2201. The origin of the library is LASO (Lanczos Algorithm with Selective Orthogonalization), which was developed on the basis of Block Lanczos method for standard eigenvalue problem for real band matrices at Texas University. We adopted D.O.F. (Degree Of Freedom) decomposition method for a parallelization of this library, and evaluated its parallel performance. (author)
Consolidity analysis for fully fuzzy functions, matrices, probability and statistics
Directory of Open Access Journals (Sweden)
Walaa Ibrahim Gabr
2015-03-01
Full Text Available The paper presents a comprehensive review of the know-how for developing the systems consolidity theory for modeling, analysis, optimization and design in fully fuzzy environment. The solving of systems consolidity theory included its development for handling new functions of different dimensionalities, fuzzy analytic geometry, fuzzy vector analysis, functions of fuzzy complex variables, ordinary differentiation of fuzzy functions and partial fraction of fuzzy polynomials. On the other hand, the handling of fuzzy matrices covered determinants of fuzzy matrices, the eigenvalues of fuzzy matrices, and solving least-squares fuzzy linear equations. The approach demonstrated to be also applicable in a systematic way in handling new fuzzy probabilistic and statistical problems. This included extending the conventional probabilistic and statistical analysis for handling fuzzy random data. Application also covered the consolidity of fuzzy optimization problems. Various numerical examples solved have demonstrated that the new consolidity concept is highly effective in solving in a compact form the propagation of fuzziness in linear, nonlinear, multivariable and dynamic problems with different types of complexities. Finally, it is demonstrated that the implementation of the suggested fuzzy mathematics can be easily embedded within normal mathematics through building special fuzzy functions library inside the computational Matlab Toolbox or using other similar software languages.
Sparse Matrices in Frame Theory
DEFF Research Database (Denmark)
Lemvig, Jakob; Krahmer, Felix; Kutyniok, Gitta
2014-01-01
Frame theory is closely intertwined with signal processing through a canon of methodologies for the analysis of signals using (redundant) linear measurements. The canonical dual frame associated with a frame provides a means for reconstruction by a least squares approach, but other dual frames...... yield alternative reconstruction procedures. The novel paradigm of sparsity has recently entered the area of frame theory in various ways. Of those different sparsity perspectives, we will focus on the situations where frames and (not necessarily canonical) dual frames can be written as sparse matrices...
The Inverse of Banded Matrices
2013-01-01
indexed entries all zeros. In this paper, generalizing a method of Mallik (1999) [5], we give the LU factorization and the inverse of the matrix Br,n (if it...r ≤ i ≤ r, 1 ≤ j ≤ r, with the remaining un-indexed entries all zeros. In this paper generalizing a method of Mallik (1999) [5...matrices and applications to piecewise cubic approximation, J. Comput. Appl. Math. 8 (4) (1982) 285–288. [5] R.K. Mallik , The inverse of a lower
Fusion algebra and fusing matrices
International Nuclear Information System (INIS)
Gao Yihong; Li Miao; Yu Ming.
1989-09-01
We show that the Wilson line operators in topological field theories form a fusion algebra. In general, the fusion algebra is a relation among the fusing (F) matrices. In the case of the SU(2) WZW model, some special F matrix elements are found in this way, and the remaining F matrix elements are then determined up to a sign. In addition, the S(j) modular transformation of the one point blocks on the torus is worked out. Our results are found to agree with those obtained from the quantum group method. (author). 24 refs
Transfer matrices for multilayer structures
International Nuclear Information System (INIS)
Baquero, R.
1988-08-01
We consider four of the transfer matrices defined to deal with multilayer structures. We deduce algorithms to calculate them numerically, in a simple and neat way. We illustrate their application to semi-infinite systems using SGFM formulae. These algorithms are of fast convergence and allow a calculation of bulk-, surface- and inner-layers band structure in good agreement with much more sophisticated calculations. Supermatrices, interfaces and multilayer structures can be calculated in this way with a small computational effort. (author). 10 refs
Orthogonal polynomials and random matrices
Deift, Percy
2000-01-01
This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal of the course was to prove universality for a variety of statistical quantities arising in the theory of random matrix models. The central question was the following: Why do very general ensembles of random n {\\times} n matrices exhibit universal behavior as n {\\rightarrow} {\\infty}? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems.
Transversals of Complex Polynomial Vector Fields
DEFF Research Database (Denmark)
Dias, Kealey
Vector fields in the complex plane are defined by assigning the vector determined by the value P(z) to each point z in the complex plane, where P is a polynomial of one complex variable. We consider special families of so-called rotated vector fields that are determined by a polynomial multiplied...... by rotational constants. Transversals are a certain class of curves for such a family of vector fields that represent the bifurcation states for this family of vector fields. More specifically, transversals are curves that coincide with a homoclinic separatrix for some rotation of the vector field. Given...... a concrete polynomial, it seems to take quite a bit of work to prove that it is generic, i.e. structurally stable. This has been done for a special class of degree d polynomial vector fields having simple equilibrium points at the d roots of unity, d odd. In proving that such vector fields are generic...
Floor response spectra for multi-degree-of-freedom systems by Fourier transform
International Nuclear Information System (INIS)
Scanlan, R.H.; Sachs, K.
1975-01-01
A method of generating floor response spectra from a given ground response spectrum is given. This time-saving approach makes use of Fourier spectrum techniques and the randomness of phase angles. In matrix form a structure having many degrees-of-freedom is described by the equation of motion with M, C, K as the mass-, damping-, and stiffness matrices and Z being the acceleration time history of the earthquake and I a direction vector. If the Fourier spectrum FZ of the ground motion is known, then by standard methods the Fourier spectrum of the equipment response can be obtained. The assumption of random phase angles for the synthetic time history Z seems reasonable. The response is then also a superposition of cosine waves. Good agreement with time history methods is obtained. This method is much faster than time history methods, which are being used in most applications
Rigid Body Attitude Control Based on a Manifold Representation of Direction Cosine Matrices
International Nuclear Information System (INIS)
Nakath, David; Clemens, Joachim; Rachuy, Carsten
2017-01-01
Autonomous systems typically actively observe certain aspects of their surroundings, which makes them dependent on a suitable controller. However, building an attitude controller for three degrees of freedom is a challenging task, mainly due to singularities in the different parametrizations of the three dimensional rotation group SO (3). Thus, we propose an attitude controller based on a manifold representation of direction cosine matrices: In state space, the attitude is globally and uniquely represented as a direction cosine matrix R ∈ SO (3). However, differences in the state space, i.e., the attitude errors, are exposed to the controller in the vector space ℝ 3 . This is achieved by an operator, which integrates the matrix logarithm mapping from SO (3) to so(3) and the map from so(3) to ℝ 3 . Based on this representation, we derive a proportional and derivative feedback controller, whose output has an upper bound to prevent actuator saturation. Additionally, the feedback is preprocessed by a particle filter to account for measurement and state transition noise. We evaluate our approach in a simulator in three different spacecraft maneuver scenarios: (i) stabilizing, (ii) rest-to-rest, and (iii) nadir-pointing. The controller exhibits stable behavior from initial attitudes near and far from the setpoint. Furthermore, it is able to stabilize a spacecraft and can be used for nadir-pointing maneuvers. (paper)
Hypercyclic Abelian Semigroups of Matrices on Cn
International Nuclear Information System (INIS)
Ayadi, Adlene; Marzougui, Habib
2010-07-01
We give a complete characterization of existence of dense orbit for any abelian semigroup of matrices on C n . For finitely generated semigroups, this characterization is explicit and is used to determine the minimal number of matrices in normal form over C which forms a hypercyclic abelian semigroup on C n . In particular, we show that no abelian semigroup generated by n matrices on C n can be hypercyclic. (author)
Pathological rate matrices: from primates to pathogens
Directory of Open Access Journals (Sweden)
Knight Rob
2008-12-01
Full Text Available Abstract Background Continuous-time Markov models allow flexible, parametrically succinct descriptions of sequence divergence. Non-reversible forms of these models are more biologically realistic but are challenging to develop. The instantaneous rate matrices defined for these models are typically transformed into substitution probability matrices using a matrix exponentiation algorithm that employs eigendecomposition, but this algorithm has characteristic vulnerabilities that lead to significant errors when a rate matrix possesses certain 'pathological' properties. Here we tested whether pathological rate matrices exist in nature, and consider the suitability of different algorithms to their computation. Results We used concatenated protein coding gene alignments from microbial genomes, primate genomes and independent intron alignments from primate genomes. The Taylor series expansion and eigendecomposition matrix exponentiation algorithms were compared to the less widely employed, but more robust, Padé with scaling and squaring algorithm for nucleotide, dinucleotide, codon and trinucleotide rate matrices. Pathological dinucleotide and trinucleotide matrices were evident in the microbial data set, affecting the eigendecomposition and Taylor algorithms respectively. Even using a conservative estimate of matrix error (occurrence of an invalid probability, both Taylor and eigendecomposition algorithms exhibited substantial error rates: ~100% of all exonic trinucleotide matrices were pathological to the Taylor algorithm while ~10% of codon positions 1 and 2 dinucleotide matrices and intronic trinucleotide matrices, and ~30% of codon matrices were pathological to eigendecomposition. The majority of Taylor algorithm errors derived from occurrence of multiple unobserved states. A small number of negative probabilities were detected from the Pad�� algorithm on trinucleotide matrices that were attributable to machine precision. Although the Pad
Quantum Hilbert matrices and orthogonal polynomials
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Berg, Christian
2009-01-01
Using the notion of quantum integers associated with a complex number q≠0 , we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little q -Jacobi polynomials when |q|<1 , and for the special value they are closely related to Hankel matrice...
The construction of factorized S-matrices
International Nuclear Information System (INIS)
Chudnovsky, D.V.
1981-01-01
We study the relationships between factorized S-matrices given as representations of the Zamolodchikov algebra and exactly solvable models constructed using the Baxter method. Several new examples of symmetric and non-symmetric factorized S-matrices are proposed. (orig.)
Skew-adjacency matrices of graphs
Cavers, M.; Cioaba, S.M.; Fallat, S.; Gregory, D.A.; Haemers, W.H.; Kirkland, S.J.; McDonald, J.J.; Tsatsomeros, M.
2012-01-01
The spectra of the skew-adjacency matrices of a graph are considered as a possible way to distinguish adjacency cospectral graphs. This leads to the following topics: graphs whose skew-adjacency matrices are all cospectral; relations between the matchings polynomial of a graph and the characteristic
On Investigating GMRES Convergence using Unitary Matrices
Czech Academy of Sciences Publication Activity Database
Duintjer Tebbens, Jurjen; Meurant, G.; Sadok, H.; Strakoš, Z.
2014-01-01
Roč. 450, 1 June (2014), s. 83-107 ISSN 0024-3795 Grant - others:GA AV ČR(CZ) M100301201; GA MŠk(CZ) LL1202 Institutional support: RVO:67985807 Keywords : GMRES convergence * unitary matrices * unitary spectra * normal matrices * Krylov residual subspace * Schur parameters Subject RIV: BA - General Mathematics Impact factor: 0.939, year: 2014
Exact Inverse Matrices of Fermat and Mersenne Circulant Matrix
Directory of Open Access Journals (Sweden)
Yanpeng Zheng
2015-01-01
Full Text Available The well known circulant matrices are applied to solve networked systems. In this paper, circulant and left circulant matrices with the Fermat and Mersenne numbers are considered. The nonsingularity of these special matrices is discussed. Meanwhile, the exact determinants and inverse matrices of these special matrices are presented.
Directory of Open Access Journals (Sweden)
Fabiana T. Rodrigues
2010-06-01
Full Text Available In this work, the modifications promoted by alkaline hydrolysis and glutaraldehyde (GA crosslinking on type I collagen found in porcine skin have been studied. Collagen matrices were obtained from the alkaline hydrolysis of porcine skin, with subsequent GA crosslinking in different concentrations and reaction times. The elastin content determination showed that independent of the treatment, elastin was present in the matrices. Results obtained from in vitro trypsin degradation indicated that with the increase of GA concentration and reaction time, the degradation rate decreased. From thermogravimetry and differential scanning calorimetry analysis it can be observed that the collagen in the matrices becomes more resistant to thermal degradation as a consequence of the increasing crosslink degree. Scanning electron microscopy analysis indicated that after the GA crosslinking, collagen fibers become more organized and well-defined. Therefore, the preparations of porcine skin matrices with different degradation rates, which can be used in soft tissue reconstruction, are viable.
PRIMITIVE MATRICES AND GENERATORS OF PSEUDO RANDOM SEQUENCES OF GALOIS
Directory of Open Access Journals (Sweden)
A. Beletsky
2014-04-01
Full Text Available In theory and practice of information cryptographic protection one of the key problems is the forming a binary pseudo-random sequences (PRS with a maximum length with acceptable statistical characteristics. PRS generators are usually implemented by linear shift register (LSR of maximum period with linear feedback [1]. In this paper we extend the concept of LSR, assuming that each of its rank (memory cell can be in one of the following condition. Let’s call such registers “generalized linear shift register.” The research goal is to develop algorithms for constructing Galois and Fibonacci generalized matrix of n-order over the field , which uniquely determined both the structure of corresponding generalized of n-order LSR maximal period, and formed on their basis Galois PRS generators of maximum length. Thus the article presents the questions of formation the primitive generalized Fibonacci and Galois arbitrary order matrix over the prime field . The synthesis of matrices is based on the use of irreducible polynomials of degree and primitive elements of the extended field generated by polynomial. The constructing methods of Galois and Fibonacci conjugated primitive matrices are suggested. The using possibilities of such matrices in solving the problem of constructing generalized generators of Galois pseudo-random sequences are discussed.
Community Detection for Correlation Matrices
Directory of Open Access Journals (Sweden)
Mel MacMahon
2015-04-01
Full Text Available A challenging problem in the study of complex systems is that of resolving, without prior information, the emergent, mesoscopic organization determined by groups of units whose dynamical activity is more strongly correlated internally than with the rest of the system. The existing techniques to filter correlations are not explicitly oriented towards identifying such modules and can suffer from an unavoidable information loss. A promising alternative is that of employing community detection techniques developed in network theory. Unfortunately, this approach has focused predominantly on replacing network data with correlation matrices, a procedure that we show to be intrinsically biased because of its inconsistency with the null hypotheses underlying the existing algorithms. Here, we introduce, via a consistent redefinition of null models based on random matrix theory, the appropriate correlation-based counterparts of the most popular community detection techniques. Our methods can filter out both unit-specific noise and system-wide dependencies, and the resulting communities are internally correlated and mutually anticorrelated. We also implement multiresolution and multifrequency approaches revealing hierarchically nested subcommunities with “hard” cores and “soft” peripheries. We apply our techniques to several financial time series and identify mesoscopic groups of stocks which are irreducible to a standard, sectorial taxonomy; detect “soft stocks” that alternate between communities; and discuss implications for portfolio optimization and risk management.
Community Detection for Correlation Matrices
MacMahon, Mel; Garlaschelli, Diego
2015-04-01
A challenging problem in the study of complex systems is that of resolving, without prior information, the emergent, mesoscopic organization determined by groups of units whose dynamical activity is more strongly correlated internally than with the rest of the system. The existing techniques to filter correlations are not explicitly oriented towards identifying such modules and can suffer from an unavoidable information loss. A promising alternative is that of employing community detection techniques developed in network theory. Unfortunately, this approach has focused predominantly on replacing network data with correlation matrices, a procedure that we show to be intrinsically biased because of its inconsistency with the null hypotheses underlying the existing algorithms. Here, we introduce, via a consistent redefinition of null models based on random matrix theory, the appropriate correlation-based counterparts of the most popular community detection techniques. Our methods can filter out both unit-specific noise and system-wide dependencies, and the resulting communities are internally correlated and mutually anticorrelated. We also implement multiresolution and multifrequency approaches revealing hierarchically nested subcommunities with "hard" cores and "soft" peripheries. We apply our techniques to several financial time series and identify mesoscopic groups of stocks which are irreducible to a standard, sectorial taxonomy; detect "soft stocks" that alternate between communities; and discuss implications for portfolio optimization and risk management.
Tsang, Leung; Chan, Chi Hou; Kong, Jin AU; Joseph, James
1992-01-01
Complete polarimetric signatures of a canopy of dielectric cylinders overlying a homogeneous half space are studied with the first and second order solutions of the vector radiative transfer theory. The vector radiative transfer equations contain a general nondiagonal extinction matrix and a phase matrix. The energy conservation issue is addressed by calculating the elements of the extinction matrix and the elements of the phase matrix in a manner that is consistent with energy conservation. Two methods are used. In the first method, the surface fields and the internal fields of the dielectric cylinder are calculated by using the fields of an infinite cylinder. The phase matrix is calculated and the extinction matrix is calculated by summing the absorption and scattering to ensure energy conservation. In the second method, the method of moments is used to calculate the elements of the extinction and phase matrices. The Mueller matrix based on the first order and second order multiple scattering solutions of the vector radiative transfer equation are calculated. Results from the two methods are compared. The vector radiative transfer equations, combined with the solution based on method of moments, obey both energy conservation and reciprocity. The polarimetric signatures, copolarized and depolarized return, degree of polarization, and phase differences are studied as a function of the orientation, sizes, and dielectric properties of the cylinders. It is shown that second order scattering is generally important for vegetation canopy at C band and can be important at L band for some cases.
2D vector-cyclic deformable templates
DEFF Research Database (Denmark)
Schultz, Nette; Conradsen, Knut
1998-01-01
In this paper the theory of deformable templates is a vector cycle in 2D is described. The deformable template model originated in (Grenander, 1983) and was further investigated in (Grenander et al., 1991). A template vector distribution is induced by parameter distribution from transformation...... matrices applied to the vector cycle. An approximation in the parameter distribution is introduced. The main advantage by using the deformable template model is the ability to simulate a wide range of objects trained by e.g. their biological variations, and thereby improve restoration, segmentation...... and probabillity measurement. The case study concerns estimation of meat percent in pork carcasses. Given two cross-sectional images - one at the front and one near the ham of the carcass - the areas of lean and fat and a muscle in the lean area are measured automatically by the deformable templates....
The Antitriangular Factorization of Saddle Point Matrices
Pestana, J.
2014-01-01
Mastronardi and Van Dooren [SIAM J. Matrix Anal. Appl., 34 (2013), pp. 173-196] recently introduced the block antitriangular ("Batman") decomposition for symmetric indefinite matrices. Here we show the simplification of this factorization for saddle point matrices and demonstrate how it represents the common nullspace method. We show that rank-1 updates to the saddle point matrix can be easily incorporated into the factorization and give bounds on the eigenvalues of matrices important in saddle point theory. We show the relation of this factorization to constraint preconditioning and how it transforms but preserves the structure of block diagonal and block triangular preconditioners. © 2014 Society for Industrial and Applied Mathematics.
Polynomial sequences generated by infinite Hessenberg matrices
Directory of Open Access Journals (Sweden)
Verde-Star Luis
2017-01-01
Full Text Available We show that an infinite lower Hessenberg matrix generates polynomial sequences that correspond to the rows of infinite lower triangular invertible matrices. Orthogonal polynomial sequences are obtained when the Hessenberg matrix is tridiagonal. We study properties of the polynomial sequences and their corresponding matrices which are related to recurrence relations, companion matrices, matrix similarity, construction algorithms, and generating functions. When the Hessenberg matrix is also Toeplitz the polynomial sequences turn out to be of interpolatory type and we obtain additional results. For example, we show that every nonderogative finite square matrix is similar to a unique Toeplitz-Hessenberg matrix.
Computing the real-time Green's Functions of large Hamiltonian matrices
Iitaka, Toshiaki
1998-01-01
A numerical method is developed for calculating the real time Green's functions of very large sparse Hamiltonian matrices, which exploits the numerical solution of the inhomogeneous time-dependent Schroedinger equation. The method has a clear-cut structure reflecting the most naive definition of the Green's functions, and is very suitable to parallel and vector supercomputers. The effectiveness of the method is illustrated by applying it to simple lattice models. An application of this method...
A new method for calculation of traces of Dirac γ-matrices in Minkowski space
International Nuclear Information System (INIS)
Bondarev, Alexander L.
2006-01-01
This paper presents some relations for orthonormal bases in the Minkowski space and isotropic tetrads constructed from the vectors of these bases. As an example of an application of the obtained formulae, in particular recursion relations, a new method is proposed to calculate traces of Dirac γ-matrices in the Minkowski space. Compared to the classical algorithms, the new method results in more compact expressions for the traces. Specifically, it may be easily implemented as a simple yet efficient computer algorithm
The analytic structure of trigonometric S-matrices
International Nuclear Information System (INIS)
Hollowood, T.J.
1994-01-01
S-matrices associated to the vector representations of the quantum groups for the classical Lie algebras are constructed. For the a m-1 and c m algebras the complete S-matrix is found by an application of the bootstrap equations. It is shown that the simplest form for the S-matrix which generalizes that of the Gross-Neveu model is not consistent for the non-simply-laced algebras due to the existence of unexplained singularities on the physical strip. However, a form which generalizes the S-matrix of the principal chiral model is shown to be consistent via an argument which uses a novel application of the Coleman-Thun mechanism. The analysis also gives a correct description of the analytic structure of the S-matrix of the principle chiral model for c m . (orig.)
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)
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
Synchronous correlation matrices and Connes’ embedding conjecture
Energy Technology Data Exchange (ETDEWEB)
Dykema, Kenneth J., E-mail: kdykema@math.tamu.edu [Department of Mathematics, Texas A& M University, College Station, Texas 77843-3368 (United States); Paulsen, Vern, E-mail: vern@math.uh.edu [Department of Mathematics, University of Houston, Houston, Texas 77204 (United States)
2016-01-15
In the work of Paulsen et al. [J. Funct. Anal. (in press); preprint arXiv:1407.6918], the concept of synchronous quantum correlation matrices was introduced and these were shown to correspond to traces on certain C*-algebras. In particular, synchronous correlation matrices arose in their study of various versions of quantum chromatic numbers of graphs and other quantum versions of graph theoretic parameters. In this paper, we develop these ideas further, focusing on the relations between synchronous correlation matrices and microstates. We prove that Connes’ embedding conjecture is equivalent to the equality of two families of synchronous quantum correlation matrices. We prove that if Connes’ embedding conjecture has a positive answer, then the tracial rank and projective rank are equal for every graph. We then apply these results to more general non-local games.
Discrete canonical transforms that are Hadamard matrices
International Nuclear Information System (INIS)
Healy, John J; Wolf, Kurt Bernardo
2011-01-01
The group Sp(2,R) of symplectic linear canonical transformations has an integral kernel which has quadratic and linear phases, and which is realized by the geometric paraxial optical model. The discrete counterpart of this model is a finite Hamiltonian system that acts on N-point signals through N x N matrices whose elements also have a constant absolute value, although they do not form a representation of that group. Those matrices that are also unitary are Hadamard matrices. We investigate the manifolds of these N x N matrices under the Sp(2,R) equivalence imposed by the model, and find them to be on two-sided cosets. By means of an algorithm we determine representatives that lead to collections of mutually unbiased bases.
ESTIMATION OF FUNCTIONALS OF SPARSE COVARIANCE MATRICES.
Fan, Jianqing; Rigollet, Philippe; Wang, Weichen
High-dimensional statistical tests often ignore correlations to gain simplicity and stability leading to null distributions that depend on functionals of correlation matrices such as their Frobenius norm and other ℓ r norms. Motivated by the computation of critical values of such tests, we investigate the difficulty of estimation the functionals of sparse correlation matrices. Specifically, we show that simple plug-in procedures based on thresholded estimators of correlation matrices are sparsity-adaptive and minimax optimal over a large class of correlation matrices. Akin to previous results on functional estimation, the minimax rates exhibit an elbow phenomenon. Our results are further illustrated in simulated data as well as an empirical study of data arising in financial econometrics.
The Antitriangular Factorization of Saddle Point Matrices
Pestana, J.; Wathen, A. J.
2014-01-01
Mastronardi and Van Dooren [SIAM J. Matrix Anal. Appl., 34 (2013), pp. 173-196] recently introduced the block antitriangular ("Batman") decomposition for symmetric indefinite matrices. Here we show the simplification of this factorization for saddle
Flux Jacobian Matrices For Equilibrium Real Gases
Vinokur, Marcel
1990-01-01
Improved formulation includes generalized Roe average and extension to three dimensions. Flux Jacobian matrices derived for use in numerical solutions of conservation-law differential equations of inviscid flows of ideal gases extended to real gases. Real-gas formulation of these matrices retains simplifying assumptions of thermodynamic and chemical equilibrium, but adds effects of vibrational excitation, dissociation, and ionization of gas molecules via general equation of state.
Supercritical fluid extraction behaviour of polymer matrices
International Nuclear Information System (INIS)
Sujatha, K.; Kumar, R.; Sivaraman, N.; Srinivasan, T.G.; Vasudeva Rao, P.R.
2007-01-01
Organic compounds present in polymeric matrices such as neoprene, surgical gloves and PVC were co-extracted during the removal of uranium using supercritical fluid extraction (SFE) technique. Hence SFE studies of these matrices were carried out to establish the extracted species using HPLC, IR and mass spectrometry techniques. The initial study indicated that uranium present in the extract could be purified from the co-extracted organic species. (author)
Seismic structural response analysis using consistent mass matrices having dynamic coupling
International Nuclear Information System (INIS)
Shaw, D.E.
1977-01-01
The basis for the theoretical development of this paper is the linear matrix equations of motion for an unconstrained structure subject to support excitation. The equations are formulated in terms of absolute displacement, velocity and acceleration vectors. By means of a transformation of the absolute response vectors into displacements, velocities and accelerations relative to the support motions, the homogeneous equations become non-homogeneous and the non-homogeneous boundary conditions become homogeneous with relative displacements, velocities and accelerations being zero at support points. The forcing function or inertial loading vector is shown to consist of two parts. The first part is comprised of the mass matrix times the suppport acceleration function times a vector of structural displacements resulting from a unit vector of support displacements in the direction of excitation. This inertial loading corresponds to the classical seismic loading vector and is indeed the only loading vector for lumped-mass systems. The second part of he inertial loading vectors consists of the mass matrix times the support acceleration function times a vector of structural accelerations resulting from unit support accelerations in the direction of excitation. This term is not present in classical seismic analysis formulations and results from the presence of off-diagonal terms in the mass matrices which give rise to dynamic coupling through the mass matrix. Thus, for lumped-mass models, the classical formulation of the inertial loading vector is correct. However, if dynamic coupling terms are included through off-diagonal terms in the mass matrix, an additional inertia loading vector must be considered
Xu, Danfeng; Gu, Bing; Rui, Guanghao; Zhan, Qiwen; Cui, Yiping
2016-02-22
We present an arbitrary vector field with hybrid polarization based on the combination of a pair of orthogonal elliptically polarized base vectors on the Poincaré sphere. It is shown that the created vector field is only dependent on the latitude angle 2χ but is independent on the longitude angle 2ψ on the Poincaré sphere. By adjusting the latitude angle 2χ, which is related to two identical waveplates in a common path interferometric arrangement, one could obtain arbitrary type of vector fields. Experimentally, we demonstrate the generation of such kind of vector fields and confirm the distribution of state of polarization by the measurement of Stokes parameters. Besides, we investigate the tight focusing properties of these vector fields. It is found that the additional degree of freedom 2χ provided by arbitrary vector field with hybrid polarization allows one to control the spatial structure of polarization and to engineer the focusing field.
Protein matrices for wound dressings =
Vasconcelos, Andreia Joana Costa
Fibrous proteins such as silk fibroin (SF), keratin (K) and elastin (EL) are able to mimic the extracellular matrix (ECM) that allows their recognition under physiological conditions. The impressive mechanical properties, the environmental stability, in combination with their biocompatibility and control of morphology, provide an important basis to use these proteins in biomedical applications like protein-based wound dressings. Along time the concept of wound dressings has changed from the traditional dressings such as honey or natural fibres, used just to protect the wound from external factors, to the interactive dressings of the present. Wounds can be classified in acute that heal in the expected time frame, and chronic, which fail to heal because the orderly sequence of events is disrupted at one or more stages of the healing process. Moreover, chronic wound exudates contain high levels of tissue destructive proteolytic enzymes such as human neutrophil elastase (HNE) that need to be controlled for a proper healing. The aim of this work is to exploit the self-assemble properties of silk fibroin, keratin and elastin for the development of new protein materials to be used as wound dressings: i) evaluation of the blending effect on the physical and chemical properties of the materials; ii) development of materials with different morphologies; iii) assessment of the cytocompatibility of the protein matrices; iv) ultimately, study the ability of the developed protein matrices as wound dressings through the use of human chronic wound exudate; v) use of innovative short peptide sequences that allow to target the control of high levels of HNE found on chronic wounds. Chapter III reports the preparation of silk fibroin/keratin (SF/K) blend films by solvent casting evaporation. Two solvent systems, aqueous and acidic, were used for the preparation of films from fibroin and keratin extracted from the respective silk and wool fibres. The effect of solvent system used was
Determination of key parameters of vector multifractal vector fields
Schertzer, D. J. M.; Tchiguirinskaia, I.
2017-12-01
For too long time, multifractal analyses and simulations have been restricted to scalar-valued fields (Schertzer and Tchiguirinskaia, 2017a,b). For instance, the wind velocity multifractality has been mostly analysed in terms of scalar structure functions and with the scalar energy flux. This restriction has had the unfortunate consequences that multifractals were applicable to their full extent in geophysics, whereas it has inspired them. Indeed a key question in geophysics is the complexity of the interactions between various fields or they components. Nevertheless, sophisticated methods have been developed to determine the key parameters of scalar valued fields. In this communication, we first present the vector extensions of the universal multifractal analysis techniques to multifractals whose generator belong to a Levy-Clifford algebra (Schertzer and Tchiguirinskaia, 2015). We point out further extensions noting the increased complexity. For instance, the (scalar) index of multifractality becomes a matrice. Schertzer, D. and Tchiguirinskaia, I. (2015) `Multifractal vector fields and stochastic Clifford algebra', Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(12), p. 123127. doi: 10.1063/1.4937364. Schertzer, D. and Tchiguirinskaia, I. (2017) `An Introduction to Multifractals and Scale Symmetry Groups', in Ghanbarian, B. and Hunt, A. (eds) Fractals: Concepts and Applications in Geosciences. CRC Press, p. (in press). Schertzer, D. and Tchiguirinskaia, I. (2017b) `Pandora Box of Multifractals: Barely Open ?', in Tsonis, A. A. (ed.) 30 Years of Nonlinear Dynamics in Geophysics. Berlin: Springer, p. (in press).
MERSENNE AND HADAMARD MATRICES CALCULATION BY SCARPIS METHOD
Directory of Open Access Journals (Sweden)
N. A. Balonin
2014-05-01
Full Text Available Purpose. The paper deals with the problem of basic generalizations of Hadamard matrices associated with maximum determinant matrices or not optimal by determinant matrices with orthogonal columns (weighing matrices, Mersenne and Euler matrices, ets.; calculation methods for the quasi-orthogonal local maximum determinant Mersenne matrices are not studied enough sufficiently. The goal of this paper is to develop the theory of Mersenne and Hadamard matrices on the base of generalized Scarpis method research. Methods. Extreme solutions are found in general by minimization of maximum for absolute values of the elements of studied matrices followed by their subsequent classification according to the quantity of levels and their values depending on orders. Less universal but more effective methods are based on structural invariants of quasi-orthogonal matrices (Silvester, Paley, Scarpis methods, ets.. Results. Generalizations of Hadamard and Belevitch matrices as a family of quasi-orthogonal matrices of odd orders are observed; they include, in particular, two-level Mersenne matrices. Definitions of section and layer on the set of generalized matrices are proposed. Calculation algorithms for matrices of adjacent layers and sections by matrices of lower orders are described. Approximation examples of the Belevitch matrix structures up to 22-nd critical order by Mersenne matrix of the third order are given. New formulation of the modified Scarpis method to approximate Hadamard matrices of high orders by lower order Mersenne matrices is proposed. Williamson method is described by example of one modular level matrices approximation by matrices with a small number of levels. Practical relevance. The efficiency of developing direction for the band-pass filters creation is justified. Algorithms for Mersenne matrices design by Scarpis method are used in developing software of the research program complex. Mersenne filters are based on the suboptimal by
A Brief Historical Introduction to Matrices and Their Applications
Debnath, L.
2014-01-01
This paper deals with the ancient origin of matrices, and the system of linear equations. Included are algebraic properties of matrices, determinants, linear transformations, and Cramer's Rule for solving the system of algebraic equations. Special attention is given to some special matrices, including matrices in graph theory and electrical…
Generalized Selection Weighted Vector Filters
Directory of Open Access Journals (Sweden)
Rastislav Lukac
2004-09-01
Full Text Available This paper introduces a class of nonlinear multichannel filters capable of removing impulsive noise in color images. The here-proposed generalized selection weighted vector filter class constitutes a powerful filtering framework for multichannel signal processing. Previously defined multichannel filters such as vector median filter, basic vector directional filter, directional-distance filter, weighted vector median filters, and weighted vector directional filters are treated from a global viewpoint using the proposed framework. Robust order-statistic concepts and increased degree of freedom in filter design make the proposed method attractive for a variety of applications. Introduced multichannel sigmoidal adaptation of the filter parameters and its modifications allow to accommodate the filter parameters to varying signal and noise statistics. Simulation studies reported in this paper indicate that the proposed filter class is computationally attractive, yields excellent performance, and is able to preserve fine details and color information while efficiently suppressing impulsive noise. This paper is an extended version of the paper by Lukac et al. presented at the 2003 IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing (NSIP '03 in Grado, Italy.
Directory of Open Access Journals (Sweden)
P. S. Timashev
2016-01-01
Full Text Available Aim. Controlled treatment of the physico-chemical and mechanical properties of a three-dimensional crosslinked matrix based on reactive chitosan. Materials and methods. The three-dimensional matrices were obtained using photosensitive composition based on allyl chitosan (5 wt%, poly(ethylene glycol diacrylate (8 wt% and the photoinitiator Irgacure 2959 (1 wt% by laser stereolithography setting. The kinetic swelling curves were constructed for structures in the base and salt forms of chitosan using gravimetric method and the contact angles were measured using droplet spreading. The supercritical fl uid setting (40 °C, 12 MPa was used to process matrices during 1.5 hours. Using nanohardness Piuma Nanoindenter we calculated values of Young’s modulus. The study of cytotoxicity was performed by direct contact with the culture of the NIH 3T3 mouse fi broblast cell line. Results. Architectonics of matrices fully repeats the program model. Matrices are uniform throughout and retain their shape after being transferred to the base form. Matrices compressed by 5% after treatment in supercritical carbon dioxide (scCO2 . The elastic modulus of matrices after scCO2 treatment is 4 times higher than the original matrix. The kinetic swelling curves have similar form. In this case the maximum degree of swelling for matrices in base form is 2–2.5 times greater than that of matrices in salt form. There was a surface hydrophobization after the material was transferred to the base form: the contact angle is 94°, and for the salt form it is 66°. The basic form absorbs liquid approximately 1.6 times faster. The fi lm thickness was increased in the area of contact with the liquid droplets after absorption by 133 and 87% for the base and the salt forms, respectively. Treatment of samples in scCO2 reduces their cytotoxicity from 2 degree of reaction (initial samples down to 1 degree of reaction. Conclusion. The use of supercritical carbon dioxide for scaffolds
Bayesian Nonparametric Clustering for Positive Definite Matrices.
Cherian, Anoop; Morellas, Vassilios; Papanikolopoulos, Nikolaos
2016-05-01
Symmetric Positive Definite (SPD) matrices emerge as data descriptors in several applications of computer vision such as object tracking, texture recognition, and diffusion tensor imaging. Clustering these data matrices forms an integral part of these applications, for which soft-clustering algorithms (K-Means, expectation maximization, etc.) are generally used. As is well-known, these algorithms need the number of clusters to be specified, which is difficult when the dataset scales. To address this issue, we resort to the classical nonparametric Bayesian framework by modeling the data as a mixture model using the Dirichlet process (DP) prior. Since these matrices do not conform to the Euclidean geometry, rather belongs to a curved Riemannian manifold,existing DP models cannot be directly applied. Thus, in this paper, we propose a novel DP mixture model framework for SPD matrices. Using the log-determinant divergence as the underlying dissimilarity measure to compare these matrices, and further using the connection between this measure and the Wishart distribution, we derive a novel DPM model based on the Wishart-Inverse-Wishart conjugate pair. We apply this model to several applications in computer vision. Our experiments demonstrate that our model is scalable to the dataset size and at the same time achieves superior accuracy compared to several state-of-the-art parametric and nonparametric clustering algorithms.
Raster images vectorization system
Genytė, Jurgita
2006-01-01
The problem of raster images vectorization was analyzed and researched in this work. Existing vectorization systems are quite expensive, the results are inaccurate, and the manual vectorization of a large number of drafts is impossible. That‘s why our goal was to design and develop a new raster images vectorization system using our suggested automatic vectorization algorithm and the way to record results in a new universal vectorial file format. The work consists of these main parts: analysis...
International Nuclear Information System (INIS)
Pavicic, Mladen; Merlet, Jean-Pierre; McKay, Brendan; Megill, Norman D
2005-01-01
We give a constructive and exhaustive definition of Kochen-Specker (KS) vectors in a Hilbert space of any dimension as well as of all the remaining vectors of the space. KS vectors are elements of any set of orthonormal states, i.e., vectors in an n-dimensional Hilbert space, H n , n≥3, to which it is impossible to assign 1s and 0s in such a way that no two mutually orthogonal vectors from the set are both assigned 1 and that not all mutually orthogonal vectors are assigned 0. Our constructive definition of such KS vectors is based on algorithms that generate MMP diagrams corresponding to blocks of orthogonal vectors in R n , on algorithms that single out those diagrams on which algebraic (0)-(1) states cannot be defined, and on algorithms that solve nonlinear equations describing the orthogonalities of the vectors by means of statistically polynomially complex interval analysis and self-teaching programs. The algorithms are limited neither by the number of dimensions nor by the number of vectors. To demonstrate the power of the algorithms, all four-dimensional KS vector systems containing up to 24 vectors were generated and described, all three-dimensional vector systems containing up to 30 vectors were scanned, and several general properties of KS vectors were found
Random matrices and random difference equations
International Nuclear Information System (INIS)
Uppuluri, V.R.R.
1975-01-01
Mathematical models leading to products of random matrices and random difference equations are discussed. A one-compartment model with random behavior is introduced, and it is shown how the average concentration in the discrete time model converges to the exponential function. This is of relevance to understanding how radioactivity gets trapped in bone structure in blood--bone systems. The ideas are then generalized to two-compartment models and mammillary systems, where products of random matrices appear in a natural way. The appearance of products of random matrices in applications in demography and control theory is considered. Then random sequences motivated from the following problems are studied: constant pulsing and random decay models, random pulsing and constant decay models, and random pulsing and random decay models
Quantum Entanglement and Reduced Density Matrices
Purwanto, Agus; Sukamto, Heru; Yuwana, Lila
2018-05-01
We investigate entanglement and separability criteria of multipartite (n-partite) state by examining ranks of its reduced density matrices. Firstly, we construct the general formula to determine the criterion. A rank of origin density matrix always equals one, meanwhile ranks of reduced matrices have various ranks. Next, separability and entanglement criterion of multipartite is determined by calculating ranks of reduced density matrices. In this article we diversify multipartite state criteria into completely entangled state, completely separable state, and compound state, i.e. sub-entangled state and sub-entangledseparable state. Furthermore, we also shorten the calculation proposed by the previous research to determine separability of multipartite state and expand the methods to be able to differ multipartite state based on criteria above.
Forecasting Covariance Matrices: A Mixed Frequency Approach
DEFF Research Database (Denmark)
Halbleib, Roxana; Voev, Valeri
This paper proposes a new method for forecasting covariance matrices of financial returns. The model mixes volatility forecasts from a dynamic model of daily realized volatilities estimated with high-frequency data with correlation forecasts based on daily data. This new approach allows for flexi......This paper proposes a new method for forecasting covariance matrices of financial returns. The model mixes volatility forecasts from a dynamic model of daily realized volatilities estimated with high-frequency data with correlation forecasts based on daily data. This new approach allows...... for flexible dependence patterns for volatilities and correlations, and can be applied to covariance matrices of large dimensions. The separate modeling of volatility and correlation forecasts considerably reduces the estimation and measurement error implied by the joint estimation and modeling of covariance...
Advanced incomplete factorization algorithms for Stiltijes matrices
Energy Technology Data Exchange (ETDEWEB)
Il`in, V.P. [Siberian Division RAS, Novosibirsk (Russian Federation)
1996-12-31
The modern numerical methods for solving the linear algebraic systems Au = f with high order sparse matrices A, which arise in grid approximations of multidimensional boundary value problems, are based mainly on accelerated iterative processes with easily invertible preconditioning matrices presented in the form of approximate (incomplete) factorization of the original matrix A. We consider some recent algorithmic approaches, theoretical foundations, experimental data and open questions for incomplete factorization of Stiltijes matrices which are {open_quotes}the best{close_quotes} ones in the sense that they have the most advanced results. Special attention is given to solving the elliptic differential equations with strongly variable coefficients, singular perturbated diffusion-convection and parabolic equations.
Draisma, J.; Horobet, E.; Ottaviani, G.; Sturmfels, B.; Thomas, R.R.; Zhi, L.; Watt, M.
2014-01-01
The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low rank matrices, the Eckart-Young Theorem states that this map is given by the singular value decomposition. This article develops a theory of such nearest
Symmetry of anomalous dimension matrices for colour evolution of hard scattering processes
International Nuclear Information System (INIS)
Seymour, Michael H.
2005-01-01
In a recent paper, Dokshitzer and Marchesini rederived the anomalous dimension matrix for colour evolution of gg→gg scattering, first derived by Kidonakis, Oderda and Sterman. They noted a weird symmetry that it possesses under interchange of internal (colour group) and external (scattering angle) degrees of freedom and speculated that this may be related to an embedding into a context that correlates internal and external variables such as string theory. In this short note, I point out another symmetry possessed by all the colour evolution anomalous dimension matrices calculated to date. It is more prosaic, but equally unexpected, and may also point to the fact that colour evolution might be understood in some deeper theoretical framework. To my knowledge it has not been pointed out elsewhere, or anticipated by any of the authors calculating these matrices. It is simply that, in a suitably chosen colour basis, they are complex symmetric matrices
Wishart and anti-Wishart random matrices
International Nuclear Information System (INIS)
Janik, Romuald A; Nowak, Maciej A
2003-01-01
We provide a compact exact representation for the distribution of the matrix elements of the Wishart-type random matrices A † A, for any finite number of rows and columns of A, without any large N approximations. In particular, we treat the case when the Wishart-type random matrix contains redundant, non-random information, which is a new result. This representation is of interest for a procedure for reconstructing the redundant information hidden in Wishart matrices, with potential applications to numerous models based on biological, social and artificial intelligence networks
Topological expansion of the chain of matrices
International Nuclear Information System (INIS)
Eynard, B.; Ferrer, A. Prats
2009-01-01
We solve the loop equations to all orders in 1/N 2 , for the Chain of Matrices matrix model (with possibly an external field coupled to the last matrix of the chain). We show that the topological expansion of the free energy, is, like for the 1 and 2-matrix model, given by the symplectic invariants of [19]. As a consequence, we find the double scaling limit explicitly, and we discuss modular properties, large N asymptotics. We also briefly discuss the limit of an infinite chain of matrices (matrix quantum mechanics).
Partitioning sparse rectangular matrices for parallel processing
Energy Technology Data Exchange (ETDEWEB)
Kolda, T.G.
1998-05-01
The authors are interested in partitioning sparse rectangular matrices for parallel processing. The partitioning problem has been well-studied in the square symmetric case, but the rectangular problem has received very little attention. They will formalize the rectangular matrix partitioning problem and discuss several methods for solving it. They will extend the spectral partitioning method for symmetric matrices to the rectangular case and compare this method to three new methods -- the alternating partitioning method and two hybrid methods. The hybrid methods will be shown to be best.
Directory of Open Access Journals (Sweden)
Mok Tik
2014-06-01
Full Text Available This study formulates regression of vector data that will enable statistical analysis of various geodetic phenomena such as, polar motion, ocean currents, typhoon/hurricane tracking, crustal deformations, and precursory earthquake signals. The observed vector variable of an event (dependent vector variable is expressed as a function of a number of hypothesized phenomena realized also as vector variables (independent vector variables and/or scalar variables that are likely to impact the dependent vector variable. The proposed representation has the unique property of solving the coefficients of independent vector variables (explanatory variables also as vectors, hence it supersedes multivariate multiple regression models, in which the unknown coefficients are scalar quantities. For the solution, complex numbers are used to rep- resent vector information, and the method of least squares is deployed to estimate the vector model parameters after transforming the complex vector regression model into a real vector regression model through isomorphism. Various operational statistics for testing the predictive significance of the estimated vector parameter coefficients are also derived. A simple numerical example demonstrates the use of the proposed vector regression analysis in modeling typhoon paths.
Directory of Open Access Journals (Sweden)
Akira R Kinjo
Full Text Available Position-specific scoring matrices (PSSMs are useful for detecting weak homology in protein sequence analysis, and they are thought to contain some essential signatures of the protein families. In order to elucidate what kind of ingredients constitute such family-specific signatures, we apply singular value decomposition to a set of PSSMs and examine the properties of dominant right and left singular vectors. The first right singular vectors were correlated with various amino acid indices including relative mutability, amino acid composition in protein interior, hydropathy, or turn propensity, depending on proteins. A significant correlation between the first left singular vector and a measure of site conservation was observed. It is shown that the contribution of the first singular component to the PSSMs act to disfavor potentially but falsely functionally important residues at conserved sites. The second right singular vectors were highly correlated with hydrophobicity scales, and the corresponding left singular vectors with contact numbers of protein structures. It is suggested that sequence alignment with a PSSM is essentially equivalent to threading supplemented with functional information. In addition, singular vectors may be useful for analyzing and annotating the characteristics of conserved sites in protein families.
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander; Genton, Marc G.; Sun, Ying
2015-01-01
We approximate large non-structured Matérn covariance matrices of size n×n in the H-matrix format with a log-linear computational cost and storage O(kn log n), where rank k ≪ n is a small integer. Applications are: spatial statistics, machine learning and image analysis, kriging and optimal design.
Theoretical origin of quark mass matrices
International Nuclear Information System (INIS)
Mohapatra, R.N.
1987-01-01
This paper presents the theoretical origin of specific quark mass matrices in the grand unified theories. The author discusses the first natural derivation of the Stech-type mass matrix in unified gauge theories. A solution to the strong CP-problem is provided
Malware Analysis Using Visualized Image Matrices
Directory of Open Access Journals (Sweden)
KyoungSoo Han
2014-01-01
Full Text Available This paper proposes a novel malware visual analysis method that contains not only a visualization method to convert binary files into images, but also a similarity calculation method between these images. The proposed method generates RGB-colored pixels on image matrices using the opcode sequences extracted from malware samples and calculates the similarities for the image matrices. Particularly, our proposed methods are available for packed malware samples by applying them to the execution traces extracted through dynamic analysis. When the images are generated, we can reduce the overheads by extracting the opcode sequences only from the blocks that include the instructions related to staple behaviors such as functions and application programming interface (API calls. In addition, we propose a technique that generates a representative image for each malware family in order to reduce the number of comparisons for the classification of unknown samples and the colored pixel information in the image matrices is used to calculate the similarities between the images. Our experimental results show that the image matrices of malware can effectively be used to classify malware families both statically and dynamically with accuracy of 0.9896 and 0.9732, respectively.
Moment matrices, border bases and radical computation
B. Mourrain; J.B. Lasserre; M. Laurent (Monique); P. Rostalski; P. Trebuchet (Philippe)
2013-01-01
htmlabstractIn this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is nte. The aim is to combine approaches for solving a system of polynomial equations with dual methods which involve moment matrices and
Moment matrices, border bases and radical computation
Lasserre, J.B.; Laurent, M.; Mourrain, B.; Rostalski, P.; Trébuchet, P.
2013-01-01
In this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming its complex (resp. real) variety is finite. The aim is to combine approaches for solving a system of polynomial equations with dual methods which involve moment matrices and semi-definite
Moment matrices, border bases and radical computation
B. Mourrain; J.B. Lasserre; M. Laurent (Monique); P. Rostalski; P. Trebuchet (Philippe)
2011-01-01
htmlabstractIn this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is nte. The aim is to combine approaches for solving a system of polynomial equations with dual methods which involve moment matrices and
Malware analysis using visualized image matrices.
Han, KyoungSoo; Kang, BooJoong; Im, Eul Gyu
2014-01-01
This paper proposes a novel malware visual analysis method that contains not only a visualization method to convert binary files into images, but also a similarity calculation method between these images. The proposed method generates RGB-colored pixels on image matrices using the opcode sequences extracted from malware samples and calculates the similarities for the image matrices. Particularly, our proposed methods are available for packed malware samples by applying them to the execution traces extracted through dynamic analysis. When the images are generated, we can reduce the overheads by extracting the opcode sequences only from the blocks that include the instructions related to staple behaviors such as functions and application programming interface (API) calls. In addition, we propose a technique that generates a representative image for each malware family in order to reduce the number of comparisons for the classification of unknown samples and the colored pixel information in the image matrices is used to calculate the similarities between the images. Our experimental results show that the image matrices of malware can effectively be used to classify malware families both statically and dynamically with accuracy of 0.9896 and 0.9732, respectively.
Generation speed in Raven's Progressive Matrices Test
Verguts, T.; Boeck, P. De; Maris, E.G.G.
1999-01-01
In this paper, we investigate the role of response fluency on a well-known intelligence test, Raven's (1962) Advanced Progressive Matrices (APM) test. Critical in solving this test is finding rules that govern the items. Response fluency is conceptualized as generation speed or the speed at which a
Inversion of General Cyclic Heptadiagonal Matrices
Directory of Open Access Journals (Sweden)
A. A. Karawia
2013-01-01
Full Text Available We describe a reliable symbolic computational algorithm for inverting general cyclic heptadiagonal matrices by using parallel computing along with recursion. The computational cost of it is operations. The algorithm is implementable to the Computer Algebra System (CAS such as MAPLE, MATLAB, and MATHEMATICA. Two examples are presented for the sake of illustration.
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-11-30
We approximate large non-structured Matérn covariance matrices of size n×n in the H-matrix format with a log-linear computational cost and storage O(kn log n), where rank k ≪ n is a small integer. Applications are: spatial statistics, machine learning and image analysis, kriging and optimal design.
U.S. Department of Health & Human Services — VectorBase is a Bioinformatics Resource Center for invertebrate vectors. It is one of four Bioinformatics Resource Centers funded by NIAID to provide web-based...
Fortran code for generating random probability vectors, unitaries, and quantum states
Directory of Open Access Journals (Sweden)
Jonas eMaziero
2016-03-01
Full Text Available The usefulness of generating random configurations is recognized in many areas of knowledge. Fortran was born for scientific computing and has been one of the main programming languages in this area since then. And several ongoing projects targeting towards its betterment indicate that it will keep this status in the decades to come. In this article, we describe Fortran codes produced, or organized, for the generation of the following random objects: numbers, probability vectors, unitary matrices, and quantum state vectors and density matrices. Some matrix functions are also included and may be of independent interest.
Generalization of concurrence vectors
International Nuclear Information System (INIS)
Yu Changshui; Song Heshan
2004-01-01
In this Letter, based on the generalization of concurrence vectors for bipartite pure state with respect to employing tensor product of generators of the corresponding rotation groups, we generalize concurrence vectors to the case of mixed states; a new criterion of separability of multipartite pure states is given out, for which we define a concurrence vector; we generalize the vector to the case of multipartite mixed state and give out a good measure of free entanglement
Convexity and Marginal Vectors
van Velzen, S.; Hamers, H.J.M.; Norde, H.W.
2002-01-01
In this paper we construct sets of marginal vectors of a TU game with the property that if the marginal vectors from these sets are core elements, then the game is convex.This approach leads to new upperbounds on the number of marginal vectors needed to characterize convexity.An other result is that
DEFF Research Database (Denmark)
Becciolini, Diego; Franzosi, Diogo Buarque; Foadi, Roshan
2015-01-01
We analyze the Large Hadron Collider (LHC) phenomenology of heavy vector resonances with a $SU(2)_L\\times SU(2)_R$ spectral global symmetry. This symmetry partially protects the electroweak S-parameter from large contributions of the vector resonances. The resulting custodial vector model spectrum...
On the uncertainty relations for vector-valued operators
International Nuclear Information System (INIS)
Chistyakov, A.L.
1976-01-01
In analogy with the expression for the Heisenberg incertainty principle in terms of dispersions by means of the Weyl inequality, in the case of one-dimensional quantum mechanical quantities, the principle for many-dimensional quantities can be expressed in terms of generalized dispersions and covariance matrices by means of inequalities similar to the Weyl unequality. The proofs of these inequalities are given in an abstract form, not only for the physical vector quantities, but also for arbitrary vector-valued operators with commuting self-adjoint components
Rotations with Rodrigues' vector
International Nuclear Information System (INIS)
Pina, E
2011-01-01
The rotational dynamics was studied from the point of view of Rodrigues' vector. This vector is defined here by its connection with other forms of parametrization of the rotation matrix. The rotation matrix was expressed in terms of this vector. The angular velocity was computed using the components of Rodrigues' vector as coordinates. It appears to be a fundamental matrix that is used to express the components of the angular velocity, the rotation matrix and the angular momentum vector. The Hamiltonian formalism of rotational dynamics in terms of this vector uses the same matrix. The quantization of the rotational dynamics is performed with simple rules if one uses Rodrigues' vector and similar formal expressions for the quantum operators that mimic the Hamiltonian classical dynamics.
On Skew Circulant Type Matrices Involving Any Continuous Fibonacci Numbers
Directory of Open Access Journals (Sweden)
Zhaolin Jiang
2014-01-01
inverse matrices of them by constructing the transformation matrices. Furthermore, the maximum column sum matrix norm, the spectral norm, the Euclidean (or Frobenius norm, and the maximum row sum matrix norm and bounds for the spread of these matrices are given, respectively.
Waller, Niels G
2016-01-01
For a fixed set of standardized regression coefficients and a fixed coefficient of determination (R-squared), an infinite number of predictor correlation matrices will satisfy the implied quadratic form. I call such matrices fungible correlation matrices. In this article, I describe an algorithm for generating positive definite (PD), positive semidefinite (PSD), or indefinite (ID) fungible correlation matrices that have a random or fixed smallest eigenvalue. The underlying equations of this algorithm are reviewed from both algebraic and geometric perspectives. Two simulation studies illustrate that fungible correlation matrices can be profitably used in Monte Carlo research. The first study uses PD fungible correlation matrices to compare penalized regression algorithms. The second study uses ID fungible correlation matrices to compare matrix-smoothing algorithms. R code for generating fungible correlation matrices is presented in the supplemental materials.
Evolutionary Games with Randomly Changing Payoff Matrices
Yakushkina, Tatiana; Saakian, David B.; Bratus, Alexander; Hu, Chin-Kun
2015-06-01
Evolutionary games are used in various fields stretching from economics to biology. In most of these games a constant payoff matrix is assumed, although some works also consider dynamic payoff matrices. In this article we assume a possibility of switching the system between two regimes with different sets of payoff matrices. Potentially such a model can qualitatively describe the development of bacterial or cancer cells with a mutator gene present. A finite population evolutionary game is studied. The model describes the simplest version of annealed disorder in the payoff matrix and is exactly solvable at the large population limit. We analyze the dynamics of the model, and derive the equations for both the maximum and the variance of the distribution using the Hamilton-Jacobi equation formalism.
Introduction to random matrices theory and practice
Livan, Giacomo; Vivo, Pierpaolo
2018-01-01
Modern developments of Random Matrix Theory as well as pedagogical approaches to the standard core of the discipline are surprisingly hard to find in a well-organized, readable and user-friendly fashion. This slim and agile book, written in a pedagogical and hands-on style, without sacrificing formal rigor fills this gap. It brings Ph.D. students in Physics, as well as more senior practitioners, through the standard tools and results on random matrices, with an eye on most recent developments that are not usually covered in introductory texts. The focus is mainly on random matrices with real spectrum. The main guiding threads throughout the book are the Gaussian Ensembles. In particular, Wigner’s semicircle law is derived multiple times to illustrate several techniques (e.g., Coulomb gas approach, replica theory). Most chapters are accompanied by Matlab codes (stored in an online repository) to guide readers through the numerical check of most analytical results.
Teaching Fourier optics through ray matrices
International Nuclear Information System (INIS)
Moreno, I; Sanchez-Lopez, M M; Ferreira, C; Davis, J A; Mateos, F
2005-01-01
In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics provided by the wave theory, but it is a complementary tool useful to simplify many aspects of Fourier optics and to relate them to geometrical optics
The recurrence sequences via Sylvester matrices
Karaduman, Erdal; Deveci, Ömür
2017-07-01
In this work, we define the Pell-Jacobsthal-Slyvester sequence and the Jacobsthal-Pell-Slyvester sequence by using the Slyvester matrices which are obtained from the characteristic polynomials of the Pell and Jacobsthal sequences and then, we study the sequences defined modulo m. Also, we obtain the cyclic groups and the semigroups from the generating matrices of these sequences when read modulo m and then, we derive the relationships among the orders of the cyclic groups and the periods of the sequences. Furthermore, we redefine Pell-Jacobsthal-Slyvester sequence and the Jacobsthal-Pell-Slyvester sequence by means of the elements of the groups and then, we examine them in the finite groups.
Linear Matrix Inequalities for Analysis and Control of Linear Vector Second-Order Systems
DEFF Research Database (Denmark)
Adegas, Fabiano Daher; Stoustrup, Jakob
2015-01-01
the Lyapunov matrix and the system matrices by introducing matrix multipliers, which potentially reduce conservativeness in hard control problems. Multipliers facilitate the usage of parameter-dependent Lyapunov functions as certificates of stability of uncertain and time-varying vector second-order systems......SUMMARY Many dynamical systems are modeled as vector second-order differential equations. This paper presents analysis and synthesis conditions in terms of LMI with explicit dependence in the coefficient matrices of vector second-order systems. These conditions benefit from the separation between....... The conditions introduced in this work have the potential to increase the practice of analyzing and controlling systems directly in vector second-order form. Copyright © 2014 John Wiley & Sons, Ltd....
Joint Matrices Decompositions and Blind Source Separation
Czech Academy of Sciences Publication Activity Database
Chabriel, G.; Kleinsteuber, M.; Moreau, E.; Shen, H.; Tichavský, Petr; Yeredor, A.
2014-01-01
Roč. 31, č. 3 (2014), s. 34-43 ISSN 1053-5888 R&D Projects: GA ČR GA102/09/1278 Institutional support: RVO:67985556 Keywords : joint matrices decomposition * tensor decomposition * blind source separation Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 5.852, year: 2014 http://library.utia.cas.cz/separaty/2014/SI/tichavsky-0427607.pdf
Tensor Permutation Matrices in Finite Dimensions
Christian, Rakotonirina
2005-01-01
We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows us to construct a tensor permutation matrix, which is a generalisation of tensor commutation matrix, has been established. The expression of an element of a tensor commutation matrix has been generalised in the case of any element of a tensor permutation ma...
Fast Approximate Joint Diagonalization Incorporating Weight Matrices
Czech Academy of Sciences Publication Activity Database
Tichavský, Petr; Yeredor, A.
2009-01-01
Roč. 57, č. 3 (2009), s. 878-891 ISSN 1053-587X R&D Projects: GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : autoregressive processes * blind source separation * nonstationary random processes Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 2.212, year: 2009 http://library.utia.cas.cz/separaty/2009/SI/tichavsky-fast approximate joint diagonalization incorporating weight matrices.pdf
Photoluminescence of nanocrystals embedded in oxide matrices
International Nuclear Information System (INIS)
Estrada, C.; Gonzalez, J.A.; Kunold, A.; Reyes-Esqueda, J.A.; Pereyra, P.
2006-12-01
We used the theory of finite periodic systems to explain the photoluminescence spectra dependence on the average diameter of nanocrystals embedded in oxide matrices. Because of the broad matrix band gap, the photoluminescence response is basically determined by isolated nanocrystals and sequences of a few of them. With this model we were able to reproduce the shape and displacement of the experimentally observed photoluminescence spectra. (author)
Equiangular tight frames and unistochastic matrices
Czech Academy of Sciences Publication Activity Database
Goyeneche, D.; Turek, Ondřej
2017-01-01
Roč. 50, č. 24 (2017), č. článku 245304. ISSN 1751-8113 R&D Projects: GA ČR GA17-01706S Institutional support: RVO:61389005 Keywords : equiangular tight frames * unistochastic matrices * SIC POVM Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.857, year: 2016
Simplifications of rational matrices by using UML
Tasić, Milan B.; Stanimirović, Ivan P.
2013-01-01
The simplification process on rational matrices consists of simplifying each entry represented by a rational function. We follow the classic approach of dividing the numerator and denominator polynomials by their common GCD polynomial, and provide the activity diagram in UML for this process. A rational matrix representation as the quotient of a polynomial matrix and a polynomial is also discussed here and illustrated via activity diagrams. Also, a class diagram giving the links between the c...
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-01-07
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-01-05
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.
PHAGOCYTOSIS AND REMODELING OF COLLAGEN MATRICES
Abraham, Leah C.; Dice, J Fred.; Lee, Kyongbum; Kaplan, David L.
2007-01-01
The biodegradation of collagen and the deposition of new collagen-based extracellular matrices are of central importance in tissue remodeling and function. Similarly, for collagen-based biomaterials used in tissue engineering, the degradation of collagen scaffolds with accompanying cellular infiltration and generation of new extracellular matrix is critical for integration of in vitro grown tissues in vivo. In earlier studies we observed significant impact of collagen structure on primary lun...
Preconditioners for regularized saddle point matrices
Czech Academy of Sciences Publication Activity Database
Axelsson, Owe
2011-01-01
Roč. 19, č. 2 (2011), s. 91-112 ISSN 1570-2820 Institutional research plan: CEZ:AV0Z30860518 Keywords : saddle point matrices * preconditioning * regularization * eigenvalue clustering Subject RIV: BA - General Mathematics Impact factor: 0.533, year: 2011 http://www.degruyter.com/view/j/jnma.2011.19.issue-2/jnum.2011.005/jnum.2011.005. xml
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander; Genton, Marc G.; Sun, Ying; Tempone, Raul
2015-01-01
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander; Genton, Marc G.; Sun, Ying; Tempone, Raul
2015-01-01
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.
Localized bound states of fermions interacting via massive vector bosons
International Nuclear Information System (INIS)
Ionescu, D.C.; Reinhardt, J.; Mueller, B.; Greiner, W.; Soff, G.
1988-11-01
A model for composite consisting of fermions with internal degrees of freedom interacting via intermediate vector bosons (IVB) is constructed. We find highly localized, low-mass bound states in the Hartree-Fock approximation. We investigate the dependence of these states as function of the coupling constant and vector boson mass. In the limit of infinite vector boson mass the interaction is described by Fermi-type contact forces. (orig.)
Vector optical fields with bipolar symmetry of linear polarization.
Pan, Yue; Li, Yongnan; Li, Si-Min; Ren, Zhi-Cheng; Si, Yu; Tu, Chenghou; Wang, Hui-Tian
2013-09-15
We focus on a new kind of vector optical field with bipolar symmetry of linear polarization instead of cylindrical and elliptical symmetries, enriching members of family of vector optical fields. We design theoretically and generate experimentally the demanded vector optical fields and then explore some novel tightly focusing properties. The geometric configurations of states of polarization provide additional degrees of freedom assisting in engineering the field distribution at the focus to the specific applications such as lithography, optical trapping, and material processing.
Compact stars in vector-tensor-Horndeski theory of gravity
Energy Technology Data Exchange (ETDEWEB)
Momeni, Davood; Myrzakulov, Kairat; Myrzakulov, Ratbay [Eurasian National University, Department of General and Theoretical Physics, Eurasian International Center for Theoretical Physics, Astana (Kazakhstan); Faizal, Mir [University of British Columbia-Okanagan, Irving K. Barber School of Arts and Sciences, Kelowna, BC (Canada); University of Lethbridge, Department of Physics and Astronomy, Lethbridge, AB (Canada)
2017-01-15
In this paper, we will analyze a theory of modified gravity, in which the field content of general relativity will be increased to include a vector field. We will use the Horndeski formalism to non-minimally couple this vector field to the metric. As we will be using the Horndeski formalism, this theory will not contain Ostrogradsky ghost degree of freedom. We will analyze compact stars using this vector-tensor-Horndeski theory. (orig.)
Transition Effect Matrices and Quantum Markov Chains
Gudder, Stan
2009-06-01
A transition effect matrix (TEM) is a quantum generalization of a classical stochastic matrix. By employing a TEM we obtain a quantum generalization of a classical Markov chain. We first discuss state and operator dynamics for a quantum Markov chain. We then consider various types of TEMs and vector states. In particular, we study invariant, equilibrium and singular vector states and investigate projective, bistochastic, invertible and unitary TEMs.
Gaussian vector fields on triangulated surfaces
DEFF Research Database (Denmark)
Ipsen, John H
2016-01-01
proven to be very useful to resolve the complex interplay between in-plane ordering of membranes and membrane conformations. In the present work we have developed a procedure for realistic representations of Gaussian models with in-plane vector degrees of freedoms on a triangulated surface. The method...
DEFF Research Database (Denmark)
Wood, Johanna
2016-01-01
, empirical data relevant to the development of the degree adverb function is presented and possible relevant constructions identified. It is argued that the degree adverb function of that possibly occurs later than the historical dictionaries indicate. The degree adverb function of this is challenging...
Group inverses of M-matrices and their applications
Kirkland, Stephen J
2013-01-01
Group inverses for singular M-matrices are useful tools not only in matrix analysis, but also in the analysis of stochastic processes, graph theory, electrical networks, and demographic models. Group Inverses of M-Matrices and Their Applications highlights the importance and utility of the group inverses of M-matrices in several application areas. After introducing sample problems associated with Leslie matrices and stochastic matrices, the authors develop the basic algebraic and spectral properties of the group inverse of a general matrix. They then derive formulas for derivatives of matrix f
Supergravity inspired vector curvaton
International Nuclear Information System (INIS)
Dimopoulos, Konstantinos
2007-01-01
It is investigated whether a massive Abelian vector field, whose gauge kinetic function is growing during inflation, can be responsible for the generation of the curvature perturbation in the Universe. Particle production is studied and it is shown that the vector field can obtain a scale-invariant superhorizon spectrum of perturbations with a reasonable choice of kinetic function. After inflation the vector field begins coherent oscillations, during which it corresponds to pressureless isotropic matter. When the vector field dominates the Universe, its perturbations give rise to the observed curvature perturbation following the curvaton scenario. It is found that this is possible if, after the end of inflation, the mass of the vector field increases at a phase transition at temperature of order 1 TeV or lower. Inhomogeneous reheating, whereby the vector field modulates the decay rate of the inflaton, is also studied
Becciolini, Diego; Franzosi, Diogo Buarque; Foadi, Roshan; Frandsen, Mads T.; Hapola, Tuomas; Sannino, Francesco
2015-07-01
We analyze the Large Hadron Collider (LHC) phenomenology of heavy vector resonances with a S U (2 )L×S U (2 )R spectral global symmetry. This symmetry partially protects the electroweak S parameter from large contributions of the vector resonances. The resulting custodial vector model spectrum and interactions with the standard model fields lead to distinct signatures at the LHC in the diboson, dilepton, and associated Higgs channels.
HITZER, Eckhard MS
2002-01-01
This paper treats the fundamentals of the vector differential calculus part of universal geometric calculus. Geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. In order to make the treatment self-contained, I first compile all important geometric algebra relationships,which are necesssary for vector differential calculus. Then differentiation by vectors is introduced and a host of major ve...
Directory of Open Access Journals (Sweden)
Jean-François Degbomont
2010-10-01
Full Text Available This paper addresses the symbolic representation of non-convex real polyhedra, i.e., sets of real vectors satisfying arbitrary Boolean combinations of linear constraints. We develop an original data structure for representing such sets, based on an implicit and concise encoding of a known structure, the Real Vector Automaton. The resulting formalism provides a canonical representation of polyhedra, is closed under Boolean operators, and admits an efficient decision procedure for testing the membership of a vector.
A new approach to radiative transfer theory using Jones's vectors. I
International Nuclear Information System (INIS)
Fymat, A.L.; Vasudevan, R.
1975-01-01
Radiative transfer of partially polarized radiation in an anisotropically scattering, inhomogeneous atmosphere containing arbitrary polydispersion of particles is described using Jones's amplitude vectors and matrices. This novel approach exploits the close analogy between the quantum mechanical states of spin 1/2 systems and the polarization states of electromagnetic radiation described by Jones's vector, and draws on the methodology of such spin 1/2 systems. The complete equivalence between the transport equation for Jones's vectors and the classical radiative transfer equation for Stokes's intensity vectors is demonstrated in two independent ways after deriving the transport equations for the polarization coherency matrices and for the quaternions corresponding to the Jones's vectors. A compact operator formulation of the theory is provided, and used to derive the necessary equations for both a local and a global description of the transport of Jones's vectors. Lastly, the integro-differential equations for the amplitude reflection and transmission matrices are derived, and related to the usual corresponding equations. The present formulation is the most succinct and the most convenient one for both theoretical and experimental studies. It yields a simpler analysis than the classical formulation since it reduces by a factor of two the dimensionality of transfer problems. It preserves information on phases, and thus can be used directly across the entire electromagnetic spectrum without any further conversion into intensities. (Auth.)
A matrix formulation of Frobenius power series solutions using products of 4X4 matrices
Directory of Open Access Journals (Sweden)
Jeremy Mandelkern
2015-08-01
Full Text Available In Coddington and Levison [7, p. 119, Thm. 4.1] and Balser [4, p. 18-19, Thm. 5], matrix formulations of Frobenius theory, near a regular singular point, are given using 2X2 matrix recurrence relations yielding fundamental matrices consisting of two linearly independent solutions together with their quasi-derivatives. In this article we apply a reformulation of these matrix methods to the Bessel equation of nonintegral order. The reformulated approach of this article differs from [7] and [4] by its implementation of a new ``vectorization'' procedure that yields recurrence relations of an altogether different form: namely, it replaces the implicit 2X2 matrix recurrence relations of both [7] and [4] by explicit 4X4 matrix recurrence relations that are implemented by means only of 4X4 matrix products. This new idea of using a vectorization procedure may further enable the development of symbolic manipulator programs for matrix forms of the Frobenius theory.
Dynamical analogy of the Cabibbo-Kobayashi-Maskawa matrices (with CP-violation)
International Nuclear Information System (INIS)
Beshtoev, Kh.M.
1997-01-01
The dynamical analogy of the Cabibbo-Kobayashi-Maskawa matrices is built, i.e., the phenomenological expansion of the weak interaction theory by the inclusion of four doublets of the charged-vector bosons B ± , C ± , D ± , E ± , leading to transitions between the quark families, and of four doublets of the charged-vector bosons X 1 ± , X 2 ± , X 3 ± , X 4 ± , leading to transitions between the lepton families, is suggested. The bosons E ± , X 4 ± realize CP-violation. This expansion works only at a tree level. An estimation of the boson masses is performed. The quasi-elastic processes proceeding through an exchange of the bosons and the production cross sections are given
Finding a Hadamard matrix by simulated annealing of spin vectors
Bayu Suksmono, Andriyan
2017-05-01
Reformulation of a combinatorial problem into optimization of a statistical-mechanics system enables finding a better solution using heuristics derived from a physical process, such as by the simulated annealing (SA). In this paper, we present a Hadamard matrix (H-matrix) searching method based on the SA on an Ising model. By equivalence, an H-matrix can be converted into a seminormalized Hadamard (SH) matrix, whose first column is unit vector and the rest ones are vectors with equal number of -1 and +1 called SH-vectors. We define SH spin vectors as representation of the SH vectors, which play a similar role as the spins on Ising model. The topology of the lattice is generalized into a graph, whose edges represent orthogonality relationship among the SH spin vectors. Starting from a randomly generated quasi H-matrix Q, which is a matrix similar to the SH-matrix without imposing orthogonality, we perform the SA. The transitions of Q are conducted by random exchange of {+, -} spin-pair within the SH-spin vectors that follow the Metropolis update rule. Upon transition toward zeroth energy, the Q-matrix is evolved following a Markov chain toward an orthogonal matrix, at which the H-matrix is said to be found. We demonstrate the capability of the proposed method to find some low-order H-matrices, including the ones that cannot trivially be constructed by the Sylvester method.
Release and diffusional modeling of metronidazole lipid matrices.
Ozyazici, Mine; Gökçe, Evren H; Ertan, Gökhan
2006-07-01
In this study, the first aim was to investigate the swelling and relaxation properties of lipid matrix on diffusional exponent (n). The second aim was to determine the desired release profile of metronidazole lipid matrix tablets. We prepared metronidazole lipid matrix granules using Carnauba wax, Beeswax, Stearic acid, Cutina HR, Precirol ATO 5, and Compritol ATO 888 by hot fusion method and pressed the tablets of these granules. In vitro release test was performed using a standard USP dissolution apparatus I (basket method) with a stirring rate of 100 rpm at 37 degrees C in 900 ml of 0.1 N hydrochloric acid, adjusted to pH 1.2, as medium for the formulations' screening. Hardness, diameter-height ratio, friability, and swelling ratio were determined. Target release profile of metronidazole was also drawn. Stearic acid showed the highest and Carnauba wax showed the lowest release rates in all formulations used. Swelling ratios were calculated after the dissolution of tablets as 9.24%, 6.03%, 1.74%, and 1.07% for Cutina HR, Beeswax, Precirol ATO 5, and Compritol ATO 888, respectively. There was erosion in Stearic acid, but neither erosion nor swelling in Carnauba wax, was detected. According to the power law analysis, the diffusion mechanism was expressed as pure Fickian for Stearic acid and Carnauba wax and the coupling of Fickian and relaxation contributions for other Cutina HR, Beeswax, Compritol ATO 888, and Precirol ATO 5 tablets. It was found that Beeswax (kd=2.13) has a very close drug release rate with the target profile (kt=1.95). Our results suggested that swelling and relaxation properties of lipid matrices should be examined together for a correct evaluation on drug diffusion mechanism of insoluble matrices.
International Nuclear Information System (INIS)
Brown, F.B.
1981-01-01
Examination of the global algorithms and local kernels of conventional general-purpose Monte Carlo codes shows that multigroup Monte Carlo methods have sufficient structure to permit efficient vectorization. A structured multigroup Monte Carlo algorithm for vector computers is developed in which many particle events are treated at once on a cell-by-cell basis. Vectorization of kernels for tracking and variance reduction is described, and a new method for discrete sampling is developed to facilitate the vectorization of collision analysis. To demonstrate the potential of the new method, a vectorized Monte Carlo code for multigroup radiation transport analysis was developed. This code incorporates many features of conventional general-purpose production codes, including general geometry, splitting and Russian roulette, survival biasing, variance estimation via batching, a number of cutoffs, and generalized tallies of collision, tracklength, and surface crossing estimators with response functions. Predictions of vectorized performance characteristics for the CYBER-205 were made using emulated coding and a dynamic model of vector instruction timing. Computation rates were examined for a variety of test problems to determine sensitivities to batch size and vector lengths. Significant speedups are predicted for even a few hundred particles per batch, and asymptotic speedups by about 40 over equivalent Amdahl 470V/8 scalar codes arepredicted for a few thousand particles per batch. The principal conclusion is that vectorization of a general-purpose multigroup Monte Carlo code is well worth the significant effort required for stylized coding and major algorithmic changes
Vectors and their applications
Pettofrezzo, Anthony J
2005-01-01
Geared toward undergraduate students, this text illustrates the use of vectors as a mathematical tool in plane synthetic geometry, plane and spherical trigonometry, and analytic geometry of two- and three-dimensional space. Its rigorous development includes a complete treatment of the algebra of vectors in the first two chapters.Among the text's outstanding features are numbered definitions and theorems in the development of vector algebra, which appear in italics for easy reference. Most of the theorems include proofs, and coordinate position vectors receive an in-depth treatment. Key concept
Symbolic computer vector analysis
Stoutemyer, D. R.
1977-01-01
A MACSYMA program is described which performs symbolic vector algebra and vector calculus. The program can combine and simplify symbolic expressions including dot products and cross products, together with the gradient, divergence, curl, and Laplacian operators. The distribution of these operators over sums or products is under user control, as are various other expansions, including expansion into components in any specific orthogonal coordinate system. There is also a capability for deriving the scalar or vector potential of a vector field. Examples include derivation of the partial differential equations describing fluid flow and magnetohydrodynamics, for 12 different classic orthogonal curvilinear coordinate systems.
Speculative segmented sum for sparse matrix-vector multiplication on heterogeneous processors
DEFF Research Database (Denmark)
Liu, Weifeng; Vinter, Brian
2015-01-01
of the same chip is triggered to re-arrange the predicted partial sums for a correct resulting vector. On three heterogeneous processors from Intel, AMD and nVidia, using 20 sparse matrices as a benchmark suite, the experimental results show that our method obtains significant performance improvement over...
Determination of coefficient matrices for ARMA model
International Nuclear Information System (INIS)
Tran Dinh Tri.
1990-10-01
A new recursive algorithm for determining coefficient matrices of ARMA model from measured data is presented. The Yule-Walker equations for the case of ARMA model are derived from the ARMA innovation equation. The recursive algorithm is based on choosing appropriate form of the operator functions and suitable representation of the (n+1)-th order operator functions according to ones with the lower order. Two cases, when the order of the AR part is equal to one of the MA part, and the optimal case, were considered. (author) 5 refs
Algebraic Graph Theory Morphisms, Monoids and Matrices
Knauer, Ulrich
2011-01-01
This is a highly self-contained book about algebraic graph theory which iswritten with a view to keep the lively and unconventional atmosphere of a spoken text to communicate the enthusiasm the author feels about this subject. The focus is on homomorphisms and endomorphisms, matrices and eigenvalues. Graph models are extremely useful for almost all applications and applicators as they play an important role as structuring tools. They allow to model net structures -like roads, computers, telephones -instances of abstract data structures -likelists, stacks, trees -and functional or object orient
Coherence and extensions of stochastic matrices
Directory of Open Access Journals (Sweden)
Angelo Gilio
1995-11-01
Full Text Available In this paper a review of some general results on coherence of conditional probability assessments is given. Then, a necessary and sufficient condition on coherence of two finite families of discrete conditianal probability distributions, represented by two stochastic matrices P and Q, is obtained. Moreover, the possible extensions of the assessment (P,Q to the marginal distributions are examined and explicit formulas for them are given in some special case. Finally, a general algorithm to check coherence of (P,Q and to derive its extensions is proposed.
2D gravity and random matrices
International Nuclear Information System (INIS)
Zinn-Justin, J.
1990-01-01
Recent progress in 2D gravity coupled to d ≤ 1 matter, based on a representation of discrete gravity in terms of random matrices, is reported. The matrix problem can be solved in many cases by the introduction of suitable orthogonal polynomials. Alternatively in the continuum limit the orthogonal polynomial method can be shown to be equivalent to the construction of representation of the canonical commutation relations in terms of differential operators. In the case of pure gravity or discrete Ising-like matter the sum over topologies is reduced to the solution of non-linear differential equations. The d = 1 problem can be solved by semiclassical methods
Vector-Vector Scattering on the Lattice
Romero-López, Fernando; Urbach, Carsten; Rusetsky, Akaki
2018-03-01
In this work we present an extension of the LüScher formalism to include the interaction of particles with spin, focusing on the scattering of two vector particles. The derived formalism will be applied to Scalar QED in the Higgs Phase, where the U(1) gauge boson acquires mass.
Selection vector filter framework
Lukac, Rastislav; Plataniotis, Konstantinos N.; Smolka, Bogdan; Venetsanopoulos, Anastasios N.
2003-10-01
We provide a unified framework of nonlinear vector techniques outputting the lowest ranked vector. The proposed framework constitutes a generalized filter class for multichannel signal processing. A new class of nonlinear selection filters are based on the robust order-statistic theory and the minimization of the weighted distance function to other input samples. The proposed method can be designed to perform a variety of filtering operations including previously developed filtering techniques such as vector median, basic vector directional filter, directional distance filter, weighted vector median filters and weighted directional filters. A wide range of filtering operations is guaranteed by the filter structure with two independent weight vectors for angular and distance domains of the vector space. In order to adapt the filter parameters to varying signal and noise statistics, we provide also the generalized optimization algorithms taking the advantage of the weighted median filters and the relationship between standard median filter and vector median filter. Thus, we can deal with both statistical and deterministic aspects of the filter design process. It will be shown that the proposed method holds the required properties such as the capability of modelling the underlying system in the application at hand, the robustness with respect to errors in the model of underlying system, the availability of the training procedure and finally, the simplicity of filter representation, analysis, design and implementation. Simulation studies also indicate that the new filters are computationally attractive and have excellent performance in environments corrupted by bit errors and impulsive noise.
International Nuclear Information System (INIS)
Clark, T.E.; Love, S.T.; Nitta, Muneto; Veldhuis, T. ter; Xiong, C.
2009-01-01
Local oscillations of the brane world are manifested as massive vector fields. Their coupling to the Standard Model can be obtained using the method of nonlinear realizations of the spontaneously broken higher-dimensional space-time symmetries, and to an extent, are model independent. Phenomenological limits on these vector field parameters are obtained using LEP collider data and dark matter constraints
Complex Polynomial Vector Fields
DEFF Research Database (Denmark)
The two branches of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions...... or meromorphic (allowing poles as singularities) functions. There already exists a well-developed theory for iterative holomorphic dynamical systems, and successful relations found between iteration theory and flows of vector fields have been one of the main motivations for the recent interest in holomorphic...... vector fields. Since the class of complex polynomial vector fields in the plane is natural to consider, it is remarkable that its study has only begun very recently. There are numerous fundamental questions that are still open, both in the general classification of these vector fields, the decomposition...
Complex Polynomial Vector Fields
DEFF Research Database (Denmark)
Dias, Kealey
vector fields. Since the class of complex polynomial vector fields in the plane is natural to consider, it is remarkable that its study has only begun very recently. There are numerous fundamental questions that are still open, both in the general classification of these vector fields, the decomposition...... of parameter spaces into structurally stable domains, and a description of the bifurcations. For this reason, the talk will focus on these questions for complex polynomial vector fields.......The two branches of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions...
Yihaa Roodhiyah, Lisa’; Tjong, Tiffany; Nurhasan; Sutarno, D.
2018-04-01
The late research, linear matrices of vector finite element in two dimensional(2-D) magnetotelluric (MT) responses modeling was solved by non-sparse direct solver in TE mode. Nevertheless, there is some weakness which have to be improved especially accuracy in the low frequency (10-3 Hz-10-5 Hz) which is not achieved yet and high cost computation in dense mesh. In this work, the solver which is used is sparse direct solver instead of non-sparse direct solverto overcome the weaknesses of solving linear matrices of vector finite element metod using non-sparse direct solver. Sparse direct solver will be advantageous in solving linear matrices of vector finite element method because of the matrix properties which is symmetrical and sparse. The validation of sparse direct solver in solving linear matrices of vector finite element has been done for a homogen half-space model and vertical contact model by analytical solution. Thevalidation result of sparse direct solver in solving linear matrices of vector finite element shows that sparse direct solver is more stable than non-sparse direct solver in computing linear problem of vector finite element method especially in low frequency. In the end, the accuracy of 2D MT responses modelling in low frequency (10-3 Hz-10-5 Hz) has been reached out under the efficient allocation memory of array and less computational time consuming.
Estadísticos en términos de vectores y matrices
Directory of Open Access Journals (Sweden)
Julio Pallas González
2000-01-01
Full Text Available Es corriente definir algunos conceptos estadísticos directamente, sin usar aquellas ideas iniciales que los motivaron. A causa de ello puede parecer (sobre todo a nuestros estudiantes que no existe relación ni continuidad con otros conceptos básicos ya introducidos en Matemáticas. Esta es la razón que nos ha llevado a presentar la materia elemental (y sobradamente conocida que sigue. Concretamente, utilizando el concepto de producto escalar ordinario (y la norma inducida por él, se introducen los conceptos de varianza y de coeficiente de correlación, así como su interpretación geométrica. Posteriormente, utilizando el concepto de proyección, se presentan e interpretan los conceptos de ajuste de mínimos cuadrados, coeficiente de determinación y los de correlación parcial.
Virial expansion for almost diagonal random matrices
International Nuclear Information System (INIS)
Yevtushenko, Oleg; Kravtsov, Vladimir E
2003-01-01
Energy level statistics of Hermitian random matrices H-circumflex with Gaussian independent random entries H i≥j is studied for a generic ensemble of almost diagonal random matrices with (vertical bar H ii vertical bar 2 ) ∼ 1 and (vertical bar H i≠j vertical bar 2 ) bF(vertical bar i - j vertical bar) parallel 1. We perform a regular expansion of the spectral form-factor K(τ) = 1 + bK 1 (τ) + b 2 K 2 (τ) + c in powers of b parallel 1 with the coefficients K m (τ) that take into account interaction of (m + 1) energy levels. To calculate K m (τ), we develop a diagrammatic technique which is based on the Trotter formula and on the combinatorial problem of graph edges colouring with (m + 1) colours. Expressions for K 1 (τ) and K 2 (τ) in terms of infinite series are found for a generic function F(vertical bar i - j vertical bar ) in the Gaussian orthogonal ensemble (GOE), the Gaussian unitary ensemble (GUE) and in the crossover between them (the almost unitary Gaussian ensemble). The Rosenzweig-Porter and power-law banded matrix ensembles are considered as examples
Generalized Eigenvalues for pairs on heritian matrices
Rublein, George
1988-01-01
A study was made of certain special cases of a generalized eigenvalue problem. Let A and B be nxn matrics. One may construct a certain polynomial, P(A,B, lambda) which specializes to the characteristic polynomial of B when A equals I. In particular, when B is hermitian, that characteristic polynomial, P(I,B, lambda) has real roots, and one can ask: are the roots of P(A,B, lambda) real when B is hermitian. We consider the case where A is positive definite and show that when N equals 3, the roots are indeed real. The basic tools needed in the proof are Shur's theorem on majorization for eigenvalues of hermitian matrices and the interlacing theorem for the eigenvalues of a positive definite hermitian matrix and one of its principal (n-1)x(n-1) minors. The method of proof first reduces the general problem to one where the diagonal of B has a certain structure: either diag (B) = diag (1,1,1) or diag (1,1,-1), or else the 2 x 2 principal minors of B are all 1. According as B has one of these three structures, we use an appropriate method to replace A by a positive diagonal matrix. Since it can be easily verified that P(D,B, lambda) has real roots, the result follows. For other configurations of B, a scaling and a continuity argument are used to prove the result in general.
Adaptive Matrices for Color Texture Classification
Bunte, Kerstin; Giotis, Ioannis; Petkov, Nicolai; Biehl, Michael; Real, P; DiazPernil, D; MolinaAbril, H; Berciano, A; Kropatsch, W
2011-01-01
In this paper we introduce an integrative approach towards color texture classification learned by a supervised framework. Our approach is based on the Generalized Learning Vector Quantization (GLVQ), extended by an adaptive distance measure which is defined in the Fourier domain and 2D Gabor
Meet and Join Matrices in the Poset of Exponential Divisors
Indian Academy of Sciences (India)
... exponential divisor ( G C E D ) and the least common exponential multiple ( L C E M ) do not always exist. In this paper we embed this poset in a lattice. As an application we study the G C E D and L C E M matrices, analogues of G C D and L C M matrices, which are both special cases of meet and join matrices on lattices.
The 'golden' matrices and a new kind of cryptography
International Nuclear Information System (INIS)
Stakhov, A.P.
2007-01-01
We consider a new class of square matrices called the 'golden' matrices. They are a generalization of the classical Fibonacci Q-matrix for continuous domain. The 'golden' matrices can be used for creation of a new kind of cryptography called the 'golden' cryptography. The method is very fast and simple for technical realization and can be used for cryptographic protection of digital signals (telecommunication and measurement systems)
Generalized Perron--Frobenius Theorem for Nonsquare Matrices
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...
International Nuclear Information System (INIS)
Gerola, Adriana P.; Silva, Danielle C.; Rubira, Adley F.; Muniz, Edvani C.
2015-01-01
Modified gum Arabic (GA) hydrogels show a pH-responsive behavior making them excellent matrices to be used for oral administration of drugs. Our goal is to study the behavior of those matrices in simulated gastric and intestinal fluids. In this work we will present how the methacrylation degree of GA, by using glycidyl methacrylate, can affect the properties of these hydrogels for controlled release. The drug used in this work is the curcumin (Cur). Cur is associated with numerous pharmacological activities, but their application is limited by the low water solubility. We will present some studies involving the formation of host-guest complexes between Cur and natural cyclodextrins. Both modified GA and hydrogels were characterized by different techniques. The kinetics release of Cur complex-containing modified GA hydrogels was studied to have an insight on the release mechanism and rate constants. Toxicity studies on undifferentiated and differentiated Caco-2 were also carried out. (author)
Fractal vector optical fields.
Pan, Yue; Gao, Xu-Zhen; Cai, Meng-Qiang; Zhang, Guan-Lin; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian
2016-07-15
We introduce the concept of a fractal, which provides an alternative approach for flexibly engineering the optical fields and their focal fields. We propose, design, and create a new family of optical fields-fractal vector optical fields, which build a bridge between the fractal and vector optical fields. The fractal vector optical fields have polarization states exhibiting fractal geometry, and may also involve the phase and/or amplitude simultaneously. The results reveal that the focal fields exhibit self-similarity, and the hierarchy of the fractal has the "weeding" role. The fractal can be used to engineer the focal field.
Noisy covariance matrices and portfolio optimization II
Pafka, Szilárd; Kondor, Imre
2003-03-01
Recent studies inspired by results from random matrix theory (Galluccio et al.: Physica A 259 (1998) 449; Laloux et al.: Phys. Rev. Lett. 83 (1999) 1467; Risk 12 (3) (1999) 69; Plerou et al.: Phys. Rev. Lett. 83 (1999) 1471) found that covariance matrices determined from empirical financial time series appear to contain such a high amount of noise that their structure can essentially be regarded as random. This seems, however, to be in contradiction with the fundamental role played by covariance matrices in finance, which constitute the pillars of modern investment theory and have also gained industry-wide applications in risk management. Our paper is an attempt to resolve this embarrassing paradox. The key observation is that the effect of noise strongly depends on the ratio r= n/ T, where n is the size of the portfolio and T the length of the available time series. On the basis of numerical experiments and analytic results for some toy portfolio models we show that for relatively large values of r (e.g. 0.6) noise does, indeed, have the pronounced effect suggested by Galluccio et al. (1998), Laloux et al. (1999) and Plerou et al. (1999) and illustrated later by Laloux et al. (Int. J. Theor. Appl. Finance 3 (2000) 391), Plerou et al. (Phys. Rev. E, e-print cond-mat/0108023) and Rosenow et al. (Europhys. Lett., e-print cond-mat/0111537) in a portfolio optimization context, while for smaller r (around 0.2 or below), the error due to noise drops to acceptable levels. Since the length of available time series is for obvious reasons limited in any practical application, any bound imposed on the noise-induced error translates into a bound on the size of the portfolio. In a related set of experiments we find that the effect of noise depends also on whether the problem arises in asset allocation or in a risk measurement context: if covariance matrices are used simply for measuring the risk of portfolios with a fixed composition rather than as inputs to optimization, the
Fast multipole preconditioners for sparse matrices arising from elliptic equations
Ibeid, Huda
2017-11-09
Among optimal hierarchical algorithms for the computational solution of elliptic problems, the fast multipole method (FMM) stands out for its adaptability to emerging architectures, having high arithmetic intensity, tunable accuracy, and relaxable global synchronization requirements. We demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for satisfying conditions at finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Here, we do not discuss the well developed applications of FMM to implement matrix-vector multiplications within Krylov solvers of boundary element methods. Instead, we propose using FMM for the volume-to-volume contribution of inhomogeneous Poisson-like problems, where the boundary integral is a small part of the overall computation. Our method may be used to precondition sparse matrices arising from finite difference/element discretizations, and can handle a broader range of scientific applications. It is capable of algebraic convergence rates down to the truncation error of the discretized PDE comparable to those of multigrid methods, and it offers potentially superior multicore and distributed memory scalability properties on commodity architecture supercomputers. Compared with other methods exploiting the low-rank character of off-diagonal blocks of the dense resolvent operator, FMM-preconditioned Krylov iteration may reduce the amount of communication because it is matrix-free and exploits the tree structure of FMM. We describe our tests in reproducible detail with freely available codes and outline directions for further extensibility.
Fast multipole preconditioners for sparse matrices arising from elliptic equations
Ibeid, Huda; Yokota, Rio; Pestana, Jennifer; Keyes, David E.
2017-01-01
Among optimal hierarchical algorithms for the computational solution of elliptic problems, the fast multipole method (FMM) stands out for its adaptability to emerging architectures, having high arithmetic intensity, tunable accuracy, and relaxable global synchronization requirements. We demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for satisfying conditions at finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Here, we do not discuss the well developed applications of FMM to implement matrix-vector multiplications within Krylov solvers of boundary element methods. Instead, we propose using FMM for the volume-to-volume contribution of inhomogeneous Poisson-like problems, where the boundary integral is a small part of the overall computation. Our method may be used to precondition sparse matrices arising from finite difference/element discretizations, and can handle a broader range of scientific applications. It is capable of algebraic convergence rates down to the truncation error of the discretized PDE comparable to those of multigrid methods, and it offers potentially superior multicore and distributed memory scalability properties on commodity architecture supercomputers. Compared with other methods exploiting the low-rank character of off-diagonal blocks of the dense resolvent operator, FMM-preconditioned Krylov iteration may reduce the amount of communication because it is matrix-free and exploits the tree structure of FMM. We describe our tests in reproducible detail with freely available codes and outline directions for further extensibility.
Multiple image encryption scheme based on pixel exchange operation and vector decomposition
Xiong, Y.; Quan, C.; Tay, C. J.
2018-02-01
We propose a new multiple image encryption scheme based on a pixel exchange operation and a basic vector decomposition in Fourier domain. In this algorithm, original images are imported via a pixel exchange operator, from which scrambled images and pixel position matrices are obtained. Scrambled images encrypted into phase information are imported using the proposed algorithm and phase keys are obtained from the difference between scrambled images and synthesized vectors in a charge-coupled device (CCD) plane. The final synthesized vector is used as an input in a random phase encoding (DRPE) scheme. In the proposed encryption scheme, pixel position matrices and phase keys serve as additional private keys to enhance the security of the cryptosystem which is based on a 4-f system. Numerical simulations are presented to demonstrate the feasibility and robustness of the proposed encryption scheme.
Reversible Vector Ratchet Effect in Skyrmion Systems
Ma, Xiaoyu; Reichhardt, Charles; Reichhardt, Cynthia
Magnetic skyrmions are topological non-trivial spin textures found in several magnetic materials. Since their motion can be controlled using ultralow current densities, skyrmions are appealing for potential applications in spintronics as information carriers and processing devices. In this work, we studied the collective transport properties of driven skyrmions based on a particle-like model with molecular dynamics (MD) simulation. Our results show that ac driven skyrmions interacting with an asymmetric substrate provide a realization of a new class of ratchet system, which we call a vector ratchet, that arises due to the effect of the Magnus term on the skyrmion dynamics. In a vector ratchet, the dc motion induced by the ac drive can be described as a vector that can be rotated up to 360 degrees relative to the substrate asymmetry direction. This could represent a new method for controlling skyrmion motion for spintronic applications.
Colonization of bone matrices by cellular components
Shchelkunova, E. I.; Voropaeva, A. A.; Korel, A. V.; Mayer, D. A.; Podorognaya, V. T.; Kirilova, I. A.
2017-09-01
Practical surgery, traumatology, orthopedics, and oncology require bioengineered constructs suitable for replacement of large-area bone defects. Only rigid/elastic matrix containing recipient's bone cells capable of mitosis, differentiation, and synthesizing extracellular matrix that supports cell viability can comply with these requirements. Therefore, the development of the techniques to produce structural and functional substitutes, whose three-dimensional structure corresponds to the recipient's damaged tissues, is the main objective of tissue engineering. This is achieved by developing tissue-engineering constructs represented by cells placed on the matrices. Low effectiveness of carrier matrix colonization with cells and their uneven distribution is one of the major problems in cell culture on various matrixes. In vitro studies of the interactions between cells and material, as well as the development of new techniques for scaffold colonization by cellular components are required to solve this problem.
Matrices over runtime systems at exascale
Agullo, Emmanuel
2012-11-01
The goal of Matrices Over Runtime Systems at Exascale (MORSE) project is to design dense and sparse linear algebra methods that achieve the fastest possible time to an accurate solution on large-scale multicore systems with GPU accelerators, using all the processing power that future high end systems can make available. In this poster, we propose a framework for describing linear algebra algorithms at a high level of abstraction and delegating the actual execution to a runtime system in order to design software whose performance is portable accross architectures. We illustrate our methodology on three classes of problems: dense linear algebra, sparse direct methods and fast multipole methods. The resulting codes have been incorporated into Magma, Pastix and ScalFMM solvers, respectively. © 2012 IEEE.
Sparse random matrices: The eigenvalue spectrum revisited
International Nuclear Information System (INIS)
Semerjian, Guilhem; Cugliandolo, Leticia F.
2003-08-01
We revisit the derivation of the density of states of sparse random matrices. We derive a recursion relation that allows one to compute the spectrum of the matrix of incidence for finite trees that determines completely the low concentration limit. Using the iterative scheme introduced by Biroli and Monasson [J. Phys. A 32, L255 (1999)] we find an approximate expression for the density of states expected to hold exactly in the opposite limit of large but finite concentration. The combination of the two methods yields a very simple geometric interpretation of the tails of the spectrum. We test the analytic results with numerical simulations and we suggest an indirect numerical method to explore the tails of the spectrum. (author)
From Pauli Matrices to Quantum Ito Formula
International Nuclear Information System (INIS)
Pautrat, Yan
2005-01-01
This paper answers important questions raised by the recent description, by Attal, of a robust and explicit method to approximate basic objects of quantum stochastic calculus on bosonic Fock space by analogues on the state space of quantum spin chains. The existence of that method justifies a detailed investigation of discrete-time quantum stochastic calculus. Here we fully define and study that theory and obtain in particular a discrete-time quantum Ito formula, which one can see as summarizing the commutation relations of Pauli matrices.An apparent flaw in that approximation method is the difference in the quantum Ito formulas, discrete and continuous, which suggests that the discrete quantum stochastic calculus differs fundamentally from the continuous one and is therefore not a suitable object to approximate subtle phenomena. We show that flaw is only apparent by proving that the continuous-time quantum Ito formula is actually a consequence of its discrete-time counterpart
Noncausal Bayesian Vector Autoregression
DEFF Research Database (Denmark)
Lanne, Markku; Luoto, Jani
We propose a Bayesian inferential procedure for the noncausal vector autoregressive (VAR) model that is capable of capturing nonlinearities and incorporating effects of missing variables. In particular, we devise a fast and reliable posterior simulator that yields the predictive distribution...
Curjel, C. R.
1990-01-01
Presented are activities that help students understand the idea of a vector field. Included are definitions, flow lines, tangential and normal components along curves, flux and work, field conservation, and differential equations. (KR)
Minnesota Department of Natural Resources — This vector dataset is a detailed (1-acre minimum), hierarchically organized vegetation cover map produced by computer classification of combined two-season pairs of...
Sesquilinear uniform vector integral
Indian Academy of Sciences (India)
theory, together with his integral, dominate contemporary mathematics. ... directions belonging to Bartle and Dinculeanu (see [1], [6], [7] and [2]). ... in this manner, namely he integrated vector functions with respect to measures of bounded.
Kansas Data Access and Support Center — The Kansas Tagged Vector Contour (TVC) dataset consists of digitized contours from the 7.5 minute topographic quadrangle maps. Coverage for the state is incomplete....
Czech Academy of Sciences Publication Activity Database
Krejčí, Pavel
1991-01-01
Roč. 2, - (1991), s. 281-292 ISSN 0956-7925 Keywords : vector hysteresis operator * hysteresis potential * differential inequality Subject RIV: BA - General Mathematics http://www.math.cas.cz/~krejci/b15p.pdf
Dirac matrices for Chern-Simons gravity
Energy Technology Data Exchange (ETDEWEB)
Izaurieta, Fernando; Ramirez, Ricardo; Rodriguez, Eduardo [Departamento de Matematica y Fisica Aplicadas, Universidad Catolica de la Santisima Concepcion, Alonso de Ribera 2850, 4090541 Concepcion (Chile)
2012-10-06
A genuine gauge theory for the Poincare, de Sitter or anti-de Sitter algebras can be constructed in (2n- 1)-dimensional spacetime by means of the Chern-Simons form, yielding a gravitational theory that differs from General Relativity but shares many of its properties, such as second order field equations for the metric. The particular form of the Lagrangian is determined by a rank n, symmetric tensor invariant under the relevant algebra. In practice, the calculation of this invariant tensor can be reduced to the computation of the trace of the symmetrized product of n Dirac Gamma matrices {Gamma}{sub ab} in 2n-dimensional spacetime. While straightforward in principle, this calculation can become extremely cumbersome in practice. For large enough n, existing computer algebra packages take an inordinate long time to produce the answer or plainly fail having used up all available memory. In this talk we show that the general formula for the trace of the symmetrized product of 2n Gamma matrices {Gamma}{sub ab} can be written as a certain sum over the integer partitions s of n, with every term being multiplied by a numerical cofficient {alpha}{sub s}. We then give a general algorithm that computes the {alpha}-coefficients as the solution of a linear system of equations generated by evaluating the general formula for different sets of tensors B{sup ab} with random numerical entries. A recurrence relation between different coefficients is shown to hold and is used in a second, 'minimal' algorithm to greatly speed up the computations. Runtime of the minimal algorithm stays below 1 min on a typical desktop computer for up to n = 25, which easily covers all foreseeable applications of the trace formula.
Viscous hydrophilic injection matrices for serial crystallography
Directory of Open Access Journals (Sweden)
Gabriela Kovácsová
2017-07-01
Full Text Available Serial (femtosecond crystallography at synchrotron and X-ray free-electron laser (XFEL sources distributes the absorbed radiation dose over all crystals used for data collection and therefore allows measurement of radiation damage prone systems, including the use of microcrystals for room-temperature measurements. Serial crystallography relies on fast and efficient exchange of crystals upon X-ray exposure, which can be achieved using a variety of methods, including various injection techniques. The latter vary significantly in their flow rates – gas dynamic virtual nozzle based injectors provide very thin fast-flowing jets, whereas high-viscosity extrusion injectors produce much thicker streams with flow rates two to three orders of magnitude lower. High-viscosity extrusion results in much lower sample consumption, as its sample delivery speed is commensurate both with typical XFEL repetition rates and with data acquisition rates at synchrotron sources. An obvious viscous injection medium is lipidic cubic phase (LCP as it is used for in meso membrane protein crystallization. However, LCP has limited compatibility with many crystallization conditions. While a few other viscous media have been described in the literature, there is an ongoing need to identify additional injection media for crystal embedding. Critical attributes are reliable injection properties and a broad chemical compatibility to accommodate samples as heterogeneous and sensitive as protein crystals. Here, the use of two novel hydrogels as viscous injection matrices is described, namely sodium carboxymethyl cellulose and the thermo-reversible block polymer Pluronic F-127. Both are compatible with various crystallization conditions and yield acceptable X-ray background. The stability and velocity of the extruded stream were also analysed and the dependence of the stream velocity on the flow rate was measured. In contrast with previously characterized injection media, both new
Support vector machines applications
Guo, Guodong
2014-01-01
Support vector machines (SVM) have both a solid mathematical background and good performance in practical applications. This book focuses on the recent advances and applications of the SVM in different areas, such as image processing, medical practice, computer vision, pattern recognition, machine learning, applied statistics, business intelligence, and artificial intelligence. The aim of this book is to create a comprehensive source on support vector machine applications, especially some recent advances.
International Nuclear Information System (INIS)
Akama, K.; Hattori, T.; Yasue, M.
1991-01-01
An exotic composite vector boson V is introduced in two dynamical models of composite quarks, leptons, W, and Z. One is based on four-Fermi interactions, in which composite vector bosons are regarded as fermion-antifermion bound states and the other is based on the confining SU(2) L gauge model, in which they are given by scalar-antiscalar bound states. Both approaches describe the same effective interactions for the sector of composite quarks, leptons, W, Z, γ, and V
Melillo Fenech, Tanya
2010-01-01
A vector-borne disease is one in which the pathogenic microorganism is transmitted from an infected individual to another individual by an arthropod or other agent. The transmission depends upon the attributes and requirements of at least three different Iiving organisms : the pathologic agent which is either a virus, protozoa, bacteria or helminth (worm); the vector, which is commonly an arthropod such as ticks or mosquitoes; and the human host.
International Nuclear Information System (INIS)
Yan, Zhenya
2011-01-01
The coupled nonlinear volatility and option pricing model presented recently by Ivancevic is investigated, which generates a leverage effect, i.e., stock volatility is (negatively) correlated to stock returns, and can be regarded as a coupled nonlinear wave alternative of the Black–Scholes option pricing model. In this Letter, we analytically propose vector financial rogue waves of the coupled nonlinear volatility and option pricing model without an embedded w-learning. Moreover, we exhibit their dynamical behaviors for chosen different parameters. The vector financial rogue wave (rogon) solutions may be used to describe the possible physical mechanisms for the rogue wave phenomena and to further excite the possibility of relative researches and potential applications of vector rogue waves in the financial markets and other related fields. -- Highlights: ► We investigate the coupled nonlinear volatility and option pricing model. ► We analytically present vector financial rogue waves. ► The vector financial rogue waves may be used to describe the extreme events in financial markets. ► This results may excite the relative researches and potential applications of vector rogue waves.
Binary Positive Semidefinite Matrices and Associated Integer Polytopes
DEFF Research Database (Denmark)
Letchford, Adam N.; Sørensen, Michael Malmros
2012-01-01
We consider the positive semidefinite (psd) matrices with binary entries, along with the corresponding integer polytopes. We begin by establishing some basic properties of these matrices and polytopes. Then, we show that several families of integer polytopes in the literature-the cut, boolean qua...
CONVERGENCE OF POWERS OF CONTROLLABLE INTUITIONISTIC FUZZY MATRICES
Riyaz Ahmad Padder; P. Murugadas
2016-01-01
Convergences of powers of controllable intuitionistic fuzzy matrices have been stud¬ied. It is shown that they oscillate with period equal to 2, in general. Some equalities and sequences of inequalities about powers of controllable intuitionistic fuzzy matrices have been obtained.
Propositional matrices as alternative representation of truth values ...
African Journals Online (AJOL)
The paper considered the subject of representation of truth values in symbolic logic. An alternative representation was given based on the rows and columns properties of matrices, with the operations involving the logical connectives subjected to the laws of algebra of propositions. Matrices of various propositions detailing ...
The Modern Origin of Matrices and Their Applications
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…
Abel-grassmann's groupoids of modulo matrices
International Nuclear Information System (INIS)
Javaid, Q.; Awan, M.D.; Naqvi, S.H.A.
2016-01-01
The binary operation of usual addition is associative in all matrices over R. However, a binary operation of addition in matrices over Z/sub n/ of a nonassociative structures of AG-groupoids and AG-groups are defined and investigated here. It is shown that both these structures exist for every integer n >≥ 3. Various properties of these structures are explored like: (i) Every AG-groupoid of matrices over Z/sub n/ is transitively commutative AG-groupoid and is a cancellative AG-groupoid if n is prime. (ii) Every AG-groupoid of matrices over Z/sub n/ of Type-II is a T/sup 3/-AG-groupoid. (iii) An AG-groupoid of matrices over Z/sub n/ ; G /sub nAG/(t,u), is an AG-band, if t+u=1(mod n). (author)
СREATION OF CORRELATION FUNCTIONS OF LINEAR CONTINUOUS SYSTEMS BASED ON THEIR FUNDAMENTAL MATRICES
Directory of Open Access Journals (Sweden)
N. A. Vunder
2015-11-01
Full Text Available The paper presents a method of creating correlation matrices and functions of the state vectors and outputs of the linear continuous systems functioning under the conditions of stochastic stationary, in a broad sense, effects. Fundamental matrices form the basis of the method. We have shown that for the linear continuous systems with single dimensional input and single dimensional output the correlation output function of such system can be found as the free movement of this system generated by its initial state. This state is constructed from the variance matrix of the state vector and the transposed output matrix. We have elucidated that when a continuous system belongs to a class of multi-dimensional input – multi-dimensional output systems, the following options are available for solving the problem of creation of the correlation function of a linear system. The first option is to partition the system into separate channels. Then the approach developed for systems with onedimensional input and one-dimensional output is applied to each of the separate channels. The second option is used to preserve the vector nature of the stochastic external influence. It consists in partition of output vector to scalar components by separating output matrix into separate rows with subsequent formation of the correlation function according to the scheme for single dimensional input and single dimensional output type systems. The third option is based on the scalarization of matrix correlation output function by applying the singular value decomposition to it. That gives the possibility to form scalar majorant and minorant of correlation output functions. We have established that a key component of a computational procedure of creating the correlation function of continuous linear system is a variance matrix of the system state vector. In the case of functioning under an exogenous stochastic effect like "white noise" the variance matrix is calculated by
De Marco, N
2013-01-01
Two identical sets of calorimeters are located on both sides with respect to the beam Interaction Point (IP), 112.5 m away from it. Each set of detectors consists of a neutron (ZN) and a proton (ZP) Zero Degree Calorimeter (ZDC), positioned on remotely controlled platforms. The ZN is placed at zero degree with respect to the LHC beam axis, between the two beam pipes, while the ZP is positioned externally to the outgoing beam pipe. The spectator protons are separated from the ion beams by means of the dipole magnet D1.
Thomas, EG
2014-01-01
Physics to a Degree provides an extensive collection of problems suitable for self-study or tutorial and group work at the level of an undergraduate physics course. This novel set of exercises draws together the core elements of an undergraduate physics degree and provides students with the problem solving skills needed for general physics' examinations and for real-life situations encountered by the professional physicist. Topics include force, momentum, gravitation, Bernoulli's Theorem, magnetic fields, blackbody radiation, relativistic travel, mechanics near the speed of light, radioactive
Vectorization in quantum chemistry
International Nuclear Information System (INIS)
Saunders, V.R.
1987-01-01
It is argued that the optimal vectorization algorithm for many steps (and sub-steps) in a typical ab initio calculation of molecular electronic structure is quite strongly dependent on the target vector machine. Details such as the availability (or lack) of a given vector construct in the hardware, vector startup times and asymptotic rates must all be considered when selecting the optimal algorithm. Illustrations are drawn from: gaussian integral evaluation, fock matrix construction, 4-index transformation of molecular integrals, direct-CI methods, the matrix multiply operation. A cross comparison of practical implementations on the CDC Cyber 205, the Cray-IS and Cray-XMP machines is presented. To achieve portability while remaining optimal on a wide range of machines it is necessary to code all available algorithms in a machine independent manner, and to select the appropriate algorithm using a procedure which is based on machine dependent parameters. Most such parameters concern the timing of certain vector loop kernals, which can usually be derived from a 'bench-marking' routine executed prior to the calculation proper
Epilogue: degrees of transparency
Hengeveld, K.
2011-01-01
In this epilogue the results of the analyses of four different languages in the preceding papers are compared. It is shown that the degrees of transparency of these languages can be represented on an implicational scale, and that the features themselves can be ranked on a transparency scale as well.
Registered Nurse (Associate Degree).
Ohio State Univ., Columbus. Center on Education and Training for Employment.
This document, which is designed for use in developing a tech prep competency profile for the occupation of registered nurse (with an associate degree), lists technical competencies and competency builders for 19 units pertinent to the health technologies cluster in general and 5 units specific to the occupation of registered nurse. The following…
Vector Fields on Product Manifolds
Kurz, Stefan
2011-01-01
This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields. (ii) Horizontal and vertical vector fields are naturally isomorphic to smooth families of vector fields defined on the factors. Vector fields are regarded as derivations of the algebra of smooth functions.
Fully constrained Majorana neutrino mass matrices using Σ(72 x 3)
Energy Technology Data Exchange (ETDEWEB)
Krishnan, R.; Harrison, P.F. [Warwick Univ., Coventry (United Kingdom); Scott, W.G. [Rutherford Appleton Laboratory, Chilton, Didcot (United Kingdom)
2018-01-15
In 2002, two neutrino mixing ansatze having trimaximally mixed middle (ν{sub 2}) columns, namely tri-chi-maximal mixing (TχM) and tri-phi-maximal mixing (TφM), were proposed. In 2012, it was shown that TχM with χ = ± (π)/(16) as well as TφM with φ = ± (π)/(16) leads to the solution, sin{sup 2} θ{sub 13} = (2)/(3) sin{sup 2} (π)/(16), consistent with the latest measurements of the reactor mixing angle, θ{sub 13}. To obtain TχM{sub (χ=±(π)/(16))} and TφM{sub (φ=±(π)/(16))}, the type I see-saw framework with fully constrained Majorana neutrino mass matrices was utilised. These mass matrices also resulted in the neutrino mass ratios, m{sub 1}: m{sub 2}: m{sub 3} = ((2+√2))/(1+√(2(2+√2))): 1: ((2+√2))/(-1+√(2(2+√2))). In this paper we construct a flavour model based on the discrete group Σ(72 x 3) and obtain the aforementioned results. A Majorana neutrino mass matrix (a symmetric 3 x 3 matrix with six complex degrees of freedom) is conveniently mapped into a flavon field transforming as the complex six-dimensional representation of Σ(72 x 3). Specific vacuum alignments of the flavons are used to arrive at the desired mass matrices. (orig.)
Substituted amylose matrices for oral drug delivery
International Nuclear Information System (INIS)
Moghadam, S H; Wang, H W; El-Leithy, E Saddar; Chebli, C; Cartilier, L
2007-01-01
High amylose corn starch was used to obtain substituted amylose (SA) polymers by chemically modifying hydroxyl groups by an etherification process using 1,2-epoxypropanol. Tablets for drug-controlled release were prepared by direct compression and their release properties assessed by an in vitro dissolution test (USP XXIII no 2). The polymer swelling was characterized by measuring gravimetrically the water uptake ability of polymer tablets. SA hydrophilic matrix tablets present sequentially a burst effect, typical of hydrophilic matrices, and a near constant release, typical of reservoir systems. After the burst effect, surface pores disappear progressively by molecular association of amylose chains; this allows the creation of a polymer layer acting as a diffusion barrier and explains the peculiar behaviour of SA polymers. Several formulation parameters such as compression force, drug loading, tablet weight and insoluble diluent concentration were investigated. On the other hand, tablet thickness, scanning electron microscope analysis and mercury intrusion porosimetry showed that the high crushing strength values observed for SA tablets were due to an unusual melting process occurring during tabletting although the tablet external layer went only through densification, deformation and partial melting. In contrast, HPMC tablets did not show any traces of a melting process
LIBS analysis of artificial calcified tissues matrices.
Kasem, M A; Gonzalez, J J; Russo, R E; Harith, M A
2013-04-15
In most laser-based analytical methods, the reproducibility of quantitative measurements strongly depends on maintaining uniform and stable experimental conditions. For LIBS analysis this means that for accurate estimation of elemental concentration, using the calibration curves obtained from reference samples, the plasma parameters have to be kept as constant as possible. In addition, calcified tissues such as bone are normally less "tough" in their texture than many samples, especially metals. Thus, the ablation process could change the sample morphological features rapidly, and result in poor reproducibility statistics. In the present work, three artificial reference sample sets have been fabricated. These samples represent three different calcium based matrices, CaCO3 matrix, bone ash matrix and Ca hydroxyapatite matrix. A comparative study of UV (266 nm) and IR (1064 nm) LIBS for these three sets of samples has been performed under similar experimental conditions for the two systems (laser energy, spot size, repetition rate, irradiance, etc.) to examine the wavelength effect. The analytical results demonstrated that UV-LIBS has improved reproducibility, precision, stable plasma conditions, better linear fitting, and the reduction of matrix effects. Bone ash could be used as a suitable standard reference material for calcified tissue calibration using LIBS with a 266 nm excitation wavelength. Copyright © 2013 Elsevier B.V. All rights reserved.
Neutrino mass matrices with vanishing determinant
International Nuclear Information System (INIS)
Chauhan, Bhag C.; Pulido, Joao; Picariello, Marco
2006-01-01
We investigate the prospects for neutrinoless double beta decay, texture zeros. and equalities between neutrino mass matrix elements in scenarios with vanishing determinant mass matrices for vanishing and finite θ 13 mixing angles in normal and inverse mass hierarchies. For normal hierarchy and both zero and finite θ 13 it is found that neutrinoless double beta decay cannot be observed by any of the present or next generation experiments, while for inverse hierarchy it is, on the contrary, accessible to experiments. Regarding texture zeros and equalities between mass matrix elements, we find that in both normal and inverse hierarchies with θ 13 =0 no texture zeros nor any such equalities can exist apart from the obvious ones. For θ 13 ≠0 some texture zeros become possible. In normal hierarchy two texture zeros occur if 8.1x10 -2 ≤sinθ 13 ≤9.1x10 -2 while in inverse hierarchy three are possible, one with sinθ 13 ≥7x10 -3 and two others with sinθ 13 ≥0.18. All equalities between mass matrix elements are impossible with θ 13 ≠0
Calculating scattering matrices by wave function matching
International Nuclear Information System (INIS)
Zwierzycki, M.; Khomyakov, P.A.; Starikov, A.A.; Talanana, M.; Xu, P.X.; Karpan, V.M.; Marushchenko, I.; Brocks, G.; Kelly, P.J.; Xia, K.; Turek, I.; Bauer, G.E.W.
2008-01-01
The conductance of nanoscale structures can be conveniently related to their scattering properties expressed in terms of transmission and reflection coefficients. Wave function matching (WFM) is a transparent technique for calculating transmission and reflection matrices for any Hamiltonian that can be represented in tight-binding form. A first-principles Kohn-Sham Hamiltonian represented on a localized orbital basis or on a real space grid has such a form. WFM is based upon direct matching of the scattering-region wave function to the Bloch modes of ideal leads used to probe the scattering region. The purpose of this paper is to give a pedagogical introduction to WFM and present some illustrative examples of its use in practice. We briefly discuss WFM for calculating the conductance of atomic wires, using a real space grid implementation. A tight-binding muffin-tin orbital implementation very suitable for studying spin-dependent transport in layered magnetic materials is illustrated by looking at spin-dependent transmission through ideal and disordered interfaces. (copyright 2008 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Probing the Topology of Density Matrices
Directory of Open Access Journals (Sweden)
Charles-Edouard Bardyn
2018-02-01
Full Text Available The mixedness of a quantum state is usually seen as an adversary to topological quantization of observables. For example, exact quantization of the charge transported in a so-called Thouless adiabatic pump is lifted at any finite temperature in symmetry-protected topological insulators. Here, we show that certain directly observable many-body correlators preserve the integrity of topological invariants for mixed Gaussian quantum states in one dimension. Our approach relies on the expectation value of the many-body momentum-translation operator and leads to a physical observable—the “ensemble geometric phase” (EGP—which represents a bona fide geometric phase for mixed quantum states, in the thermodynamic limit. In cyclic protocols, the EGP provides a topologically quantized observable that detects encircled spectral singularities (“purity-gap” closing points of density matrices. While we identify the many-body nature of the EGP as a key ingredient, we propose a conceptually simple, interferometric setup to directly measure the latter in experiments with mesoscopic ensembles of ultracold atoms.
Visualizing complex (hydrological) systems with correlation matrices
Haas, J. C.
2016-12-01
When trying to understand or visualize the connections of different aspects of a complex system, this often requires deeper understanding to start with, or - in the case of geo data - complicated GIS software. To our knowledge, correlation matrices have rarely been used in hydrology (e.g. Stoll et al., 2011; van Loon and Laaha, 2015), yet they do provide an interesting option for data visualization and analysis. We present a simple, python based way - using a river catchment as an example - to visualize correlations and similarities in an easy and colorful way. We apply existing and easy to use python packages from various disciplines not necessarily linked to the Earth sciences and can thus quickly show how different aquifers work or react, and identify outliers, enabling this system to also be used for quality control of large datasets. Going beyond earlier work, we add a temporal and spatial element, enabling us to visualize how a system reacts to local phenomena such as for example a river, or changes over time, by visualizing the passing of time in an animated movie. References: van Loon, A.F., Laaha, G.: Hydrological drought severity explained by climate and catchment characteristics, Journal of Hydrology 526, 3-14, 2015, Drought processes, modeling, and mitigation Stoll, S., Hendricks Franssen, H. J., Barthel, R., Kinzelbach, W.: What can we learn from long-term groundwater data to improve climate change impact studies?, Hydrology and Earth System Sciences 15(12), 3861-3875, 2011
Decellularized matrices for cardiovascular tissue engineering.
Moroni, Francesco; Mirabella, Teodelinda
2014-01-01
Cardiovascular disease (CVD) is one of the leading causes of death in the Western world. The replacement of damaged vessels and valves has been practiced since the 1950's. Synthetic grafts, usually made of bio-inert materials, are long-lasting and mechanically relevant, but fail when it comes to "biointegration". Decellularized matrices, instead, can be considered biological grafts capable of stimulating in vivo migration and proliferation of endothelial cells (ECs), recruitment and differentiation of mural cells, finally, culminating in the formation of a biointegrated tissue. Decellularization protocols employ osmotic shock, ionic and non-ionic detergents, proteolitic digestions and DNase/RNase treatments; most of them effectively eliminate the cellular component, but show limitations in preserving the native structure of the extracellular matrix (ECM). In this review, we examine the current state of the art relative to decellularization techniques and biological performance of decellularized heart, valves and big vessels. Furthermore, we focus on the relevance of ECM components, native and resulting from decellularization, in mediating in vivo host response and determining repair and regeneration, as opposed to graft corruption.
On some Toeplitz matrices and their inversions
Directory of Open Access Journals (Sweden)
S. Dutta
2014-10-01
Full Text Available In this article, using the difference operator B(a[m], we introduce a lower triangular Toeplitz matrix T which includes several difference matrices such as Δ(1,Δ(m,B(r,s,B(r,s,t, and B(r̃,s̃,t̃,ũ in different special cases. For any x ∈ w and m∈N0={0,1,2,…}, the difference operator B(a[m] is defined by (B(a[m]xk=ak(0xk+ak-1(1xk-1+ak-2(2xk-2+⋯+ak-m(mxk-m,(k∈N0 where a[m] = {a(0, a(1, …, a(m} and a(i = (ak(i for 0 ⩽ i ⩽ m are convergent sequences of real numbers. We use the convention that any term with negative subscript is equal to zero. The main results of this article relate to the determination and applications of the inverse of the Toeplitz matrix T.
Bunyavirus-Vector Interactions
Directory of Open Access Journals (Sweden)
Kate McElroy Horne
2014-11-01
Full Text Available The Bunyaviridae family is comprised of more than 350 viruses, of which many within the Hantavirus, Orthobunyavirus, Nairovirus, Tospovirus, and Phlebovirus genera are significant human or agricultural pathogens. The viruses within the Orthobunyavirus, Nairovirus, and Phlebovirus genera are transmitted by hematophagous arthropods, such as mosquitoes, midges, flies, and ticks, and their associated arthropods not only serve as vectors but also as virus reservoirs in many cases. This review presents an overview of several important emerging or re-emerging bunyaviruses and describes what is known about bunyavirus-vector interactions based on epidemiological, ultrastructural, and genetic studies of members of this virus family.
Yurinsky, Vadim Vladimirovich
1995-01-01
Surveys the methods currently applied to study sums of infinite-dimensional independent random vectors in situations where their distributions resemble Gaussian laws. Covers probabilities of large deviations, Chebyshev-type inequalities for seminorms of sums, a method of constructing Edgeworth-type expansions, estimates of characteristic functions for random vectors obtained by smooth mappings of infinite-dimensional sums to Euclidean spaces. A self-contained exposition of the modern research apparatus around CLT, the book is accessible to new graduate students, and can be a useful reference for researchers and teachers of the subject.
Duality in vector optimization
Bot, Radu Ioan
2009-01-01
This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. After a preliminary chapter dedicated to convex analysis and minimality notions of sets with respect to partial orderings induced by convex cones a chapter on scalar conjugate duality follows. Then investigations on vector duality based on scalar conjugacy are made. Weak, strong and converse duality statements are delivered and connections to classical results from the literature are emphasized. One chapter is exclusively consecrated to the s
Multithreading in vector processors
Evangelinos, Constantinos; Kim, Changhoan; Nair, Ravi
2018-01-16
In one embodiment, a system includes a processor having a vector processing mode and a multithreading mode. The processor is configured to operate on one thread per cycle in the multithreading mode. The processor includes a program counter register having a plurality of program counters, and the program counter register is vectorized. Each program counter in the program counter register represents a distinct corresponding thread of a plurality of threads. The processor is configured to execute the plurality of threads by activating the plurality of program counters in a round robin cycle.
Free topological vector spaces
Gabriyelyan, Saak S.; Morris, Sidney A.
2016-01-01
We define and study the free topological vector space $\\mathbb{V}(X)$ over a Tychonoff space $X$. We prove that $\\mathbb{V}(X)$ is a $k_\\omega$-space if and only if $X$ is a $k_\\omega$-space. If $X$ is infinite, then $\\mathbb{V}(X)$ contains a closed vector subspace which is topologically isomorphic to $\\mathbb{V}(\\mathbb{N})$. It is proved that if $X$ is a $k$-space, then $\\mathbb{V}(X)$ is locally convex if and only if $X$ is discrete and countable. If $X$ is a metrizable space it is shown ...
Energy Technology Data Exchange (ETDEWEB)
Rejon-Barrera, Fernando [Institute for Theoretical Physics, University of Amsterdam,Science Park 904, Postbus 94485, 1090 GL, Amsterdam (Netherlands); Robbins, Daniel [Department of Physics, Texas A& M University,TAMU 4242, College Station, TX 77843 (United States)
2016-01-22
We work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field theory in arbitrary dimension. This includes a review of which tensor structures make appearances, a construction of the projectors onto the required mixed symmetry representations, and a computation of the conformal blocks for all possible operators which can be exchanged. These blocks are presented as differential operators acting upon the previously known scalar conformal blocks. Finally, we set up the bootstrap equations which implement crossing symmetry. Special attention is given to the case of conserved vectors, where several simplifications occur.
Stokes vector and its relationship to Discrete Wigner Functions of multiqubit states
Energy Technology Data Exchange (ETDEWEB)
Srinivasan, K., E-mail: sriniphysics@gmail.com; Raghavan, G.
2016-07-29
A Stokes vectors and Discrete Wigner Functions (DWF) provide two alternate ways of representing the state of multiqubit systems. A general relationship between the Stokes vector and the DWF is derived for arbitrary n-qubit states for all possible choices of quantum nets. The Stokes vector and the DWF are shown to be related through a Hadamard Matrix. Using these results, a relationship between the Stokes vector of a spin-flipped state and the DWF is derived. Finally, we also present a method to express the Minkowskian squared norm of the Stokes vector, corresponding to n-concurrence in terms of the DWF. - Highlights: • Relationship between Stokes vector (SV) and discrete Wigner function (DWF) for arbitrary multiqubit states is presented. • It is shown that SV and DWF are related to one another through Hadamard matrices. • We show that the Hadamard matrices depend on the choice of the quantum net. • Relationship between SV of the spin flipped state and the DWF is derived. • Expression to compute n-concurrence of the pure n-qubit systems purely in terms of DWF is given.
Stokes vector and its relationship to Discrete Wigner Functions of multiqubit states
International Nuclear Information System (INIS)
Srinivasan, K.; Raghavan, G.
2016-01-01
A Stokes vectors and Discrete Wigner Functions (DWF) provide two alternate ways of representing the state of multiqubit systems. A general relationship between the Stokes vector and the DWF is derived for arbitrary n-qubit states for all possible choices of quantum nets. The Stokes vector and the DWF are shown to be related through a Hadamard Matrix. Using these results, a relationship between the Stokes vector of a spin-flipped state and the DWF is derived. Finally, we also present a method to express the Minkowskian squared norm of the Stokes vector, corresponding to n-concurrence in terms of the DWF. - Highlights: • Relationship between Stokes vector (SV) and discrete Wigner function (DWF) for arbitrary multiqubit states is presented. • It is shown that SV and DWF are related to one another through Hadamard matrices. • We show that the Hadamard matrices depend on the choice of the quantum net. • Relationship between SV of the spin flipped state and the DWF is derived. • Expression to compute n-concurrence of the pure n-qubit systems purely in terms of DWF is given.
Degree distribution in discrete case
International Nuclear Information System (INIS)
Wang, Li-Na; Chen, Bin; Yan, Zai-Zai
2011-01-01
Vertex degree of many network models and real-life networks is limited to non-negative integer. By means of measure and integral, the relation of the degree distribution and the cumulative degree distribution in discrete case is analyzed. The degree distribution, obtained by the differential of its cumulative, is only suitable for continuous case or discrete case with constant degree change. When degree change is not a constant but proportional to degree itself, power-law degree distribution and its cumulative have the same exponent and the mean value is finite for power-law exponent greater than 1. -- Highlights: → Degree change is the crux for using the cumulative degree distribution method. → It suits for discrete case with constant degree change. → If degree change is proportional to degree, power-law degree distribution and its cumulative have the same exponent. → In addition, the mean value is finite for power-law exponent greater than 1.
Polarization speckles and generalized Stokes vector wave: a review [invited
DEFF Research Database (Denmark)
Takeda, Mitsuo; Wang, Wei; Hanson, Steen Grüner
2010-01-01
We review some of the statistical properties of polarization-related speckle phenomena, with an introduction of a less known concept of polarization speckles and their spatial degree of polarization. As a useful means to characterize twopoint vector field correlations, we review the generalized...... Stokes parameters proposed by Korotkova and Wolf, and introduce its time-domain representation to describe the space-time evolution of the correlation between random electric vector fields at two different space-time points. This time-domain generalized Stokes vector, with components similar to those...... of the beam coherence polarization matrix proposed by Gori, is shown to obey the wave equation in exact analogy to a coherence function of scalar fields. Because of this wave nature, the time-domain generalized Stokes vector is referred to as generalized Stokes vector wave in this paper....
Chain of matrices, loop equations and topological recursion
Orantin, Nicolas
2009-01-01
Random matrices are used in fields as different as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of them are based on the study of a matrix integral. However, this term can be confusing since the definition of a matrix integral in these two applications is not the same. These two definitions, perturbative and non-perturbative, are discussed in this chapter as well as their relation. The so-called loop equations satisfied by integrals over random matrices coupled in chain is discussed as well as their recursive solution in the perturbative case when the matrices are Hermitean.
Directory of Open Access Journals (Sweden)
A. Barrientos
2012-10-01
Full Text Available Resumen: En este trabajo se presenta un mÃ©todo para el modelado de cadenas cinemÃ¡ticas de robots que salva las dificultades asociadas a la elecciÃ³n de los sistemas de coordenadas y obtenciÃ³n de los parÃ¡metros de Denavit-Hartenberg. El mÃ©todo propuesto parte del conocimiento de la posiciÃ³n y orientaciÃ³n del extremo del robot en su configuraciÃ³n de reposo, para ir obteniendo en quÃ© se transforman Ã©stas tras los sucesivos movimientos de sus grados de libertad en secuencia descendente, desde el mÃ¡s alejado al mÃ¡s cercano a su base. Los movimientos son calculados en base a las Matrices de Desplazamiento, que permiten conocer en que se transforma un punto cuando Ã©ste es desplazado (trasladado o rotado con respecto a un eje que no pasa por el origen. A diferencia del mÃ©todo de Denavit-Hartenberg, que precisa ubicar para cada eslabÃ³n el origen y las direcciones de los vectores directores de los sistemas de referencia asociados, el mÃ©todo basado en las Matrices de Desplazamiento precisa solo identificar el eje de cada articulaciÃ³n, lo que le hace mÃ¡s simple e intuitivo que aquel. La obtenciÃ³n de las Matrices de Desplazamiento y con ellas del Modelo CinemÃ¡tico Directo a partir de los ejes de la articulaciÃ³n, puede hacerse mediante algunas simples operaciones, fÃ¡cilmente programables. Abstract: In this paper, a new method for modelling kinematic chains in Robotics is presented. This method eludes the difficulties de- rived from selecting the coordinate frames required to obtain Denavit-Hartenberg parameters. The proposed method arises from knowing the position and orientation of the end-effector of the robot in its home position. This algorithm allows obtaining their transformations according to the successive variations of its degrees of freedom in descending order from the remotest to the closest to the base.The movements are calculated based on the Displacement Matrixes by determining
International Nuclear Information System (INIS)
Millican, D.W.; McGown, L.B.
1989-01-01
Steady-state fluorescence excitation-emission matrices (EEMs), and phase-resolved EEMs (PREEMs) collected at modulation frequencies of 6, 18, and 30 MHz, were used for qualitative analysis of mixtures of benzo[k]fluoranthene (τ = 8 ns) and benzo[b]fluoranthene (τ = 29 ns) in ethanol. The EEMs of the individual components were extracted from mixture EEMs by means of wavelength component vector-gram (WCV) analysis. Phase resolution was found to be superior to steady-state measurements for extraction of the component spectra, for mixtures in which the intensity contributions from the two components are unequal
DEFF Research Database (Denmark)
2000-01-01
Using a pulsed ultrasound field, the two-dimensional velocity vector can be determined with the invention. The method uses a transversally modulated ultrasound field for probing the moving medium under investigation. A modified autocorrelation approach is used in the velocity estimation. The new...
Production of lentiviral vectors
Directory of Open Access Journals (Sweden)
Otto-Wilhelm Merten
2016-01-01
Full Text Available Lentiviral vectors (LV have seen considerably increase in use as gene therapy vectors for the treatment of acquired and inherited diseases. This review presents the state of the art of the production of these vectors with particular emphasis on their large-scale production for clinical purposes. In contrast to oncoretroviral vectors, which are produced using stable producer cell lines, clinical-grade LV are in most of the cases produced by transient transfection of 293 or 293T cells grown in cell factories. However, more recent developments, also, tend to use hollow fiber reactor, suspension culture processes, and the implementation of stable producer cell lines. As is customary for the biotech industry, rather sophisticated downstream processing protocols have been established to remove any undesirable process-derived contaminant, such as plasmid or host cell DNA or host cell proteins. This review compares published large-scale production and purification processes of LV and presents their process performances. Furthermore, developments in the domain of stable cell lines and their way to the use of production vehicles of clinical material will be presented.
Indian Academy of Sciences (India)
The Gram-Schmidt process is one of the first things one learns in a course ... We might want to stay as close to the experimental data as possible when converting these vectors to orthonormal ones demanded by the model. The process of finding the closest or- thonormal .... is obtained by writing the matrix A = [aI, an], then.
Champenois, Gilles
2007-01-01
The mnesor theory is the adaptation of vectors to artificial intelligence. The scalar field is replaced by a lattice. Addition becomes idempotent and multiplication is interpreted as a selection operation. We also show that mnesors can be the foundation for a linear calculus.
Treiman, Jay S
2014-01-01
Calculus with Vectors grew out of a strong need for a beginning calculus textbook for undergraduates who intend to pursue careers in STEM. fields. The approach introduces vector-valued functions from the start, emphasizing the connections between one-variable and multi-variable calculus. The text includes early vectors and early transcendentals and includes a rigorous but informal approach to vectors. Examples and focused applications are well presented along with an abundance of motivating exercises. All three-dimensional graphs have rotatable versions included as extra source materials and may be freely downloaded and manipulated with Maple Player; a free Maple Player App is available for the iPad on iTunes. The approaches taken to topics such as the derivation of the derivatives of sine and cosine, the approach to limits, and the use of "tables" of integration have been modified from the standards seen in other textbooks in order to maximize the ease with which students may comprehend the material. Additio...
Indian Academy of Sciences (India)
[G] Giannessi F, Theorems of alternative, quadratic programs and complementarity problems, in: Variational Inequalities and Complementarity Problems (eds) R W Cottle, F Giannessi and J L Lions (New York: Wiley) (1980) pp. 151±186. [K1] Kazmi K R, Existence of solutions for vector optimization, Appl. Math. Lett. 9 (1996).
Centers for Disease Control (CDC) Podcasts
2011-04-18
This podcast discusses emerging vector-borne pathogens, their role as prominent contributors to emerging infectious diseases, how they're spread, and the ineffectiveness of mosquito control methods. Created: 4/18/2011 by National Center for Emerging Zoonotic and Infectious Diseases (NCEZID). Date Released: 4/27/2011.
Lambda-matrices and vibrating systems
Lancaster, Peter
2002-01-01
Features aspects and solutions of problems of linear vibrating systems with a finite number of degrees of freedom. Starts with development of necessary tools in matrix theory, followed by numerical procedures for relevant matrix formulations and relevant theory of differential equations. Minimum of mathematical abstraction; assumes a familiarity with matrix theory, elementary calculus. 1966 edition.
Directory of Open Access Journals (Sweden)
Janiga-Ćmiel Anna
2016-12-01
Full Text Available The paper looks at the issues related to the research on and assessment of the contagion effect. Based on several examinations of two selected EU countries, Poland paired with one of the EU member states; it presents the interaction between their economic development. A DCC-GARCH model constructed for the purpose of the study was used to generate a covariance matrix Ht, which enabled the calculation of correlation matrices Rt. The resulting variance vectors were used to present a linear correlation model on which a further analysis of the contagion effect was based. The aim of the study was to test a contagion effect among selected EU countries in the years 2000–2014. The transmission channel under study was the GDP of a selected country. The empirical studies confirmed the existence of the contagion effect between the economic development of the Polish and selected EU economies.
Ait-Haddou, Rachid
2015-01-01
We show that the best degree reduction of a given polynomial P from degree n to m with respect to the discrete (Formula presented.)-norm is equivalent to the best Euclidean distance of the vector of h-Bézier coefficients of P from the vector
Modular Extracellular Matrices: Solutions for the Puzzle
Serban, Monica A.; Prestwich, Glenn D.
2008-01-01
The common technique of growing cells in two-dimensions (2-D) is gradually being replaced by culturing cells on matrices with more appropriate composition and stiffness, or by encapsulation of cells in three-dimensions (3-D). The universal acceptance of the new 3-D paradigm has been constrained by the absence of a commercially available, biocompatible material that offers ease of use, experimental flexibility, and a seamless transition from in vitro to in vivo applications. The challenge – the puzzle that needs a solution – is to replicate the complexity of the native extracellular matrix (ECM) environment with the minimum number of components necessary to allow cells to rebuild and replicate a given tissue. For use in drug discovery, toxicology, cell banking, and ultimately in reparative medicine, the ideal matrix would therefore need to be highly reproducible, manufacturable, approvable, and affordable. Herein we describe the development of a set of modular components that can be assembled into biomimetic materials that meet these requirements. These semi-synthetic ECMs, or sECMs, are based on hyaluronan derivatives that form covalently crosslinked, biodegradable hydrogels suitable for 3-D culture of primary and stem cells in vitro, and for tissue formation in vivo. The sECMs can be engineered to provide appropriate biological cues needed to recapitulate the complexity of a given ECM environment. Specific applications for different sECM compositions include stem cell expansion with control of differentiation, scar-free wound healing, growth factor delivery, cell delivery for osteochondral defect and liver repair, and development of vascularized tumor xenografts for personalized chemotherapy. PMID:18442709
Comparison of eigensolvers for symmetric band matrices.
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.
MATXTST, Basic Operations for Covariance Matrices
International Nuclear Information System (INIS)
Geraldo, Luiz P.; Smith, Donald
1989-01-01
1 - Description of program or function: MATXTST and MATXTST1 perform the following operations for a covariance matrix: - test for singularity; - test for positive definiteness; - compute the inverse if the matrix is non-singular; - compute the determinant; - determine the number of positive, negative, and zero eigenvalues; - examine all possible 3 X 3 cross correlations within a sub-matrix corresponding to a leading principal minor which is non-positive definite. While the two programs utilize the same input, the calculational procedures employed are somewhat different and their functions are complementary. The available input options include: i) the full covariance matrix, ii) the basic variables plus the relative covariance matrix, or iii) uncertainties in the basic variables plus the correlation matrix. 2 - Method of solution: MATXTST employs LINPACK subroutines SPOFA and SPODI to test for positive definiteness and to perform further optional calculations. Subroutine SPOFA factors a symmetric matrix M using the Cholesky algorithm to determine the elements of a matrix R which satisfies the relation M=R'R, where R' is the transposed matrix of R. Each leading principal minor of M is tested until the first one is found which is not positive definite. MATXTST1 uses LINPACK subroutines SSICO, SSIFA, and SSIDI to estimate whether the matrix is near to singularity or not (SSICO), and to perform the matrix diagonalization process (SSIFA). The algorithm used in SSIFA is generalization of the Method of Lagrange Reduction. SSIDI is used to compute the determinant and inertia of the matrix. 3 - Restrictions on the complexity of the problem: Matrices of sizes up to 50 X 50 elements can be treated by present versions of the programs
Joint Estimation of Multiple Precision Matrices with Common Structures.
Lee, Wonyul; Liu, Yufeng
Estimation of inverse covariance matrices, known as precision matrices, is important in various areas of statistical analysis. In this article, we consider estimation of multiple precision matrices sharing some common structures. In this setting, estimating each precision matrix separately can be suboptimal as it ignores potential common structures. This article proposes a new approach to parameterize each precision matrix as a sum of common and unique components and estimate multiple precision matrices in a constrained l 1 minimization framework. We establish both estimation and selection consistency of the proposed estimator in the high dimensional setting. The proposed estimator achieves a faster convergence rate for the common structure in certain cases. Our numerical examples demonstrate that our new estimator can perform better than several existing methods in terms of the entropy loss and Frobenius loss. An application to a glioblastoma cancer data set reveals some interesting gene networks across multiple cancer subtypes.
Systems of Differential Equations with Skew-Symmetric, Orthogonal Matrices
Glaister, P.
2008-01-01
The solution of a system of linear, inhomogeneous differential equations is discussed. The particular class considered is where the coefficient matrix is skew-symmetric and orthogonal, and where the forcing terms are sinusoidal. More general matrices are also considered.
Finiteness properties of congruence classes of infinite matrices
Eggermont, R.H.
2014-01-01
We look at spaces of infinite-by-infinite matrices, and consider closed subsets that are stable under simultaneous row and column operations. We prove that up to symmetry, any of these closed subsets is defined by finitely many equations.
Flexible Bayesian Dynamic Modeling of Covariance and Correlation Matrices
Lan, Shiwei; Holbrook, Andrew; Fortin, Norbert J.; Ombao, Hernando; Shahbaba, Babak
2017-01-01
Modeling covariance (and correlation) matrices is a challenging problem due to the large dimensionality and positive-definiteness constraint. In this paper, we propose a novel Bayesian framework based on decomposing the covariance matrix
Procrustes Problems for General, Triangular, and Symmetric Toeplitz Matrices
Directory of Open Access Journals (Sweden)
Juan Yang
2013-01-01
Full Text Available The Toeplitz Procrustes problems are the least squares problems for the matrix equation AX=B over some Toeplitz matrix sets. In this paper the necessary and sufficient conditions are obtained about the existence and uniqueness for the solutions of the Toeplitz Procrustes problems when the unknown matrices are constrained to the general, the triangular, and the symmetric Toeplitz matrices, respectively. The algorithms are designed and the numerical examples show that these algorithms are feasible.
An introduction to the theory of canonical matrices
Turnbull, H W
2004-01-01
Thorough and self-contained, this penetrating study of the theory of canonical matrices presents a detailed consideration of all the theory's principal features. Topics include elementary transformations and bilinear and quadratic forms; canonical reduction of equivalent matrices; subgroups of the group of equivalent transformations; and rational and classical canonical forms. The final chapters explore several methods of canonical reduction, including those of unitary and orthogonal transformations. 1952 edition. Index. Appendix. Historical notes. Bibliographies. 275 problems.
Dynamical correlations for circular ensembles of random matrices
International Nuclear Information System (INIS)
Nagao, Taro; Forrester, Peter
2003-01-01
Circular Brownian motion models of random matrices were introduced by Dyson and describe the parametric eigenparameter correlations of unitary random matrices. For symmetric unitary, self-dual quaternion unitary and an analogue of antisymmetric Hermitian matrix initial conditions, Brownian dynamics toward the unitary symmetry is analyzed. The dynamical correlation functions of arbitrary number of Brownian particles at arbitrary number of times are shown to be written in the forms of quaternion determinants, similarly as in the case of Hermitian random matrix models
Complementary Set Matrices Satisfying a Column Correlation Constraint
Wu, Di; Spasojevic, Predrag
2006-01-01
Motivated by the problem of reducing the peak to average power ratio (PAPR) of transmitted signals, we consider a design of complementary set matrices whose column sequences satisfy a correlation constraint. The design algorithm recursively builds a collection of $2^{t+1}$ mutually orthogonal (MO) complementary set matrices starting from a companion pair of sequences. We relate correlation properties of column sequences to that of the companion pair and illustrate how to select an appropriate...
Open vessel microwave digestion of food matrices (T6)
International Nuclear Information System (INIS)
Rhodes, L.; LeBlanc, G.
2002-01-01
Full text: Advancements in the field of open vessel microwave digestion continue to provide solutions for industries requiring acid digestion of large sample sizes. Those interesting in digesting food matrices are particularly interested in working with large amounts of sample and then diluting small final volumes. This paper will show the advantages of instantaneous regent addition and post-digestion evaporation when performing an open vessel digestion and evaporation methods for various food matrices will be presented along with analyte recovery data. (author)
Quantum Algorithms for Weighing Matrices and Quadratic Residues
van Dam, Wim
2000-01-01
In this article we investigate how we can employ the structure of combinatorial objects like Hadamard matrices and weighing matrices to device new quantum algorithms. We show how the properties of a weighing matrix can be used to construct a problem for which the quantum query complexity is ignificantly lower than the classical one. It is pointed out that this scheme captures both Bernstein & Vazirani's inner-product protocol, as well as Grover's search algorithm. In the second part of the ar...
Asymptotic Distribution of Eigenvalues of Weakly Dilute Wishart Matrices
Energy Technology Data Exchange (ETDEWEB)
Khorunzhy, A. [Institute for Low Temperature Physics (Ukraine)], E-mail: khorunjy@ilt.kharkov.ua; Rodgers, G. J. [Brunel University, Uxbridge, Department of Mathematics and Statistics (United Kingdom)], E-mail: g.j.rodgers@brunel.ac.uk
2000-03-15
We study the eigenvalue distribution of large random matrices that are randomly diluted. We consider two random matrix ensembles that in the pure (nondilute) case have a limiting eigenvalue distribution with a singular component at the origin. These include the Wishart random matrix ensemble and Gaussian random matrices with correlated entries. Our results show that the singularity in the eigenvalue distribution is rather unstable under dilution and that even weak dilution destroys it.
Circular Conditional Autoregressive Modeling of Vector Fields.
Modlin, Danny; Fuentes, Montse; Reich, Brian
2012-02-01
As hurricanes approach landfall, there are several hazards for which coastal populations must be prepared. Damaging winds, torrential rains, and tornadoes play havoc with both the coast and inland areas; but, the biggest seaside menace to life and property is the storm surge. Wind fields are used as the primary forcing for the numerical forecasts of the coastal ocean response to hurricane force winds, such as the height of the storm surge and the degree of coastal flooding. Unfortunately, developments in deterministic modeling of these forcings have been hindered by computational expenses. In this paper, we present a multivariate spatial model for vector fields, that we apply to hurricane winds. We parameterize the wind vector at each site in polar coordinates and specify a circular conditional autoregressive (CCAR) model for the vector direction, and a spatial CAR model for speed. We apply our framework for vector fields to hurricane surface wind fields for Hurricane Floyd of 1999 and compare our CCAR model to prior methods that decompose wind speed and direction into its N-S and W-E cardinal components.
MHD thrust vectoring of a rocket engine
Labaune, Julien; Packan, Denis; Tholin, Fabien; Chemartin, Laurent; Stillace, Thierry; Masson, Frederic
2016-09-01
In this work, the possibility to use MagnetoHydroDynamics (MHD) to vectorize the thrust of a solid propellant rocket engine exhaust is investigated. Using a magnetic field for vectoring offers a mass gain and a reusability advantage compared to standard gimbaled, elastomer-joint systems. Analytical and numerical models were used to evaluate the flow deviation with a 1 Tesla magnetic field inside the nozzle. The fluid flow in the resistive MHD approximation is calculated using the KRONOS code from ONERA, coupling the hypersonic CFD platform CEDRE and the electrical code SATURNE from EDF. A critical parameter of these simulations is the electrical conductivity, which was evaluated using a set of equilibrium calculations with 25 species. Two models were used: local thermodynamic equilibrium and frozen flow. In both cases, chlorine captures a large fraction of free electrons, limiting the electrical conductivity to a value inadequate for thrust vectoring applications. However, when using chlorine-free propergols with 1% in mass of alkali, an MHD thrust vectoring of several degrees was obtained.
Inference for High-dimensional Differential Correlation Matrices.
Cai, T Tony; Zhang, Anru
2016-01-01
Motivated by differential co-expression analysis in genomics, we consider in this paper estimation and testing of high-dimensional differential correlation matrices. An adaptive thresholding procedure is introduced and theoretical guarantees are given. Minimax rate of convergence is established and the proposed estimator is shown to be adaptively rate-optimal over collections of paired correlation matrices with approximately sparse differences. Simulation results show that the procedure significantly outperforms two other natural methods that are based on separate estimation of the individual correlation matrices. The procedure is also illustrated through an analysis of a breast cancer dataset, which provides evidence at the gene co-expression level that several genes, of which a subset has been previously verified, are associated with the breast cancer. Hypothesis testing on the differential correlation matrices is also considered. A test, which is particularly well suited for testing against sparse alternatives, is introduced. In addition, other related problems, including estimation of a single sparse correlation matrix, estimation of the differential covariance matrices, and estimation of the differential cross-correlation matrices, are also discussed.
Vector grammars and PN machines
Institute of Scientific and Technical Information of China (English)
蒋昌俊
1996-01-01
The concept of vector grammars under the string semantic is introduced.The dass of vector grammars is given,which is similar to the dass of Chomsky grammars.The regular vector grammar is divided further.The strong and weak relation between the vector grammar and scalar grammar is discussed,so the spectrum system graph of scalar and vector grammars is made.The equivalent relation between the regular vector grammar and Petri nets (also called PN machine) is pointed.The hybrid PN machine is introduced,and its language is proved equivalent to the language of the context-free vector grammar.So the perfect relation structure between vector grammars and PN machines is formed.
When Graduate Degrees Prostitute the Educational Process: Degrees Gone Wild
Lumadue, Richard T.
2006-01-01
Graduate degrees prostitute the educational process when they are sold to consumers by unaccredited degree/diploma mills as being equivalent to legitimate, bona-fide degrees awarded by accredited graduate schools. This article carefully analyzes the serious problems of bogus degrees and their association with the religious higher education…
Estimated correlation matrices and portfolio optimization
Pafka, Szilárd; Kondor, Imre
2004-11-01
Correlations of returns on various assets play a central role in financial theory and also in many practical applications. From a theoretical point of view, the main interest lies in the proper description of the structure and dynamics of correlations, whereas for the practitioner the emphasis is on the ability of the models to provide adequate inputs for the numerous portfolio and risk management procedures used in the financial industry. The theory of portfolios, initiated by Markowitz, has suffered from the “curse of dimensions” from the very outset. Over the past decades a large number of different techniques have been developed to tackle this problem and reduce the effective dimension of large bank portfolios, but the efficiency and reliability of these procedures are extremely hard to assess or compare. In this paper, we propose a model (simulation)-based approach which can be used for the systematical testing of all these dimensional reduction techniques. To illustrate the usefulness of our framework, we develop several toy models that display some of the main characteristic features of empirical correlations and generate artificial time series from them. Then, we regard these time series as empirical data and reconstruct the corresponding correlation matrices which will inevitably contain a certain amount of noise, due to the finiteness of the time series. Next, we apply several correlation matrix estimators and dimension reduction techniques introduced in the literature and/or applied in practice. As in our artificial world the only source of error is the finite length of the time series and, in addition, the “true” model, hence also the “true” correlation matrix, are precisely known, therefore in sharp contrast with empirical studies, we can precisely compare the performance of the various noise reduction techniques. One of our recurrent observations is that the recently introduced filtering technique based on random matrix theory performs
2015-09-28
buoyant underwater vehicle with an interior space in which a length of said underwater vehicle is equal to one tenth of the acoustic wavelength...underwater vehicle with an interior space in which a length of said underwater vehicle is equal to one tenth of the acoustic wavelength; an...unmanned underwater vehicle that can function as an acoustic vector sensor. (2) Description of the Prior Art [0004] It is known that a propagating
Reciprocity in Vector Acoustics
2017-03-01
Green’s Theorem to the left hand side of Equation (3.2) converts it to a surface integral that vanishes for the impedance boundary conditions one...There are situations where this assumption does not hold, such as at boundaries between layers or in an inhomogeneous layer , because the density gradient...instead of requiring one model run for each source location. Application of the vector-scalar reciprocity principle is demonstrated with analytic
Tensor Calculus: Unlearning Vector Calculus
Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita
2018-01-01
Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…
Directory of Open Access Journals (Sweden)
Lars Bergström
2011-05-01
Full Text Available People have tended to load their different conceptions of democracy with their own political ideals; in this paper it is argued that normative and definitional questions should rather be separated, so that political philosophers and political scientists may adopt the same concept of democracy, even if they disagree normatively or politically. Moreover, it is argued that we should replace an absolute notion of democracy by a relativized notion, which allows for different degrees of democraticity. This facilitates the separation of normative and conceptual issues and it is convenient in contexts in which “democratic deficits” are discussed – as e.g. when democracy is to be implemented on a supranational level. Moreover, it has the consequence that democratic deficits are not necessarily bad. DOWNLOAD THIS PAPER FROM SSRN: http://ssrn.com/abstract=1837342
International Nuclear Information System (INIS)
Frois, B.
1985-03-01
The nucleon is nothing but the fundamental state of a complex object, the Baryon. It has a great number of excited states which are significative of its quark structure. The aim of nuclear physics today is to understand the interaction dynamics in nuclei of particles whose existence is known by high energy physics. This lecture aims at defining the frontier of current comprehension in this field by some examples. First quarks and gluons are presented. Proofs of existence of pinpoint particles inside the nucleus are given. Then a direct proof of the concept validity of the nucleon orbit in the nucleus is given. Mesonic freedom degrees are also studied. Some experience examples in which meson exchange exist clearly are shown. At last, the role of subnucleonic effects in the nuclear reactions is shown [fr
A NEW METHOD OF CHANNEL FRICTION INVERSION BASED ON KALMAN FILTER WITH UNKNOWN PARAMETER VECTOR
Institute of Scientific and Technical Information of China (English)
CHENG Wei-ping; MAO Gen-hai; LIU Guo-hua
2005-01-01
Channel friction is an important parameter in hydraulic analysis.A channel friction parameter inversion method based on Kalman Filter with unknown parameter vector is proposed.Numerical simulations indicate that when the number of monitoring stations exceeds a critical value, the solution is hardly affected.In addition, Kalman Filter with unknown parameter vector is effective only at unsteady state.For the nonlinear equations, computations of sensitivity matrices are time-costly.Two simplified measures can reduce computing time, but not influence the results.One is to reduce sensitivity matrix analysis time, the other is to substitute for sensitivity matrix.
Approximating second-order vector differential operators on distorted meshes in two space dimensions
International Nuclear Information System (INIS)
Hermeline, F.
2008-01-01
A new finite volume method is presented for approximating second-order vector differential operators in two space dimensions. This method allows distorted triangle or quadrilateral meshes to be used without the numerical results being too much altered. The matrices that need to be inverted are symmetric positive definite therefore, the most powerful linear solvers can be applied. The method has been tested on a few second-order vector partial differential equations coming from elasticity and fluids mechanics areas. These numerical experiments show that it is second-order accurate and locking-free. (authors)
Generalized Inferences about the Mean Vector of Several Multivariate Gaussian Processes
Directory of Open Access Journals (Sweden)
Pilar Ibarrola
2015-01-01
Full Text Available We consider in this paper the problem of comparing the means of several multivariate Gaussian processes. It is assumed that the means depend linearly on an unknown vector parameter θ and that nuisance parameters appear in the covariance matrices. More precisely, we deal with the problem of testing hypotheses, as well as obtaining confidence regions for θ. Both methods will be based on the concepts of generalized p value and generalized confidence region adapted to our context.
On the Eigenvalues and Eigenvectors of Block Triangular Preconditioned Block Matrices
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.
International Nuclear Information System (INIS)
Chudnovsky, D.V.; Chudnovsky, G.V.
1980-01-01
We consider semi-classical approximation to factorized S-matrices. We show that this new class of matrices, called s-matrices, defines Hamiltonian structures for isospectral deformation equations. Concrete examples of factorized s-matrices are constructed and they are used to define Hamiltonian structure for general two-dimensional isospectral deformation systems. (orig.)
Adenovirus dodecahedron, as a drug delivery vector.
Directory of Open Access Journals (Sweden)
Monika Zochowska
Full Text Available BACKGROUND: Bleomycin (BLM is an anticancer antibiotic used in many cancer regimens. Its utility is limited by systemic toxicity and dose-dependent pneumonitis able to progress to lung fibrosis. The latter can affect up to nearly 50% of the total patient population, out of which 3% will die. We propose to improve BLM delivery by tethering it to an efficient delivery vector. Adenovirus (Ad dodecahedron base (DB is a particulate vector composed of 12 copies of a pentameric viral protein responsible for virus penetration. The vector efficiently penetrates the plasma membrane, is liberated in the cytoplasm and has a propensity to concentrate around the nucleus; up to 300000 particles can be observed in one cell in vitro. PRINCIPAL FINDINGS: Dodecahedron (Dd structure is preserved at up to about 50 degrees C at pH 7-8 and during dialysis, freezing and drying in the speed-vac in the presence of 150 mM ammonium sulfate, as well as during lyophilization in the presence of cryoprotectants. The vector is also stable in human serum for 2 h at 37 degrees C. We prepared a Dd-BLM conjugate which upon penetration induced death of transformed cells. Similarly to free bleomycin, Dd-BLM caused dsDNA breaks. Significantly, effective cytotoxic concentration of BLM delivered with Dd was 100 times lower than that of free bleomycin. CONCLUSIONS/SIGNIFICANCE: Stability studies show that Dds can be conveniently stored and transported, and can potentially be used for therapeutic purposes under various climates. Successful BLM delivery by Ad Dds demonstrates that the use of virus like particle (VLP results in significantly improved drug bioavailability. These experiments open new vistas for delivery of non-permeant labile drugs.
Agricultural matrices affect ground ant assemblage composition inside forest fragments.
Directory of Open Access Journals (Sweden)
Diego Santana Assis
Full Text Available The establishment of agricultural matrices generally involves deforestation, which leads to fragmentation of the remaining forest. This fragmentation can affect forest dynamics both positively and negatively. Since most animal species are affected, certain groups can be used to measure the impact of such fragmentation. This study aimed to measure the impacts of agricultural crops (matrices on ant communities of adjacent lower montane Atlantic rainforest fragments. We sampled nine forest fragments at locations surrounded by different agricultural matrices, namely: coffee (3 replicates; sugarcane (3; and pasture (3. At each site we installed pitfall traps along a 500 m transect from the interior of the matrix to the interior of the fragment (20 pitfall traps ~25 m apart. Each transect was partitioned into four categories: interior of the matrix; edge of the matrix; edge of the fragment; and interior of the fragment. For each sample site, we measured ant species richness and ant community composition within each transect category. Ant richness and composition differed between fragments and matrices. Each sample location had a specific composition of ants, probably because of the influence of the nature and management of the agricultural matrices. Species composition in the coffee matrix had the highest similarity to its corresponding fragment. The variability in species composition within forest fragments surrounded by pasture was greatest when compared with forest fragments surrounded by sugarcane or, to a lesser extent, coffee. Functional guild composition differed between locations, but the most representative guild was 'generalist' both in the agricultural matrices and forest fragments. Our results are important for understanding how agricultural matrices act on ant communities, and also, how these isolated forest fragments could act as an island of biodiversity in an 'ocean of crops'.
Agricultural matrices affect ground ant assemblage composition inside forest fragments.
Assis, Diego Santana; Dos Santos, Iracenir Andrade; Ramos, Flavio Nunes; Barrios-Rojas, Katty Elena; Majer, Jonathan David; Vilela, Evaldo Ferreira
2018-01-01
The establishment of agricultural matrices generally involves deforestation, which leads to fragmentation of the remaining forest. This fragmentation can affect forest dynamics both positively and negatively. Since most animal species are affected, certain groups can be used to measure the impact of such fragmentation. This study aimed to measure the impacts of agricultural crops (matrices) on ant communities of adjacent lower montane Atlantic rainforest fragments. We sampled nine forest fragments at locations surrounded by different agricultural matrices, namely: coffee (3 replicates); sugarcane (3); and pasture (3). At each site we installed pitfall traps along a 500 m transect from the interior of the matrix to the interior of the fragment (20 pitfall traps ~25 m apart). Each transect was partitioned into four categories: interior of the matrix; edge of the matrix; edge of the fragment; and interior of the fragment. For each sample site, we measured ant species richness and ant community composition within each transect category. Ant richness and composition differed between fragments and matrices. Each sample location had a specific composition of ants, probably because of the influence of the nature and management of the agricultural matrices. Species composition in the coffee matrix had the highest similarity to its corresponding fragment. The variability in species composition within forest fragments surrounded by pasture was greatest when compared with forest fragments surrounded by sugarcane or, to a lesser extent, coffee. Functional guild composition differed between locations, but the most representative guild was 'generalist' both in the agricultural matrices and forest fragments. Our results are important for understanding how agricultural matrices act on ant communities, and also, how these isolated forest fragments could act as an island of biodiversity in an 'ocean of crops'.
Hierarchal scalar and vector tetrahedra
International Nuclear Information System (INIS)
Webb, J.P.; Forghani, B.
1993-01-01
A new set of scalar and vector tetrahedral finite elements are presented. The elements are hierarchal, allowing mixing of polynomial orders; scalar orders up to 3 and vector orders up to 2 are defined. The vector elements impose tangential continuity on the field but not normal continuity, making them suitable for representing the vector electric or magnetic field. Further, the scalar and vector elements are such that they can easily be used in the same mesh, a requirement of many quasi-static formulations. Results are presented for two 50 Hz problems: the Bath Cube, and TEAM Problem 7
Leishmaniasis vector behaviour in Kenya
International Nuclear Information System (INIS)
Mutinga, M.J.
1980-01-01
Leishmaniasis in Kenya exists in two forms: cutaneous and visceral. The vectors of visceral leishmaniasis have been the subject of investigation by various researchers since World War II, when the outbreak of the disease was first noticed. The vectors of cutaneous leishmaniasis were first worked on only a decade ago after the discovery of the disease focus in Mt. Elgon. The vector behaviour of these diseases, namely Phlebotomus pedifer, the vector of cutaneous leishmaniasis, and Phlebotomus martini, the vector of visceral leishmaniasis, are discussed in detail. P. pedifer has been found to breed and bite inside caves, whereas P. martini mainly bites inside houses. (author)
Theoretical Properties for Neural Networks with Weight Matrices of Low Displacement Rank
Zhao, Liang; Liao, Siyu; Wang, Yanzhi; Li, Zhe; Tang, Jian; Pan, Victor; Yuan, Bo
2017-01-01
Recently low displacement rank (LDR) matrices, or so-called structured matrices, have been proposed to compress large-scale neural networks. Empirical results have shown that neural networks with weight matrices of LDR matrices, referred as LDR neural networks, can achieve significant reduction in space and computational complexity while retaining high accuracy. We formally study LDR matrices in deep learning. First, we prove the universal approximation property of LDR neural networks with a ...
Degree-degree correlations in random graphs with heavy-tailed degrees
Hofstad, van der R.W.; Litvak, N.
2014-01-01
Mixing patterns in large self-organizing networks, such as the Internet, the World Wide Web, social, and biological networks are often characterized by degree-degree dependencies between neighboring nodes. In assortative networks, the degree-degree dependencies are positive (nodes with similar
Degree-Degree Dependencies in Random Graphs with Heavy-Tailed Degrees
van der Hofstad, Remco; Litvak, Nelly
2014-01-01
Mixing patterns in large self-organizing networks, such as the Internet, the World Wide Web, social, and biological networks are often characterized by degree-degree dependencies between neighboring nodes. In assortative networks, the degree-degree dependencies are positive (nodes with similar
Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations
Directory of Open Access Journals (Sweden)
Han Guo
2012-01-01
Full Text Available Hierarchical (H- matrices method is a general mathematical framework providing a highly compact representation and efficient numerical arithmetic. When applied in integral-equation- (IE- based computational electromagnetics, H-matrices can be regarded as a fast algorithm; therefore, both the CPU time and memory requirement are reduced significantly. Its kernel independent feature also makes it suitable for any kind of integral equation. To solve H-matrices system, Krylov iteration methods can be employed with appropriate preconditioners, and direct solvers based on the hierarchical structure of H-matrices are also available along with high efficiency and accuracy, which is a unique advantage compared to other fast algorithms. In this paper, a novel sparse approximate inverse (SAI preconditioner in multilevel fashion is proposed to accelerate the convergence rate of Krylov iterations for solving H-matrices system in electromagnetic applications, and a group of parallel fast direct solvers are developed for dealing with multiple right-hand-side cases. Finally, numerical experiments are given to demonstrate the advantages of the proposed multilevel preconditioner compared to conventional “single level” preconditioners and the practicability of the fast direct solvers for arbitrary complex structures.
MALDI matrices for low molecular weight compounds: an endless story?
Calvano, Cosima Damiana; Monopoli, Antonio; Cataldi, Tommaso R I; Palmisano, Francesco
2018-04-23
Since its introduction in the 1980s, matrix-assisted laser desorption/ionization mass spectrometry (MALDI MS) has gained a prominent role in the analysis of high molecular weight biomolecules such as proteins, peptides, oligonucleotides, and polysaccharides. Its application to low molecular weight compounds has remained for long time challenging due to the spectral interferences produced by conventional organic matrices in the low m/z window. To overcome this problem, specific sample preparation such as analyte/matrix derivatization, addition of dopants, or sophisticated deposition technique especially useful for imaging experiments, have been proposed. Alternative approaches based on second generation (rationally designed) organic matrices, ionic liquids, and inorganic matrices, including metallic nanoparticles, have been the object of intense and continuous research efforts. Definite evidences are now provided that MALDI MS represents a powerful and invaluable analytical tool also for small molecules, including their quantification, thus opening new, exciting applications in metabolomics and imaging mass spectrometry. This review is intended to offer a concise critical overview of the most recent achievements about MALDI matrices capable of specifically address the challenging issue of small molecules analysis. Graphical abstract An ideal Book of matrices for MALDI MS of small molecules.
DEFF Research Database (Denmark)
More, Simon J.; Bicout, Dominique; Bøtner, Anette
2017-01-01
After a request from the Europea n Commission, EFSA’s Panel on Animal Health and Welfaresummarised the main characteristics of 36 vector-borne disease s (VBDs) in 36 web-based storymaps.The risk of introduction in the EU through movement of livestock or pets was assessed for eac h of the36 VBDs......-agents for which the rate of introduction wasestimated to be very low, no further asse ssments were made. Due to the uncertainty related to someparameters used for the risk assessment or the instable or unpredictability disease situation in some ofthe source regions, it is recommended to update the assessment when...
International Nuclear Information System (INIS)
Rodríguez, Yeinzon; Navarro, Andrés A.
2017-01-01
An alternative for the construction of fundamental theories is the introduction of Galileons. These are fields whose action leads to non higher than second-order equations of motion. As this is a necessary but not sufficient condition to make the Hamiltonian bounded from below, as long as the action is not degenerate, the Galileon construction is a way to avoid pathologies both at the classical and quantum levels. Galileon actions are, therefore, of great interest in many branches of physics, specially in high energy physics and cosmology. This proceedings contribution presents the generalities of the construction of both scalar and vector Galileons following two different but complimentary routes. (paper)
International Nuclear Information System (INIS)
Otsason, J.
1998-01-01
The Vector Pipeline project linking the Chicago supply hub to markets in eastern Canada, the northeastern U.S. and the Mid-Atlantic states, is described. Subsidiary objectives of the promoters are to match market timing to upstream pipelines and market requirements, and to provide low cost expandability to complement upstream expandability. The presentation includes description of the project, costs, leased facilities, rates and tariffs, right of way considerations, storage facilities and a project schedule. Construction is to begin in March 1999 and the line should be in service in November 1999
Using Covariant Lyapunov Vectors to Understand Spatiotemporal Chaos in Fluids
Paul, Mark; Xu, Mu; Barbish, Johnathon; Mukherjee, Saikat
2017-11-01
The spatiotemporal chaos of fluids present many difficult and fascinating challenges. Recent progress in computing covariant Lyapunov vectors for a variety of model systems has made it possible to probe fundamental ideas from dynamical systems theory including the degree of hyperbolicity, the fractal dimension, the dimension of the inertial manifold, and the decomposition of the dynamics into a finite number of physical modes and spurious modes. We are interested in building upon insights such as these for fluid systems. We first demonstrate the power of covariant Lyapunov vectors using a system of maps on a lattice with a nonlinear coupling. We then compute the covariant Lyapunov vectors for chaotic Rayleigh-Bénard convection for experimentally accessible conditions. We show that chaotic convection is non-hyperbolic and we quantify the spatiotemporal features of the spectrum of covariant Lyapunov vectors. NSF DMS-1622299 and DARPA/DSO Models, Dynamics, and Learning (MoDyL).
Stability of Picard Bundle Over Moduli Space of Stable Vector ...
Indian Academy of Sciences (India)
Abstract. Answering a question of [BV] it is proved that the Picard bundle on the moduli space of stable vector bundles of rank two, on a Riemann surface of genus at least three, with fixed determinant of odd degree is stable.
Vector-vector production in photon-photon interactions
International Nuclear Information System (INIS)
Ronan, M.T.
1988-01-01
Measurements of exclusive untagged /rho/ 0 /rho/ 0 , /rho//phi/, K/sup *//bar K//sup */, and /rho/ω production and tagged /rho/ 0 /rho/ 0 production in photon-photon interactions by the TPC/Two-Gamma experiment are reviewed. Comparisons to the results of other experiments and to models of vector-vector production are made. Fits to the data following a four quark model prescription for vector meson pair production are also presented. 10 refs., 9 figs
Nano-Fiber Reinforced Enhancements in Composite Polymer Matrices
Chamis, Christos C.
2009-01-01
Nano-fibers are used to reinforce polymer matrices to enhance the matrix dependent properties that are subsequently used in conventional structural composites. A quasi isotropic configuration is used in arranging like nano-fibers through the thickness to ascertain equiaxial enhanced matrix behavior. The nano-fiber volume ratios are used to obtain the enhanced matrix strength properties for 0.01,0.03, and 0.05 nano-fiber volume rates. These enhanced nano-fiber matrices are used with conventional fiber volume ratios of 0.3 and 0.5 to obtain the composite properties. Results show that nano-fiber enhanced matrices of higher than 0.3 nano-fiber volume ratio are degrading the composite properties.
Square matrices of order 2 theory, applications, and problems
Pop, Vasile
2017-01-01
This unique and innovative book presents an exciting and complete detail of all the important topics related to the theory of square matrices of order 2. The readers exploring every detailed aspect of matrix theory are gently led toward understanding advanced topics. They will follow every notion of matrix theory with ease, accumulating a thorough understanding of algebraic and geometric aspects of matrices of order 2. The prime jewel of this book is its offering of an unusual collection of problems, theoretically motivated, most of which are new, original, and seeing the light of publication for the first time in the literature. Nearly all of the exercises are presented with detailed solutions and vary in difficulty from easy to more advanced. Many problems are particularly challenging. These, and not only these, invite the reader to unleash their creativity and research capabilities and to discover their own methods of attacking a problem. Matrices have a vast practical importance to mathematics, science, a...
Two-mode Gaussian density matrices and squeezing of photons
International Nuclear Information System (INIS)
Tucci, R.R.
1992-01-01
In this paper, the authors generalize to 2-mode states the 1-mode state results obtained in a previous paper. The authors study 2-mode Gaussian density matrices. The authors find a linear transformation which maps the two annihilation operators, one for each mode, into two new annihilation operators that are uncorrelated and unsqueezed. This allows the authors to express the density matrix as a product of two 1-mode density matrices. The authors find general conditions under which 2-mode Gaussian density matrices become pure states. Possible pure states include the 2-mode squeezed pure states commonly mentioned in the literature, plus other pure states never mentioned before. The authors discuss the entropy and thermodynamic laws (Second Law, Fundamental Equation, and Gibbs-Duhem Equation) for the 2-mode states being considered
A Workshop on Algebraic Design Theory and Hadamard Matrices
2015-01-01
This volume develops the depth and breadth of the mathematics underlying the construction and analysis of Hadamard matrices and their use in the construction of combinatorial designs. At the same time, it pursues current research in their numerous applications in security and cryptography, quantum information, and communications. Bridges among diverse mathematical threads and extensive applications make this an invaluable source for understanding both the current state of the art and future directions. The existence of Hadamard matrices remains one of the most challenging open questions in combinatorics. Substantial progress on their existence has resulted from advances in algebraic design theory using deep connections with linear algebra, abstract algebra, finite geometry, number theory, and combinatorics. Hadamard matrices arise in a very diverse set of applications. Starting with applications in experimental design theory and the theory of error-correcting codes, they have found unexpected and important ap...
Asymmetric correlation matrices: an analysis of financial data
Livan, G.; Rebecchi, L.
2012-06-01
We analyse the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non-symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson correlation matrices to the realm of complex eigenvalues. We employ some recent random matrix theory results on the average eigenvalue density of this type of matrix to distinguish between noise and non-trivial correlation structures, and we focus on financial data as a case study. Namely, we employ daily prices of stocks belonging to the American and British stock exchanges, and look for the emergence of correlations between two such markets in the eigenvalue spectrum of their non-symmetric correlation matrix. We find several non trivial results when considering time-lagged correlations over short lags, and we corroborate our findings by additionally studying the asymmetric correlation matrix of the principal components of our datasets.
Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices
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.
Physical properties of the Schur complement of local covariance matrices
International Nuclear Information System (INIS)
Haruna, L F; Oliveira, M C de
2007-01-01
General properties of global covariance matrices representing bipartite Gaussian states can be decomposed into properties of local covariance matrices and their Schur complements. We demonstrate that given a bipartite Gaussian state ρ 12 described by a 4 x 4 covariance matrix V, the Schur complement of a local covariance submatrix V 1 of it can be interpreted as a new covariance matrix representing a Gaussian operator of party 1 conditioned to local parity measurements on party 2. The connection with a partial parity measurement over a bipartite quantum state and the determination of the reduced Wigner function is given and an operational process of parity measurement is developed. Generalization of this procedure to an n-partite Gaussian state is given, and it is demonstrated that the n - 1 system state conditioned to a partial parity projection is given by a covariance matrix such that its 2 x 2 block elements are Schur complements of special local matrices
Somoano, Brian; Chan, Joanna; Morganroth, Greg
2011-01-01
Facial rejuvenation using local anesthesia has evolved in the past decade as a safer option for patients seeking fewer complications and minimal downtime. Mini- and short-scar face lifts using more conservative incision lengths and extent of undermining can be effective in the younger patient with lower face laxity and minimal loose, elastotic neck skin. By incorporating both an anterior and posterior approach and using an incision length between the mini and more traditional face lift, the Vertical Vector Face Lift can achieve longer-lasting and natural results with lesser cost and risk. Submentoplasty and liposuction of the neck and jawline, fundamental components of the vertical vector face lift, act synergistically with superficial musculoaponeurotic system plication to reestablish a more youthful, sculpted cervicomental angle, even in patients with prominent jowls. Dramatic results can be achieved in the right patient by combining with other procedures such as injectable fillers, chin implants, laser resurfacing, or upper and lower blepharoplasties. © 2011 Wiley Periodicals, Inc.
Vector control in leishmaniasis.
Kishore, K; Kumar, V; Kesari, S; Dinesh, D S; Kumar, A J; Das, P; Bhattacharya, S K
2006-03-01
Indoor residual spraying is a simple and cost effective method of controlling endophilic vectors and DDT remains the insecticide of choice for the control of leishmaniasis. However resistance to insecticide is likely to become more widespread in the population especially in those areas in which insecticide has been used for years. In this context use of slow release emulsified suspension (SRES) may be the best substitute. In this review spraying frequencies of DDT and new schedule of spray have been discussed. Role of biological control and environment management in the control of leishmaniasis has been emphasized. Allethrin (coil) 0.1 and 1.6 per cent prallethrin (liquid) have been found to be effective repellents against Phlebotomus argentipes, the vector of Indian kalaazar. Insecticide impregnated bednets is another area which requires further research on priority basis for the control of leishmaniasis. Role of satellite remote sensing for early prediction of disease by identifying the sandflygenic conditions cannot be undermined. In future synthetic pheromons can be exploited in the control of leishmaniasis.
Experimental demonstration of vector E x vector B plasma divertor
International Nuclear Information System (INIS)
Strait, E.J.; Kerst, D.W.; Sprott, J.C.
1977-01-01
The vector E x vector B drift due to an applied radial electric field in a tokamak with poloidal divertor can speed the flow of plasma out of the scrape-off region, and provide a means of externally controlling the flow rate and thus the width of the density fall-off. An experiment in the Wisconsin levitated toroidal octupole, using vector E x vector B drifts alone, demonstrates divertor-like behavior, including 70% reduction of plasma density near the wall and 40% reduction of plasma flux to the wall, with no adverse effects on confinement of the main plasma
Enumeration of Combinatorial Classes of Single Variable Complex Polynomial Vector Fields
DEFF Research Database (Denmark)
Dias, Kealey
A vector field in the space of degree d monic, centered single variable complex polynomial vector fields has a combinatorial structure which can be fully described by a combinatorial data set consisting of an equivalence relation and a marked subset on the integers mod 2d-2, satisfying certain...
Spherical cap modelling of Orsted magnetic field vectors over southern Africa
CSIR Research Space (South Africa)
Kotze, PB
2001-01-01
Full Text Available Vector magnetic field observations by the Orsted satellite during geomagnetic quiet conditions around January 1, 2000, have been employed to derive a spherical cap harmonic model (Haines, 1985) over the southern African region between 10 degrees...
Random Matrices for Information Processing – A Democratic Vision
DEFF Research Database (Denmark)
Cakmak, Burak
The thesis studies three important applications of random matrices to information processing. Our main contribution is that we consider probabilistic systems involving more general random matrix ensembles than the classical ensembles with iid entries, i.e. models that account for statistical...... dependence between the entries. Specifically, the involved matrices are invariant or fulfill a certain asymptotic freeness condition as their dimensions grow to infinity. Informally speaking, all latent variables contribute to the system model in a democratic fashion – there are no preferred latent variables...
An algebraic model for quark mass matrices with heavy top
International Nuclear Information System (INIS)
Krolikowski, W.; Warsaw Univ.
1991-01-01
In terms of an intergeneration U(3) algebra, a numerical model is constructed for quark mass matrices, predicting the top-quark mass around 170 GeV and the CP-violating phase around 75 deg. The CKM matrix is nonsymmetric in moduli with |V ub | being very small. All moduli are consistent with their experimental limits. The model is motivated by the author's previous work on three replicas of the Dirac particle, presumably resulting into three generations of leptons and quarks. The paper may be also viewed as an introduction to a new method of intrinsic dynamical description of lepton and quark mass matrices. (author)
ON MATRICES ARISING IN RETARDED DELAY DIFFERENTIAL SYSTEMS
Directory of Open Access Journals (Sweden)
S DJEZZAR
2002-12-01
Full Text Available Dans cet article, on considère une classe de système différentiels retardés et à laquelle on associe une matrice système sur R[s,z], l'anneau des polynômes à deux indéterminés s et z. Ensuite, en utilisant la notion de la matrice forme de Smith sur R[s,z], on étend un résultat de caractérisation obtenu précédemment [5] sur les formes canoniques, à un cas plus général.
Soft landing of size selected clusters in rare gas matrices
International Nuclear Information System (INIS)
Lau, J.T; Wurth, W.; Ehrke, H-U.; Achleitner, A.
2003-01-01
Soft landing of mass selected clusters in rare gas matrices is a technique used to preserve mass selection in cluster deposition. To prevent fragmentation upon deposition, the substrate is covered with rare gas matrices to dissipate the cluster kinetic energy upon impact. Theoretical and experimental studies demonstrate the power of this technique. Besides STM, optical absorption, excitation, and fluorescence experiments, x-ray absorption at core levels can be used as a tool to study soft landing conditions, as will be shown here. X-ray absorption spectroscopy is also well suited to follow diffusion and agglomeration of clusters on surfaces via energy shifts in core level absorption
Positive projections of symmetric matrices and Jordan algebras
DEFF Research Database (Denmark)
Fuglede, Bent; Jensen, Søren Tolver
2013-01-01
An elementary proof is given that the projection from the space of all symmetric p×p matrices onto a linear subspace is positive if and only if the subspace is a Jordan algebra. This solves a problem in a statistical model.......An elementary proof is given that the projection from the space of all symmetric p×p matrices onto a linear subspace is positive if and only if the subspace is a Jordan algebra. This solves a problem in a statistical model....
On the Wigner law in dilute random matrices
Khorunzhy, A.; Rodgers, G. J.
1998-12-01
We consider ensembles of N × N symmetric matrices whose entries are weakly dependent random variables. We show that random dilution can change the limiting eigenvalue distribution of such matrices. We prove that under general and natural conditions the normalised eigenvalue counting function coincides with the semicircle (Wigner) distribution in the limit N → ∞. This can be explained by the observation that dilution (or more generally, random modulation) eliminates the weak dependence (or correlations) between random matrix entries. It also supports our earlier conjecture that the Wigner distribution is stable to random dilution and modulation.
Degree of mapping for general relativistic kinks
International Nuclear Information System (INIS)
Harriot, Tina A.; Williams, J.G.
2005-01-01
The Finkelstein-Misner metrical kinks of general relativity are homo topically nontrivial light cone configurations that can occur on space-time hypersurfaces. The number of kinks corresponds to the winding number of a timelike vector field that that is determined from the metric. This paper uses the usual Euclidean integral formula for degree of mapping as a starting point and so produces a covariant formula that can be applied to counting general relativistic kinks in any dimension. The kink number is calculated for some simple-to-visualize examples in 2 + 1 dimensions. These include hypersurfaces of differing topologies and so have relevance to mechanisms of topology change in semi-classical theories of quantum gravity
Video Vectorization via Tetrahedral Remeshing.
Wang, Chuan; Zhu, Jie; Guo, Yanwen; Wang, Wenping
2017-02-09
We present a video vectorization method that generates a video in vector representation from an input video in raster representation. A vector-based video representation offers the benefits of vector graphics, such as compactness and scalability. The vector video we generate is represented by a simplified tetrahedral control mesh over the spatial-temporal video volume, with color attributes defined at the mesh vertices. We present novel techniques for simplification and subdivision of a tetrahedral mesh to achieve high simplification ratio while preserving features and ensuring color fidelity. From an input raster video, our method is capable of generating a compact video in vector representation that allows a faithful reconstruction with low reconstruction errors.
Hyperbolic-symmetry vector fields.
Gao, Xu-Zhen; Pan, Yue; Cai, Meng-Qiang; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian
2015-12-14
We present and construct a new kind of orthogonal coordinate system, hyperbolic coordinate system. We present and design a new kind of local linearly polarized vector fields, which is defined as the hyperbolic-symmetry vector fields because the points with the same polarization form a series of hyperbolae. We experimentally demonstrate the generation of such a kind of hyperbolic-symmetry vector optical fields. In particular, we also study the modified hyperbolic-symmetry vector optical fields with the twofold and fourfold symmetric states of polarization when introducing the mirror symmetry. The tight focusing behaviors of these vector fields are also investigated. In addition, we also fabricate micro-structures on the K9 glass surfaces by several tightly focused (modified) hyperbolic-symmetry vector fields patterns, which demonstrate that the simulated tightly focused fields are in good agreement with the fabricated micro-structures.
Optimality Conditions in Vector Optimization
Jiménez, Manuel Arana; Lizana, Antonio Rufián
2011-01-01
Vector optimization is continuously needed in several science fields, particularly in economy, business, engineering, physics and mathematics. The evolution of these fields depends, in part, on the improvements in vector optimization in mathematical programming. The aim of this Ebook is to present the latest developments in vector optimization. The contributions have been written by some of the most eminent researchers in this field of mathematical programming. The Ebook is considered essential for researchers and students in this field.
Symmetric vectors and algebraic classification
International Nuclear Information System (INIS)
Leibowitz, E.
1980-01-01
The concept of symmetric vector field in Riemannian manifolds, which arises in the study of relativistic cosmological models, is analyzed. Symmetric vectors are tied up with the algebraic properties of the manifold curvature. A procedure for generating a congruence of symmetric fields out of a given pair is outlined. The case of a three-dimensional manifold of constant curvature (''isotropic universe'') is studied in detail, with all its symmetric vector fields being explicitly constructed
THE ALGORITHM AND PROGRAM OF M-MATRICES SEARCH AND STUDY
Directory of Open Access Journals (Sweden)
Y. N. Balonin
2013-05-01
Full Text Available The algorithm and software for search and study of orthogonal bases matrices – minimax matrices (M-matrix are considered. The algorithm scheme is shown, comments on calculation blocks are given, and interface of the MMatrix software system developed with participation of the authors is explained. The results of the universal algorithm work are presented as Hadamard matrices, Belevitch matrices (C-matrices, conference matrices and matrices of even and odd orders complementary and closely related to those ones by their properties, in particular, the matrix of the 22-th order for which there is no C-matrix. Examples of portraits for alternative matrices of the 255-th and the 257-th orders are given corresponding to the sequences of Mersenne and Fermat numbers. A new way to get Hadamard matrices is explained, different from the previously known procedures based on iterative processes and calculations of Lagrange symbols, with theoretical and practical meaning.
Vector continued fractions using a generalized inverse
International Nuclear Information System (INIS)
Haydock, Roger; Nex, C M M; Wexler, Geoffrey
2004-01-01
A real vector space combined with an inverse (involution) for vectors is sufficient to define a vector continued fraction whose parameters consist of vector shifts and changes of scale. The choice of sign for different components of the vector inverse permits construction of vector analogues of the Jacobi continued fraction. These vector Jacobi fractions are related to vector and scalar-valued polynomial functions of the vectors, which satisfy recurrence relations similar to those of orthogonal polynomials. The vector Jacobi fraction has strong convergence properties which are demonstrated analytically, and illustrated numerically
Migration of vectorized iterative solvers to distributed memory architectures
Energy Technology Data Exchange (ETDEWEB)
Pommerell, C. [AT& T Bell Labs., Murray Hill, NJ (United States); Ruehl, R. [CSCS-ETH, Manno (Switzerland)
1994-12-31
Both necessity and opportunity motivate the use of high-performance computers for iterative linear solvers. Necessity results from the size of the problems being solved-smaller problems are often better handled by direct methods. Opportunity arises from the formulation of the iterative methods in terms of simple linear algebra operations, even if this {open_quote}natural{close_quotes} parallelism is not easy to exploit in irregularly structured sparse matrices and with good preconditioners. As a result, high-performance implementations of iterative solvers have attracted a lot of interest in recent years. Most efforts are geared to vectorize or parallelize the dominating operation-structured or unstructured sparse matrix-vector multiplication, or to increase locality and parallelism by reformulating the algorithm-reducing global synchronization in inner products or local data exchange in preconditioners. Target architectures for iterative solvers currently include mostly vector supercomputers and architectures with one or few optimized (e.g., super-scalar and/or super-pipelined RISC) processors and hierarchical memory systems. More recently, parallel computers with physically distributed memory and a better price/performance ratio have been offered by vendors as a very interesting alternative to vector supercomputers. However, programming comfort on such distributed memory parallel processors (DMPPs) still lags behind. Here the authors are concerned with iterative solvers and their changing computing environment. In particular, they are considering migration from traditional vector supercomputers to DMPPs. Application requirements force one to use flexible and portable libraries. They want to extend the portability of iterative solvers rather than reimplementing everything for each new machine, or even for each new architecture.
Characterizing protein conformations by correlation analysis of coarse-grained contact matrices
Lindsay, Richard J.; Siess, Jan; Lohry, David P.; McGee, Trevor S.; Ritchie, Jordan S.; Johnson, Quentin R.; Shen, Tongye
2018-01-01
We have developed a method to capture the essential conformational dynamics of folded biopolymers using statistical analysis of coarse-grained segment-segment contacts. Previously, the residue-residue contact analysis of simulation trajectories was successfully applied to the detection of conformational switching motions in biomolecular complexes. However, the application to large protein systems (larger than 1000 amino acid residues) is challenging using the description of residue contacts. Also, the residue-based method cannot be used to compare proteins with different sequences. To expand the scope of the method, we have tested several coarse-graining schemes that group a collection of consecutive residues into a segment. The definition of these segments may be derived from structural and sequence information, while the interaction strength of the coarse-grained segment-segment contacts is a function of the residue-residue contacts. We then perform covariance calculations on these coarse-grained contact matrices. We monitored how well the principal components of the contact matrices is preserved using various rendering functions. The new method was demonstrated to assist the reduction of the degrees of freedom for describing the conformation space, and it potentially allows for the analysis of a system that is approximately tenfold larger compared with the corresponding residue contact-based method. This method can also render a family of similar proteins into the same conformational space, and thus can be used to compare the structures of proteins with different sequences.
Lee, Ken Voon
2013-04-01
The purpose of this action research was to increase the mastery level of Form Five Social Science students in Tawau II National Secondary School in the operations of addition, subtraction and multiplication of matrices in Mathematics. A total of 30 students were involved. Preliminary findings through the analysis of pre-test results and questionnaire had identified the main problem faced in which the students felt confused with the application of principles of the operations of matrices when performing these operations. Therefore, an action research was conducted using an intervention programme called "G.P.S Matrices" to overcome the problem. This programme was divided into three phases. 'Gift of Matrices' phase aimed at forming matrix teaching aids. The second and third phases were 'Positioning the Elements of Matrices' and 'Strenghtening the Concept of Matrices'. These two phases were aimed at increasing the level of understanding and memory of the students towards the principles of matrix operations. Besides, this third phase was also aimed at creating an interesting learning environment. A comparison between the results of pre-test and post-test had shown a remarkable improvement in students' performances after implementing the programme. In addition, the analysis of interview findings also indicated a positive feedback on the changes in students' attitude, particularly in the aspect of students' understanding level. Moreover, the level of students' memory also increased following the use of the concrete matrix teaching aids created in phase one. Besides, teachers felt encouraging when conducive learning environment was created through students' presentation activity held in third phase. Furthermore, students were voluntarily involved in these student-centred activities. In conclusion, this research findings showed an increase in the mastery level of students in these three matrix operations and thus the objective of the research had been achieved.
International Nuclear Information System (INIS)
Nelson, Ann E.; Walsh, Jonathan
2008-01-01
We show that for a force mediated by a vector particle coupled to a conserved U(1) charge, the apparent range and strength can depend on the size and density of the source, and the proximity to other sources. This chameleon effect is due to screening from a light charged scalar. Such screening can weaken astrophysical constraints on new gauge bosons. As an example we consider the constraints on chameleonic gauged B-L. We show that although Casimir measurements greatly constrain any B-L force much stronger than gravity with range longer than 0.1 μm, there remains an experimental window for a long-range chameleonic B-L force. Such a force could be much stronger than gravity, and long or infinite range in vacuum, but have an effective range near the surface of the earth which is less than a micron.
Architecture and Vector Control
DEFF Research Database (Denmark)
von Seidlein, Lorenz; Knols, Bart GJ; Kirby, Matthew
2012-01-01
, closing of eaves and insecticide treated bednets. All of these interventions have an effect on the indoor climate. Temperature, humidity and airflow are critical for a comfortable climate. Air-conditioning and fans allow us to control indoor climate, but many people in Africa and Asia who carry the brunt...... of vector-borne diseases have no access to electricity. Many houses in the hot, humid regions of Asia have adapted to the environment, they are built of porous materials and are elevated on stilts features which allow a comfortable climate even in the presence of bednets and screens. In contrast, many...... buildings in Africa and Asia in respect to their indoor climate characteristics and finally, show how state-of-the-art 3D modelling can predict climate characteristics and help to optimize buildings....
International Nuclear Information System (INIS)
Ginelli, Francesco; Politi, Antonio; Chaté, Hugues; Livi, Roberto
2013-01-01
Recent years have witnessed a growing interest in covariant Lyapunov vectors (CLVs) which span local intrinsic directions in the phase space of chaotic systems. Here, we review the basic results of ergodic theory, with a specific reference to the implications of Oseledets’ theorem for the properties of the CLVs. We then present a detailed description of a ‘dynamical’ algorithm to compute the CLVs and show that it generically converges exponentially in time. We also discuss its numerical performance and compare it with other algorithms presented in the literature. We finally illustrate how CLVs can be used to quantify deviations from hyperbolicity with reference to a dissipative system (a chain of Hénon maps) and a Hamiltonian model (a Fermi–Pasta–Ulam chain). This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)
Schur complements of matrices with acyclic bipartite graphs
DEFF Research Database (Denmark)
Britz, Thomas Johann; Olesky, D.D.; van den Driessche, P.
2005-01-01
Bipartite graphs are used to describe the generalized Schur complements of real matrices having nos quare submatrix with two or more nonzero diagonals. For any matrix A with this property, including any nearly reducible matrix, the sign pattern of each generalized Schur complement is shown to be ...
BMP-silk composite matrices heal critically sized femoral defects
Kirker-Head, C.; Karageorgiou, V.; Hofmann, S.; Fajardo, R.; Betz, O.; Merkle, H.P.; Hilbe, M.; Rechenberg, von B.; McCool, J.; Abrahamsen, L.; Nazarian, A.; Cory, E.; Curtis, M.; Kaplan, D.L.; Meinel, L.
2007-01-01
Clinical drawbacks of bone grafting prompt the search for alternative bone augmentation technologies such as use of growth and differentiation factors, gene therapy, and cell therapy. Osteopromotive matrices are frequently employed for the local delivery and controlled release of these augmentation
Which matrices are immune against the transportation paradox
Deineko, Vladimir G.; Klinz, Bettina; Woeginger, Gerhard
2003-01-01
We characterize the m×n cost matrices of the transportation problem for which there exist supplies and demands such that the transportation paradox arises. Our characterization is fairly simple and can be verified within O(mn) computational steps. Moreover, we discuss the corresponding question for
A definition of column reduced proper rational matrices
Czech Academy of Sciences Publication Activity Database
Ruiz-León, J. J.; Castellanos, A.; Ramos-Velasco, Luis Enrique
2002-01-01
Roč. 75, č. 3 (2002), s. 195-203 ISSN 0020-7179 R&D Projects: GA AV ČR KSK1019101 Institutional research plan: CEZ:AV0Z1075907 Keywords : linear systems * columm reduced polynomial matrices * decoupling Subject RIV: BC - Control Systems Theory Impact factor: 0.861, year: 2002
Construction of MDS self-dual codes from orthogonal matrices
Shi, Minjia; Sok, Lin; Solé, Patrick
2016-01-01
In this paper, we give algorithms and methods of construction of self-dual codes over finite fields using orthogonal matrices. Randomization in the orthogonal group, and code extension are the main tools. Some optimal, almost MDS, and MDS self-dual codes over both small and large prime fields are constructed.
Designer matrices for intestinal stem cell and organoid culture
Gjorevski, Nikolce; Sachs, Norman; Manfrin, Andrea; Giger, Sonja; Bragina, Maiia E.; Ordóñez-Morán, Paloma; Clevers, Hans; Lutolf, Matthias P.
2016-01-01
Epithelial organoids recapitulate multiple aspects of real organs, making them promising models of organ development, function and disease. However, the full potential of organoids in research and therapy has remained unrealized, owing to the poorly defined animal-derived matrices in which they are
More about unphysical zeroes in quark mass matrices
Energy Technology Data Exchange (ETDEWEB)
Emmanuel-Costa, David, E-mail: david.costa@tecnico.ulisboa.pt [Departamento de Física and Centro de Física Teórica de Partículas - CFTP, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, 1049-001 Lisboa (Portugal); González Felipe, Ricardo, E-mail: ricardo.felipe@tecnico.ulisboa.pt [Departamento de Física and Centro de Física Teórica de Partículas - CFTP, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, 1049-001 Lisboa (Portugal); ISEL - Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa, Rua Conselheiro Emídio Navarro, 1959-007 Lisboa (Portugal)
2017-01-10
We look for all weak bases that lead to texture zeroes in the quark mass matrices and contain a minimal number of parameters in the framework of the standard model. Since there are ten physical observables, namely, six nonvanishing quark masses, three mixing angles and one CP phase, the maximum number of texture zeroes in both quark sectors is altogether nine. The nine zero entries can only be distributed between the up- and down-quark sectors in matrix pairs with six and three texture zeroes or five and four texture zeroes. In the weak basis where a quark mass matrix is nonsingular and has six zeroes in one sector, we find that there are 54 matrices with three zeroes in the other sector, obtainable through right-handed weak basis transformations. It is also found that all pairs composed of a nonsingular matrix with five zeroes and a nonsingular and nondecoupled matrix with four zeroes simply correspond to a weak basis choice. Without any further assumptions, none of these pairs of up- and down-quark mass matrices has physical content. It is shown that all non-weak-basis pairs of quark mass matrices that contain nine zeroes are not compatible with current experimental data. The particular case of the so-called nearest-neighbour-interaction pattern is also discussed.
Eudragit E100 and Polysaccharide Polymer Blends as Matrices for ...
African Journals Online (AJOL)
Purpose: To compare the effects of two states of polymer/polymer blending (dry and aqueous/lyophilized) on the physicomechanical properties of tablets, containing blends of locust bean gum (LB) with Eudragit® E100 (E100) and sodium carboxymethylcellulose (SCMC) as matrices. Methods: LB, SCMC and E100 were ...
On the nonnegative inverse eigenvalue problem of traditional matrices
Directory of Open Access Journals (Sweden)
Alimohammad Nazari
2014-07-01
Full Text Available In this paper, at first for a given set of real or complex numbers $\\sigma$ with nonnegativesummation, we introduce some special conditions that with them there is no nonnegativetridiagonal matrix in which $\\sigma$ is its spectrum. In continue we present some conditions forexistence such nonnegative tridiagonal matrices.
Dirac Matrices and Feynman’s Rest of the Universe
Directory of Open Access Journals (Sweden)
Young S. Kim
2012-10-01
Full Text Available There are two sets of four-by-four matrices introduced by Dirac. The first set consists of fifteen Majorana matrices derivable from his four γ matrices. These fifteen matrices can also serve as the generators of the group SL(4, r. The second set consists of ten generators of the Sp(4 group which Dirac derived from two coupled harmonic oscillators. It is shown possible to extend the symmetry of Sp(4 to that of SL(4, r if the area of the phase space of one of the oscillators is allowed to become smaller without a lower limit. While there are no restrictions on the size of phase space in classical mechanics, Feynman’s rest of the universe makes this Sp(4-to-SL(4, r transition possible. The ten generators are for the world where quantum mechanics is valid. The remaining five generators belong to the rest of the universe. It is noted that the groups SL(4, r and Sp(4 are locally isomorphic to the Lorentz groups O(3, 3 and O(3, 2 respectively. This allows us to interpret Feynman’s rest of the universe in terms of space-time symmetry.
REFLECTIONS The Matrices of Race, Class and Gender: how they ...
African Journals Online (AJOL)
REFLECTIONS The Matrices of Race, Class and Gender: how they. Nova Smith. Full Text: EMAIL FULL TEXT EMAIL FULL TEXT · DOWNLOAD FULL TEXT DOWNLOAD FULL TEXT · http://dx.doi.org/10.4314/safere.v3i1.23950 · AJOL African Journals Online. HOW TO USE AJOL... for Researchers · for Librarians ...
A Role for M-Matrices in Modelling Population Growth
James, Glyn; Rumchev, Ventsi
2006-01-01
Adopting a discrete-time cohort-type model to represent the dynamics of a population, the problem of achieving a desired total size of the population under a balanced growth (contraction) and the problem of maintaining the desired size, once achieved, are studied. Properties of positive-time systems and M-matrices are used to develop the results,…
Quantitative mass spectrometry of unconventional human biological matrices
Dutkiewicz, Ewelina P.; Urban, Pawel L.
2016-10-01
The development of sensitive and versatile mass spectrometric methodology has fuelled interest in the analysis of metabolites and drugs in unconventional biological specimens. Here, we discuss the analysis of eight human matrices-hair, nail, breath, saliva, tears, meibum, nasal mucus and skin excretions (including sweat)-by mass spectrometry (MS). The use of such specimens brings a number of advantages, the most important being non-invasive sampling, the limited risk of adulteration and the ability to obtain information that complements blood and urine tests. The most often studied matrices are hair, breath and saliva. This review primarily focuses on endogenous (e.g. potential biomarkers, hormones) and exogenous (e.g. drugs, environmental contaminants) small molecules. The majority of analytical methods used chromatographic separation prior to MS; however, such a hyphenated methodology greatly limits analytical throughput. On the other hand, the mass spectrometric methods that exclude chromatographic separation are fast but suffer from matrix interferences. To enable development of quantitative assays for unconventional matrices, it is desirable to standardize the protocols for the analysis of each specimen and create appropriate certified reference materials. Overcoming these challenges will make analysis of unconventional human biological matrices more common in a clinical setting. This article is part of the themed issue 'Quantitative mass spectrometry'.
Variation in Raven's Progressive Matrices Scores across Time and Place
Brouwers, Symen A.; Van de Vijver, Fons J. R.; Van Hemert, Dianne A.
2009-01-01
The paper describes a cross-cultural and historical meta-analysis of Raven's Progressive Matrices. Data were analyzed of 798 samples from 45 countries (N = 244,316), which were published between 1944 and 2003. Country-level indicators of educational permeation (which involves a broad set of interrelated educational input and output factors that…
Eudragit E100 and Polysaccharide Polymer Blends as Matrices for ...
African Journals Online (AJOL)
Methods: LB, SCMC and E100 were blended in their dry (as purchased) state or modified by aqueous blending and subsequent lyophilization, prior to use as matrices in tablets. ... pullulan from Aureobasidium pullulans, 3-(3,4- .... the frozen polymer before sublimation and drying). Subsequently, milling generated a more.
Higher dimensional unitary braid matrices: Construction, associated structures and entanglements
International Nuclear Information System (INIS)
Abdesselam, B.; Chakrabarti, A.; Dobrev, V.K.; Mihov, S.G.
2007-03-01
We construct (2n) 2 x (2n) 2 unitary braid matrices R-circumflex for n ≥ 2 generalizing the class known for n = 1. A set of (2n) x (2n) matrices (I, J,K,L) are defined. R-circumflex is expressed in terms of their tensor products (such as K x J), leading to a canonical formulation for all n. Complex projectors P ± provide a basis for our real, unitary R-circumflex. Baxterization is obtained. Diagonalizations and block- diagonalizations are presented. The loss of braid property when R-circumflex (n > 1) is block-diagonalized in terms of R-circumflex (n = 1) is pointed out and explained. For odd dimension (2n + 1) 2 x (2n + 1) 2 , a previously constructed braid matrix is complexified to obtain unitarity. R-circumflexLL- and R-circumflexTT- algebras, chain Hamiltonians, potentials for factorizable S-matrices, complex non-commutative spaces are all studied briefly in the context of our unitary braid matrices. Turaev construction of link invariants is formulated for our case. We conclude with comments concerning entanglements. (author)
The algebraic structure of lax equations for infinite matrices
Helminck, G.F.
2002-01-01
In this paper we discuss the algebraic structure of the tower of differential difference equations that one can associate with any commutative subalgebra of $M_k(\\mathbb{C})$. These equations can be formulated conveniently in so-called Lax equations for infinite upper- resp. lowertriangular matrices
Resistant lower rank approximation of matrices by iterative majorization
Verboon, Peter; Heiser, Willem
2011-01-01
It is commonly known that many techniques for data analysis based on the least squares criterion are very sensitive to outliers in the data. Gabriel and Odoroff (1984) suggested a resistant approach for lower rank approximation of matrices. In this approach, weights are used to diminish the
Systematics of quark mass matrices in the standard electroweak model
International Nuclear Information System (INIS)
Frampton, P.H.; Jarlskog, C.; Stockholm Univ.
1985-01-01
It is shown that the quark mass matrices in the standard electroweak model satisfy the empirical relation M = M' + O(lambda 2 ), where M(M') refers to the mass matrix of the charge 2/3 (-1/3) quarks normalized to the largest eigenvalue, msub(t) (msub(b)), and lambda = Vsub(us) approx.= 0.22. (orig.)
Model-independent analysis with BPM correlation matrices
International Nuclear Information System (INIS)
Irwin, J.; Wang, C.X.; Yan, Y.T.; Bane, K.; Cai, Y.; Decker, F.; Minty, M.; Stupakov, G.; Zimmermann, F.
1998-06-01
The authors discuss techniques for Model-Independent Analysis (MIA) of a beamline using correlation matrices of physical variables and Singular Value Decomposition (SVD) of a beamline BPM matrix. The beamline matrix is formed from BPM readings for a large number of pulses. The method has been applied to the Linear Accelerator of the SLAC Linear Collider (SLC)
Swinburne, Thomas D.; Perez, Danny
2018-05-01
A massively parallel method to build large transition rate matrices from temperature-accelerated molecular dynamics trajectories is presented. Bayesian Markov model analysis is used to estimate the expected residence time in the known state space, providing crucial uncertainty quantification for higher-scale simulation schemes such as kinetic Monte Carlo or cluster dynamics. The estimators are additionally used to optimize where exploration is performed and the degree of temperature acceleration on the fly, giving an autonomous, optimal procedure to explore the state space of complex systems. The method is tested against exactly solvable models and used to explore the dynamics of C15 interstitial defects in iron. Our uncertainty quantification scheme allows for accurate modeling of the evolution of these defects over timescales of several seconds.
Patel, Vivek; Joseph, Gravil; Patel, Amit; Patel, Samik; Bustin, Devin; Mawson, David; Tuesta, Luis M.; Puentes, Rocio; Ghosh, Mousumi
2010-01-01
Abstract Trauma to the spinal cord produces endogenously irreversible tissue and functional loss, requiring the application of therapeutic approaches to achieve meaningful restoration. Cellular strategies, in particular Schwann-cell implantation, have shown promise in overcoming many of the obstacles facing successful repair of the injured spinal cord. Here, we show that the implantation of Schwann cells as cell suspensions with in-situ gelling laminin:collagen matrices after spinal-cord contusion significantly enhances long-term cell survival but not proliferation, as well as improves graft vascularization and the degree of axonal in-growth over the standard implantation vehicle, minimal media. The use of a matrix to suspend cells prior to implantation should be an important consideration for achieving improved survival and effectiveness of cellular therapies for future clinical application. PMID:20144012
International Nuclear Information System (INIS)
Hemmady, Sameer; Zheng, Xing; Hart, James; Antonsen, Thomas M. Jr.; Ott, Edward; Anlage, Steven M.
2006-01-01
Statistical fluctuations in the eigenvalues of the scattering, impedance, and admittance matrices of two-port wave-chaotic systems are studied experimentally using a chaotic microwave cavity. These fluctuations are universal in that their properties are dependent only upon the degree of loss in the cavity. We remove the direct processes introduced by the nonideally coupled driving ports through a matrix normalization process that involves the radiation-impedance matrix of the two driving ports. We find good agreement between the experimentally obtained marginal probability density functions (PDFs) of the eigenvalues of the normalized impedance, admittance, and scattering matrix and those from random matrix theory (RMT). We also experimentally study the evolution of the joint PDF of the eigenphases of the normalized scattering matrix as a function of loss. Experimental agreement with the theory by Brouwer and Beenakker for the joint PDF of the magnitude of the eigenvalues of the normalized scattering matrix is also shown
Applicability of non-invasively collected matrices for human biomonitoring
Directory of Open Access Journals (Sweden)
Nickmilder Marc
2009-03-01
Full Text Available Abstract With its inclusion under Action 3 in the Environment and Health Action Plan 2004–2010 of the European Commission, human biomonitoring is currently receiving an increasing amount of attention from the scientific community as a tool to better quantify human exposure to, and health effects of, environmental stressors. Despite the policy support, however, there are still several issues that restrict the routine application of human biomonitoring data in environmental health impact assessment. One of the main issues is the obvious need to routinely collect human samples for large-scale surveys. Particularly the collection of invasive samples from susceptible populations may suffer from ethical and practical limitations. Children, pregnant women, elderly, or chronically-ill people are among those that would benefit the most from non-invasive, repeated or routine sampling. Therefore, the use of non-invasively collected matrices for human biomonitoring should be promoted as an ethically appropriate, cost-efficient and toxicologically relevant alternative for many biomarkers that are currently determined in invasively collected matrices. This review illustrates that several non-invasively collected matrices are widely used that can be an valuable addition to, or alternative for, invasively collected matrices such as peripheral blood sampling. Moreover, a well-informed choice of matrix can provide an added value for human biomonitoring, as different non-invasively collected matrices can offer opportunities to study additional aspects of exposure to and effects from environmental contaminants, such as repeated sampling, historical overview of exposure, mother-child transfer of substances, or monitoring of substances with short biological half-lives.
Polymer Percolation Threshold in Multi-Component HPMC Matrices Tablets
Directory of Open Access Journals (Sweden)
Maryam Maghsoodi
2011-06-01
Full Text Available Introduction: The percolation theory studies the critical points or percolation thresholds of the system, where onecomponent of the system undergoes a geometrical phase transition, starting to connect the whole system. The application of this theory to study the release rate of hydrophilic matrices allows toexplain the changes in release kinetics of swellable matrix type system and results in a clear improvement of the design of controlled release dosage forms. Methods: In this study, the percolation theory has been applied to multi-component hydroxypropylmethylcellulose (HPMC hydrophilic matrices. Matrix tablets have been prepared using phenobarbital as drug,magnesium stearate as a lubricant employing different amount of lactose and HPMC K4M as a fillerandmatrix forming material, respectively. Ethylcelullose (EC as a polymeric excipient was also examined. Dissolution studies were carried out using the paddle method. In order to estimate the percolation threshold, the behaviour of the kinetic parameters with respect to the volumetric fraction of HPMC at time zero, was studied. Results: In both HPMC/lactose and HPMC/EC/lactose matrices, from the point of view of the percolation theory, the optimum concentration for HPMC, to obtain a hydrophilic matrix system for the controlled release of phenobarbital is higher than 18.1% (v/v HPMC. Above 18.1% (v/v HPMC, an infinite cluster of HPMC would be formed maintaining integrity of the system and controlling the drug release from the matrices. According to results, EC had no significant influence on the HPMC percolation threshold. Conclusion: This may be related to broad functionality of the swelling hydrophilic matrices.
Dynamical R Matrices of Elliptic Quantum Groups and Connection Matrices for the q-KZ Equations
Directory of Open Access Journals (Sweden)
Hitoshi Konno
2006-12-01
Full Text Available For any affine Lie algebra ${mathfrak g}$, we show that any finite dimensional representation of the universal dynamical $R$ matrix ${cal R}(lambda$ of the elliptic quantum group ${cal B}_{q,lambda}({mathfrak g}$ coincides with a corresponding connection matrix for the solutions of the $q$-KZ equation associated with $U_q({mathfrak g}$. This provides a general connection between ${cal B}_{q,lambda}({mathfrak g}$ and the elliptic face (IRF or SOS models. In particular, we construct vector representations of ${cal R}(lambda$ for ${mathfrak g}=A_n^{(1}$, $B_n^{(1}$, $C_n^{(1}$, $D_n^{(1}$, and show that they coincide with the face weights derived by Jimbo, Miwa and Okado. We hence confirm the conjecture by Frenkel and Reshetikhin.
Simplified Representation of Vector Fields
Telea, Alexandru; Wijk, Jarke J. van
1999-01-01
Vector field visualization remains a difficult task. Although many local and global visualization methods for vector fields such as flow data exist, they usually require extensive user experience on setting the visualization parameters in order to produce images communicating the desired insight. We
Estimation of Motion Vector Fields
DEFF Research Database (Denmark)
Larsen, Rasmus
1993-01-01
This paper presents an approach to the estimation of 2-D motion vector fields from time varying image sequences. We use a piecewise smooth model based on coupled vector/binary Markov random fields. We find the maximum a posteriori solution by simulated annealing. The algorithm generate sample...... fields by means of stochastic relaxation implemented via the Gibbs sampler....
GPU Accelerated Vector Median Filter
Aras, Rifat; Shen, Yuzhong
2011-01-01
Noise reduction is an important step for most image processing tasks. For three channel color images, a widely used technique is vector median filter in which color values of pixels are treated as 3-component vectors. Vector median filters are computationally expensive; for a window size of n x n, each of the n(sup 2) vectors has to be compared with other n(sup 2) - 1 vectors in distances. General purpose computation on graphics processing units (GPUs) is the paradigm of utilizing high-performance many-core GPU architectures for computation tasks that are normally handled by CPUs. In this work. NVIDIA's Compute Unified Device Architecture (CUDA) paradigm is used to accelerate vector median filtering. which has to the best of our knowledge never been done before. The performance of GPU accelerated vector median filter is compared to that of the CPU and MPI-based versions for different image and window sizes, Initial findings of the study showed 100x improvement of performance of vector median filter implementation on GPUs over CPU implementations and further speed-up is expected after more extensive optimizations of the GPU algorithm .
Archimedeanization of ordered vector spaces
Emelyanov, Eduard Yu.
2014-01-01
In the case of an ordered vector space with an order unit, the Archimedeanization method has been developed recently by V.I Paulsen and M. Tomforde. We present a general version of the Archimedeanization which covers arbitrary ordered vector spaces.
Vector superconductivity in cosmic strings
International Nuclear Information System (INIS)
Dvali, G.R.; Mahajan, S.M.
1992-03-01
We argue that in most realistic cases, the usual Witten-type bosonic superconductivity of the cosmic string is automatically (independent of the existence of superconducting currents) accompanied by the condensation of charged gauge vector bosons in the core giving rise to a new vector type superconductivity. The value of the charged vector condensate is related with the charged scalar expectation value, and vanishes only if the latter goes to zero. The mechanism for the proposed vector superconductivity, differing fundamentally from those in the literature, is delineated using the simplest realistic example of the two Higgs doublet standard model interacting with the extra cosmic string. It is shown that for a wide range of parameters, for which the string becomes scalarly superconducting, W boson condensates (the sources of vector superconductivity) are necessarily excited. (author). 14 refs
The True Gravitational Degrees Of Freedom
International Nuclear Information System (INIS)
Murchadha, N. o
2011-01-01
More than 50 years ago it was realized that General Relativity could be expressed in Hamiltonian form. Unfortunately, just like electromagnetism and Yang-Mills theory, the Einstein equations split into evolution equations and constraints which complicates matters. The 4 constraints are expressions of the gauge freedom of the theory, general covariance. One can cleanly pose initial data for the gravitational field, but this data has to satisfy the constraints. To find the independent degrees of freedom, one needs to factor the initial data by the constraints. There are many ways of doing this. I can do so in such a way as to implement the model suggested by Poincare for a well-posed dynamical system: Pick a configuration space and give the free initial data as a point of the configuration space and a tangent vector at the same point. Now, the evolution equations should give a unique curve in the same configuration space. This gives a natural definition of what I call the true gravitational degrees of freedom. (author)
Flach, J.; van der Waal, M.B.; van den Nieuwboer, M.; Claassen, H.J.H.M.; Larsen, O.F.A.
2017-01-01
Full Article Figures & data References Supplemental Citations Metrics Reprints & Permissions PDF ABSTRACT Probiotic microorganisms are increasingly incorporated into food matrices in order to confer proposed health benefits on the consumer. It is important that the health benefits,
Emerging vector borne diseases – incidence through vectors
Directory of Open Access Journals (Sweden)
Sara eSavic
2014-12-01
Full Text Available Vector borne diseases use to be a major public health concern only in tropical and subtropical areas, but today they are an emerging threat for the continental and developed countries also. Nowdays, in intercontinetal countries, there is a struggle with emerging diseases which have found their way to appear through vectors. Vector borne zoonotic diseases occur when vectors, animal hosts, climate conditions, pathogens and susceptible human population exist at the same time, at the same place. Global climate change is predicted to lead to an increase in vector borne infectious diseases and disease outbreaks. It could affect the range and popultion of pathogens, host and vectors, transmission season, etc. Reliable surveilance for diseases that are most likely to emerge is required. Canine vector borne diseases represent a complex group of diseases including anaplasmosis, babesiosis, bartonellosis, borreliosis, dirofilariosis, erlichiosis, leishmaniosis. Some of these diseases cause serious clinical symptoms in dogs and some of them have a zoonotic potential with an effect to public health. It is expected from veterinarians in coordination with medical doctors to play a fudamental role at primeraly prevention and then treatment of vector borne diseases in dogs. The One Health concept has to be integrated into the struggle against emerging diseases.During a four year period, from 2009-2013, a total number of 551 dog samples were analysed for vector borne diseases (borreliosis, babesiosis, erlichiosis, anaplasmosis, dirofilariosis and leishmaniasis in routine laboratory work. The analysis were done by serological tests – ELISA for borreliosis, dirofilariosis and leishmaniasis, modified Knott test for dirofilariosis and blood smear for babesiosis, erlichiosis and anaplasmosis. This number of samples represented 75% of total number of samples that were sent for analysis for different diseases in dogs. Annually, on avarege more then half of the samples
Efficient linear algebra routines for symmetric matrices stored in packed form.
Ahlrichs, Reinhart; Tsereteli, Kakha
2002-01-30
Quantum chemistry methods require various linear algebra routines for symmetric matrices, for example, diagonalization or Cholesky decomposition for positive matrices. We present a small set of these basic routines that are efficient and minimize memory requirements.
Pieper, J.S.; Oosterhof, A.; Dijkstra, Pieter J.; Veerkamp, J.H.; van Kuppevelt, T.H.
1999-01-01
Porous collagen matrices with defined physical, chemical and biological characteristics are interesting materials for tissue engineering. Attachment of glycosaminoglycans (GAGs) may add to these characteristics and valorize collagen. In this study, porous type I collagen matrices were crosslinked
Multi-color incomplete Cholesky conjugate gradient methods for vector computers. Ph.D. Thesis
Poole, E. L.
1986-01-01
In this research, we are concerned with the solution on vector computers of linear systems of equations, Ax = b, where A is a larger, sparse symmetric positive definite matrix. We solve the system using an iterative method, the incomplete Cholesky conjugate gradient method (ICCG). We apply a multi-color strategy to obtain p-color matrices for which a block-oriented ICCG method is implemented on the CYBER 205. (A p-colored matrix is a matrix which can be partitioned into a pXp block matrix where the diagonal blocks are diagonal matrices). This algorithm, which is based on a no-fill strategy, achieves O(N/p) length vector operations in both the decomposition of A and in the forward and back solves necessary at each iteration of the method. We discuss the natural ordering of the unknowns as an ordering that minimizes the number of diagonals in the matrix and define multi-color orderings in terms of disjoint sets of the unknowns. We give necessary and sufficient conditions to determine which multi-color orderings of the unknowns correpond to p-color matrices. A performance model is given which is used both to predict execution time for ICCG methods and also to compare an ICCG method to conjugate gradient without preconditioning or another ICCG method. Results are given from runs on the CYBER 205 at NASA's Langley Research Center for four model problems.
On the Reduction of Vector and Axial-Vector Fields in a Meson Effective Action at O(p4)
International Nuclear Information System (INIS)
Bel'kov, A.A.; Lanev, A.V.; Schaale, A.
1994-01-01
Starting from an effective NJL-type quark interaction we have derived an effective meson action for the pseudoscalar sector. The vector and axial-vector degrees of freedom have been integrated out, applying the static equations of motion. As the results we have found a (reduced) pseudoscalar meson Lagrangian of the Gasser-Leutwyler type with modified structure coefficients L i . This method has been also used to construct the reduced weak and electromagnetic-weak currents. The application of the reduced Lagrangian and currents has been considered in physical processes. 36 refs., 1 fig., 1 tab
Enhancing poxvirus vectors vaccine immunogenicity.
García-Arriaza, Juan; Esteban, Mariano
2014-01-01
Attenuated recombinant poxvirus vectors expressing heterologous antigens from pathogens are currently at various stages in clinical trials with the aim to establish their efficacy. This is because these vectors have shown excellent safety profiles, significant immunogenicity against foreign expressed antigens and are able to induce protective immune responses. In view of the limited efficacy triggered by some poxvirus strains used in clinical trials (i.e, ALVAC in the RV144 phase III clinical trial for HIV), and of the restrictive replication capacity of the highly attenuated vectors like MVA and NYVAC, there is a consensus that further improvements of these vectors should be pursuit. In this review we considered several strategies that are currently being implemented, as well as new approaches, to improve the immunogenicity of the poxvirus vectors. This includes heterologous prime/boost protocols, use of co-stimulatory molecules, deletion of viral immunomodulatory genes still present in the poxvirus genome, enhancing virus promoter strength, enhancing vector replication capacity, optimizing expression of foreign heterologous sequences, and the combined use of adjuvants. An optimized poxvirus vector triggering long-lasting immunity with a high protective efficacy against a selective disease should be sought.
Stable piecewise polynomial vector fields
Directory of Open Access Journals (Sweden)
Claudio Pessoa
2012-09-01
Full Text Available Let $N={y>0}$ and $S={y<0}$ be the semi-planes of $mathbb{R}^2$ having as common boundary the line $D={y=0}$. Let $X$ and $Y$ be polynomial vector fields defined in $N$ and $S$, respectively, leading to a discontinuous piecewise polynomial vector field $Z=(X,Y$. This work pursues the stability and the transition analysis of solutions of $Z$ between $N$ and $S$, started by Filippov (1988 and Kozlova (1984 and reformulated by Sotomayor-Teixeira (1995 in terms of the regularization method. This method consists in analyzing a one parameter family of continuous vector fields $Z_{epsilon}$, defined by averaging $X$ and $Y$. This family approaches $Z$ when the parameter goes to zero. The results of Sotomayor-Teixeira and Sotomayor-Machado (2002 providing conditions on $(X,Y$ for the regularized vector fields to be structurally stable on planar compact connected regions are extended to discontinuous piecewise polynomial vector fields on $mathbb{R}^2$. Pertinent genericity results for vector fields satisfying the above stability conditions are also extended to the present case. A procedure for the study of discontinuous piecewise vector fields at infinity through a compactification is proposed here.
Chikungunya Virus–Vector Interactions
Directory of Open Access Journals (Sweden)
Lark L. Coffey
2014-11-01
Full Text Available Chikungunya virus (CHIKV is a mosquito-borne alphavirus that causes chikungunya fever, a severe, debilitating disease that often produces chronic arthralgia. Since 2004, CHIKV has emerged in Africa, Indian Ocean islands, Asia, Europe, and the Americas, causing millions of human infections. Central to understanding CHIKV emergence is knowledge of the natural ecology of transmission and vector infection dynamics. This review presents current understanding of CHIKV infection dynamics in mosquito vectors and its relationship to human disease emergence. The following topics are reviewed: CHIKV infection and vector life history traits including transmission cycles, genetic origins, distribution, emergence and spread, dispersal, vector competence, vector immunity and microbial interactions, and co-infection by CHIKV and other arboviruses. The genetics of vector susceptibility and host range changes, population heterogeneity and selection for the fittest viral genomes, dual host cycling and its impact on CHIKV adaptation, viral bottlenecks and intrahost diversity, and adaptive constraints on CHIKV evolution are also discussed. The potential for CHIKV re-emergence and expansion into new areas and prospects for prevention via vector control are also briefly reviewed.
de Jong, J. T. A.; Kuijken, K.; Applegate, D.; Begeman, K.; Belikov, A.; Blake, C.; Bout, J.; Boxhoorn, D.; Buddelmeijer, H.; Buddendiek, A.; Cacciato, M.; Capaccioli, M.; Choi, A.; Cordes, O.; Covone, G.; Dall'Ora, M.; Edge, A.; Erben, T.; Franse, J.; Getman, F.; Grado, A.; Harnois-Deraps, J.; Helmich, E.; Herbonnet, R.; Heymans, C.; Hildebrandt, H.; Hoekstra, H.; Huang, Z.; Irisarri, N.; Joachimi, B.; Köhlinger, F.; Kitching, T.; La Barbera, F.; Lacerda, P.; McFarland, J.; Miller, L.; Nakajima, R.; Napolitano, N. R.; Paolillo, M.; Peacock, J.; Pila-Diez, B.; Puddu, E.; Radovich, M.; Rifatto, A.; Schneider, P.; Schrabback, T.; Sifon, C.; Sikkema, G.; Simon, P.; Sutherland, W.; Tudorica, A.; Valentijn, E.; van der Burg, R.; van Uitert, E.; van Waerbeke, L.; Velander, M.; Kleijn, G. V.; Viola, M.; Vriend, W.-J.
2013-01-01
The Kilo-Degree Survey (KiDS), a 1500-square-degree optical imaging survey with the recently commissioned OmegaCAM wide-field imager on the VLT Survey Telescope (VST), is described. KiDS will image two fields in u-,g-,r- and i-bands and, together with the VIKING survey, produce nine-band (u- to
Research Degrees as Professional Education?
Barnacle, Robyn; Dall'Alba, Gloria
2011-01-01
There is an increasing trend within higher education and, more specifically, in higher degrees by research, to treat a professional skills set as a desirable graduate outcome. The increasing value that is being placed on a professional skills set in large part reflects growing interest around the world in the role of research degrees in labour…
Violation of vector dominance in the vector manifestation
International Nuclear Information System (INIS)
Sasaki, Chihiro
2003-01-01
The vector manifestation (VM) is a new pattern for realizing the chiral symmetry in QCD. In the VM, the massless vector meson becomes the chiral partner of pion at the critical point, in contrast with the restoration based on the linear sigma model. Including the intrinsic temperature dependences of the parameters of the hidden local symmetry (HLS) Lagrangian determined from the underlying QCD through the Wilsonian matching together with the hadronic thermal corrections, we present a new prediction of the VM on the direct photon-π-π coupling which measures the validity of the vector dominance (VD) of the electromagnetic form factor of the pion. We find that the VD is largely violated at the critical temperature, which indicates that the assumption of the VD made in several analysis on the dilepton spectra in hot matter may need to be weakened for consistently including the effect of the dropping mass of the vector meson. (author)
Lohe, M. A.
2018-06-01
We generalize the Watanabe–Strogatz (WS) transform, which acts on the Kuramoto model in d = 2 dimensions, to a higher-dimensional vector transform which operates on vector oscillator models of synchronization in any dimension , for the case of identical frequency matrices. These models have conserved quantities constructed from the cross ratios of inner products of the vector variables, which are invariant under the vector transform, and have trajectories which lie on the unit sphere S d‑1. Application of the vector transform leads to a partial integration of the equations of motion, leaving independent equations to be solved, for any number of nodes N. We discuss properties of complete synchronization and use the reduced equations to derive a stability condition for completely synchronized trajectories on S d‑1. We further generalize the vector transform to a mapping which acts in and in particular preserves the unit ball , and leaves invariant the cross ratios constructed from inner products of vectors in . This mapping can be used to partially integrate a system of vector oscillators with trajectories in , and for d = 2 leads to an extension of the Kuramoto system to a system of oscillators with time-dependent amplitudes and trajectories in the unit disk. We find an inequivalent generalization of the Möbius map which also preserves but leaves invariant a different set of cross ratios, this time constructed from the vector norms. This leads to a different extension of the Kuramoto model with trajectories in the complex plane that can be partially integrated by means of fractional linear transformations.
On the norms of r-circulant matrices with generalized Fibonacci numbers
Directory of Open Access Journals (Sweden)
Amara Chandoul
2017-01-01
Full Text Available In this paper, we obtain a generalization of [6, 8]. Firstly, we consider the so-called r-circulant matrices with generalized Fibonacci numbers and then found lower and upper bounds for the Euclidean and spectral norms of these matrices. Afterwards, we present some bounds for the spectral norms of Hadamard and Kronecker product of these matrices.
Emerging Vector-Borne Diseases - Incidence through Vectors.
Savić, Sara; Vidić, Branka; Grgić, Zivoslav; Potkonjak, Aleksandar; Spasojevic, Ljubica
2014-01-01
Vector-borne diseases use to be a major public health concern only in tropical and subtropical areas, but today they are an emerging threat for the continental and developed countries also. Nowadays, in intercontinental countries, there is a struggle with emerging diseases, which have found their way to appear through vectors. Vector-borne zoonotic diseases occur when vectors, animal hosts, climate conditions, pathogens, and susceptible human population exist at the same time, at the same place. Global climate change is predicted to lead to an increase in vector-borne infectious diseases and disease outbreaks. It could affect the range and population of pathogens, host and vectors, transmission season, etc. Reliable surveillance for diseases that are most likely to emerge is required. Canine vector-borne diseases represent a complex group of diseases including anaplasmosis, babesiosis, bartonellosis, borreliosis, dirofilariosis, ehrlichiosis, and leishmaniosis. Some of these diseases cause serious clinical symptoms in dogs and some of them have a zoonotic potential with an effect to public health. It is expected from veterinarians in coordination with medical doctors to play a fundamental role at primarily prevention and then treatment of vector-borne diseases in dogs. The One Health concept has to be integrated into the struggle against emerging diseases. During a 4-year period, from 2009 to 2013, a total number of 551 dog samples were analyzed for vector-borne diseases (borreliosis, babesiosis, ehrlichiosis, anaplasmosis, dirofilariosis, and leishmaniasis) in routine laboratory work. The analysis was done by serological tests - ELISA for borreliosis, dirofilariosis, and leishmaniasis, modified Knott test for dirofilariosis, and blood smear for babesiosis, ehrlichiosis, and anaplasmosis. This number of samples represented 75% of total number of samples that were sent for analysis for different diseases in dogs. Annually, on average more then half of the samples
Padman, Rachael
2010-04-01
Making UK undergraduate physics degrees longer must have seemed like a good idea at the time. Back in the early 1990s the standard three-year Bachelor's physics degree (four years in Scotland) was under pressure at both ends. The A-level curriculum - one of the requirements for entry onto a degree course - was being increasingly modularized, and dumbed down. Physics students were arriving at university less well prepared than in the past and there was an increasing awareness that graduates of five-year continental degree courses were better equipped for a professional scientific career than those in the UK. At the same time, local education authorities in the UK were required to provide full funding for a first degree, whether for three or four years.
Uniform Recovery Bounds for Structured Random Matrices in Corrupted Compressed Sensing
Zhang, Peng; Gan, Lu; Ling, Cong; Sun, Sumei
2018-04-01
We study the problem of recovering an $s$-sparse signal $\\mathbf{x}^{\\star}\\in\\mathbb{C}^n$ from corrupted measurements $\\mathbf{y} = \\mathbf{A}\\mathbf{x}^{\\star}+\\mathbf{z}^{\\star}+\\mathbf{w}$, where $\\mathbf{z}^{\\star}\\in\\mathbb{C}^m$ is a $k$-sparse corruption vector whose nonzero entries may be arbitrarily large and $\\mathbf{w}\\in\\mathbb{C}^m$ is a dense noise with bounded energy. The aim is to exactly and stably recover the sparse signal with tractable optimization programs. In this paper, we prove the uniform recovery guarantee of this problem for two classes of structured sensing matrices. The first class can be expressed as the product of a unit-norm tight frame (UTF), a random diagonal matrix and a bounded columnwise orthonormal matrix (e.g., partial random circulant matrix). When the UTF is bounded (i.e. $\\mu(\\mathbf{U})\\sim1/\\sqrt{m}$), we prove that with high probability, one can recover an $s$-sparse signal exactly and stably by $l_1$ minimization programs even if the measurements are corrupted by a sparse vector, provided $m = \\mathcal{O}(s \\log^2 s \\log^2 n)$ and the sparsity level $k$ of the corruption is a constant fraction of the total number of measurements. The second class considers randomly sub-sampled orthogonal matrix (e.g., random Fourier matrix). We prove the uniform recovery guarantee provided that the corruption is sparse on certain sparsifying domain. Numerous simulation results are also presented to verify and complement the theoretical results.
DEFF Research Database (Denmark)
Davis, Christopher James; Kedlaya, Kiran
2014-01-01
We study the kernel and cokernel of the Frobenius map on the p-typical Witt vectors of a commutative ring, not necessarily of characteristic p. We give many equivalent conditions to surjectivity of the Frobenius map on both finite and infinite length Witt vectors. In particular, surjectivity...... on finite Witt vectors turns out to be stable under certain integral extensions; this provides a clean formulation of a strong generalization of Faltings’s almost purity theorem from p-adic Hodge theory, incorporating recent improvements by Kedlaya–Liu and by Scholze....
Vector boson scattering at CLIC
Energy Technology Data Exchange (ETDEWEB)
Kilian, Wolfgang; Fleper, Christian [Department Physik, Universitaet Siegen, 57068 Siegen (Germany); Reuter, Juergen [DESY Theory Group, 22603 Hamburg (Germany); Sekulla, Marco [Institut fuer Theoretische Physik, Karlsruher Institut fuer Technologie, 76131 Karlsruhe (Germany)
2016-07-01
Linear colliders operating in a range of multiple TeV are able to investigate the details of vector boson scattering and electroweak symmetry breaking. We calculate cross sections with the Monte Carlo generator WHIZARD for vector boson scattering processes at the future linear e{sup +} e{sup -} collider CLIC. By finding suitable cuts, the vector boson scattering signal processes are isolated from the background. Finally, we are able to determine exclusion sensitivities on the non-Standard Model parameters of the relevant dimension eight operators.
Vector control of induction machines
Robyns, Benoit
2012-01-01
After a brief introduction to the main law of physics and fundamental concepts inherent in electromechanical conversion, ""Vector Control of Induction Machines"" introduces the standard mathematical models for induction machines - whichever rotor technology is used - as well as several squirrel-cage induction machine vector-control strategies. The use of causal ordering graphs allows systematization of the design stage, as well as standardization of the structure of control devices. ""Vector Control of Induction Machines"" suggests a unique approach aimed at reducing parameter sensitivity for
Vectors of rickettsiae in Africa.
Bitam, Idir
2012-12-01
Vector-borne diseases are caused by parasites, bacteria, or viruses transmitted by the bites of hematophagous arthropods. In Africa, there has been a recent emergence of new diseases and the re-emergence of existing diseases, usually with changes in disease epidemiology (e.g., geographical distribution, prevalence, and pathogenicity). In Africa, rickettsioses are recognized as important emerging vector-borne infections in humans. Rickettsial diseases are transmitted by different types of arthropods, ticks, fleas, lice, and mites. This review will examine the roles of these different arthropod vectors and their geographical distributions. Copyright © 2012 Elsevier GmbH. All rights reserved.
Recommendation on vectors and vector-transmitted diseases
Netherlands Food and Consumer Product Safety Authority
2009-01-01
In view of their increasing risk of introduction and their possible implications in causing major disease outbreaks, vectors, as well as vector-transmitted diseases like dengue, West Nile disease, Lyme disease and bluetongue need to be recognised as a threat to public and animal health and to the economy, also in the Netherlands. There has been an increase in the incidence of these diseases in the past two to three decades. Climate changes and changes in the use of land, water managemen...
Vector manifestation and violation of vector dominance in hot matter
International Nuclear Information System (INIS)
Harada, Masayasu; Sasaki, Chihiro
2004-01-01
We show the details of the calculation of the hadronic thermal corrections to the two-point functions in the effective field theory of QCD for pions and vector mesons based on the hidden local symmetry (HLS) in hot matter using the background field gauge. We study the temperature dependence of the pion velocity in the low-temperature region determined from the hadronic thermal corrections, and show that, due to the presence of the dynamical vector meson, the pion velocity is smaller than the speed of the light already at one-loop level, in contrast to the result obtained in the ordinary chiral perturbation theory including only the pion at one-loop. Including the intrinsic temperature dependences of the parameters of the HLS Lagrangian determined from the underlying QCD through the Wilsonian matching, we show how the vector manifestation (VM), in which the massless vector meson becomes the chiral partner of pion, is realized at the critical temperature. We present a new prediction of the VM on the direct photon-π-π coupling which measures the validity of the vector dominance (VD) of the electromagnetic form factor of the pion: we find that the VD is largely violated at the critical temperature, which indicates that the assumption of the VD made in several analyses on the dilepton spectra in hot matter may need to be weakened for consistently including the effect of the dropping mass of the vector meson
Vector independent transmission of the vector-borne bluetongue virus.
van der Sluijs, Mirjam Tineke Willemijn; de Smit, Abraham J; Moormann, Rob J M
2016-01-01
Bluetongue is an economically important disease of ruminants. The causative agent, Bluetongue virus (BTV), is mainly transmitted by insect vectors. This review focuses on vector-free BTV transmission, and its epizootic and economic consequences. Vector-free transmission can either be vertical, from dam to fetus, or horizontal via direct contract. For several BTV-serotypes, vertical (transplacental) transmission has been described, resulting in severe congenital malformations. Transplacental transmission had been mainly associated with live vaccine strains. Yet, the European BTV-8 strain demonstrated a high incidence of transplacental transmission in natural circumstances. The relevance of transplacental transmission for the epizootiology is considered limited, especially in enzootic areas. However, transplacental transmission can have a substantial economic impact due to the loss of progeny. Inactivated vaccines have demonstrated to prevent transplacental transmission. Vector-free horizontal transmission has also been demonstrated. Since direct horizontal transmission requires close contact of animals, it is considered only relevant for within-farm spreading of BTV. The genetic determinants which enable vector-free transmission are present in virus strains circulating in the field. More research into the genetic changes which enable vector-free transmission is essential to better evaluate the risks associated with outbreaks of new BTV serotypes and to design more appropriate control measures.
Stabilization and solidification of Pb in cement matrices
International Nuclear Information System (INIS)
Gollmann, Maria A.C.; Silva, Marcia M. da; Santos, Joao H. Z. dos; Masuero, Angela B.
2010-01-01
Pb was incorporated to a series of cement matrices, which were submitted to different cure time and pH. Pb content leached to aqueous solution was monitored by atomic absorption spectroscopy. The block resistance was evaluated by unconfined compressive strength at 7 and 28 ages. Data are discussed in terms of metal mobility along the cement block monitored by X-ray fluorescence (XRF) spectrometry. The Pb incorporated matrices have shown that a long cure time is more suitable for avoiding metal leaching. For a longer cure period the action of the metal is higher and there is a decreasing in the compressive strength. The XRF analyses show that there is a lower Ca concentration in the matrix in which Pb was added. (author)
Multigroup P8 - elastic scattering matrices of main reactor elements
International Nuclear Information System (INIS)
Garg, S.B.; Shukla, V.K.
1979-01-01
To study the effect of anisotropic scattering phenomenon on shielding and neutronics of nuclear reactors multigroup P8-elastic scattering matrices have been generated for H, D, He, 6 Li, 7 Li, 10 B, C, N, O, Na, Cr, Fe, Ni, 233 U, 235 U, 238 U, 239 Pu, 240 Pu, 241 Pu and 242 Pu using their angular distribution, Legendre coefficient and elastic scattering cross-section data from the basic ENDF/B library. Two computer codes HSCAT and TRANS have been developed to complete this task for BESM-6 and CDC-3600 computers. These scattering matrices can be directly used as input to the transport theory codes ANISN and DOT. (auth.)
Properties of Zero-Free Transfer Function Matrices
D. O. Anderson, Brian; Deistler, Manfred
Transfer functions of linear, time-invariant finite-dimensional systems with more outputs than inputs, as arise in factor analysis (for example in econometrics), have, for state-variable descriptions with generic entries in the relevant matrices, no finite zeros. This paper gives a number of characterizations of such systems (and indeed square discrete-time systems with no zeros), using state-variable, impulse response, and matrix-fraction descriptions. Key properties include the ability to recover the input values at any time from a bounded interval of output values, without any knowledge of an initial state, and an ability to verify the no-zero property in terms of a property of the impulse response coefficient matrices. Results are particularized to cases where the transfer function matrix in question may or may not have a zero at infinity or a zero at zero.
Determination of chromium in biological matrices by neutron activation
International Nuclear Information System (INIS)
McClendon, L.T.
1978-01-01
Chromium is recognized to be an essential trace element in several biological systems. It exists in many biological materials in a variety of chemical forms and very low concentration levels which cause problems for many analytical techniques. Both instrumental and destructive neutron activation analysis were used to determine the chromium concentration in Orchard Leaves, SRM 1571, Brewers Yeast, SRM 1569, and Bovine Liver, SRM 1577. Some of the problems inherent with determining chromium in certain biological matrices and the data obtained here at the National Bureau of Standards using this technique are discussed. The results obtained from dissolution of brewers yeast in a closed system as described in the DNAA procedure are in good agreement with the INAA results. The same phenomenon existed in the determination of chromium in bovine liver. The radiochemical procedure described for chromium (DNAA) provides the analyst with a simple, rapid and selective technique for chromium determination in a variety of matrices. (T.G.)
NDMA formation kinetics from three pharmaceuticals in four water matrices.
Shen, Ruqiao; Andrews, Susan A
2011-11-01
N, N-nitrosodimethylamine (NDMA) is an emerging disinfection by-product (DBP) that has been widely detected in many drinking water systems and commonly associated with the chloramine disinfection process. Some amine-based pharmaceuticals have been demonstrated to form NDMA during chloramination, but studies regarding the reaction kinetics are largely lacking. This study investigates the NDMA formation kinetics from ranitidine, chlorphenamine, and doxylamine under practical chloramine disinfection conditions. The formation profile was monitored in both lab-grade water and real water matrices, and a statistical model is proposed to describe and predict the NDMA formation from selected pharmaceuticals in various water matrices. The results indicate the significant impact of water matrix components and reaction time on the NDMA formation from selected pharmaceuticals, and provide fresh insights on the estimation of ultimate NDMA formation potential from pharmaceutical precursors. Copyright © 2011 Elsevier Ltd. All rights reserved.
Quark mass matrices in left-right symmetric gauge theories
International Nuclear Information System (INIS)
Ecker, G.; Grimus, W.; Konetschny, W.
1981-01-01
The most general left-right symmetry for SU(2)sub(L) x SU(2)sub(R) x U(1) gauge theories with any number of flavours and with at most two scalar multiplets transforming as anti qq bilinears is analyzed. In order to get additional constraints on the structure of quark mass matrices all possible horizontal groups (continuous or discrete) are investigated. A complete classification of physically inequivalent quark mass matrices is given for four and six flavours. It is argued that the methods and results are also applicable in the case of dynamical symmetry breaking. Parity invariance and horizontal symmetry are shown to imply CP conservation on the Lagrangian level. For all non-trivial three-generation models there is spontaneous CP violation which in most cases turns out to be naturally small. (Auth.)
Generalised Wigner surmise for (2 X 2) random matrices
International Nuclear Information System (INIS)
Chau Huu-Tai, P.; Van Isacker, P.; Smirnova, N.A.
2001-01-01
We present new analytical results concerning the spectral distributions for (2 x 2) random real symmetric matrices which generalize the Wigner surmise. The study of the statistical properties of spectra of realistic many-body Hamiltonians requires consideration of a random matrix ensemble whose elements are not independent or whose distribution is not invariant under orthogonal transformation of a chosen basis. In this letter we have concentrated on the properties of (2 x 2) real symmetric matrices whose elements are independent Gaussian variables with zero means but do not belong to the GOE. We have derived the distribution of eigenvalues for such a matrix, the nearest-neighbour spacing distribution which generalizes the Wigner surmise and we have calculated some important moments. (authors)
Likelihood Approximation With Hierarchical Matrices For Large Spatial Datasets
Litvinenko, Alexander
2017-09-03
We use available measurements to estimate the unknown parameters (variance, smoothness parameter, and covariance length) of a covariance function by maximizing the joint Gaussian log-likelihood function. To overcome cubic complexity in the linear algebra, we approximate the discretized covariance function in the hierarchical (H-) matrix format. The H-matrix format has a log-linear computational cost and storage O(kn log n), where the rank k is a small integer and n is the number of locations. The H-matrix technique allows us to work with general covariance matrices in an efficient way, since H-matrices can approximate inhomogeneous covariance functions, with a fairly general mesh that is not necessarily axes-parallel, and neither the covariance matrix itself nor its inverse have to be sparse. We demonstrate our method with Monte Carlo simulations and an application to soil moisture data. The C, C++ codes and data are freely available.
HadISST (1-degree)/HadISST (1-degree)
National Oceanic and Atmospheric Administration, Department of Commerce — Monthly version of HadISST sea surface temperature component (1-degree). See Rayner, N. A., Parker, D. E., Horton, E. B., Folland, C. K., Alexander, L. V., Rowell,...
Sports drug testing using complementary matrices: Advantages and limitations.
Thevis, Mario; Geyer, Hans; Tretzel, Laura; Schänzer, Wilhelm
2016-10-25
Today, routine doping controls largely rely on testing whole blood, serum, and urine samples. These matrices allow comprehensively covering inorganic as well as low and high molecular mass organic analytes relevant to doping controls and are collecting and transferring from sampling sites to accredited anti-doping laboratories under standardized conditions. Various aspects including time and cost-effectiveness as well as intrusiveness and invasiveness of the sampling procedure but also analyte stability and breadth of the contained information have been motivation to consider and assess values potentially provided and added to modern sports drug testing programs by alternative matrices. Such alternatives could be dried blood spots (DBS), dried plasma spots (DPS), oral fluid (OF), exhaled breath (EB), and hair. In this review, recent developments and test methods concerning these alternative matrices and expected or proven contributions as well as limitations of these specimens in the context of the international anti-doping fight are presented and discussed, guided by current regulations for prohibited substances and methods of doping as established by the World Anti-Doping Agency (WADA). Focusing on literature published between 2011 and 2015, examples for doping control analytical assays concerning non-approved substances, anabolic agents, peptide hormones/growth factors/related substances and mimetics, β 2 -agonists, hormone and metabolic modulators, diuretics and masking agents, stimulants, narcotics, cannabinoids, glucocorticoids, and beta-blockers were selected to outline the advantages and limitations of the aforementioned alternative matrices as compared to conventional doping control samples (i.e. urine and blood/serum). Copyright © 2016 Elsevier B.V. All rights reserved.
Contributions to Large Covariance and Inverse Covariance Matrices Estimation
Kang, Xiaoning
2016-01-01
Estimation of covariance matrix and its inverse is of great importance in multivariate statistics with broad applications such as dimension reduction, portfolio optimization, linear discriminant analysis and gene expression analysis. However, accurate estimation of covariance or inverse covariance matrices is challenging due to the positive definiteness constraint and large number of parameters, especially in the high-dimensional cases. In this thesis, I develop several approaches for estimat...
Limit sets for the discrete spectrum of complex Jacobi matrices
International Nuclear Information System (INIS)
Golinskii, L B; Egorova, I E
2005-01-01
The discrete spectrum of complex Jacobi matrices that are compact perturbations of the discrete Laplacian is studied. The precise stabilization rate (in the sense of order) of the matrix elements ensuring the finiteness of the discrete spectrum is found. An example of a Jacobi matrix with discrete spectrum having a unique limit point is constructed. These results are discrete analogues of Pavlov's well-known results on Schroedinger operators with complex potential on a half-axis.
Electrospun Phospholipid Fibers as Micro-Encapsulation and Antioxidant Matrices
DEFF Research Database (Denmark)
Shekarforoush, Elhamalsadat; Mendes, Ana Carina Loureiro; Baj, Vanessa
2017-01-01
Electrospun phospholipid (asolectin) microfibers were investigated as antioxidants and encapsulation matrices for curcumin and vanillin. These phospholipid microfibers exhibited antioxidant properties which increased after the encapsulation of both curcumin and vanillin. The total antioxidant...... capacity (TAC) and the total phenolic content (TPC) of curcumin/phospholipid and vanillin/phospholipid microfibers remained stable over time at different temperatures (refrigerated, ambient) and pressures (vacuum, ambient). ¹H-NMR confirmed the chemical stability of both encapsulated curcumin and vanillin...
Parallel decompositions of Mueller matrices and polarimetric subtraction
Directory of Open Access Journals (Sweden)
Gil J.J.
2010-06-01
Full Text Available From a general formulation of the physically realizable parallel decompositions of the Mueller matrix M of a given depolarizing system, a procedure for determining the set of pure Mueller matrices susceptible to be subtracted from M is presented. This procedure provides a way to check if a given pure Mueller matrix N can be subtracted from M or not. If this check is positive, the value of the relative cross section of the subtracted component is also determined.
Von Willebrand protein binds to extracellular matrices independently of collagen.
Wagner, D D; Urban-Pickering, M; Marder, V J
1984-01-01
Von Willebrand protein is present in the extracellular matrix of endothelial cells where it codistributes with fibronectin and types IV and V collagen. Bacterial collagenase digestion of endothelial cells removed fibrillar collagen, but the pattern of fibronectin and of von Willebrand protein remained undisturbed. Exogenous von Willebrand protein bound to matrices of different cells, whether rich or poor in collagen. von Willebrand protein also decorated the matrix of cells grown in the prese...
Procedure for the analysis of americium in complex matrices
International Nuclear Information System (INIS)
Knab, D.
1978-02-01
A radioanalytical procedure for the analysis of americium in complex matrices has been developed. Clean separations of americium can be obtained from up to 100 g of sample ash, regardless of the starting material. The ability to analyze large masses of material provides the increased sensitivity necessary to detect americium in many environmental samples. The procedure adequately decontaminates from rare earth elements and natural radioactive nuclides that interfere with the alpha spectrometric measurements
Computation of the q -th roots of circulant matrices
Directory of Open Access Journals (Sweden)
Pakizeh Mohammadi Khanghah
2014-05-01
Full Text Available In this paper, we investigate the reduced form of circulant matrices and we show that the problem of computing the $q$-th roots of a nonsingular circulant matrix $A$ can be reduced to that of computing the $q$-th roots of two half size matrices $B-C$ and $B+C$.
Factoring symmetric indefinite matrices on high-performance architectures
Jones, Mark T.; Patrick, Merrell L.
1990-01-01
The Bunch-Kaufman algorithm is the method of choice for factoring symmetric indefinite matrices in many applications. However, the Bunch-Kaufman algorithm does not take advantage of high-performance architectures such as the Cray Y-MP. Three new algorithms, based on Bunch-Kaufman factorization, that take advantage of such architectures are described. Results from an implementation of the third algorithm are presented.
A Robust Incomplete Factorization Preconditioner for Positive Definite Matrices
Czech Academy of Sciences Publication Activity Database
Benzi, M.; Tůma, Miroslav
2003-01-01
Roč. 10, - (2003), s. 385-400 ISSN 1070-5325 R&D Projects: GA AV ČR IAA2030801; GA AV ČR IAA1030103 Institutional research plan: AV0Z1030915 Keywords : sparse linear systems * positive definite matrices * preconditioned conjugate gradient s * incomplete factorization * A-orthogonalization * SAINV Subject RIV: BA - General Mathematics Impact factor: 1.042, year: 2003
Interactions between Food Additive Silica Nanoparticles and Food Matrices
Directory of Open Access Journals (Sweden)
Mi-Ran Go
2017-06-01
Full Text Available Nanoparticles (NPs have been widely utilized in the food industry as additives with their beneficial characteristics, such as improving sensory property and processing suitability, enhancing functional and nutritional values, and extending shelf-life of foods. Silica is used as an anti-caking agent to improve flow property of powered ingredients and as a carrier for flavors or active compounds in food. Along with the rapid development of nanotechnology, the sizes of silica fall into nanoscale, thereby raising concerns about the potential toxicity of nano-sized silica materials. There have been a number of studies carried out to investigate possible adverse effects of NPs on the gastrointestinal tract. The interactions between NPs and surrounding food matrices should be also taken into account since the interactions can affect their bioavailability, efficacy, and toxicity. In the present study, we investigated the interactions between food additive silica NPs and food matrices, such as saccharides, proteins, lipids, and minerals. Quantitative analysis was performed to determine food component-NP corona using HPLC, fluorescence quenching, GC-MS, and ICP-AES. The results demonstrate that zeta potential and hydrodynamic radius of silica NPs changed in the presence of all food matrices, but their solubility was not affected. However, quantitative analysis on the interactions revealed that a small portion of food matrices interacted with silica NPs and the interactions were highly dependent on the type of food component. Moreover, minor nutrients could also affect the interactions, as evidenced by higher NP interaction with honey rather than with a simple sugar mixture containing an equivalent amount of fructose, glucose, sucrose, and maltose. These findings provide fundamental information to extend our understanding about the interactions between silica NPs and food components and to predict the interaction effect on the safety aspects of food
Discrete ergodic Jacobi matrices: Spectral properties and Quantum dynamical bounds
Han, Rui
2017-01-01
In this thesis we study discrete quasiperiodic Jacobi operators as well as ergodic operators driven by more general zero topological entropy dynamics. Such operators are deeply connected to physics (quantum Hall effect and graphene) and have enjoyed great attention from mathematics (e.g. several of Simon’s problems). The thesis has two main themes. First, to study spectral properties of quasiperiodic Jacobi matrices, in particular when off-diagonal sampling function has non-zero winding numbe...
Non-dense domain operator matrices and Cauchy problems
International Nuclear Information System (INIS)
Lalaoui Rhali, S.
2002-12-01
In this work, we study Cauchy problems with non-dense domain operator matrices. By assuming that the entries of an unbounded operator matrix are Hille-Yosida operators, we give a necessary and sufficient condition ensuring that the part of this operator matrix generates a semigroup in the closure of its domain. This allows us to prove the well-posedness of the corresponding Cauchy problem. Our results are applied to delay and neutral differential equations. (author)
Updating Stiffness and Hysteretic Damping Matrices Using Measured Modal Data
Directory of Open Access Journals (Sweden)
Jiashang Jiang
2018-01-01
Full Text Available A new direct method for the finite element (FE matrix updating problem in a hysteretic (or material damping model based on measured incomplete vibration modal data is presented. With this method, the optimally approximated stiffness and hysteretic damping matrices can be easily constructed. The physical connectivity of the original model is preserved and the measured modal data are embedded in the updated model. The numerical results show that the proposed method works well.
Updating Stiffness and Hysteretic Damping Matrices Using Measured Modal Data
Jiashang Jiang; Yongxin Yuan
2018-01-01
A new direct method for the finite element (FE) matrix updating problem in a hysteretic (or material) damping model based on measured incomplete vibration modal data is presented. With this method, the optimally approximated stiffness and hysteretic damping matrices can be easily constructed. The physical connectivity of the original model is preserved and the measured modal data are embedded in the updated model. The numerical results show that the proposed method works well.
Wound care matrices for chronic leg ulcers: role in therapy
Directory of Open Access Journals (Sweden)
Sano H
2015-07-01
Full Text Available Hitomi Sano,1 Sachio Kouraba,2 Rei Ogawa11Department of Plastic, Reconstructive, and Aesthetic Surgery, Nippon Medical School, Tokyo, Japan; 2Sapporo Wound Care and Anti-Aging Laboratory, Sapporo, JapanAbstract: Chronic leg ulcers are a significant health care concern. Although deep wounds are usually treated by flap transfers, the operation is invasive and associates with serious complications. Skin grafts may be a less invasive means of covering wounds. However, skin grafts cannot survive on deep defects unless high-quality granulation tissue can first be generated in the defects. Technologies that generate high-quality granulation tissue are needed. One possibility is to use wound care matrices, which are bioengineered skin and soft tissue substitutes. Because they all support the healing process by providing a premade extracellular matrix material, these matrices can be termed “extracellular matrix replacement therapies”. The matrix promotes wound healing by acting as a scaffold for regeneration, attracting host cytokines to the wound, stimulating wound epithelialization and angiogenesis, and providing the wound bed with bioactive components. This therapy has lasting benefits as it not only helps large skin defects to be closed with thin skin grafts or patch grafts but also restores cosmetic appearance and proper function. In particular, since it acts as a layer that slides over the subcutaneous fascia, it provides skin elasticity, tear resistance, and texture. Several therapies and products employing wound care matrices for wound management have been developed recently. Some of these can be applied in combination with negative pressure wound therapy or beneficial materials that promote wound healing and can be incorporated into the matrix. To date, the clinical studies on these approaches suggest that wound care matrices promote spontaneous wound healing or can be used to facilitate skin grafting, thereby avoiding the need to use
Estimating correlation and covariance matrices by weighting of market similarity
Michael C. M\\"unnix; Rudi Sch\\"afer; Oliver Grothe
2010-01-01
We discuss a weighted estimation of correlation and covariance matrices from historical financial data. To this end, we introduce a weighting scheme that accounts for similarity of previous market conditions to the present one. The resulting estimators are less biased and show lower variance than either unweighted or exponentially weighted estimators. The weighting scheme is based on a similarity measure which compares the current correlation structure of the market to the structures at past ...
Vectorization at the KENO-IV code
International Nuclear Information System (INIS)
Asai, K.; Higuchi, K.; Katakura, J.
1986-01-01
The multigroup criticality safety code KENO-IV has been vectorized and tested on the FACOM VP-100 vector processor. At first, the vectorized KENO-IV on a scalar processor was slower than the original one by a factor of 1.4 because of the overhead introduced by vectorization. Making modifications of algorithms and techniques for vectorization, the vectorized version has become faster than the original one by a factor of 1.4 on the vector processor. For further speedup of the code, some improvements on compiler and hardware, especially on addition of Monte Carlo pipelines to the vector processor, are discussed
Estimation of Fuzzy Measures Using Covariance Matrices in Gaussian Mixtures
Directory of Open Access Journals (Sweden)
Nishchal K. Verma
2012-01-01
Full Text Available This paper presents a novel computational approach for estimating fuzzy measures directly from Gaussian mixtures model (GMM. The mixture components of GMM provide the membership functions for the input-output fuzzy sets. By treating consequent part as a function of fuzzy measures, we derived its coefficients from the covariance matrices found directly from GMM and the defuzzified output constructed from both the premise and consequent parts of the nonadditive fuzzy rules that takes the form of Choquet integral. The computational burden involved with the solution of λ-measure is minimized using Q-measure. The fuzzy model whose fuzzy measures were computed using covariance matrices found in GMM has been successfully applied on two benchmark problems and one real-time electric load data of Indian utility. The performance of the resulting model for many experimental studies including the above-mentioned application is found to be better and comparable to recent available fuzzy models. The main contribution of this paper is the estimation of fuzzy measures efficiently and directly from covariance matrices found in GMM, avoiding the computational burden greatly while learning them iteratively and solving polynomial equations of order of the number of input-output variables.
Unified triminimal parametrizations of quark and lepton mixing matrices
International Nuclear Information System (INIS)
He Xiaogang; Li Shiwen; Ma Boqiang
2009-01-01
We present a detailed study on triminimal parametrizations of quark and lepton mixing matrices with different basis matrices. We start with a general discussion on the triminimal expansion of the mixing matrix and on possible unified quark and lepton parametrization using quark-lepton complementarity. We then consider several interesting basis matrices and compare the triminimal parametrizations with the Wolfenstein-like parametrizations. The usual Wolfenstein parametrization for quark mixing is a triminimal expansion around the unit matrix as the basis. The corresponding quark-lepton complementarity lepton mixing matrix is a triminimal expansion around the bimaximal basis. Current neutrino oscillation data show that the lepton mixing matrix is very well represented by the tribimaximal mixing. It is natural to take it as an expanding basis. The corresponding zeroth order basis for quark mixing in this case makes the triminimal expansion converge much faster than the usual Wolfenstein parametrization. The triminimal expansion based on tribimaximal mixing can be converted to the Wolfenstein-like parametrizations discussed in the literature. We thus have a unified description between different kinds of parametrizations for quark and lepton sectors: the standard parametrizations, the Wolfenstein-like parametrizations, and the triminimal parametrizations.
Likelihood Approximation With Parallel Hierarchical Matrices For Large Spatial Datasets
Litvinenko, Alexander
2017-11-01
The main goal of this article is to introduce the parallel hierarchical matrix library HLIBpro to the statistical community. We describe the HLIBCov package, which is an extension of the HLIBpro library for approximating large covariance matrices and maximizing likelihood functions. We show that an approximate Cholesky factorization of a dense matrix of size $2M\\\\times 2M$ can be computed on a modern multi-core desktop in few minutes. Further, HLIBCov is used for estimating the unknown parameters such as the covariance length, variance and smoothness parameter of a Matérn covariance function by maximizing the joint Gaussian log-likelihood function. The computational bottleneck here is expensive linear algebra arithmetics due to large and dense covariance matrices. Therefore covariance matrices are approximated in the hierarchical ($\\\\H$-) matrix format with computational cost $\\\\mathcal{O}(k^2n \\\\log^2 n/p)$ and storage $\\\\mathcal{O}(kn \\\\log n)$, where the rank $k$ is a small integer (typically $k<25$), $p$ the number of cores and $n$ the number of locations on a fairly general mesh. We demonstrate a synthetic example, where the true values of known parameters are known. For reproducibility we provide the C++ code, the documentation, and the synthetic data.
Study of remobilization polycyclic aromatic hydrocarbons (PAHs) in contaminated matrices
International Nuclear Information System (INIS)
Belkessam, L.; Vessigaud, S.; Laboudigue, A.; Vessigaud, S.; Perrin-Ganier, C.; Schiavon, M.; Denys, S.
2005-01-01
Polycyclic aromatic hydrocarbons (PAHs) originate from many pyrolysis processes. They are widespread environmental pollutants because some of them present toxic and genotoxic properties. In coal pyrolysis sites such as former manufactured gas plants and coke production plants, coal tar is a major source of PAHs. The management of such sites requires better understanding of the mechanisms that control release of PAHs to the biosphere. Determining total PAH concentrations is not sufficient since it does not inform about the pollutants availability to environmental processes. The fate and transport of PAHs in soil are governed by sorption and microbial processes which are well documented. Globally, enhancing retention of the compounds by a solid matrix reduces the risk of pollutant dispersion, but decreases their accessibility to microbial microflora. Conversely, the remobilization of organics from contaminated solid matrices represents a potential hazard since these pollutants can reach groundwater resources. However the available data are often obtained from laboratory experiments in which many field parameters can not be taken into account (long term, temperature, co-pollution, ageing phenomenon, heterogenous distribution of pollution). The present work focuses on the influence assessment and understanding of some of these parameters on PAHs remobilization from heavily polluted matrices in near-field conditions (industrial contaminated matrices, high contact time, ..). Results concerning effects of temperature and physical state of pollution (dispersed among the soil or condensed in small clusters or in coal tar) are presented. (authors)
Linear algebra and matrices topics for a second course
Shapiro, Helene
2015-01-01
Linear algebra and matrix theory are fundamental tools for almost every area of mathematics, both pure and applied. This book combines coverage of core topics with an introduction to some areas in which linear algebra plays a key role, for example, block designs, directed graphs, error correcting codes, and linear dynamical systems. Notable features include a discussion of the Weyr characteristic and Weyr canonical forms, and their relationship to the better-known Jordan canonical form; the use of block cyclic matrices and directed graphs to prove Frobenius's theorem on the structure of the eigenvalues of a nonnegative, irreducible matrix; and the inclusion of such combinatorial topics as BIBDs, Hadamard matrices, and strongly regular graphs. Also included are McCoy's theorem about matrices with property P, the Bruck-Ryser-Chowla theorem on the existence of block designs, and an introduction to Markov chains. This book is intended for those who are familiar with the linear algebra covered in a typical first c...
Likelihood Approximation With Parallel Hierarchical Matrices For Large Spatial Datasets
Litvinenko, Alexander; Sun, Ying; Genton, Marc G.; Keyes, David E.
2017-01-01
The main goal of this article is to introduce the parallel hierarchical matrix library HLIBpro to the statistical community. We describe the HLIBCov package, which is an extension of the HLIBpro library for approximating large covariance matrices and maximizing likelihood functions. We show that an approximate Cholesky factorization of a dense matrix of size $2M\\times 2M$ can be computed on a modern multi-core desktop in few minutes. Further, HLIBCov is used for estimating the unknown parameters such as the covariance length, variance and smoothness parameter of a Matérn covariance function by maximizing the joint Gaussian log-likelihood function. The computational bottleneck here is expensive linear algebra arithmetics due to large and dense covariance matrices. Therefore covariance matrices are approximated in the hierarchical ($\\H$-) matrix format with computational cost $\\mathcal{O}(k^2n \\log^2 n/p)$ and storage $\\mathcal{O}(kn \\log n)$, where the rank $k$ is a small integer (typically $k<25$), $p$ the number of cores and $n$ the number of locations on a fairly general mesh. We demonstrate a synthetic example, where the true values of known parameters are known. For reproducibility we provide the C++ code, the documentation, and the synthetic data.
Raven's matrices and working memory: a dual-task approach.
Rao, K Venkata; Baddeley, Alan
2013-01-01
Raven's Matrices Test was developed as a "pure" measure of Spearman's concept of general intelligence, g. Subsequent research has attempted to specify the processes underpinning performance, some relating it to the concept of working memory and proposing a crucial role for the central executive, with the nature of other components currently unclear. Up to this point, virtually all work has been based on correlational analysis of number of correct solutions, sometimes related to possible strategies. We explore the application to this problem of the concurrent task methodology used widely in developing the concept of multicomponent working memory. Participants attempted to solve problems from the matrices under baseline conditions, or accompanied by backward counting or verbal repetition tasks, assumed to disrupt the central executive and phonological loop components of working memory, respectively. As in other uses of this method, number of items correct showed little effect, while solution time measures gave very clear evidence of an important role for the central executive, but no evidence for phonological loop involvement. We conclude that this and related concurrent task techniques hold considerable promise for the analysis of Raven's matrices and potentially for other established psychometric tests.
Large deviations of the maximum eigenvalue in Wishart random matrices
International Nuclear Information System (INIS)
Vivo, Pierpaolo; Majumdar, Satya N; Bohigas, Oriol
2007-01-01
We analytically compute the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x N) Wishart matrix W = X T X (where X is a rectangular M x N matrix with independent Gaussian entries) are smaller than the mean value (λ) = N/c decreases for large N as ∼exp[-β/2 N 2 Φ - (2√c + 1: c)], where β = 1, 2 corresponds respectively to real and complex Wishart matrices, c = N/M ≤ 1 and Φ - (x; c) is a rate (sometimes also called large deviation) function that we compute explicitly. The result for the anti-Wishart case (M < N) simply follows by exchanging M and N. We also analytically determine the average spectral density of an ensemble of Wishart matrices whose eigenvalues are constrained to be smaller than a fixed barrier. Numerical simulations are in excellent agreement with the analytical predictions
Large deviations of the maximum eigenvalue in Wishart random matrices
Energy Technology Data Exchange (ETDEWEB)
Vivo, Pierpaolo [School of Information Systems, Computing and Mathematics, Brunel University, Uxbridge, Middlesex, UB8 3PH (United Kingdom) ; Majumdar, Satya N [Laboratoire de Physique Theorique et Modeles Statistiques (UMR 8626 du CNRS), Universite Paris-Sud, Batiment 100, 91405 Orsay Cedex (France); Bohigas, Oriol [Laboratoire de Physique Theorique et Modeles Statistiques (UMR 8626 du CNRS), Universite Paris-Sud, Batiment 100, 91405 Orsay Cedex (France)
2007-04-20
We analytically compute the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x N) Wishart matrix W = X{sup T}X (where X is a rectangular M x N matrix with independent Gaussian entries) are smaller than the mean value ({lambda}) = N/c decreases for large N as {approx}exp[-{beta}/2 N{sup 2}{phi}{sub -} (2{radical}c + 1: c)], where {beta} = 1, 2 corresponds respectively to real and complex Wishart matrices, c = N/M {<=} 1 and {phi}{sub -}(x; c) is a rate (sometimes also called large deviation) function that we compute explicitly. The result for the anti-Wishart case (M < N) simply follows by exchanging M and N. We also analytically determine the average spectral density of an ensemble of Wishart matrices whose eigenvalues are constrained to be smaller than a fixed barrier. Numerical simulations are in excellent agreement with the analytical predictions.
Geometry and arithmetic of factorized S-matrices
International Nuclear Information System (INIS)
Freund, P.G.O.
1995-01-01
In realistic four-dimensional quantum field theories integrability is elusive. Relativity, when combined with quantum theory does not permit an infinity of local conservation laws except for free fields, for which the S-matrix is trivial S = 1. In two space-time dimensions, where forward and backward scattering are the only possibilities, nontrivial S-matrices are possible even in integrable theories. Such S-matrices are known to factorize [1]. This means that there is no particle production, so that the 4-point amplitudes determine all higher n-point amplitudes. In our recent work [2, 3, 4, 5, 6] we found that in such integrable two-dimensional theories, even the input 4-point amplitudes are determined by a simple principle. Roughly speaking these amplitudes describe the S-wave scattering which one associates with free motion on certain quantum-symmetric spaces. The trivial S-matrix of free field theory describes the absence of scattering which one associates with free motion on a euclidean space, itself a symmetric space. As is well known [7, 8, 9], for curved symmetric spaces the S-matrices for S-wave scattering are no longer trivial, but rather they are determined by the Harish-Chandra c-functions of these spaces [10]. The quantum deformation of this situation is what appears when one considers excitation scattering in two-dimensional integrable models. (orig.)
Large-deviation theory for diluted Wishart random matrices
Castillo, Isaac Pérez; Metz, Fernando L.
2018-03-01
Wishart random matrices with a sparse or diluted structure are ubiquitous in the processing of large datasets, with applications in physics, biology, and economy. In this work, we develop a theory for the eigenvalue fluctuations of diluted Wishart random matrices based on the replica approach of disordered systems. We derive an analytical expression for the cumulant generating function of the number of eigenvalues IN(x ) smaller than x ∈R+ , from which all cumulants of IN(x ) and the rate function Ψx(k ) controlling its large-deviation probability Prob[IN(x ) =k N ] ≍e-N Ψx(k ) follow. Explicit results for the mean value and the variance of IN(x ) , its rate function, and its third cumulant are discussed and thoroughly compared to numerical diagonalization, showing very good agreement. The present work establishes the theoretical framework put forward in a recent letter [Phys. Rev. Lett. 117, 104101 (2016), 10.1103/PhysRevLett.117.104101] as an exact and compelling approach to deal with eigenvalue fluctuations of sparse random matrices.
Threshold partitioning of sparse matrices and applications to Markov chains
Energy Technology Data Exchange (ETDEWEB)
Choi, Hwajeong; Szyld, D.B. [Temple Univ., Philadelphia, PA (United States)
1996-12-31
It is well known that the order of the variables and equations of a large, sparse linear system influences the performance of classical iterative methods. In particular if, after a symmetric permutation, the blocks in the diagonal have more nonzeros, classical block methods have a faster asymptotic rate of convergence. In this paper, different ordering and partitioning algorithms for sparse matrices are presented. They are modifications of PABLO. In the new algorithms, in addition to the location of the nonzeros, the values of the entries are taken into account. The matrix resulting after the symmetric permutation has dense blocks along the diagonal, and small entries in the off-diagonal blocks. Parameters can be easily adjusted to obtain, for example, denser blocks, or blocks with elements of larger magnitude. In particular, when the matrices represent Markov chains, the permuted matrices are well suited for block iterative methods that find the corresponding probability distribution. Applications to three types of methods are explored: (1) Classical block methods, such as Block Gauss Seidel. (2) Preconditioned GMRES, where a block diagonal preconditioner is used. (3) Iterative aggregation method (also called aggregation/disaggregation) where the partition obtained from the ordering algorithm with certain parameters is used as an aggregation scheme. In all three cases, experiments are presented which illustrate the performance of the methods with the new orderings. The complexity of the new algorithms is linear in the number of nonzeros and the order of the matrix, and thus adding little computational effort to the overall solution.
Vector Monte Carlo simulations on atmospheric scattering of polarization qubits.
Li, Ming; Lu, Pengfei; Yu, Zhongyuan; Yan, Lei; Chen, Zhihui; Yang, Chuanghua; Luo, Xiao
2013-03-01
In this paper, a vector Monte Carlo (MC) method is proposed to study the influence of atmospheric scattering on polarization qubits for satellite-based quantum communication. The vector MC method utilizes a transmittance method to solve the photon free path for an inhomogeneous atmosphere and random number sampling to determine whether the type of scattering is aerosol scattering or molecule scattering. Simulations are performed for downlink and uplink. The degrees and the rotations of polarization are qualitatively and quantitatively obtained, which agree well with the measured results in the previous experiments. The results show that polarization qubits are well preserved in the downlink and uplink, while the number of received single photons is less than half of the total transmitted single photons for both links. Moreover, our vector MC method can be applied for the scattering of polarized light in other inhomogeneous random media.
Galiatsatos, P. G.; Tennyson, J.
2012-11-01
The most time consuming step within the framework of the UK R-matrix molecular codes is that of the diagonalization of the inner region Hamiltonian matrix (IRHM). Here we present the method that we follow to speed up this step. We use shared memory machines (SMM), distributed memory machines (DMM), the OpenMP directive based parallel language, the MPI function based parallel language, the sparse matrix diagonalizers ARPACK and PARPACK, a variation for real symmetric matrices of the official coordinate sparse matrix format and finally a parallel sparse matrix-vector product (PSMV). The efficient application of the previous techniques rely on two important facts: the sparsity of the matrix is large enough (more than 98%) and in order to get back converged results we need a small only part of the matrix spectrum.
Ait-Haddou, Rachid
2015-06-04
We show that the best degree reduction of a given polynomial P from degree n to m with respect to the discrete (Formula presented.)-norm is equivalent to the best Euclidean distance of the vector of h-Bézier coefficients of P from the vector of degree raised h-Bézier coefficients of polynomials of degree m. Moreover, we demonstrate the adequacy of h-Bézier curves for approaching the problem of weighted discrete least squares approximation. Applications to discrete orthogonal polynomials are also presented. © 2015 Springer Science+Business Media Dordrecht
GRE Enzymes for Vector Analysis
U.S. Environmental Protection Agency — Microbial enzyme data that were collected during the 2004-2006 EMAP-GRE program. These data were then used by Moorhead et al (2016) in their ecoenzyme vector...
Scanning vector Hall probe microscopy
International Nuclear Information System (INIS)
Cambel, V.; Gregusova, D.; Fedor, J.; Kudela, R.; Bending, S.J.
2004-01-01
We have developed a scanning vector Hall probe microscope for mapping magnetic field vector over magnetic samples. The microscope is based on a micromachined Hall sensor and the cryostat with scanning system. The vector Hall sensor active area is ∼5x5 μm 2 . It is realized by patterning three Hall probes on the tilted faces of GaAs pyramids. Data from these 'tilted' Hall probes are used to reconstruct the full magnetic field vector. The scanning area of the microscope is 5x5 mm 2 , space resolution 2.5 μm, field resolution ∼1 μT Hz -1/2 at temperatures 10-300 K
DEFF Research Database (Denmark)
Pihl, Michael Johannes
The main purpose of this PhD project is to develop an ultrasonic method for 3D vector flow imaging. The motivation is to advance the field of velocity estimation in ultrasound, which plays an important role in the clinic. The velocity of blood has components in all three spatial dimensions, yet...... are (vx, vy, vz) = (-0.03, 95, 1.0) ± (9, 6, 1) cm/s compared with the expected (0, 96, 0) cm/s. Afterwards, 3D vector flow images from a cross-sectional plane of the vessel are presented. The out of plane velocities exhibit the expected 2D circular-symmetric parabolic shape. The experimental results...... verify that the 3D TO method estimates the complete 3D velocity vectors, and that the method is suitable for 3D vector flow imaging....
DEFF Research Database (Denmark)
Holbek, Simon
, if this significant reduction in the element count can still provide precise and robust 3-D vector flow estimates in a plane. The study concludes that the RC array is capable of estimating precise 3-D vector flow both in a plane and in a volume, despite the low channel count. However, some inherent new challenges...... ultrasonic vector flow estimation and bring it a step closer to a clinical application. A method for high frame rate 3-D vector flow estimation in a plane using the transverse oscillation method combined with a 1024 channel 2-D matrix array is presented. The proposed method is validated both through phantom...... hampers the task of real-time processing. In a second study, some of the issue with the 2-D matrix array are solved by introducing a 2-D row-column (RC) addressing array with only 62 + 62 elements. It is investigated both through simulations and via experimental setups in various flow conditions...
Transcriptional Silencing of Retroviral Vectors
DEFF Research Database (Denmark)
Lund, Anders Henrik; Duch, M.; Pedersen, F.S.
1996-01-01
. Extinction of long-term vector expression has been observed after implantation of transduced hematopoietic cells as well as fibroblasts, myoblasts and hepatocytes. Here we review the influence of vector structure, integration site and cell type on transcriptional silencing. While down-regulation of proviral...... transcription is known from a number of cellular and animal models, major insight has been gained from studies in the germ line and embryonal cells of the mouse. Key elements for the transfer and expression of retroviral vectors, such as the viral transcriptional enhancer and the binding site for the t......RNA primer for reverse transcription may have a major influence on transcriptional silencing. Alterations of these elements of the vector backbone as well as the use of internal promoter elements from housekeeping genes may contribute to reduce transcriptional silencing. The use of cell culture and animal...
High Accuracy Vector Helium Magnetometer
National Aeronautics and Space Administration — The proposed HAVHM instrument is a laser-pumped helium magnetometer with both triaxial vector and omnidirectional scalar measurement capabilities in a single...
Degree-degree correlations in directed networks with heavy-tailed degrees
van der Hoorn, W.L.F.; Litvak, Nelli
2013-01-01
In network theory, Pearson's correlation coefficients are most commonly used to measure the degree assortativity of a network. We investigate the behavior of these coefficients in the setting of directed networks with heavy-tailed degree sequences. We prove that for graphs where the in- and
Degree-degree dependencies in directed networks with heavy-tailed degrees
van der Hoorn, W.L.F.; Litvak, Nelly
2015-01-01
In network theory, Pearson’s correlation coefficients are most commonly used to measure the degree assortativity of a network. We investigate the behavior of these coefficients in the setting of directed networks with heavy-tailed degree sequences. We prove that for graphs where the in- and
Liu, Yongbin; He, Bing; Liu, Fang; Lu, Siliang; Zhao, Yilei
2016-12-01
Fault pattern identification is a crucial step for the intelligent fault diagnosis of real-time health conditions in monitoring a mechanical system. However, many challenges exist in extracting the effective feature from vibration signals for fault recognition. A new feature fusion method is proposed in this study to extract new features using kernel joint approximate diagonalization of eigen-matrices (KJADE). In the method, the input space that is composed of original features is mapped into a high-dimensional feature space by nonlinear mapping. Then, the new features can be estimated through the eigen-decomposition of the fourth-order cumulative kernel matrix obtained from the feature space. Therefore, the proposed method could be used to reduce data redundancy because it extracts the inherent pattern structure of different fault classes as it is nonlinear by nature. The integration evaluation factor of between-class and within-class scatters (SS) is employed to depict the clustering performance quantitatively, and the new feature subset extracted by the proposed method is fed into a multi-class support vector machine for fault pattern identification. Finally, the effectiveness of the proposed method is verified by experimental vibration signals with different bearing fault types and severities. Results of several cases show that the KJADE algorithm is efficient in feature fusion for bearing fault identification.
Model selection with multiple regression on distance matrices leads to incorrect inferences.
Directory of Open Access Journals (Sweden)
Ryan P Franckowiak
Full Text Available In landscape genetics, model selection procedures based on Information Theoretic and Bayesian principles have been used with multiple regression on distance matrices (MRM to test the relationship between multiple vectors of pairwise genetic, geographic, and environmental distance. Using Monte Carlo simulations, we examined the ability of model selection criteria based on Akaike's information criterion (AIC, its small-sample correction (AICc, and the Bayesian information criterion (BIC to reliably rank candidate models when applied with MRM while varying the sample size. The results showed a serious problem: all three criteria exhibit a systematic bias toward selecting unnecessarily complex models containing spurious random variables and erroneously suggest a high level of support for the incorrectly ranked best model. These problems effectively increased with increasing sample size. The failure of AIC, AICc, and BIC was likely driven by the inflated sample size and different sum-of-squares partitioned by MRM, and the resulting effect on delta values. Based on these findings, we strongly discourage the continued application of AIC, AICc, and BIC for model selection with MRM.